0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n157.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 09:52:09 CST 2018
82.40/82.61	% done 9888 iterations in 82.407s
82.40/82.61	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
82.40/82.61	% SZS output start Refutation
82.40/82.61	tff(fact_1__096abs_A_I2_A_K_Ax_J_A_094_A2_A_060_061_A1_A_094_A2_096, axiom,
82.40/82.61	  (ord_less_eq(real,
82.40/82.61	               power_power(real,
82.40/82.61	                           abs_abs(real,
82.40/82.61	                                   times_times(real,
82.40/82.61	                                               number_number_of(real,
82.40/82.61	                                                                bit0(
82.40/82.61	                                                                bit1(pls))),
82.40/82.61	                                               x)),
82.40/82.61	                           number_number_of(nat,bit0(bit1(pls)))),
82.40/82.61	               power_power(real,one_one(real),
82.40/82.61	                           number_number_of(nat,bit0(bit1(pls))))))).
82.40/82.61	tff('0', plain,
82.40/82.61	    ord_less_eq(real, 
82.40/82.61	      power_power(real, 
82.40/82.61	        abs_abs(real, 
82.40/82.61	          times_times(real, number_number_of(real, bit0(bit1(pls))), x)), 
82.40/82.61	        number_number_of(nat, bit0(bit1(pls)))), 
82.40/82.61	      power_power(real, one_one(real), 
82.40/82.61	        number_number_of(nat, bit0(bit1(pls))))),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [fact_1__096abs_A_I2_A_K_Ax_J_A_094_A2_A_060_061_A1_A_094_A2_096])).
82.40/82.61	tff(arity_RealDef_Oreal___Rings_Osemiring__1, axiom, (semiring_1(real))).
82.40/82.61	tff('1', plain, semiring_1(real),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [arity_RealDef_Oreal___Rings_Osemiring__1])).
82.40/82.61	tff(fact_7_one__power2, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (semiring_1(A) =>
82.40/82.61	      (power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls)))) =
82.40/82.61	       one_one(A))))).
82.40/82.61	tff('2', plain,
82.40/82.61	    ![X2 : $tType]:
82.40/82.61	      (power_power(X2, one_one(X2), number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	        = one_one(X2)
82.40/82.61	       | ~ semiring_1(X2)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_7_one__power2])).
82.40/82.61	tff('3', plain,
82.40/82.61	    (~ $true
82.40/82.61	     | power_power(real, one_one(real), 
82.40/82.61	         number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	        = one_one(real)),
82.40/82.61	    inference('sup-', [status(thm)], ['1', '2'])).
82.40/82.61	tff('4', plain,
82.40/82.61	    power_power(real, one_one(real), number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	     = one_one(real),
82.40/82.61	    inference('simplify', [status(thm)], ['3'])).
82.40/82.61	tff('5', plain,
82.40/82.61	    ord_less_eq(real, 
82.40/82.61	      power_power(real, 
82.40/82.61	        abs_abs(real, 
82.40/82.61	          times_times(real, number_number_of(real, bit0(bit1(pls))), x)), 
82.40/82.61	        number_number_of(nat, bit0(bit1(pls)))), one_one(real)),
82.40/82.61	    inference('demod', [status(thm)], ['0', '4'])).
82.40/82.61	tff(arity_RealDef_Oreal___Rings_Ocomm__semiring__1, axiom,
82.40/82.61	  (comm_semiring_1(real))).
82.40/82.61	tff('6', plain, comm_semiring_1(real),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [arity_RealDef_Oreal___Rings_Ocomm__semiring__1])).
82.40/82.61	tff(fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (comm_semiring_1(A) =>
82.40/82.61	      (![X:A]:
82.40/82.61	         (times_times(A,X,X) =
82.40/82.61	          power_power(A,X,number_number_of(nat,bit0(bit1(pls))))))))).
82.40/82.61	tff('7', plain,
82.40/82.61	    ![X12 : $tType, X13 : X12]:
82.40/82.61	      (times_times(X12, X13, X13)
82.40/82.61	        = power_power(X12, X13, number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	       | ~ comm_semiring_1(X12)),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])).
82.40/82.61	tff('8', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      (~ $true
82.40/82.61	       | times_times(real, X0, X0)
82.40/82.61	          = power_power(real, X0, number_number_of(nat, bit0(bit1(pls))))),
82.40/82.61	    inference('sup-', [status(thm)], ['6', '7'])).
82.40/82.61	tff('9', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      times_times(real, X0, X0)
82.40/82.61	       = power_power(real, X0, number_number_of(nat, bit0(bit1(pls)))),
82.40/82.61	    inference('simplify', [status(thm)], ['8'])).
82.40/82.61	tff(arity_RealDef_Oreal___Int_Onumber__ring, axiom, (number_ring(real))).
82.40/82.61	tff('10', plain, number_ring(real),
82.40/82.61	    inference('cnf', [status(esa)], [arity_RealDef_Oreal___Int_Onumber__ring])).
82.40/82.61	tff(fact_10_numeral__1__eq__1, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (number_ring(A) => (number_number_of(A,bit1(pls)) = one_one(A))))).
82.40/82.61	tff('11', plain,
82.40/82.61	    ![X9 : $tType]:
82.40/82.61	      (number_number_of(X9, bit1(pls)) = one_one(X9) | ~ number_ring(X9)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_10_numeral__1__eq__1])).
82.40/82.61	tff('12', plain,
82.40/82.61	    (~ $true | number_number_of(real, bit1(pls)) = one_one(real)),
82.40/82.61	    inference('sup-', [status(thm)], ['10', '11'])).
82.40/82.61	tff('13', plain, number_number_of(real, bit1(pls)) = one_one(real),
82.40/82.61	    inference('simplify', [status(thm)], ['12'])).
82.40/82.61	tff('14', plain,
82.40/82.61	    ord_less_eq(real, 
82.40/82.61	      times_times(real, 
82.40/82.61	        abs_abs(real, 
82.40/82.61	          times_times(real, number_number_of(real, bit0(bit1(pls))), x)), 
82.40/82.61	        abs_abs(real, 
82.40/82.61	          times_times(real, number_number_of(real, bit0(bit1(pls))), x))), 
82.40/82.61	      number_number_of(real, bit1(pls))),
82.40/82.61	    inference('demod', [status(thm)], ['5', '9', '13'])).
82.40/82.61	tff(fact_57_power2__abs, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (linordered_idom(A) =>
82.40/82.61	      (![A1:A]:
82.40/82.61	         (power_power(A,abs_abs(A,A1),number_number_of(nat,bit0(bit1(pls)))) =
82.40/82.61	          power_power(A,A1,number_number_of(nat,bit0(bit1(pls))))))))).
82.40/82.61	tff('15', plain,
82.40/82.61	    ![X86 : $tType, X87 : X86]:
82.40/82.61	      (power_power(X86, abs_abs(X86, X87), 
82.40/82.61	         number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	        = power_power(X86, X87, number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	       | ~ linordered_idom(X86)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_57_power2__abs])).
82.40/82.61	tff('16', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      (times_times(real, abs_abs(real, X0), abs_abs(real, X0))
82.40/82.61	        = power_power(real, X0, number_number_of(nat, bit0(bit1(pls))))
82.40/82.61	       | ~ linordered_idom(real)),
82.40/82.61	    inference('sup+', [status(thm)], ['9', '15'])).
82.40/82.61	tff(arity_RealDef_Oreal___Rings_Olinordered__idom, axiom,
82.40/82.61	  (linordered_idom(real))).
82.40/82.61	tff('17', plain, linordered_idom(real),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [arity_RealDef_Oreal___Rings_Olinordered__idom])).
82.40/82.61	tff('18', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      (times_times(real, abs_abs(real, X0), abs_abs(real, X0))
82.40/82.61	        = times_times(real, X0, X0)
82.40/82.61	       | ~ $true),
82.40/82.61	    inference('demod', [status(thm)], ['16', '9', '17'])).
82.40/82.61	tff('19', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      times_times(real, abs_abs(real, X0), abs_abs(real, X0))
82.40/82.61	       = times_times(real, X0, X0),
82.40/82.61	    inference('simplify', [status(thm)], ['18'])).
82.40/82.61	tff('20', plain,
82.40/82.61	    ord_less_eq(real, 
82.40/82.61	      times_times(real, 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit1(pls))), x), 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit1(pls))), x)), 
82.40/82.61	      number_number_of(real, bit1(pls))),
82.40/82.61	    inference('demod', [status(thm)], ['14', '19'])).
82.40/82.61	tff(fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (comm_semiring_1(A) =>
82.40/82.61	      (![B:A,A1:A]: (times_times(A,A1,B) = times_times(A,B,A1)))))).
82.40/82.61	tff('21', plain,
82.40/82.61	    ![X152 : $tType, X153 : X152, X154 : X152]:
82.40/82.61	      (times_times(X152, X154, X153) = times_times(X152, X153, X154)
82.40/82.61	       | ~ comm_semiring_1(X152)),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])).
82.40/82.61	tff('22', plain,
82.40/82.61	    ![X0 : real, X1 : real]:
82.40/82.61	      (~ $true | times_times(real, X1, X0) = times_times(real, X0, X1)),
82.40/82.61	    inference('sup-', [status(thm)], ['6', '21'])).
82.40/82.61	tff('23', plain,
82.40/82.61	    ![X0 : real, X1 : real]:
82.40/82.61	      times_times(real, X1, X0) = times_times(real, X0, X1),
82.40/82.61	    inference('simplify', [status(thm)], ['22'])).
82.40/82.61	tff(fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (comm_semiring_1(A) =>
82.40/82.61	      (![Rx:A,Ly:A,Lx:A]:
82.40/82.61	         (times_times(A,times_times(A,Lx,Ly),Rx) =
82.40/82.61	          times_times(A,Lx,times_times(A,Ly,Rx))))))).
82.40/82.61	tff('24', plain,
82.40/82.61	    ![X140 : $tType, X141 : X140, X142 : X140, X143 : X140]:
82.40/82.61	      (times_times(X140, times_times(X140, X141, X142), X143)
82.40/82.61	        = times_times(X140, X141, times_times(X140, X142, X143))
82.40/82.61	       | ~ comm_semiring_1(X140)),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])).
82.40/82.61	tff('25', plain,
82.40/82.61	    ![X0 : real, X1 : real, X2 : real]:
82.40/82.61	      (~ $true
82.40/82.61	       | times_times(real, times_times(real, X2, X1), X0)
82.40/82.61	          = times_times(real, X2, times_times(real, X1, X0))),
82.40/82.61	    inference('sup-', [status(thm)], ['6', '24'])).
82.40/82.61	tff('26', plain,
82.40/82.61	    ![X0 : real, X1 : real, X2 : real]:
82.40/82.61	      times_times(real, times_times(real, X2, X1), X0)
82.40/82.61	       = times_times(real, X2, times_times(real, X1, X0)),
82.40/82.61	    inference('simplify', [status(thm)], ['25'])).
82.40/82.61	tff('27', plain,
82.40/82.61	    ![X0 : real, X1 : real, X2 : real]:
82.40/82.61	      times_times(real, times_times(real, X1, X0), X2)
82.40/82.61	       = times_times(real, X0, times_times(real, X1, X2)),
82.40/82.61	    inference('sup+', [status(thm)], ['23', '26'])).
82.40/82.61	tff(fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (comm_semiring_1(A) =>
82.40/82.61	      (![Ry:A,Rx:A,Lx:A]:
82.40/82.61	         (times_times(A,Lx,times_times(A,Rx,Ry)) =
82.40/82.61	          times_times(A,Rx,times_times(A,Lx,Ry))))))).
82.40/82.61	tff('28', plain,
82.40/82.61	    ![X148 : $tType, X149 : X148, X150 : X148, X151 : X148]:
82.40/82.61	      (times_times(X148, X150, times_times(X148, X149, X151))
82.40/82.61	        = times_times(X148, X149, times_times(X148, X150, X151))
82.40/82.61	       | ~ comm_semiring_1(X148)),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])).
82.40/82.61	tff('29', plain,
82.40/82.61	    ![X0 : real, X1 : real, X2 : real]:
82.40/82.61	      (~ $true
82.40/82.61	       | times_times(real, X2, times_times(real, X1, X0))
82.40/82.61	          = times_times(real, X1, times_times(real, X2, X0))),
82.40/82.61	    inference('sup-', [status(thm)], ['6', '28'])).
82.40/82.61	tff('30', plain,
82.40/82.61	    ![X0 : real, X1 : real, X2 : real]:
82.40/82.61	      times_times(real, X2, times_times(real, X1, X0))
82.40/82.61	       = times_times(real, X1, times_times(real, X2, X0)),
82.40/82.61	    inference('simplify', [status(thm)], ['29'])).
82.40/82.61	tff('31', plain,
82.40/82.61	    ord_less_eq(real, 
82.40/82.61	      times_times(real, number_number_of(real, bit0(bit1(pls))), 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit1(pls))), 
82.40/82.61	          times_times(real, x, x))), number_number_of(real, bit1(pls))),
82.40/82.61	    inference('demod', [status(thm)], ['20', '27', '30', '30'])).
82.40/82.61	tff(conj_0, conjecture,
82.40/82.61	  (ord_less_eq(real,
82.40/82.61	               times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),
82.40/82.61	                           power_power(real,x,
82.40/82.61	                                       number_number_of(nat,bit0(bit1(pls))))),
82.40/82.61	               one_one(real)))).
82.40/82.61	tff(zf_stmt_0, negated_conjecture,
82.40/82.61	  (~
82.40/82.61	    ord_less_eq(real,
82.40/82.61	                times_times(real,
82.40/82.61	                            number_number_of(real,bit0(bit0(bit1(pls)))),
82.40/82.61	                            power_power(real,x,
82.40/82.61	                                        number_number_of(nat,bit0(bit1(pls))))),
82.40/82.61	                one_one(real)))).
82.40/82.61	tff('32', plain,
82.40/82.61	    ~ ord_less_eq(real, 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit0(bit1(pls)))), 
82.40/82.61	          power_power(real, x, number_number_of(nat, bit0(bit1(pls))))), 
82.40/82.61	        one_one(real)),
82.40/82.61	    inference('cnf', [status(esa)], [zf_stmt_0])).
82.40/82.61	tff('33', plain,
82.40/82.61	    ~ ord_less_eq(real, 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit0(bit1(pls)))), 
82.40/82.61	          power_power(real, x, number_number_of(nat, bit0(bit1(pls))))), 
82.40/82.61	        number_number_of(real, bit1(pls))),
82.40/82.61	    inference('demod', [status(thm)], ['32', '13'])).
82.40/82.61	tff('34', plain,
82.40/82.61	    ~ ord_less_eq(real, 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit0(bit1(pls)))), 
82.40/82.61	          times_times(real, x, x)), number_number_of(real, bit1(pls))),
82.40/82.61	    inference('demod', [status(thm)], ['33', '9'])).
82.40/82.61	tff('35', plain,
82.40/82.61	    ~ ord_less_eq(real, 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit0(bit1(pls)))), 
82.40/82.61	          times_times(real, x, x)), number_number_of(real, bit1(pls))),
82.40/82.61	    inference('sup-', [status(thm)], ['23', '34'])).
82.40/82.61	tff(arity_Int_Oint___Rings_Ocomm__semiring__1, axiom, (comm_semiring_1(int))).
82.40/82.61	tff('36', plain, comm_semiring_1(int),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [arity_Int_Oint___Rings_Ocomm__semiring__1])).
82.40/82.61	tff('37', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      (~ $true | times_times(int, X1, X0) = times_times(int, X0, X1)),
82.40/82.61	    inference('sup-', [status(thm)], ['36', '21'])).
82.40/82.61	tff('38', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      times_times(int, X1, X0) = times_times(int, X0, X1),
82.40/82.61	    inference('simplify', [status(thm)], ['37'])).
82.40/82.61	tff(fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (comm_semiring_1(A) => (![A1:A]: (times_times(A,A1,one_one(A)) = A1))))).
82.40/82.61	tff('39', plain,
82.40/82.61	    ![X165 : $tType, X166 : X165]:
82.40/82.61	      (times_times(X165, X166, one_one(X165)) = X166
82.40/82.61	       | ~ comm_semiring_1(X165)),
82.40/82.61	    inference('cnf', [status(esa)],
82.40/82.61	              [fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])).
82.40/82.61	tff('40', plain,
82.40/82.61	    ![X0 : int]: (~ $true | times_times(int, X0, one_one(int)) = X0),
82.40/82.61	    inference('sup-', [status(thm)], ['36', '39'])).
82.40/82.61	tff(fact_68_one__is__num__one, axiom,
82.40/82.61	  (one_one(int) = number_number_of(int,bit1(pls)))).
82.40/82.61	tff('41', plain, one_one(int) = number_number_of(int, bit1(pls)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_68_one__is__num__one])).
82.40/82.61	tff('42', plain,
82.40/82.61	    ![X0 : int]:
82.40/82.61	      (~ $true | times_times(int, X0, number_number_of(int, bit1(pls))) = X0),
82.40/82.61	    inference('demod', [status(thm)], ['40', '41'])).
82.40/82.61	tff('43', plain,
82.40/82.61	    ![X0 : int]: times_times(int, X0, number_number_of(int, bit1(pls))) = X0,
82.40/82.61	    inference('simplify', [status(thm)], ['42'])).
82.40/82.61	tff('44', plain,
82.40/82.61	    ![X0 : int]: times_times(int, number_number_of(int, bit1(pls)), X0) = X0,
82.40/82.61	    inference('sup+', [status(thm)], ['38', '43'])).
82.40/82.61	tff(fact_21_mult__Bit0, axiom,
82.40/82.61	  (![L1:int,K3:int]:
82.40/82.61	     (times_times(int,bit0(K3),L1) = bit0(times_times(int,K3,L1))))).
82.40/82.61	tff('45', plain,
82.40/82.61	    ![X27 : int, X28 : int]:
82.40/82.61	      times_times(int, bit0(X27), X28) = bit0(times_times(int, X27, X28)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_21_mult__Bit0])).
82.40/82.61	tff('46', plain,
82.40/82.61	    ![X0 : int]:
82.40/82.61	      times_times(int, bit0(number_number_of(int, bit1(pls))), X0) = bit0(X0),
82.40/82.61	    inference('sup+', [status(thm)], ['44', '45'])).
82.40/82.61	tff('47', plain,
82.40/82.61	    ![X0 : int]:
82.40/82.61	      bit0(X0) = times_times(int, X0, bit0(number_number_of(int, bit1(pls)))),
82.40/82.61	    inference('sup+', [status(thm)], ['46', '38'])).
82.40/82.61	tff(fact_23_mult__number__of__left, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (number_ring(A) =>
82.40/82.61	      (![Z:A,W:int,V:int]:
82.40/82.61	         (times_times(A,number_number_of(A,V),
82.40/82.61	                      times_times(A,number_number_of(A,W),Z)) =
82.40/82.61	          times_times(A,number_number_of(A,times_times(int,V,W)),Z)))))).
82.40/82.61	tff('48', plain,
82.40/82.61	    ![X32 : $tType, X33 : int, X34 : int, X35 : X32]:
82.40/82.61	      (times_times(X32, number_number_of(X32, X33), 
82.40/82.61	         times_times(X32, number_number_of(X32, X34), X35))
82.40/82.61	        = times_times(X32, 
82.40/82.61	            number_number_of(X32, times_times(int, X33, X34)), X35)
82.40/82.61	       | ~ number_ring(X32)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_23_mult__number__of__left])).
82.40/82.61	tff('49', plain,
82.40/82.61	    ![X0 : real, X1 : int, X2 : int]:
82.40/82.61	      (~ $true
82.40/82.61	       | times_times(real, number_number_of(real, X2), 
82.40/82.61	           times_times(real, number_number_of(real, X1), X0))
82.40/82.61	          = times_times(real, 
82.40/82.61	              number_number_of(real, times_times(int, X2, X1)), X0)),
82.40/82.61	    inference('sup-', [status(thm)], ['10', '48'])).
82.40/82.61	tff('50', plain,
82.40/82.61	    ![X0 : real, X1 : int, X2 : int]:
82.40/82.61	      times_times(real, number_number_of(real, X2), 
82.40/82.61	        times_times(real, number_number_of(real, X1), X0))
82.40/82.61	       = times_times(real, number_number_of(real, times_times(int, X2, X1)), 
82.40/82.61	           X0),
82.40/82.61	    inference('simplify', [status(thm)], ['49'])).
82.40/82.61	tff('51', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      times_times(int, bit0(X0), X1) = bit0(times_times(int, X1, X0)),
82.40/82.61	    inference('sup+', [status(thm)], ['38', '45'])).
82.40/82.61	tff('52', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      times_times(int, bit0(X0), X1) = times_times(int, bit0(X1), X0),
82.40/82.61	    inference('sup+', [status(thm)], ['51', '45'])).
82.40/82.61	tff('53', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      times_times(int, bit0(X1), X0) = times_times(int, X1, bit0(X0)),
82.40/82.61	    inference('sup+', [status(thm)], ['52', '38'])).
82.40/82.61	tff('54', plain,
82.40/82.61	    ![X0 : real]: (~ $true | times_times(real, X0, one_one(real)) = X0),
82.40/82.61	    inference('sup-', [status(thm)], ['6', '39'])).
82.40/82.61	tff('55', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      (~ $true
82.40/82.61	       | times_times(real, X0, number_number_of(real, bit1(pls))) = X0),
82.40/82.61	    inference('demod', [status(thm)], ['54', '13'])).
82.40/82.61	tff('56', plain,
82.40/82.61	    ![X0 : real]:
82.40/82.61	      times_times(real, X0, number_number_of(real, bit1(pls))) = X0,
82.40/82.61	    inference('simplify', [status(thm)], ['55'])).
82.40/82.61	tff(fact_24_arith__simps_I32_J, axiom,
82.40/82.61	  (![A:$tType]:
82.40/82.61	     (number_ring(A) =>
82.40/82.61	      (![W:int,V:int]:
82.40/82.61	         (times_times(A,number_number_of(A,V),number_number_of(A,W)) =
82.40/82.61	          number_number_of(A,times_times(int,V,W))))))).
82.40/82.61	tff('57', plain,
82.40/82.61	    ![X36 : $tType, X37 : int, X38 : int]:
82.40/82.61	      (times_times(X36, number_number_of(X36, X37), 
82.40/82.61	         number_number_of(X36, X38))
82.40/82.61	        = number_number_of(X36, times_times(int, X37, X38))
82.40/82.61	       | ~ number_ring(X36)),
82.40/82.61	    inference('cnf', [status(esa)], [fact_24_arith__simps_I32_J])).
82.40/82.61	tff('58', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      (~ $true
82.40/82.61	       | times_times(real, number_number_of(real, X1), 
82.40/82.61	           number_number_of(real, X0))
82.40/82.61	          = number_number_of(real, times_times(int, X1, X0))),
82.40/82.61	    inference('sup-', [status(thm)], ['10', '57'])).
82.40/82.61	tff('59', plain,
82.40/82.61	    ![X0 : int, X1 : int]:
82.40/82.61	      times_times(real, number_number_of(real, X1), 
82.40/82.61	        number_number_of(real, X0))
82.40/82.61	       = number_number_of(real, times_times(int, X1, X0)),
82.40/82.61	    inference('simplify', [status(thm)], ['58'])).
82.40/82.61	tff('60', plain,
82.40/82.61	    ![X0 : int]:
82.40/82.61	      number_number_of(real, X0)
82.40/82.61	       = number_number_of(real, times_times(int, X0, bit1(pls))),
82.40/82.61	    inference('sup+', [status(thm)], ['56', '59'])).
82.40/82.61	tff('61', plain,
82.40/82.61	    ![X0 : int]:
82.40/82.61	      number_number_of(real, bit0(X0))
82.40/82.61	       = number_number_of(real, times_times(int, X0, bit0(bit1(pls)))),
82.40/82.61	    inference('sup+', [status(thm)], ['53', '60'])).
82.40/82.61	tff('62', plain,
82.40/82.61	    ~ ord_less_eq(real, 
82.40/82.61	        times_times(real, number_number_of(real, bit0(bit1(pls))), 
82.40/82.61	          times_times(real, number_number_of(real, bit0(bit1(pls))), 
82.40/82.61	            times_times(real, x, x))), number_number_of(real, bit1(pls))),
82.40/82.61	    inference('demod', [status(thm)], ['35', '47', '50', '61', '44'])).
82.40/82.61	tff('63', plain, ~ $true, inference('sup-', [status(thm)], ['31', '62'])).
82.40/82.61	tff('64', plain, $false, inference('simplify', [status(thm)], ['63'])).
82.40/82.61	
82.40/82.61	% SZS output end Refutation
82.40/82.62	EOF
