0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : purification_ext
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --ho-purify ext \
0.00/0.01	  --ho-ext-axiom \
0.00/0.01	  --restrict-hidden-sup-at-vars \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n044.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% 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 08:27:38 CST 2018
50.81/51.02	% done 3748 iterations in 50.814s
50.81/51.02	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
50.81/51.02	% SZS output start Refutation
50.81/51.02	tff(conj_0, conjecture,
50.81/51.02	  (div_mod(int,
50.81/51.02	           aa(int,int,aa(int,fun(int,int),plus_plus(int),l),
50.81/51.02	              aa(int,int,aa(int,fun(int,int),plus_plus(int),i),
50.81/51.02	                 iprod(int,ks,e))),
50.81/51.02	           d) =
50.81/51.02	   div_mod(int,
50.81/51.02	           aa(int,int,aa(int,fun(int,int),plus_plus(int),l),
50.81/51.02	              aa(int,int,aa(int,fun(int,int),plus_plus(int),j),
50.81/51.02	                 iprod(int,ks,e))),
50.81/51.02	           d))).
50.81/51.02	tff(zf_stmt_0, negated_conjecture,
50.81/51.02	  (div_mod(int,
50.81/51.02	           aa(int,int,aa(int,fun(int,int),plus_plus(int),l),
50.81/51.02	              aa(int,int,aa(int,fun(int,int),plus_plus(int),i),
50.81/51.02	                 iprod(int,ks,e))),
50.81/51.02	           d) !=
50.81/51.02	   div_mod(int,
50.81/51.02	           aa(int,int,aa(int,fun(int,int),plus_plus(int),l),
50.81/51.02	              aa(int,int,aa(int,fun(int,int),plus_plus(int),j),
50.81/51.02	                 iprod(int,ks,e))),
50.81/51.02	           d))).
50.81/51.02	tff('0', plain,
50.81/51.02	    div_mod(int, 
50.81/51.02	      aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
50.81/51.02	          iprod(int, ks, e))), d)
50.81/51.02	     != div_mod(int, 
50.81/51.02	          aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
50.81/51.02	            aa(int, int, aa(int, fun(int, int), plus_plus(int), j), 
50.81/51.02	              iprod(int, ks, e))), d),
50.81/51.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.81/51.02	tff(fact_0_assms_I3_J, axiom,
50.81/51.02	  (div_mod(int,i,divisor(a)) = div_mod(int,j,divisor(a)))).
50.81/51.02	tff('1', plain, div_mod(int, i, divisor(a)) = div_mod(int, j, divisor(a)),
50.81/51.02	    inference('cnf', [status(esa)], [fact_0_assms_I3_J])).
50.81/51.02	tff(fact_3_Dvd, axiom, (a = dvd(d,l,ks1))).
50.81/51.02	tff('2', plain, a = dvd(d, l, ks1),
50.81/51.02	    inference('cnf', [status(esa)], [fact_3_Dvd])).
50.81/51.02	tff(fact_21_divisor_Osimps_I2_J, axiom,
50.81/51.02	  (![Ks:list(int),I1:int,D:int]: (divisor(dvd(D,I1,Ks)) = D))).
50.81/51.02	tff('3', plain,
50.81/51.02	    ![X76 : int, X77 : int, X78 : list(int)]:
50.81/51.02	      divisor(dvd(X76, X77, X78)) = X76,
50.81/51.02	    inference('cnf', [status(esa)], [fact_21_divisor_Osimps_I2_J])).
50.81/51.02	tff('4', plain, divisor(a) = d, inference('sup+', [status(thm)], ['2', '3'])).
50.81/51.02	tff('5', plain, div_mod(int, i, d) = div_mod(int, j, d),
50.81/51.02	    inference('demod', [status(thm)], ['1', '4', '4'])).
50.81/51.02	tff(fact_9_mod__add__left__eq, axiom,
50.81/51.02	  (![A:$tType]:
50.81/51.02	     (semiring_div(A) =>
50.81/51.02	      (![C1:A,B2:A,A1:A]:
50.81/51.02	         (div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),A1),B2),C1) =
50.81/51.02	          div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),div_mod(A,A1,C1)),B2),
50.81/51.02	                  C1)))))).
50.81/51.02	tff('6', plain,
50.81/51.02	    ![X27 : $tType, X28 : X27, X29 : X27, X30 : X27]:
50.81/51.02	      (div_mod(X27, 
50.81/51.02	         aa(X27, X27, aa(X27, fun(X27, X27), plus_plus(X27), X28), X30), X29)
50.81/51.02	        = div_mod(X27, 
50.81/51.02	            aa(X27, X27, 
50.81/51.02	              aa(X27, fun(X27, X27), plus_plus(X27), div_mod(X27, X28, X29)), 
50.81/51.02	              X30), X29)
50.81/51.02	       | ~ semiring_div(X27)),
50.81/51.02	    inference('cnf', [status(esa)], [fact_9_mod__add__left__eq])).
50.81/51.02	tff('7', plain,
50.81/51.02	    ![X0 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         aa(int, int, aa(int, fun(int, int), plus_plus(int), j), X0), d)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, 
50.81/51.02	              aa(int, fun(int, int), plus_plus(int), div_mod(int, i, d)), X0), 
50.81/51.02	            d)
50.81/51.02	       | ~ semiring_div(int)),
50.81/51.02	    inference('sup+', [status(thm)], ['5', '6'])).
50.81/51.02	tff(arity_Int_Oint___Divides_Osemiring__div, axiom, (semiring_div(int))).
50.81/51.02	tff('8', plain, semiring_div(int),
50.81/51.02	    inference('cnf', [status(esa)], [arity_Int_Oint___Divides_Osemiring__div])).
50.81/51.02	tff('9', plain,
50.81/51.02	    ![X0 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         aa(int, int, aa(int, fun(int, int), plus_plus(int), j), X0), d)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, 
50.81/51.02	              aa(int, fun(int, int), plus_plus(int), div_mod(int, i, d)), X0), 
50.81/51.02	            d)
50.81/51.02	       | ~ $true),
50.81/51.02	    inference('demod', [status(thm)], ['7', '8'])).
50.81/51.02	tff('10', plain,
50.81/51.02	    ![X0 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), j), X0), d)
50.81/51.02	       = div_mod(int, 
50.81/51.02	           aa(int, int, 
50.81/51.02	             aa(int, fun(int, int), plus_plus(int), div_mod(int, i, d)), X0), 
50.81/51.02	           d),
50.81/51.02	    inference('simplify', [status(thm)], ['9'])).
50.81/51.02	tff(fact_8_mod__add__right__eq, axiom,
50.81/51.02	  (![A:$tType]:
50.81/51.02	     (semiring_div(A) =>
50.81/51.02	      (![C1:A,B2:A,A1:A]:
50.81/51.02	         (div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),A1),B2),C1) =
50.81/51.02	          div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),A1),div_mod(A,B2,C1)),
50.81/51.02	                  C1)))))).
50.81/51.02	tff('11', plain,
50.81/51.02	    ![X23 : $tType, X24 : X23, X25 : X23, X26 : X23]:
50.81/51.02	      (div_mod(X23, 
50.81/51.02	         aa(X23, X23, aa(X23, fun(X23, X23), plus_plus(X23), X24), X25), X26)
50.81/51.02	        = div_mod(X23, 
50.81/51.02	            aa(X23, X23, aa(X23, fun(X23, X23), plus_plus(X23), X24), 
50.81/51.02	              div_mod(X23, X25, X26)), X26)
50.81/51.02	       | ~ semiring_div(X23)),
50.81/51.02	    inference('cnf', [status(esa)], [fact_8_mod__add__right__eq])).
50.81/51.02	tff(fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, axiom,
50.81/51.02	  (![A:$tType]:
50.81/51.02	     (comm_semiring_1(A) =>
50.81/51.02	      (![A1:A]: (aa(A,A,times_times(A,one_one(A)),A1) = A1))))).
50.81/51.02	tff('12', plain,
50.81/51.02	    ![X237 : $tType, X238 : X237]:
50.81/51.02	      (aa(X237, X237, times_times(X237, one_one(X237)), X238) = X238
50.81/51.02	       | ~ comm_semiring_1(X237)),
50.81/51.02	    inference('cnf', [status(esa)],
50.81/51.02	              [fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])).
50.81/51.02	tff(fact_72_zmod__simps_I3_J, axiom,
50.81/51.02	  (![C1:int,B2:int,A1:int]:
50.81/51.02	     (div_mod(int,aa(int,int,times_times(int,A1),div_mod(int,B2,C1)),C1) =
50.81/51.02	      div_mod(int,aa(int,int,times_times(int,A1),B2),C1)))).
50.81/51.02	tff('13', plain,
50.81/51.02	    ![X279 : int, X280 : int, X281 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, times_times(int, X279), div_mod(int, X280, X281)), X281)
50.81/51.02	       = div_mod(int, aa(int, int, times_times(int, X279), X280), X281),
50.81/51.02	    inference('cnf', [status(esa)], [fact_72_zmod__simps_I3_J])).
50.81/51.02	tff(fact_4_mod__mod__trivial, axiom,
50.81/51.02	  (![A:$tType]:
50.81/51.02	     (semiring_div(A) =>
50.81/51.02	      (![B2:A,A1:A]: (div_mod(A,div_mod(A,A1,B2),B2) = div_mod(A,A1,B2)))))).
50.81/51.02	tff('14', plain,
50.81/51.02	    ![X6 : $tType, X7 : X6, X8 : X6]:
50.81/51.02	      (div_mod(X6, div_mod(X6, X7, X8), X8) = div_mod(X6, X7, X8)
50.81/51.02	       | ~ semiring_div(X6)),
50.81/51.02	    inference('cnf', [status(esa)], [fact_4_mod__mod__trivial])).
50.81/51.02	tff('15', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         div_mod(int, aa(int, int, times_times(int, X2), X1), X0), X0)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, times_times(int, X2), div_mod(int, X1, X0)), X0)
50.81/51.02	       | ~ semiring_div(int)),
50.81/51.02	    inference('sup+', [status(thm)], ['13', '14'])).
50.81/51.02	tff('16', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         div_mod(int, aa(int, int, times_times(int, X2), X1), X0), X0)
50.81/51.02	        = div_mod(int, aa(int, int, times_times(int, X2), X1), X0)
50.81/51.02	       | ~ $true),
50.81/51.02	    inference('demod', [status(thm)], ['15', '13', '8'])).
50.81/51.02	tff('17', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int]:
50.81/51.02	      div_mod(int, div_mod(int, aa(int, int, times_times(int, X2), X1), X0), 
50.81/51.02	        X0)
50.81/51.02	       = div_mod(int, aa(int, int, times_times(int, X2), X1), X0),
50.81/51.02	    inference('simplify', [status(thm)], ['16'])).
50.81/51.02	tff('18', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      (div_mod(int, div_mod(int, X0, X1), X1)
50.81/51.02	        = div_mod(int, aa(int, int, times_times(int, one_one(int)), X0), X1)
50.81/51.02	       | ~ comm_semiring_1(int)),
50.81/51.02	    inference('sup+', [status(thm)], ['12', '17'])).
50.81/51.02	tff(arity_Int_Oint___Rings_Ocomm__semiring__1, axiom, (comm_semiring_1(int))).
50.81/51.02	tff('19', plain, comm_semiring_1(int),
50.81/51.02	    inference('cnf', [status(esa)],
50.81/51.02	              [arity_Int_Oint___Rings_Ocomm__semiring__1])).
50.81/51.02	tff('20', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      (div_mod(int, div_mod(int, X0, X1), X1)
50.81/51.02	        = div_mod(int, aa(int, int, times_times(int, one_one(int)), X0), X1)
50.81/51.02	       | ~ $true),
50.81/51.02	    inference('demod', [status(thm)], ['18', '19'])).
50.81/51.02	tff('21', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      div_mod(int, div_mod(int, X0, X1), X1)
50.81/51.02	       = div_mod(int, aa(int, int, times_times(int, one_one(int)), X0), X1),
50.81/51.02	    inference('simplify', [status(thm)], ['20'])).
50.81/51.02	tff('22', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      (div_mod(int, div_mod(int, X0, X1), X1) = div_mod(int, X0, X1)
50.81/51.02	       | ~ comm_semiring_1(int)),
50.81/51.02	    inference('sup+', [status(thm)], ['12', '21'])).
50.81/51.02	tff('23', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      (div_mod(int, div_mod(int, X0, X1), X1) = div_mod(int, X0, X1)
50.81/51.02	       | ~ $true),
50.81/51.02	    inference('demod', [status(thm)], ['22', '19'])).
50.81/51.02	tff('24', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      div_mod(int, div_mod(int, X0, X1), X1) = div_mod(int, X0, X1),
50.81/51.02	    inference('simplify', [status(thm)], ['23'])).
50.81/51.02	tff('25', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         div_mod(int, 
50.81/51.02	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0), 
50.81/51.02	         X0)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), 
50.81/51.02	              div_mod(int, X1, X0)), X0)
50.81/51.02	       | ~ semiring_div(int)),
50.81/51.02	    inference('sup+', [status(thm)], ['11', '24'])).
50.81/51.02	tff('26', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), 
50.81/51.02	              div_mod(int, X1, X0)), X0)
50.81/51.02	       | ~ $true),
50.81/51.02	    inference('demod', [status(thm)], ['25', '24', '8'])).
50.81/51.02	tff('27', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0)
50.81/51.02	       = div_mod(int, 
50.81/51.02	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), 
50.81/51.02	             div_mod(int, X1, X0)), X0),
50.81/51.02	    inference('simplify', [status(thm)], ['26'])).
50.81/51.02	tff('28', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X1), 
50.81/51.02	          aa(int, int, 
50.81/51.02	            aa(int, fun(int, int), plus_plus(int), div_mod(int, i, d)), X0)), 
50.81/51.02	        d)
50.81/51.02	       = div_mod(int, 
50.81/51.02	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X1), 
50.81/51.02	             div_mod(int, 
50.81/51.02	               aa(int, int, aa(int, fun(int, int), plus_plus(int), j), X0), 
50.81/51.02	               d)), d),
50.81/51.02	    inference('sup+', [status(thm)], ['10', '27'])).
50.81/51.02	tff('29', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X1), 
50.81/51.02	          aa(int, int, 
50.81/51.02	            aa(int, fun(int, int), plus_plus(int), div_mod(int, i, d)), X0)), 
50.81/51.02	        d)
50.81/51.02	       = div_mod(int, 
50.81/51.02	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X1), 
50.81/51.02	             aa(int, int, aa(int, fun(int, int), plus_plus(int), j), X0)), d),
50.81/51.02	    inference('demod', [status(thm)], ['28', '27'])).
50.81/51.02	tff('30', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int, X3 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         aa(int, int, aa(int, fun(int, int), plus_plus(int), X3), 
50.81/51.02	           aa(int, int, 
50.81/51.02	             aa(int, fun(int, int), plus_plus(int), div_mod(int, X2, X0)), 
50.81/51.02	             X1)), X0)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, aa(int, fun(int, int), plus_plus(int), X3), 
50.81/51.02	              div_mod(int, 
50.81/51.02	                aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), 
50.81/51.02	                X0)), X0)
50.81/51.02	       | ~ semiring_div(int)),
50.81/51.02	    inference('sup+', [status(thm)], ['6', '27'])).
50.81/51.02	tff('31', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int, X3 : int]:
50.81/51.02	      (div_mod(int, 
50.81/51.02	         aa(int, int, aa(int, fun(int, int), plus_plus(int), X3), 
50.81/51.02	           aa(int, int, 
50.81/51.02	             aa(int, fun(int, int), plus_plus(int), div_mod(int, X2, X0)), 
50.81/51.02	             X1)), X0)
50.81/51.02	        = div_mod(int, 
50.81/51.02	            aa(int, int, aa(int, fun(int, int), plus_plus(int), X3), 
50.81/51.02	              aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1)), 
50.81/51.02	            X0)
50.81/51.02	       | ~ $true),
50.81/51.02	    inference('demod', [status(thm)], ['30', '27', '8'])).
50.81/51.02	tff('32', plain,
50.81/51.02	    ![X0 : int, X1 : int, X2 : int, X3 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X3), 
50.81/51.02	          aa(int, int, 
50.81/51.02	            aa(int, fun(int, int), plus_plus(int), div_mod(int, X2, X0)), X1)), 
50.81/51.02	        X0)
50.81/51.02	       = div_mod(int, 
50.81/51.02	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X3), 
50.81/51.02	             aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1)), 
50.81/51.02	           X0),
50.81/51.02	    inference('simplify', [status(thm)], ['31'])).
50.81/51.02	tff('33', plain,
50.81/51.02	    ![X0 : int, X1 : int]:
50.81/51.02	      div_mod(int, 
50.81/51.02	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X1), 
50.81/51.02	          aa(int, int, aa(int, fun(int, int), plus_plus(int), i), X0)), d)
50.81/51.03	       = div_mod(int, 
50.81/51.03	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X1), 
50.81/51.03	             aa(int, int, aa(int, fun(int, int), plus_plus(int), j), X0)), d),
50.81/51.03	    inference('demod', [status(thm)], ['29', '32'])).
50.81/51.03	tff('34', plain,
50.81/51.03	    div_mod(int, 
50.81/51.03	      aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
50.81/51.03	        aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
50.81/51.03	          iprod(int, ks, e))), d)
50.81/51.03	     != div_mod(int, 
50.81/51.03	          aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
50.81/51.03	            aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
50.81/51.03	              iprod(int, ks, e))), d),
50.81/51.03	    inference('demod', [status(thm)], ['0', '33'])).
50.81/51.03	tff('35', plain, $false, inference('simplify', [status(thm)], ['34'])).
50.81/51.03	
50.81/51.03	% SZS output end Refutation
50.81/51.03	EOF
