TSTP Solution File: GRP768-1 by SNARK---20120808r022

View Problem - 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  * 
%------------------------------------------------------------------------------