TSTP Solution File: GRP768-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP768-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:40:41 EDT 2022
% Result : Unsatisfiable 1.37s 1.59s
% Output : Refutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 113 ( 113 unt; 0 nHn; 9 RR)
% Number of literals : 113 ( 112 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 206 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos01,axiom,
product(X,one) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(sos02,axiom,
product(one,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos03,axiom,
product(X,difference(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos04,axiom,
difference(X,product(X,Y)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos05,axiom,
quotient(product(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos06,axiom,
product(quotient(X,Y),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos07,axiom,
difference(X,product(product(X,Y),Z)) = quotient(product(Y,product(Z,X)),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(sos09,axiom,
i(X) = difference(X,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(sos10,axiom,
j(X) = quotient(one,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos11,axiom,
product(i(X),X) = product(X,j(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos12,axiom,
eta(X) = product(i(X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(sos13,axiom,
product(i(i(X)),Y) = product(eta(X),product(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
cnf(sos14,axiom,
product(X,product(eta(X),Y)) = product(j(j(X)),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
cnf(sos15,axiom,
product(X,product(Y,eta(X))) = product(product(X,Y),eta(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
cnf(sos16,axiom,
product(eta(X),product(Y,Z)) = product(product(eta(X),Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
cnf(sos19,axiom,
t(X,Y) = quotient(product(X,Y),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
cnf(goals,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(23,plain,
quotient(product(eta(x0),product(x1,x2)),eta(x0)) != product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),
inference('REWRITE',[status(thm)],[goals,sos19,theory(equality)]) ).
cnf(24,plain,
eta(X) = product(X,j(X)),
inference('REWRITE',[status(thm)],[sos11,sos12,theory(equality)]) ).
cnf(26,plain,
product(X,i(X)) = one,
inference('PARAMODULATE',[status(thm)],[sos03,sos09,theory(equality)]) ).
cnf(27,plain,
difference(X,X) = one,
inference('PARAMODULATE',[status(thm)],[sos04,sos01,theory(equality)]) ).
cnf(30,plain,
quotient(X,difference(Y,X)) = Y,
inference('PARAMODULATE',[status(thm)],[sos05,sos03,theory(equality)]) ).
cnf(31,plain,
product(j(X),X) = one,
inference('PARAMODULATE',[status(thm)],[sos06,sos10,theory(equality)]) ).
cnf(32,plain,
difference(quotient(X,Y),X) = Y,
inference('PARAMODULATE',[status(thm)],[sos04,sos06,theory(equality)]) ).
cnf(38,plain,
difference(X,eta(X)) = j(X),
inference('PARAMODULATE',[status(thm)],[sos04,24,theory(equality)]) ).
cnf(40,plain,
i(i(X)) = product(eta(X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos13,sos01,theory(equality)]),sos01,theory(equality)]) ).
cnf(45,plain,
difference(eta(X),product(i(i(X)),Y)) = product(X,Y),
inference('PARAMODULATE',[status(thm)],[sos04,sos13,theory(equality)]) ).
cnf(50,plain,
product(X,eta(X)) = j(j(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos14,sos01,theory(equality)]),sos01,theory(equality)]) ).
cnf(51,plain,
product(X,Y) = product(j(j(X)),difference(eta(X),Y)),
inference('PARAMODULATE',[status(thm)],[sos14,sos03,theory(equality)]) ).
cnf(53,plain,
difference(X,product(j(j(X)),Y)) = product(eta(X),Y),
inference('PARAMODULATE',[status(thm)],[sos04,sos14,theory(equality)]) ).
cnf(59,plain,
difference(X,product(product(X,Y),eta(X))) = product(Y,eta(X)),
inference('PARAMODULATE',[status(thm)],[sos04,sos15,theory(equality)]) ).
cnf(61,plain,
product(X,eta(eta(X))) = product(product(X,i(eta(X))),eta(X)),
inference('PARAMODULATE',[status(thm)],[sos15,sos12,theory(equality)]) ).
cnf(62,plain,
product(i(i(X)),product(Y,eta(X))) = product(eta(X),product(product(X,Y),eta(X))),
inference('PARAMODULATE',[status(thm)],[sos13,sos15,theory(equality)]) ).
cnf(64,plain,
difference(X,product(product(X,eta(Y)),Z)) = product(eta(Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos05,sos16,theory(equality)]),sos07,theory(equality)]) ).
cnf(65,plain,
difference(product(eta(X),Y),product(eta(X),product(Y,Z))) = Z,
inference('PARAMODULATE',[status(thm)],[sos04,sos16,theory(equality)]) ).
cnf(71,plain,
difference(eta(X),product(product(eta(X),Y),Z)) = product(Y,Z),
inference('PARAMODULATE',[status(thm)],[sos04,sos16,theory(equality)]) ).
cnf(72,plain,
product(eta(X),product(difference(eta(X),Y),Z)) = product(Y,Z),
inference('PARAMODULATE',[status(thm)],[sos16,sos03,theory(equality)]) ).
cnf(75,plain,
product(eta(X),product(product(X,Y),Z)) = product(product(i(i(X)),Y),Z),
inference('PARAMODULATE',[status(thm)],[sos16,sos13,theory(equality)]) ).
cnf(76,plain,
product(i(i(X)),product(Y,eta(X))) = product(product(i(i(X)),Y),eta(X)),
inference('REWRITE',[status(thm)],[62,75,theory(equality)]) ).
cnf(87,plain,
difference(X,product(product(X,Y),quotient(Z,X))) = quotient(product(Y,Z),X),
inference('PARAMODULATE',[status(thm)],[sos07,sos06,theory(equality)]) ).
cnf(93,plain,
product(product(eta(x0),x1),quotient(x2,eta(x0))) != product(product(eta(x0),quotient(x1,eta(x0))),product(eta(x0),quotient(x2,eta(x0)))),
inference('REWRITE',[status(thm)],[23,sos16,71,87,theory(equality)]) ).
cnf(121,plain,
X = product(j(j(X)),i(eta(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos14,26,theory(equality)]),sos01,theory(equality)]) ).
cnf(122,plain,
eta(X) = product(product(eta(X),Y),i(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos16,26,theory(equality)]),sos01,theory(equality)]) ).
cnf(123,plain,
product(eta(X),product(i(eta(X)),Y)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos16,26,theory(equality)]),sos02,theory(equality)]) ).
cnf(126,plain,
i(j(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos04,31,theory(equality)]),sos09,theory(equality)]) ).
cnf(128,plain,
eta(X) = eta(j(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos13,31,theory(equality)]),sos01,sos12,126,theory(equality)]) ).
cnf(132,plain,
j(i(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos10,30,theory(equality)]),sos09,theory(equality)]) ).
cnf(149,plain,
i(X) = product(eta(X),j(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[40,128,theory(equality)]),126,theory(equality)]) ).
cnf(159,plain,
product(i(i(X)),eta(X)) = product(eta(X),j(j(X))),
inference('PARAMODULATE',[status(thm)],[sos13,50,theory(equality)]) ).
cnf(166,plain,
X = product(i(i(X)),eta(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[149,128,theory(equality)]),159,126,theory(equality)]) ).
cnf(196,plain,
product(X,i(eta(X))) = i(i(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos13,121,theory(equality)]),40,128,126,theory(equality)]) ).
cnf(197,plain,
product(X,eta(eta(X))) = X,
inference('REWRITE',[status(thm)],[61,166,196,theory(equality)]) ).
cnf(201,plain,
one = eta(eta(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos04,197,theory(equality)]),27,theory(equality)]) ).
cnf(208,plain,
i(eta(X)) = j(eta(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[38,201,theory(equality)]),sos09,theory(equality)]) ).
cnf(221,plain,
difference(product(eta(X),Y),eta(X)) = i(Y),
inference('PARAMODULATE',[status(thm)],[sos04,122,theory(equality)]) ).
cnf(263,plain,
difference(j(j(X)),product(X,Y)) = difference(eta(X),Y),
inference('PARAMODULATE',[status(thm)],[sos04,51,theory(equality)]) ).
cnf(267,plain,
product(X,difference(eta(X),Y)) = product(i(i(X)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos13,51,theory(equality)]),sos13,128,126,theory(equality)]) ).
cnf(269,plain,
difference(eta(X),Y) = product(i(eta(X)),Y),
inference('PARAMODULATE',[status(thm)],[sos04,123,theory(equality)]) ).
cnf(343,plain,
difference(X,eta(Y)) = i(difference(eta(Y),X)),
inference('PARAMODULATE',[status(thm)],[221,sos03,theory(equality)]) ).
cnf(348,plain,
difference(i(eta(X)),difference(eta(X),Y)) = Y,
inference('PARAMODULATE',[status(thm)],[sos04,269,theory(equality)]) ).
cnf(349,plain,
difference(eta(X),difference(i(eta(X)),Y)) = Y,
inference('PARAMODULATE',[status(thm)],[sos03,269,theory(equality)]) ).
cnf(358,plain,
difference(eta(X),Y) = product(X,difference(i(i(X)),Y)),
inference('PARAMODULATE',[status(thm)],[45,sos03,theory(equality)]) ).
cnf(359,plain,
difference(eta(X),product(i(X),Y)) = product(j(X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,126,theory(equality)]),128,theory(equality)]) ).
cnf(436,plain,
difference(X,difference(eta(X),product(X,Y))) = product(eta(X),Y),
inference('REWRITE',[status(thm)],[53,126,128,359,theory(equality)]) ).
cnf(462,plain,
difference(X,difference(eta(X),product(X,product(difference(eta(X),Y),Z)))) = product(Y,Z),
inference('REWRITE',[status(thm)],[72,436,theory(equality)]) ).
cnf(471,plain,
difference(X,product(product(X,eta(Y)),Z)) = difference(Y,difference(eta(Y),product(Y,Z))),
inference('REWRITE',[status(thm)],[64,436,theory(equality)]) ).
cnf(489,plain,
difference(X,difference(eta(X),product(X,product(Y,Z)))) = product(difference(X,difference(eta(X),product(X,Y))),Z),
inference('REWRITE',[status(thm)],[sos16,436,theory(equality)]) ).
cnf(491,plain,
difference(difference(X,difference(eta(X),product(X,Y))),difference(X,difference(eta(X),product(X,product(Y,Z))))) = Z,
inference('REWRITE',[status(thm)],[65,436,theory(equality)]) ).
cnf(515,plain,
product(i(i(X)),Y) = difference(X,difference(eta(X),product(X,product(X,Y)))),
inference('REWRITE',[status(thm)],[sos13,436,theory(equality)]) ).
cnf(516,plain,
product(difference(x0,difference(eta(x0),product(x0,x1))),quotient(x2,eta(x0))) != product(difference(x0,difference(eta(x0),product(x0,quotient(x1,eta(x0))))),difference(x0,difference(eta(x0),product(x0,quotient(x2,eta(x0)))))),
inference('REWRITE',[status(thm)],[93,436,theory(equality)]) ).
cnf(578,plain,
difference(eta(X),difference(X,difference(eta(X),product(X,Y)))) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[59,201,theory(equality)]),sos01,436,theory(equality)]) ).
cnf(613,plain,
difference(j(j(X)),Y) = difference(eta(X),difference(X,Y)),
inference('PARAMODULATE',[status(thm)],[263,sos03,theory(equality)]) ).
cnf(614,plain,
difference(j(j(X)),difference(eta(X),product(X,Y))) = Y,
inference('REWRITE',[status(thm)],[578,613,theory(equality)]) ).
cnf(626,plain,
difference(X,product(i(i(X)),Y)) = difference(eta(X),Y),
inference('PARAMODULATE',[status(thm)],[sos04,267,theory(equality)]) ).
cnf(641,plain,
difference(eta(X),product(Y,eta(X))) = product(difference(eta(X),Y),eta(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[59,267,theory(equality)]),626,76,theory(equality)]) ).
cnf(685,plain,
difference(i(eta(X)),Y) = difference(X,difference(eta(X),product(X,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[348,sos04,theory(equality)]),436,theory(equality)]) ).
cnf(694,plain,
product(i(i(X)),Y) = difference(i(eta(X)),product(X,Y)),
inference('REWRITE',[status(thm)],[515,685,theory(equality)]) ).
cnf(739,plain,
difference(i(eta(X)),product(difference(eta(X),Y),Z)) = product(Y,Z),
inference('REWRITE',[status(thm)],[462,685,theory(equality)]) ).
cnf(769,plain,
difference(X,product(product(X,eta(Y)),Z)) = difference(i(eta(Y)),Z),
inference('REWRITE',[status(thm)],[471,685,theory(equality)]) ).
cnf(779,plain,
difference(i(eta(X)),Y) = product(eta(X),Y),
inference('REWRITE',[status(thm)],[436,685,theory(equality)]) ).
cnf(780,plain,
difference(i(eta(X)),product(Y,Z)) = product(difference(i(eta(X)),Y),Z),
inference('REWRITE',[status(thm)],[489,685,theory(equality)]) ).
cnf(786,plain,
difference(difference(i(eta(X)),Y),difference(i(eta(X)),product(Y,Z))) = Z,
inference('REWRITE',[status(thm)],[491,685,theory(equality)]) ).
cnf(800,plain,
difference(i(eta(x0)),product(x1,quotient(x2,eta(x0)))) != difference(i(eta(x0)),product(quotient(x1,eta(x0)),difference(i(eta(x0)),quotient(x2,eta(x0))))),
inference('REWRITE',[status(thm)],[516,780,685,theory(equality)]) ).
cnf(859,plain,
difference(X,difference(eta(X),Y)) = difference(i(i(X)),Y),
inference('PARAMODULATE',[status(thm)],[sos04,358,theory(equality)]) ).
cnf(869,plain,
difference(i(eta(X)),Y) = difference(i(i(X)),product(X,Y)),
inference('REWRITE',[status(thm)],[685,859,theory(equality)]) ).
cnf(870,plain,
difference(j(j(X)),difference(eta(X),Y)) = difference(eta(X),difference(i(i(X)),Y)),
inference('PARAMODULATE',[status(thm)],[263,358,theory(equality)]) ).
cnf(907,plain,
difference(j(j(X)),difference(eta(X),Y)) = difference(X,Y),
inference('PARAMODULATE',[status(thm)],[614,sos03,theory(equality)]) ).
cnf(908,plain,
difference(X,Y) = difference(eta(X),difference(i(i(X)),Y)),
inference('REWRITE',[status(thm)],[870,907,theory(equality)]) ).
cnf(956,plain,
difference(X,product(product(X,Y),j(X))) = quotient(Y,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[87,sos01,theory(equality)]),sos10,theory(equality)]) ).
cnf(1012,plain,
difference(i(eta(x0)),product(x1,product(x2,i(eta(x0))))) != difference(i(eta(x0)),product(product(x1,i(eta(x0))),difference(i(eta(x0)),product(x2,i(eta(x0)))))),
inference('REWRITE',[status(thm)],[800,349,780,208,779,956,theory(equality)]) ).
cnf(1095,plain,
difference(difference(X,product(product(X,Y),j(X))),Y) = X,
inference('REWRITE',[status(thm)],[32,956,theory(equality)]) ).
cnf(1251,plain,
difference(product(X,i(eta(Y))),X) = eta(Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1095,779,theory(equality)]),349,780,208,theory(equality)]) ).
cnf(1255,plain,
difference(product(X,eta(Y)),X) = i(eta(Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1095,269,theory(equality)]),348,641,132,theory(equality)]) ).
cnf(1265,plain,
product(product(X,i(eta(Y))),eta(Y)) = X,
inference('PARAMODULATE',[status(thm)],[sos03,1251,theory(equality)]) ).
cnf(1390,plain,
difference(eta(X),product(Y,Z)) = product(difference(eta(X),Y),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos03,739,theory(equality)]),269,theory(equality)]) ).
cnf(1408,plain,
difference(difference(eta(X),Y),difference(eta(X),product(Y,Z))) = Z,
inference('PARAMODULATE',[status(thm)],[sos04,1390,theory(equality)]) ).
cnf(1427,plain,
i(X) = difference(i(eta(Y)),i(product(X,eta(Y)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[769,26,theory(equality)]),sos09,theory(equality)]) ).
cnf(1428,plain,
product(X,difference(i(eta(Y)),Z)) = product(product(X,eta(Y)),Z),
inference('PARAMODULATE',[status(thm)],[sos03,769,theory(equality)]) ).
cnf(1453,plain,
difference(eta(X),i(Y)) = i(product(Y,eta(X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos03,1427,theory(equality)]),269,theory(equality)]) ).
cnf(1459,plain,
j(difference(eta(X),i(Y))) = product(Y,eta(X)),
inference('PARAMODULATE',[status(thm)],[132,1453,theory(equality)]) ).
cnf(1497,plain,
j(difference(eta(X),i(product(Y,i(eta(X)))))) = Y,
inference('REWRITE',[status(thm)],[1265,1459,theory(equality)]) ).
cnf(1528,plain,
difference(j(difference(eta(X),i(Y))),Y) = i(eta(X)),
inference('REWRITE',[status(thm)],[1255,1459,theory(equality)]) ).
cnf(1533,plain,
product(X,difference(i(eta(Y)),Z)) = difference(eta(difference(eta(Y),i(X))),product(difference(i(X),eta(Y)),Z)),
inference('REWRITE',[status(thm)],[1428,343,359,1459,theory(equality)]) ).
cnf(1535,plain,
difference(i(eta(x0)),product(x1,product(x2,i(eta(x0))))) != difference(i(eta(x0)),difference(eta(difference(eta(x0),i(product(x1,i(eta(x0)))))),product(difference(i(product(x1,i(eta(x0)))),eta(x0)),product(x2,i(eta(x0)))))),
inference('REWRITE',[status(thm)],[1012,1533,theory(equality)]) ).
cnf(1637,plain,
difference(i(eta(X)),difference(X,Y)) = difference(i(i(X)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos03,908,theory(equality)]),779,theory(equality)]) ).
cnf(1665,plain,
difference(difference(eta(X),Y),difference(eta(X),Z)) = difference(Y,Z),
inference('PARAMODULATE',[status(thm)],[1408,sos03,theory(equality)]) ).
cnf(1716,plain,
difference(difference(i(eta(X)),Y),difference(i(eta(X)),Z)) = difference(Y,Z),
inference('PARAMODULATE',[status(thm)],[786,sos03,theory(equality)]) ).
cnf(1924,plain,
difference(i(eta(difference(eta(X),i(Y)))),i(eta(X))) = difference(difference(i(Y),eta(X)),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1637,1528,theory(equality)]),343,126,128,theory(equality)]) ).
cnf(1932,plain,
difference(X,difference(eta(Y),Z)) = difference(difference(i(eta(Y)),X),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1665,sos04,theory(equality)]),779,theory(equality)]) ).
cnf(1934,plain,
difference(i(eta(x0)),product(x1,product(x2,i(eta(x0))))) != difference(difference(difference(i(product(x1,i(eta(x0)))),eta(x0)),product(x1,i(eta(x0)))),product(difference(i(product(x1,i(eta(x0)))),eta(x0)),product(x2,i(eta(x0))))),
inference('REWRITE',[status(thm)],[1535,1924,1932,theory(equality)]) ).
cnf(2124,plain,
i(X) = difference(eta(Y),i(product(X,i(eta(Y))))),
inference('PARAMODULATE',[status(thm)],[126,1497,theory(equality)]) ).
cnf(2299,plain,
difference(i(eta(X)),i(Y)) = i(product(Y,i(eta(X)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[sos03,2124,theory(equality)]),779,theory(equality)]) ).
cnf(2302,plain,
$false,
inference('REWRITE',[status(thm)],[1934,1716,694,869,sos09,27,1932,2299,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP768-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 03:51:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.46 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 *
% 0.20/0.47 *
% 0.20/0.47 #<PACKAGE "SNARK-USER">
% 0.20/0.47 *
% 0.20/0.47 SNARK-TPTP-OPTIONS
% 0.20/0.47 *
% 0.20/0.48 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48 (USE-FACTORING :POS)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48 (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48 *
% 0.20/0.48 "."
% 0.20/0.48 *
% 0.20/0.48 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T03:51:20
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n020.cluster.edu at 2022-06-14T03:51:20
% 0.20/0.49
% 0.20/0.49 ; Recognized right identity assertion (= (|product| ?X |one|) ?X).
% 1.37/1.59 ; Recognized left identity assertion (= (|product| |one| ?X) ?X).
% 1.37/1.59
% 1.37/1.59 #||
% 1.37/1.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/1.59 % SZS output start Refutation
% See solution above
% 1.37/1.61 ||#
% 1.37/1.61
% 1.37/1.61 ; Summary of computation:
% 1.37/1.61 ; 7682 formulas have been input or derived (from 269 formulas).
% 1.37/1.61 ; 2302 (30%) were retained. Of these,
% 1.37/1.61 ; 1458 (63%) were simplified or subsumed later,
% 1.37/1.61 ; 844 (37%) are still being kept.
% 1.37/1.61 ;
% 1.37/1.61 ; Run time in seconds excluding printing time:
% 1.37/1.61 ; 0.003 0% Read assertion file (1 call)
% 1.37/1.61 ; 0.001 0% Assert (20 calls)
% 1.37/1.61 ; 0.349 31% Process new row (7,527 calls)
% 1.37/1.61 ; 0.016 1% Resolution (536 calls)
% 1.37/1.61 ; 0.092 8% Paramodulation (268 calls)
% 1.37/1.61 ; 0.280 25% Forward simplification (6,837 calls)
% 1.37/1.61 ; 0.158 14% Backward simplification (2,299 calls)
% 1.37/1.61 ; 0.142 13% Ordering (16,765 calls)
% 1.37/1.61 ; 0.000 0% Sortal reasoning (32 calls)
% 1.37/1.61 ; 0.000 0% Purity testing (1 call)
% 1.37/1.61 ; 0.068 6% Other
% 1.37/1.61 ; 1.109 Total
% 1.37/1.61 ; 1.134 Real time
% 1.37/1.61 ;
% 1.37/1.61 ; Term-hash-array has 7,481 terms in all.
% 1.37/1.61 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.37/1.61 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.37/1.61 ; Path-index has 3,027 entries (3,048 at peak, 8,170 added, 5,143 deleted).
% 1.37/1.61 ; Path-index has 20,814 nodes (20,881 at peak, 29,410 added, 8,596 deleted).
% 1.37/1.61 ; Trie-index has 3,027 entries (3,048 at peak, 8,170 added, 5,143 deleted).
% 1.37/1.61 ; Trie-index has 24,395 nodes (24,606 at peak, 71,685 added, 47,290 deleted).
% 1.37/1.61 ; Retrieved 72,560 generalization terms in 96,971 calls.
% 1.37/1.61 ; Retrieved 6,047 instance terms in 2,714 calls.
% 1.37/1.61 ; Retrieved 17,430 unifiable terms in 1,889 calls.
% 1.37/1.61 ;
% 1.37/1.61 ; The agenda of backward simplifiable rows to process has 1 entry:
% 1.37/1.61 ; 1 with value 0
% 1.37/1.61 ; The agenda of rows to process has 41 entries:
% 1.37/1.61 ; 5 with value 23 6 with value 27 3 with value 32
% 1.37/1.61 ; 1 with value 24 4 with value 28 2 with value 34
% 1.37/1.61 ; 3 with value 25 5 with value 29 2 with value 40
% 1.37/1.61 ; 5 with value 26 4 with value 30 1 with value 44
% 1.37/1.61 ; The agenda of rows to give has 710 entries:
% 1.37/1.61 ; 27 with value (4 23) 11 with value (4 43) 1 with value (4 68)
% 1.37/1.61 ; 29 with value (4 24) 9 with value (4 44) 1 with value (4 69)
% 1.37/1.61 ; 27 with value (4 25) 11 with value (4 45) 1 with value (4 71)
% 1.37/1.61 ; 46 with value (4 26) 4 with value (4 46) 1 with value (4 73)
% 1.37/1.61 ; 43 with value (4 27) 5 with value (4 47) 1 with value (4 74)
% 1.37/1.61 ; 35 with value (4 28) 3 with value (4 48) 2 with value (4 75)
% 1.37/1.61 ; 34 with value (4 29) 4 with value (4 49) 1 with value (4 77)
% 1.37/1.61 ; 47 with value (4 30) 4 with value (4 50) 1 with value (4 78)
% 1.37/1.61 ; 42 with value (4 31) 2 with value (4 51) 1 with value (4 81)
% 1.37/1.61 ; 45 with value (4 32) 2 with value (4 53) 1 with value (4 82)
% 1.37/1.61 ; 32 with value (4 33) 3 with value (4 54) 1 with value (4 86)
% 1.37/1.61 ; 38 with value (4 34) 4 with value (4 55) 1 with value (4 89)
% 1.37/1.61 ; 33 with value (4 35) 1 with value (4 57) 1 with value (4 90)
% 1.37/1.61 ; 34 with value (4 36) 3 with value (4 59) 1 with value (4 91)
% 1.37/1.61 ; 25 with value (4 37) 2 with value (4 61) 1 with value (4 92)
% 1.37/1.61 ; 15 with value (4 38) 2 with value (4 62) 1 with value (4 93)
% 1.37/1.61 ; 18 with value (4 39) 1 with value (4 64) 1 with value (4 94)
% 1.37/1.61 ; 19 with value (4 40) 1 with value (4 66) 1 with value (4 95)
% 1.37/1.61 ; 12 with value (4 41) 2 with value (4 67) 1 with value (4 111)
% 1.37/1.61 ; 15 with value (4 42)
% 1.37/1.61 Evaluation took:
% 1.37/1.61 1.135 seconds of real time
% 1.37/1.61 1.033063 seconds of user run time
% 1.37/1.61 0.099175 seconds of system run time
% 1.37/1.61 [Run times include 0.121 seconds GC run time.]
% 1.37/1.61 0 calls to %EVAL
% 1.37/1.61 0 page faults and
% 1.37/1.61 91,775,448 bytes consed.
% 1.37/1.61 :PROOF-FOUND
% 1.37/1.61 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T03:51:21
% 1.37/1.61 :PROOF-FOUND
% 1.37/1.61 *
%------------------------------------------------------------------------------