TSTP Solution File: GRP441-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP441-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n018.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 11:38:52 EDT 2022
% Result : Unsatisfiable 7.34s 7.56s
% Output : Refutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 2
% Syntax : Number of clauses : 127 ( 127 unt; 0 nHn; 2 RR)
% Number of literals : 127 ( 126 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 579 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(U,multiply(X,Z))))))) = U,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(3,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(V,Z))))),U)))) = V,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(4,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(Y,U)))))),multiply(multiply(V,W),inverse(multiply(X1,multiply(X,W))))))) = X1,
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(inverse(Z),U),inverse(multiply(V,multiply(W,U))))),V)),W)))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(9,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),U),inverse(multiply(V,multiply(W,U))))),V))),multiply(multiply(W,X1),inverse(multiply(Y1,multiply(X,X1))))))) = Y1,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(10,plain,
inverse(multiply(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(V,Z))))),U))),multiply(W,multiply(multiply(inverse(W),multiply(multiply(V,X1),inverse(multiply(Y1,multiply(Z1,X1))))),Y1)))) = Z1,
inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).
cnf(11,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),U),inverse(multiply(V,multiply(W,U))))),V))),multiply(multiply(W,multiply(multiply(inverse(X),X1),inverse(multiply(Y1,multiply(Z1,X1))))),Y1)))) = Z1,
inference('PARAMODULATE',[status(thm)],[3,3,theory(equality)]) ).
cnf(12,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),multiply(multiply(Z,U),inverse(multiply(V,multiply(W,U))))),V)),W)))) = multiply(X1,multiply(Y1,multiply(multiply(inverse(Y1),Z1),inverse(multiply(Z,multiply(X1,Z1)))))),
inference('PARAMODULATE',[status(thm)],[3,4,theory(equality)]) ).
cnf(292,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(U),multiply(X,Z)))))) = U,
inference('PARAMODULATE',[status(thm)],[5,12,theory(equality)]) ).
cnf(293,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(U,multiply(X,Z)))))) = multiply(V,multiply(W,multiply(multiply(inverse(W),X1),inverse(multiply(U,multiply(V,X1)))))),
inference('PARAMODULATE',[status(thm)],[12,12,theory(equality)]) ).
cnf(405,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(inverse(V),Z))))),U))) = V,
inference('PARAMODULATE',[status(thm)],[292,single_axiom,theory(equality)]) ).
cnf(406,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(inverse(V),multiply(X,U)))))),inverse(multiply(inverse(W),V))))) = W,
inference('PARAMODULATE',[status(thm)],[292,292,theory(equality)]) ).
cnf(614,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(inverse(Z),Y))))) = Z,
inference('PARAMODULATE',[status(thm)],[406,292,theory(equality)]) ).
cnf(666,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(inverse(multiply(V,multiply(multiply(inverse(V),multiply(W,multiply(multiply(inverse(W),X1),inverse(multiply(inverse(Y1),multiply(inverse(Z1),X1)))))),inverse(multiply(inverse(U1),Y1))))),multiply(X,U)))))),inverse(U1)))) = Z1,
inference('PARAMODULATE',[status(thm)],[406,406,theory(equality)]) ).
cnf(685,plain,
inverse(multiply(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,multiply(V,Z))))),U))),multiply(W,multiply(multiply(inverse(W),multiply(multiply(V,multiply(multiply(inverse(X1),multiply(Y1,multiply(multiply(inverse(Y1),Z1),inverse(multiply(inverse(U1),multiply(V1,Z1)))))),inverse(multiply(inverse(W1),U1)))),inverse(W1))),V1)))) = X1,
inference('PARAMODULATE',[status(thm)],[10,406,theory(equality)]) ).
cnf(739,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,inverse(multiply(inverse(U),Z)))),inverse(U)))) = X,
inference('PARAMODULATE',[status(thm)],[292,614,theory(equality)]) ).
cnf(740,plain,
multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(Z,inverse(multiply(inverse(U),Z)))),inverse(U)))) = Y,
inference('PARAMODULATE',[status(thm)],[614,614,theory(equality)]) ).
cnf(741,plain,
multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(U,multiply(inverse(V),Z))))),U))) = V,
inference('PARAMODULATE',[status(thm)],[614,single_axiom,theory(equality)]) ).
cnf(755,plain,
multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(inverse(Z),X))))) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[406,614,theory(equality)]),739,theory(equality)]) ).
cnf(828,plain,
multiply(multiply(X,multiply(Y,inverse(multiply(inverse(Z),Y)))),multiply(U,multiply(inverse(U),inverse(Z)))) = X,
inference('PARAMODULATE',[status(thm)],[755,614,theory(equality)]) ).
cnf(833,plain,
multiply(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,multiply(inverse(U),Y))))),multiply(V,multiply(inverse(V),Z))) = U,
inference('PARAMODULATE',[status(thm)],[755,single_axiom,theory(equality)]) ).
cnf(930,plain,
multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),multiply(U,multiply(inverse(U),Z))) = X,
inference('PARAMODULATE',[status(thm)],[828,3,theory(equality)]) ).
cnf(952,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),inverse(U)))) = multiply(V,multiply(W,multiply(multiply(inverse(W),X1),inverse(multiply(multiply(U,multiply(Y1,inverse(multiply(Z,Y1)))),multiply(V,X1)))))),
inference('PARAMODULATE',[status(thm)],[293,930,theory(equality)]) ).
cnf(1017,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,inverse(multiply(U,Z)))),U))) = X,
inference('PARAMODULATE',[status(thm)],[739,3,theory(equality)]) ).
cnf(1022,plain,
multiply(multiply(X,multiply(Y,inverse(multiply(multiply(multiply(inverse(inverse(Z)),multiply(U,inverse(multiply(V,U)))),V),Y)))),Z) = X,
inference('PARAMODULATE',[status(thm)],[930,1017,theory(equality)]) ).
cnf(1030,plain,
inverse(multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(Z,X)))))) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[single_axiom,1017,theory(equality)]),1017,theory(equality)]) ).
cnf(1040,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(multiply(Z,U)))),Z)))) = U,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[3,1017,theory(equality)]),1017,theory(equality)]) ).
cnf(1110,plain,
inverse(multiply(multiply(X,multiply(inverse(X),inverse(multiply(Y,Z)))),multiply(U,multiply(inverse(U),Y)))) = Z,
inference('PARAMODULATE',[status(thm)],[1030,1030,theory(equality)]) ).
cnf(1113,plain,
multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,Y))))) = multiply(U,multiply(V,multiply(inverse(V),inverse(multiply(Z,U))))),
inference('PARAMODULATE',[status(thm)],[614,1030,theory(equality)]) ).
cnf(1115,plain,
inverse(multiply(multiply(X,multiply(inverse(X),Y)),multiply(Z,multiply(inverse(Z),inverse(U))))) = multiply(U,multiply(V,inverse(multiply(Y,V)))),
inference('PARAMODULATE',[status(thm)],[1030,930,theory(equality)]) ).
cnf(1188,plain,
multiply(inverse(X),multiply(X,multiply(multiply(Y,multiply(Z,inverse(multiply(U,Z)))),U))) = Y,
inference('PARAMODULATE',[status(thm)],[740,3,theory(equality)]) ).
cnf(1189,plain,
multiply(multiply(X,multiply(multiply(Y,multiply(Z,inverse(multiply(U,Z)))),U)),multiply(V,multiply(inverse(V),inverse(Y)))) = X,
inference('PARAMODULATE',[status(thm)],[755,1188,theory(equality)]) ).
cnf(1626,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),U)))) = multiply(V,multiply(multiply(inverse(V),W),inverse(multiply(Z,multiply(U,W))))),
inference('PARAMODULATE',[status(thm)],[1040,single_axiom,theory(equality)]) ).
cnf(1665,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(Z))),U)))) = multiply(V,multiply(multiply(inverse(V),multiply(W,multiply(multiply(inverse(W),X1),inverse(multiply(inverse(Y1),multiply(U,X1)))))),inverse(multiply(inverse(Z),Y1)))),
inference('PARAMODULATE',[status(thm)],[1040,406,theory(equality)]) ).
cnf(1712,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),multiply(U,multiply(V,multiply(multiply(inverse(V),multiply(multiply(inverse(U),W),inverse(multiply(X1,multiply(Y1,W))))),X1))))))) = multiply(Z1,multiply(multiply(inverse(Z1),multiply(multiply(Y1,U1),inverse(multiply(V1,multiply(Z,U1))))),V1)),
inference('PARAMODULATE',[status(thm)],[1040,10,theory(equality)]) ).
cnf(1906,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),inverse(U)))) = multiply(V,multiply(W,multiply(multiply(inverse(W),X1),inverse(multiply(multiply(Y1,multiply(multiply(inverse(Y1),Z1),inverse(multiply(Z,multiply(inverse(U),Z1))))),multiply(V,X1)))))),
inference('PARAMODULATE',[status(thm)],[293,833,theory(equality)]) ).
cnf(1925,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),U),inverse(multiply(V,multiply(W,U))))),V))),multiply(multiply(W,multiply(inverse(X),X1)),inverse(Y1))))) = multiply(Z1,multiply(multiply(inverse(Z1),U1),inverse(multiply(X1,multiply(inverse(Y1),U1))))),
inference('PARAMODULATE',[status(thm)],[9,833,theory(equality)]) ).
cnf(2068,plain,
inverse(multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,Y)))))) = Z,
inference('PARAMODULATE',[status(thm)],[1030,1113,theory(equality)]) ).
cnf(2425,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),U),inverse(multiply(V,multiply(W,U))))),V))),multiply(multiply(W,multiply(multiply(inverse(X),multiply(X1,multiply(inverse(X1),inverse(Y1)))),inverse(multiply(Z1,U1)))),Z1)))) = multiply(U1,multiply(multiply(Y1,multiply(V1,inverse(multiply(W1,V1)))),W1)),
inference('PARAMODULATE',[status(thm)],[11,1189,theory(equality)]) ).
cnf(2998,plain,
multiply(X,multiply(Y,inverse(multiply(inverse(multiply(inverse(X),Z)),Y)))) = Z,
inference('PARAMODULATE',[status(thm)],[1110,1115,theory(equality)]) ).
cnf(2999,plain,
multiply(X,multiply(Y,inverse(multiply(Z,Y)))) = multiply(X,multiply(U,inverse(multiply(Z,U)))),
inference('PARAMODULATE',[status(thm)],[1115,1115,theory(equality)]) ).
cnf(3000,plain,
multiply(multiply(X,multiply(Y,multiply(inverse(Y),Z))),multiply(U,inverse(multiply(Z,U)))) = X,
inference('PARAMODULATE',[status(thm)],[1030,1115,theory(equality)]) ).
cnf(3379,plain,
multiply(X,multiply(Y,inverse(multiply(Z,Y)))) = multiply(U,multiply(multiply(inverse(U),multiply(inverse(inverse(X)),inverse(multiply(V,Z)))),V)),
inference('PARAMODULATE',[status(thm)],[2998,1040,theory(equality)]) ).
cnf(3393,plain,
inverse(multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),inverse(Z))),U)))) = multiply(V,inverse(multiply(inverse(multiply(inverse(U),Z)),V))),
inference('PARAMODULATE',[status(thm)],[1040,2998,theory(equality)]) ).
cnf(3405,plain,
multiply(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z),U)),inverse(Z))),multiply(inverse(V),Y))))),U) = V,
inference('PARAMODULATE',[status(thm)],[833,2998,theory(equality)]) ).
cnf(3539,plain,
multiply(X,inverse(multiply(Y,X))) = multiply(Z,inverse(multiply(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2998,2999,theory(equality)]),2998,theory(equality)]) ).
cnf(3668,plain,
multiply(inverse(X),multiply(X,multiply(inverse(multiply(Y,inverse(Z))),inverse(multiply(U,inverse(multiply(Y,U))))))) = Z,
inference('PARAMODULATE',[status(thm)],[614,3539,theory(equality)]) ).
cnf(3672,plain,
multiply(X,multiply(Y,inverse(multiply(inverse(multiply(Z,inverse(multiply(U,Z)))),Y)))) = inverse(multiply(U,inverse(X))),
inference('PARAMODULATE',[status(thm)],[2998,3539,theory(equality)]) ).
cnf(3715,plain,
multiply(multiply(X,multiply(multiply(inverse(X),multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(U),multiply(V,Z)))))),inverse(multiply(inverse(W),U)))),inverse(W)) = multiply(X1,inverse(multiply(V,X1))),
inference('PARAMODULATE',[status(thm)],[3539,406,theory(equality)]) ).
cnf(3742,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(inverse(Y),inverse(Z))))),X) = Z,
inference('PARAMODULATE',[status(thm)],[614,3000,theory(equality)]) ).
cnf(3919,plain,
multiply(X,multiply(inverse(X),inverse(Y))) = multiply(Z,multiply(inverse(Z),inverse(Y))),
inference('PARAMODULATE',[status(thm)],[2998,3742,theory(equality)]) ).
cnf(3920,plain,
multiply(inverse(multiply(X,Y)),X) = multiply(inverse(multiply(inverse(Z),Y)),inverse(Z)),
inference('PARAMODULATE',[status(thm)],[3742,2998,theory(equality)]) ).
cnf(3971,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(multiply(inverse(X),Z),inverse(multiply(U,V)))),U))) = multiply(Z,multiply(W,multiply(inverse(W),inverse(V)))),
inference('PARAMODULATE',[status(thm)],[405,3742,theory(equality)]) ).
cnf(4084,plain,
multiply(inverse(multiply(X,multiply(multiply(Y,multiply(multiply(Z,multiply(U,multiply(multiply(inverse(U),multiply(multiply(inverse(Z),V),inverse(multiply(W,multiply(X1,V))))),W))),multiply(multiply(X1,multiply(multiply(inverse(Y),Y1),inverse(multiply(Z1,multiply(U1,Y1))))),Z1))),multiply(U1,inverse(V1))))),X) = V1,
inference('PARAMODULATE',[status(thm)],[3742,11,theory(equality)]) ).
cnf(4086,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Z,multiply(inverse(Z),Y)),
inference('PARAMODULATE',[status(thm)],[3919,3,theory(equality)]) ).
cnf(4364,plain,
multiply(inverse(multiply(X,Y)),X) = multiply(inverse(multiply(Z,Y)),Z),
inference('PARAMODULATE',[status(thm)],[3920,3920,theory(equality)]) ).
cnf(4387,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),inverse(multiply(inverse(multiply(U,V)),U))))) = multiply(multiply(X,Z),V),
inference('PARAMODULATE',[status(thm)],[292,4364,theory(equality)]) ).
cnf(4417,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4364,1017,theory(equality)]),1017,theory(equality)]) ).
cnf(4458,plain,
multiply(inverse(X),inverse(Y)) = multiply(inverse(multiply(Z,multiply(Y,multiply(multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(W,multiply(inverse(X),V))))),W)))),Z),
inference('PARAMODULATE',[status(thm)],[4364,741,theory(equality)]) ).
cnf(4474,plain,
multiply(inverse(multiply(X,Y)),multiply(Z,multiply(multiply(inverse(Z),multiply(U,multiply(multiply(inverse(U),X),inverse(multiply(inverse(V),multiply(inverse(multiply(W,Y)),W)))))),inverse(multiply(inverse(X1),V))))) = X1,
inference('PARAMODULATE',[status(thm)],[406,4364,theory(equality)]) ).
cnf(4475,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,multiply(U,multiply(multiply(inverse(U),multiply(V,multiply(multiply(inverse(V),W),inverse(multiply(inverse(X1),multiply(Y,W)))))),inverse(multiply(inverse(X),X1)))))),Z),
inference('PARAMODULATE',[status(thm)],[4364,406,theory(equality)]) ).
cnf(4501,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(multiply(Z,multiply(U,multiply(multiply(inverse(U),multiply(multiply(inverse(Z),V),inverse(multiply(W,multiply(X1,V))))),W))),multiply(multiply(X1,X),inverse(multiply(Y1,multiply(inverse(multiply(Z1,Y)),Z1))))))) = Y1,
inference('PARAMODULATE',[status(thm)],[9,4364,theory(equality)]) ).
cnf(4502,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),U),inverse(multiply(V,multiply(W,U))))),V))),multiply(multiply(W,X1),inverse(multiply(inverse(multiply(Y1,Z1)),Y1)))))) = inverse(multiply(multiply(X,X1),Z1)),
inference('PARAMODULATE',[status(thm)],[9,4364,theory(equality)]) ).
cnf(4526,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Y,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[4086,4417,theory(equality)]) ).
cnf(4533,plain,
multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('PARAMODULATE',[status(thm)],[755,4417,theory(equality)]) ).
cnf(4540,plain,
multiply(inverse(inverse(multiply(X,inverse(multiply(inverse(Y),X))))),multiply(inverse(Z),Z)) = Y,
inference('PARAMODULATE',[status(thm)],[614,4417,theory(equality)]) ).
cnf(4551,plain,
multiply(inverse(X),multiply(X,multiply(multiply(inverse(Y),Y),Z))) = inverse(multiply(U,inverse(multiply(Z,U)))),
inference('PARAMODULATE',[status(thm)],[1188,4417,theory(equality)]) ).
cnf(4691,plain,
multiply(X,multiply(inverse(X),inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),Y))))))) = Z,
inference('PARAMODULATE',[status(thm)],[614,4526,theory(equality)]) ).
cnf(4692,plain,
inverse(multiply(X,multiply(inverse(X),inverse(inverse(multiply(Y,inverse(multiply(Z,Y)))))))) = Z,
inference('PARAMODULATE',[status(thm)],[2068,4526,theory(equality)]) ).
cnf(4697,plain,
multiply(multiply(multiply(inverse(inverse(X)),multiply(Y,inverse(multiply(Z,Y)))),Z),multiply(inverse(U),U)) = X,
inference('PARAMODULATE',[status(thm)],[1017,4526,theory(equality)]) ).
cnf(4699,plain,
multiply(X,multiply(inverse(X),inverse(multiply(multiply(inverse(Y),Y),Z)))) = multiply(inverse(multiply(U,Z)),U),
inference('PARAMODULATE',[status(thm)],[4364,4526,theory(equality)]) ).
cnf(4700,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4526,4526,theory(equality)]),4533,theory(equality)]) ).
cnf(4701,plain,
inverse(multiply(multiply(inverse(X),X),Y)) = multiply(inverse(multiply(Z,Y)),Z),
inference('REWRITE',[status(thm)],[4699,4700,theory(equality)]) ).
cnf(4702,plain,
inverse(inverse(inverse(multiply(X,inverse(multiply(Y,X)))))) = Y,
inference('REWRITE',[status(thm)],[4692,4700,theory(equality)]) ).
cnf(4703,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(Y),X))))) = Y,
inference('REWRITE',[status(thm)],[4691,4700,theory(equality)]) ).
cnf(4705,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[4540,4703,theory(equality)]) ).
cnf(4706,plain,
multiply(multiply(inverse(inverse(X)),multiply(Y,inverse(multiply(Z,Y)))),Z) = X,
inference('REWRITE',[status(thm)],[4697,4705,theory(equality)]) ).
cnf(4708,plain,
multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),Z) = X,
inference('REWRITE',[status(thm)],[1022,4706,theory(equality)]) ).
cnf(4709,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[4706,4708,theory(equality)]) ).
cnf(4710,plain,
inverse(multiply(X,inverse(multiply(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[4702,4709,theory(equality)]) ).
cnf(4716,plain,
multiply(inverse(X),multiply(X,multiply(inverse(multiply(Y,inverse(Z))),Y))) = Z,
inference('REWRITE',[status(thm)],[3668,4710,theory(equality)]) ).
cnf(4719,plain,
multiply(inverse(X),multiply(X,multiply(multiply(inverse(Y),Y),Z))) = Z,
inference('REWRITE',[status(thm)],[4551,4710,theory(equality)]) ).
cnf(4721,plain,
multiply(X,multiply(Y,inverse(multiply(Z,Y)))) = inverse(multiply(Z,inverse(X))),
inference('REWRITE',[status(thm)],[3672,4710,theory(equality)]) ).
cnf(4723,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(X))) = Y,
inference('REWRITE',[status(thm)],[2998,4721,theory(equality)]) ).
cnf(4724,plain,
multiply(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,multiply(inverse(U),Y))))),Z) = U,
inference('REWRITE',[status(thm)],[3405,4723,theory(equality)]) ).
cnf(4725,plain,
multiply(inverse(X),inverse(Y)) = multiply(inverse(multiply(Z,multiply(Y,X))),Z),
inference('REWRITE',[status(thm)],[4458,4724,theory(equality)]) ).
cnf(4729,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(multiply(inverse(Z),multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(inverse(W),multiply(Y,V)))))),inverse(multiply(inverse(X),W)))),inverse(Z)),
inference('REWRITE',[status(thm)],[4475,4725,theory(equality)]) ).
cnf(4732,plain,
multiply(inverse(multiply(X,inverse(Y))),X) = Y,
inference('REWRITE',[status(thm)],[4084,11,4725,theory(equality)]) ).
cnf(4733,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[4716,4732,theory(equality)]) ).
cnf(4734,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[4719,4733,theory(equality)]) ).
cnf(4760,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('REWRITE',[status(thm)],[4701,4734,theory(equality)]) ).
cnf(4761,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('REWRITE',[status(thm)],[4725,4760,theory(equality)]) ).
cnf(4986,plain,
multiply(inverse(X),Y) = inverse(multiply(Z,multiply(multiply(inverse(Z),multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(inverse(W),multiply(Y,V)))))),inverse(multiply(inverse(X),W))))),
inference('REWRITE',[status(thm)],[4729,4761,theory(equality)]) ).
cnf(4987,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(inverse(multiply(V,W)),multiply(X,U)))))),inverse(W)))) = V,
inference('REWRITE',[status(thm)],[666,4761,4986,theory(equality)]) ).
cnf(4992,plain,
inverse(multiply(X,multiply(Y,multiply(inverse(multiply(multiply(Z,X),Y)),U)))) = multiply(V,multiply(multiply(inverse(V),multiply(W,multiply(multiply(inverse(W),X1),inverse(multiply(inverse(Y1),multiply(U,X1)))))),inverse(multiply(inverse(Z),Y1)))),
inference('REWRITE',[status(thm)],[1665,4761,theory(equality)]) ).
cnf(4993,plain,
inverse(multiply(X,multiply(Y,multiply(inverse(multiply(multiply(Z,X),Y)),U)))) = multiply(V,inverse(multiply(inverse(multiply(inverse(U),Z)),V))),
inference('REWRITE',[status(thm)],[3393,4761,theory(equality)]) ).
cnf(5001,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(multiply(Z,multiply(U,multiply(multiply(inverse(U),multiply(multiply(inverse(Z),V),inverse(multiply(W,multiply(X1,V))))),W))),multiply(multiply(X1,X),inverse(multiply(Y1,inverse(Y))))))) = Y1,
inference('REWRITE',[status(thm)],[4501,4760,theory(equality)]) ).
cnf(5004,plain,
inverse(multiply(X,multiply(multiply(Y,multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(inverse(Y),U),inverse(multiply(V,multiply(W,U))))),V))),multiply(multiply(W,X1),Y1)))) = inverse(multiply(multiply(X,X1),Y1)),
inference('REWRITE',[status(thm)],[4502,4709,4760,theory(equality)]) ).
cnf(5005,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[5001,4709,4761,4760,5004,theory(equality)]) ).
cnf(5025,plain,
inverse(multiply(X,inverse(Y))) = multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(X,multiply(inverse(Y),U))))),
inference('REWRITE',[status(thm)],[1925,4700,5004,theory(equality)]) ).
cnf(5048,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),inverse(U)))) = multiply(Z,inverse(U)),
inference('REWRITE',[status(thm)],[1906,292,5025,theory(equality)]) ).
cnf(5052,plain,
multiply(X,inverse(Y)) = multiply(Z,multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(multiply(Y,multiply(W,inverse(multiply(X,W)))),multiply(Z,V)))))),
inference('REWRITE',[status(thm)],[952,5048,theory(equality)]) ).
cnf(5173,plain,
multiply(inverse(multiply(X,Y)),multiply(Z,multiply(multiply(inverse(Z),multiply(U,multiply(multiply(inverse(U),X),multiply(Y,V)))),inverse(multiply(inverse(W),V))))) = W,
inference('REWRITE',[status(thm)],[4474,4709,4761,4760,theory(equality)]) ).
cnf(5211,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),U))) = multiply(multiply(X,Z),U),
inference('REWRITE',[status(thm)],[4387,4709,4760,theory(equality)]) ).
cnf(5222,plain,
multiply(X,inverse(multiply(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[5173,4733,4760,5211,theory(equality)]) ).
cnf(5224,plain,
inverse(multiply(X,multiply(Y,multiply(inverse(multiply(multiply(Z,X),Y)),U)))) = multiply(inverse(U),Z),
inference('REWRITE',[status(thm)],[4993,5222,theory(equality)]) ).
cnf(5225,plain,
multiply(inverse(X),Y) = multiply(Z,multiply(multiply(inverse(Z),multiply(U,multiply(multiply(inverse(U),V),inverse(multiply(inverse(W),multiply(X,V)))))),inverse(multiply(inverse(Y),W)))),
inference('REWRITE',[status(thm)],[4992,5224,theory(equality)]) ).
cnf(5226,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[4986,5225,theory(equality)]) ).
cnf(5288,plain,
multiply(multiply(inverse(X),Y),inverse(Y)) = multiply(Z,inverse(multiply(X,Z))),
inference('REWRITE',[status(thm)],[3715,5225,theory(equality)]) ).
cnf(5326,plain,
multiply(X,inverse(Y)) = multiply(multiply(Z,U),inverse(multiply(multiply(Y,multiply(V,inverse(multiply(X,V)))),multiply(Z,U)))),
inference('REWRITE',[status(thm)],[5052,5211,theory(equality)]) ).
cnf(5333,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[4987,5222,5211,theory(equality)]) ).
cnf(5334,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[5288,5333,theory(equality)]) ).
cnf(5338,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference('REWRITE',[status(thm)],[5326,5334,theory(equality)]) ).
cnf(5455,plain,
inverse(multiply(X,Y)) = multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(X,multiply(Y,U))))),
inference('REWRITE',[status(thm)],[1626,4700,5211,theory(equality)]) ).
cnf(5523,plain,
inverse(multiply(X,inverse(Y))) = multiply(Z,multiply(multiply(inverse(Z),multiply(multiply(Y,U),inverse(multiply(V,multiply(X,U))))),V)),
inference('REWRITE',[status(thm)],[1712,4700,4733,5226,5455,5211,theory(equality)]) ).
cnf(5587,plain,
inverse(multiply(X,multiply(inverse(Y),multiply(multiply(Y,Z),U)))) = inverse(multiply(multiply(X,Z),U)),
inference('REWRITE',[status(thm)],[5004,4733,5226,5455,5211,theory(equality)]) ).
cnf(5597,plain,
inverse(multiply(multiply(inverse(X),multiply(multiply(X,inverse(multiply(multiply(inverse(Y),Z),multiply(multiply(inverse(Z),U),V)))),inverse(Y))),U)) = V,
inference('REWRITE',[status(thm)],[685,4761,4733,5226,5455,5211,theory(equality)]) ).
cnf(5667,plain,
multiply(X,inverse(Y)) = multiply(Z,multiply(multiply(inverse(Z),multiply(X,inverse(multiply(U,Y)))),U)),
inference('REWRITE',[status(thm)],[3379,5333,5338,4709,theory(equality)]) ).
cnf(5670,plain,
inverse(multiply(X,inverse(Y))) = multiply(multiply(Y,Z),inverse(multiply(X,Z))),
inference('REWRITE',[status(thm)],[5523,5667,theory(equality)]) ).
cnf(5724,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(Z))) = multiply(Y,inverse(Z)),
inference('REWRITE',[status(thm)],[3971,5667,4700,theory(equality)]) ).
cnf(5726,plain,
inverse(multiply(X,Y)) = inverse(multiply(multiply(X,multiply(Y,Z)),inverse(Z))),
inference('REWRITE',[status(thm)],[5455,5338,5724,theory(equality)]) ).
cnf(5757,plain,
multiply(inverse(X),multiply(multiply(X,Y),Z)) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[2425,5005,5226,5726,5587,4761,5333,5338,4709,5670,5667,4700,theory(equality)]) ).
cnf(5760,plain,
multiply(multiply(inverse(X),Y),multiply(multiply(inverse(Y),X),Z)) = Z,
inference('REWRITE',[status(thm)],[5597,4709,5211,5226,4761,5757,theory(equality)]) ).
cnf(5907,plain,
multiply(X,Y) = multiply(Z,multiply(multiply(inverse(Z),X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5757,5760,theory(equality)]),4709,theory(equality)]) ).
cnf(5942,plain,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[5211,5907,theory(equality)]) ).
cnf(5943,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_3,5942,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP441-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.13 % Command : run-snark %s %d
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 06:34:28 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 *
% 0.20/0.48 *
% 0.20/0.48 #<PACKAGE "SNARK-USER">
% 0.20/0.48 *
% 0.20/0.48 SNARK-TPTP-OPTIONS
% 0.20/0.48 *
% 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/sandbox2/benchmark/theBenchmark.p 2022-06-14T06:34:28
% 0.20/0.48 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-06-14T06:34:28
% 7.34/7.56
% 7.34/7.56
% 7.34/7.56 #||
% 7.34/7.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.34/7.56 % SZS output start Refutation
% See solution above
% 7.41/7.60 ||#
% 7.41/7.60
% 7.41/7.60 ; Summary of computation:
% 7.41/7.60 ; 15050 formulas have been input or derived (from 61 formulas).
% 7.41/7.60 ; 5943 (39%) were retained. Of these,
% 7.41/7.60 ; 5754 (97%) were simplified or subsumed later,
% 7.41/7.60 ; 189 ( 3%) are still being kept.
% 7.41/7.60 ;
% 7.41/7.60 ; Run time in seconds excluding printing time:
% 7.41/7.60 ; 0.001 0% Read assertion file (1 call)
% 7.41/7.60 ; 0.000 0% Assert (2 calls)
% 7.41/7.60 ; 1.751 25% Process new row (14,945 calls)
% 7.41/7.60 ; 0.022 0% Resolution (120 calls)
% 7.41/7.60 ; 0.541 8% Paramodulation (60 calls)
% 7.41/7.60 ; 2.568 36% Forward simplification (13,498 calls)
% 7.41/7.60 ; 1.722 24% Backward simplification (5,943 calls)
% 7.41/7.60 ; 0.383 5% Ordering (77,525 calls)
% 7.41/7.60 ; 0.000 0% Sortal reasoning (32 calls)
% 7.41/7.60 ; 0.000 0% Purity testing (1 call)
% 7.41/7.60 ; 0.086 1% Other
% 7.41/7.60 ; 7.074 Total
% 7.41/7.60 ; 7.115 Real time
% 7.41/7.60 ;
% 7.41/7.60 ; Term-hash-array has 38,393 terms in all.
% 7.41/7.60 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 7.41/7.60 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 7.41/7.60 ; Path-index has 1,073 entries (30,959 at peak, 39,708 added, 38,635 deleted).
% 7.41/7.60 ; Path-index has 39,532 nodes (46,386 at peak, 60,930 added, 21,398 deleted).
% 7.41/7.60 ; Trie-index has 1,073 entries (30,959 at peak, 39,708 added, 38,635 deleted).
% 7.41/7.60 ; Trie-index has 6,345 nodes (233,134 at peak, 295,136 added, 288,791 deleted).
% 7.41/7.60 ; Retrieved 140,827 generalization terms in 309,337 calls.
% 7.41/7.60 ; Retrieved 27,845 instance terms in 5,979 calls.
% 7.41/7.60 ; Retrieved 295,850 unifiable terms in 773 calls.
% 7.41/7.60 ;
% 7.41/7.60 ; The agenda of backward simplifiable rows to process has 58 entries:
% 7.41/7.60 ; 58 with value 0
% 7.41/7.60 ; The agenda of rows to process has 17 entries:
% 7.41/7.60 ; 1 with value 29 3 with value 31 5 with value 33
% 7.41/7.60 ; 2 with value 30 1 with value 32 5 with value 34
% 7.41/7.60 ; The agenda of rows to give has 179 entries:
% 7.41/7.60 ; 1 with value (4 25) 9 with value (4 38) 5 with value (4 51)
% 7.41/7.60 ; 1 with value (4 26) 5 with value (4 39) 3 with value (4 53)
% 7.41/7.60 ; 9 with value (4 27) 6 with value (4 40) 3 with value (4 54)
% 7.41/7.60 ; 6 with value (4 28) 12 with value (4 41) 3 with value (4 55)
% 7.41/7.60 ; 9 with value (4 29) 6 with value (4 42) 1 with value (4 56)
% 7.41/7.60 ; 6 with value (4 30) 5 with value (4 43) 1 with value (4 58)
% 7.41/7.60 ; 3 with value (4 31) 7 with value (4 44) 1 with value (4 59)
% 7.41/7.60 ; 8 with value (4 32) 3 with value (4 45) 1 with value (4 60)
% 7.41/7.60 ; 4 with value (4 33) 6 with value (4 46) 2 with value (4 61)
% 7.41/7.60 ; 7 with value (4 34) 3 with value (4 47) 1 with value (4 62)
% 7.41/7.60 ; 11 with value (4 35) 5 with value (4 48) 1 with value (4 64)
% 7.41/7.60 ; 11 with value (4 36) 1 with value (4 49) 1 with value (4 66)
% 7.41/7.60 ; 9 with value (4 37) 3 with value (4 50)
% 7.41/7.60 Evaluation took:
% 7.41/7.60 7.117 seconds of real time
% 7.41/7.60 6.622684 seconds of user run time
% 7.41/7.60 0.494594 seconds of system run time
% 7.41/7.60 [Run times include 1.642 seconds GC run time.]
% 7.41/7.60 0 calls to %EVAL
% 7.41/7.60 0 page faults and
% 7.41/7.60 453,906,080 bytes consed.
% 7.41/7.60 :PROOF-FOUND
% 7.41/7.60 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T06:34:35
% 7.41/7.60 :PROOF-FOUND
% 7.41/7.60 *
%------------------------------------------------------------------------------