0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
0.00/0.00	% Ordering    : kbo
0.00/0.00	% 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
0.00/0.19	% Computer   : n031.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
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 08:33:23 CST 2018
4.17/4.36	% done 958 iterations in 4.161s
4.17/4.36	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
4.17/4.36	% SZS output start Refutation
4.17/4.36	tff(conj_0, conjecture,
4.17/4.36	  (div_mod(int,
4.17/4.36	           aa(int,int,aa(int,fun(int,int),plus_plus(int),l),
4.17/4.36	              aa(int,int,aa(int,fun(int,int),plus_plus(int),i),
4.17/4.36	                 iprod(int,ks,e))),
4.17/4.36	           d) =
4.17/4.36	   div_mod(int,
4.17/4.36	           aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),
4.17/4.36	              div_mod(int,
4.17/4.36	                      aa(int,int,aa(int,fun(int,int),plus_plus(int),i),
4.17/4.36	                         iprod(int,ks,e)),
4.17/4.36	                      d)),
4.17/4.36	           d))).
4.17/4.36	tff(zf_stmt_0, negated_conjecture,
4.17/4.36	  (div_mod(int,
4.17/4.36	           aa(int,int,aa(int,fun(int,int),plus_plus(int),l),
4.17/4.36	              aa(int,int,aa(int,fun(int,int),plus_plus(int),i),
4.17/4.36	                 iprod(int,ks,e))),
4.17/4.36	           d) !=
4.17/4.36	   div_mod(int,
4.17/4.36	           aa(int,int,aa(int,fun(int,int),plus_plus(int),div_mod(int,l,d)),
4.17/4.36	              div_mod(int,
4.17/4.36	                      aa(int,int,aa(int,fun(int,int),plus_plus(int),i),
4.17/4.36	                         iprod(int,ks,e)),
4.17/4.36	                      d)),
4.17/4.36	           d))).
4.17/4.36	tff('0', plain,
4.17/4.36	    div_mod(int, 
4.17/4.36	      aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
4.17/4.36	        aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
4.17/4.36	          iprod(int, ks, e))), d)
4.17/4.36	     != div_mod(int, 
4.17/4.36	          aa(int, int, 
4.17/4.36	            aa(int, fun(int, int), plus_plus(int), div_mod(int, l, d)), 
4.17/4.36	            div_mod(int, 
4.17/4.36	              aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
4.17/4.36	                iprod(int, ks, e)), d)), d),
4.17/4.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.17/4.36	tff(fact_9_mod__add__left__eq, axiom,
4.17/4.36	  (![A:$tType]:
4.17/4.36	     (semiring_div(A) =>
4.17/4.36	      (![C1:A,B2:A,A1:A]:
4.17/4.36	         (div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),A1),B2),C1) =
4.17/4.36	          div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),div_mod(A,A1,C1)),B2),
4.17/4.36	                  C1)))))).
4.17/4.36	tff('1', plain,
4.17/4.36	    ![X27 : $tType, X28 : X27, X29 : X27, X30 : X27]:
4.17/4.36	      (div_mod(X27, 
4.17/4.36	         aa(X27, X27, aa(X27, fun(X27, X27), plus_plus(X27), X28), X30), X29)
4.17/4.36	        = div_mod(X27, 
4.17/4.36	            aa(X27, X27, 
4.17/4.36	              aa(X27, fun(X27, X27), plus_plus(X27), div_mod(X27, X28, X29)), 
4.17/4.36	              X30), X29)
4.17/4.36	       | ~ semiring_div(X27)),
4.17/4.36	    inference('cnf', [status(esa)], [fact_9_mod__add__left__eq])).
4.17/4.36	tff(fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, axiom,
4.17/4.36	  (![A:$tType]:
4.17/4.36	     (comm_semiring_1(A) =>
4.17/4.36	      (![A1:A]: (aa(A,A,times_times(A,one_one(A)),A1) = A1))))).
4.17/4.36	tff('2', plain,
4.17/4.36	    ![X237 : $tType, X238 : X237]:
4.17/4.36	      (aa(X237, X237, times_times(X237, one_one(X237)), X238) = X238
4.17/4.36	       | ~ comm_semiring_1(X237)),
4.17/4.36	    inference('cnf', [status(esa)],
4.17/4.36	              [fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])).
4.17/4.36	tff(fact_72_zmod__simps_I3_J, axiom,
4.17/4.36	  (![C1:int,B2:int,A1:int]:
4.17/4.36	     (div_mod(int,aa(int,int,times_times(int,A1),div_mod(int,B2,C1)),C1) =
4.17/4.36	      div_mod(int,aa(int,int,times_times(int,A1),B2),C1)))).
4.17/4.36	tff('3', plain,
4.17/4.36	    ![X279 : int, X280 : int, X281 : int]:
4.17/4.36	      div_mod(int, 
4.17/4.36	        aa(int, int, times_times(int, X279), div_mod(int, X280, X281)), X281)
4.17/4.36	       = div_mod(int, aa(int, int, times_times(int, X279), X280), X281),
4.17/4.36	    inference('cnf', [status(esa)], [fact_72_zmod__simps_I3_J])).
4.17/4.36	tff(fact_3_mod__mod__trivial, axiom,
4.17/4.36	  (![A:$tType]:
4.17/4.36	     (semiring_div(A) =>
4.17/4.36	      (![B2:A,A1:A]: (div_mod(A,div_mod(A,A1,B2),B2) = div_mod(A,A1,B2)))))).
4.17/4.36	tff('4', plain,
4.17/4.36	    ![X6 : $tType, X7 : X6, X8 : X6]:
4.17/4.36	      (div_mod(X6, div_mod(X6, X7, X8), X8) = div_mod(X6, X7, X8)
4.17/4.36	       | ~ semiring_div(X6)),
4.17/4.36	    inference('cnf', [status(esa)], [fact_3_mod__mod__trivial])).
4.17/4.36	tff('5', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      (div_mod(int, 
4.17/4.36	         div_mod(int, aa(int, int, times_times(int, X2), X1), X0), X0)
4.17/4.36	        = div_mod(int, 
4.17/4.36	            aa(int, int, times_times(int, X2), div_mod(int, X1, X0)), X0)
4.17/4.36	       | ~ semiring_div(int)),
4.17/4.36	    inference('sup+', [status(thm)], ['3', '4'])).
4.17/4.36	tff(arity_Int_Oint___Divides_Osemiring__div, axiom, (semiring_div(int))).
4.17/4.36	tff('6', plain, semiring_div(int),
4.17/4.36	    inference('cnf', [status(esa)], [arity_Int_Oint___Divides_Osemiring__div])).
4.17/4.36	tff('7', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      (div_mod(int, 
4.17/4.36	         div_mod(int, aa(int, int, times_times(int, X2), X1), X0), X0)
4.17/4.36	        = div_mod(int, aa(int, int, times_times(int, X2), X1), X0)
4.17/4.36	       | ~ $true),
4.17/4.36	    inference('demod', [status(thm)], ['5', '3', '6'])).
4.17/4.36	tff('8', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      div_mod(int, div_mod(int, aa(int, int, times_times(int, X2), X1), X0), 
4.17/4.36	        X0)
4.17/4.36	       = div_mod(int, aa(int, int, times_times(int, X2), X1), X0),
4.17/4.36	    inference('simplify', [status(thm)], ['7'])).
4.17/4.36	tff('9', plain,
4.17/4.36	    ![X0 : int, X1 : int]:
4.17/4.36	      (div_mod(int, div_mod(int, X0, X1), X1)
4.17/4.36	        = div_mod(int, aa(int, int, times_times(int, one_one(int)), X0), X1)
4.17/4.36	       | ~ comm_semiring_1(int)),
4.17/4.36	    inference('sup+', [status(thm)], ['2', '8'])).
4.17/4.36	tff(arity_Int_Oint___Rings_Ocomm__semiring__1, axiom, (comm_semiring_1(int))).
4.17/4.36	tff('10', plain, comm_semiring_1(int),
4.17/4.36	    inference('cnf', [status(esa)],
4.17/4.36	              [arity_Int_Oint___Rings_Ocomm__semiring__1])).
4.17/4.36	tff('11', plain,
4.17/4.36	    ![X0 : int, X1 : int]:
4.17/4.36	      (div_mod(int, div_mod(int, X0, X1), X1)
4.17/4.36	        = div_mod(int, aa(int, int, times_times(int, one_one(int)), X0), X1)
4.17/4.36	       | ~ $true),
4.17/4.36	    inference('demod', [status(thm)], ['9', '10'])).
4.17/4.36	tff('12', plain,
4.17/4.36	    ![X0 : int, X1 : int]:
4.17/4.36	      div_mod(int, div_mod(int, X0, X1), X1)
4.17/4.36	       = div_mod(int, aa(int, int, times_times(int, one_one(int)), X0), X1),
4.17/4.36	    inference('simplify', [status(thm)], ['11'])).
4.17/4.36	tff('13', plain,
4.17/4.36	    ![X0 : int, X1 : int]:
4.17/4.36	      (div_mod(int, div_mod(int, X0, X1), X1) = div_mod(int, X0, X1)
4.17/4.36	       | ~ comm_semiring_1(int)),
4.17/4.36	    inference('sup+', [status(thm)], ['2', '12'])).
4.17/4.36	tff('14', plain,
4.17/4.36	    ![X0 : int, X1 : int]:
4.17/4.36	      (div_mod(int, div_mod(int, X0, X1), X1) = div_mod(int, X0, X1)
4.17/4.36	       | ~ $true),
4.17/4.36	    inference('demod', [status(thm)], ['13', '10'])).
4.17/4.36	tff('15', plain,
4.17/4.36	    ![X0 : int, X1 : int]:
4.17/4.36	      div_mod(int, div_mod(int, X0, X1), X1) = div_mod(int, X0, X1),
4.17/4.36	    inference('simplify', [status(thm)], ['14'])).
4.17/4.36	tff('16', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      (div_mod(int, 
4.17/4.36	         div_mod(int, 
4.17/4.36	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0), 
4.17/4.36	         X0)
4.17/4.36	        = div_mod(int, 
4.17/4.36	            aa(int, int, 
4.17/4.36	              aa(int, fun(int, int), plus_plus(int), div_mod(int, X2, X0)), 
4.17/4.36	              X1), X0)
4.17/4.36	       | ~ semiring_div(int)),
4.17/4.36	    inference('sup+', [status(thm)], ['1', '15'])).
4.17/4.36	tff('17', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      (div_mod(int, 
4.17/4.36	         aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0)
4.17/4.36	        = div_mod(int, 
4.17/4.36	            aa(int, int, 
4.17/4.36	              aa(int, fun(int, int), plus_plus(int), div_mod(int, X2, X0)), 
4.17/4.36	              X1), X0)
4.17/4.36	       | ~ $true),
4.17/4.36	    inference('demod', [status(thm)], ['16', '15', '6'])).
4.17/4.36	tff('18', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      div_mod(int, 
4.17/4.36	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0)
4.17/4.36	       = div_mod(int, 
4.17/4.36	           aa(int, int, 
4.17/4.36	             aa(int, fun(int, int), plus_plus(int), div_mod(int, X2, X0)), 
4.17/4.36	             X1), X0),
4.17/4.36	    inference('simplify', [status(thm)], ['17'])).
4.17/4.36	tff(fact_8_mod__add__right__eq, axiom,
4.17/4.36	  (![A:$tType]:
4.17/4.36	     (semiring_div(A) =>
4.17/4.36	      (![C1:A,B2:A,A1:A]:
4.17/4.36	         (div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),A1),B2),C1) =
4.17/4.36	          div_mod(A,aa(A,A,aa(A,fun(A,A),plus_plus(A),A1),div_mod(A,B2,C1)),
4.17/4.36	                  C1)))))).
4.17/4.36	tff('19', plain,
4.17/4.36	    ![X23 : $tType, X24 : X23, X25 : X23, X26 : X23]:
4.17/4.36	      (div_mod(X23, 
4.17/4.36	         aa(X23, X23, aa(X23, fun(X23, X23), plus_plus(X23), X24), X25), X26)
4.17/4.36	        = div_mod(X23, 
4.17/4.36	            aa(X23, X23, aa(X23, fun(X23, X23), plus_plus(X23), X24), 
4.17/4.36	              div_mod(X23, X25, X26)), X26)
4.17/4.36	       | ~ semiring_div(X23)),
4.17/4.36	    inference('cnf', [status(esa)], [fact_8_mod__add__right__eq])).
4.17/4.36	tff('20', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      (div_mod(int, 
4.17/4.36	         div_mod(int, 
4.17/4.36	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0), 
4.17/4.36	         X0)
4.17/4.36	        = div_mod(int, 
4.17/4.36	            aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), 
4.17/4.36	              div_mod(int, X1, X0)), X0)
4.17/4.36	       | ~ semiring_div(int)),
4.17/4.36	    inference('sup+', [status(thm)], ['19', '15'])).
4.17/4.36	tff('21', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      (div_mod(int, 
4.17/4.36	         aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0)
4.17/4.36	        = div_mod(int, 
4.17/4.36	            aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), 
4.17/4.36	              div_mod(int, X1, X0)), X0)
4.17/4.36	       | ~ $true),
4.17/4.36	    inference('demod', [status(thm)], ['20', '15', '6'])).
4.17/4.36	tff('22', plain,
4.17/4.36	    ![X0 : int, X1 : int, X2 : int]:
4.17/4.36	      div_mod(int, 
4.17/4.36	        aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), X1), X0)
4.17/4.36	       = div_mod(int, 
4.17/4.36	           aa(int, int, aa(int, fun(int, int), plus_plus(int), X2), 
4.17/4.36	             div_mod(int, X1, X0)), X0),
4.17/4.36	    inference('simplify', [status(thm)], ['21'])).
4.17/4.36	tff('23', plain,
4.17/4.36	    div_mod(int, 
4.17/4.36	      aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
4.17/4.36	        aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
4.17/4.36	          iprod(int, ks, e))), d)
4.17/4.36	     != div_mod(int, 
4.17/4.36	          aa(int, int, aa(int, fun(int, int), plus_plus(int), l), 
4.17/4.36	            aa(int, int, aa(int, fun(int, int), plus_plus(int), i), 
4.17/4.36	              iprod(int, ks, e))), d),
4.17/4.36	    inference('demod', [status(thm)], ['0', '18', '22'])).
4.17/4.36	tff('24', plain, $false, inference('simplify', [status(thm)], ['23'])).
4.17/4.36	
4.17/4.36	% SZS output end Refutation
4.17/4.37	EOF
