TSTP Solution File: GRP061-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP061-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n009.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 11:35:57 EDT 2022
% Result : Unsatisfiable 7.66s 7.90s
% Output : Refutation 7.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 2
% Syntax : Number of clauses : 130 ( 127 unt; 0 nHn; 5 RR)
% Number of literals : 134 ( 133 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 19 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 580 ( 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/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
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(4418,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('REWRITE',[status(thm)],[prove_these_axioms,4417,theory(equality)]) ).
cnf(4459,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(4475,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(4476,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(4502,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(4503,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(4527,plain,
multiply(X,multiply(inverse(X),Y)) = multiply(Y,multiply(inverse(Z),Z)),
inference('PARAMODULATE',[status(thm)],[4086,4417,theory(equality)]) ).
cnf(4534,plain,
multiply(X,multiply(Y,multiply(inverse(Y),inverse(multiply(inverse(Z),Z))))) = X,
inference('PARAMODULATE',[status(thm)],[755,4417,theory(equality)]) ).
cnf(4541,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(4552,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(4555,plain,
( multiply(multiply(inverse(X),X),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference('PARAMODULATE',[status(thm)],[4418,4417,theory(equality)]) ).
cnf(4693,plain,
multiply(X,multiply(inverse(X),inverse(inverse(multiply(Y,inverse(multiply(inverse(Z),Y))))))) = Z,
inference('PARAMODULATE',[status(thm)],[614,4527,theory(equality)]) ).
cnf(4694,plain,
inverse(multiply(X,multiply(inverse(X),inverse(inverse(multiply(Y,inverse(multiply(Z,Y)))))))) = Z,
inference('PARAMODULATE',[status(thm)],[2068,4527,theory(equality)]) ).
cnf(4699,plain,
multiply(multiply(multiply(inverse(inverse(X)),multiply(Y,inverse(multiply(Z,Y)))),Z),multiply(inverse(U),U)) = X,
inference('PARAMODULATE',[status(thm)],[1017,4527,theory(equality)]) ).
cnf(4701,plain,
multiply(X,multiply(inverse(X),inverse(multiply(multiply(inverse(Y),Y),Z)))) = multiply(inverse(multiply(U,Z)),U),
inference('PARAMODULATE',[status(thm)],[4364,4527,theory(equality)]) ).
cnf(4702,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4527,4527,theory(equality)]),4534,theory(equality)]) ).
cnf(4703,plain,
inverse(multiply(multiply(inverse(X),X),Y)) = multiply(inverse(multiply(Z,Y)),Z),
inference('REWRITE',[status(thm)],[4701,4702,theory(equality)]) ).
cnf(4704,plain,
inverse(inverse(inverse(multiply(X,inverse(multiply(Y,X)))))) = Y,
inference('REWRITE',[status(thm)],[4694,4702,theory(equality)]) ).
cnf(4705,plain,
inverse(inverse(multiply(X,inverse(multiply(inverse(Y),X))))) = Y,
inference('REWRITE',[status(thm)],[4693,4702,theory(equality)]) ).
cnf(4707,plain,
multiply(X,multiply(inverse(Y),Y)) = X,
inference('REWRITE',[status(thm)],[4541,4705,theory(equality)]) ).
cnf(4708,plain,
multiply(multiply(inverse(inverse(X)),multiply(Y,inverse(multiply(Z,Y)))),Z) = X,
inference('REWRITE',[status(thm)],[4699,4707,theory(equality)]) ).
cnf(4710,plain,
multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),Z) = X,
inference('REWRITE',[status(thm)],[1022,4708,theory(equality)]) ).
cnf(4711,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[4708,4710,theory(equality)]) ).
cnf(4712,plain,
inverse(multiply(X,inverse(multiply(Y,X)))) = Y,
inference('REWRITE',[status(thm)],[4704,4711,theory(equality)]) ).
cnf(4718,plain,
multiply(inverse(X),multiply(X,multiply(inverse(multiply(Y,inverse(Z))),Y))) = Z,
inference('REWRITE',[status(thm)],[3668,4712,theory(equality)]) ).
cnf(4721,plain,
multiply(inverse(X),multiply(X,multiply(multiply(inverse(Y),Y),Z))) = Z,
inference('REWRITE',[status(thm)],[4552,4712,theory(equality)]) ).
cnf(4723,plain,
multiply(X,multiply(Y,inverse(multiply(Z,Y)))) = inverse(multiply(Z,inverse(X))),
inference('REWRITE',[status(thm)],[3672,4712,theory(equality)]) ).
cnf(4725,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(X))) = Y,
inference('REWRITE',[status(thm)],[2998,4723,theory(equality)]) ).
cnf(4726,plain,
multiply(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,multiply(inverse(U),Y))))),Z) = U,
inference('REWRITE',[status(thm)],[3405,4725,theory(equality)]) ).
cnf(4727,plain,
multiply(inverse(X),inverse(Y)) = multiply(inverse(multiply(Z,multiply(Y,X))),Z),
inference('REWRITE',[status(thm)],[4459,4726,theory(equality)]) ).
cnf(4731,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)],[4476,4727,theory(equality)]) ).
cnf(4734,plain,
multiply(inverse(multiply(X,inverse(Y))),X) = Y,
inference('REWRITE',[status(thm)],[4084,11,4727,theory(equality)]) ).
cnf(4735,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference('REWRITE',[status(thm)],[4718,4734,theory(equality)]) ).
cnf(4736,plain,
multiply(multiply(inverse(X),X),Y) = Y,
inference('REWRITE',[status(thm)],[4721,4735,theory(equality)]) ).
cnf(4762,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('REWRITE',[status(thm)],[4703,4736,theory(equality)]) ).
cnf(4763,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('REWRITE',[status(thm)],[4727,4762,theory(equality)]) ).
cnf(4988,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)],[4731,4763,theory(equality)]) ).
cnf(4989,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)],[666,4763,4988,theory(equality)]) ).
cnf(4994,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)],[1665,4763,theory(equality)]) ).
cnf(4995,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)],[3393,4763,theory(equality)]) ).
cnf(5003,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)],[4502,4762,theory(equality)]) ).
cnf(5006,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)],[4503,4711,4762,theory(equality)]) ).
cnf(5007,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[5003,4711,4763,4762,5006,theory(equality)]) ).
cnf(5027,plain,
inverse(multiply(X,inverse(Y))) = multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(X,multiply(inverse(Y),U))))),
inference('REWRITE',[status(thm)],[1925,4702,5006,theory(equality)]) ).
cnf(5050,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),multiply(inverse(X),Z)),inverse(U)))) = multiply(Z,inverse(U)),
inference('REWRITE',[status(thm)],[1906,292,5027,theory(equality)]) ).
cnf(5054,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)],[952,5050,theory(equality)]) ).
cnf(5175,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)],[4475,4711,4763,4762,theory(equality)]) ).
cnf(5213,plain,
multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),U))) = multiply(multiply(X,Z),U),
inference('REWRITE',[status(thm)],[4387,4711,4762,theory(equality)]) ).
cnf(5224,plain,
multiply(X,inverse(multiply(inverse(Y),X))) = Y,
inference('REWRITE',[status(thm)],[5175,4735,4762,5213,theory(equality)]) ).
cnf(5226,plain,
inverse(multiply(X,multiply(Y,multiply(inverse(multiply(multiply(Z,X),Y)),U)))) = multiply(inverse(U),Z),
inference('REWRITE',[status(thm)],[4995,5224,theory(equality)]) ).
cnf(5227,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)],[4994,5226,theory(equality)]) ).
cnf(5228,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[4988,5227,theory(equality)]) ).
cnf(5290,plain,
multiply(multiply(inverse(X),Y),inverse(Y)) = multiply(Z,inverse(multiply(X,Z))),
inference('REWRITE',[status(thm)],[3715,5227,theory(equality)]) ).
cnf(5328,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)],[5054,5213,theory(equality)]) ).
cnf(5335,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[4989,5224,5213,theory(equality)]) ).
cnf(5336,plain,
inverse(X) = multiply(Y,inverse(multiply(X,Y))),
inference('REWRITE',[status(thm)],[5290,5335,theory(equality)]) ).
cnf(5340,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference('REWRITE',[status(thm)],[5328,5336,theory(equality)]) ).
cnf(5457,plain,
inverse(multiply(X,Y)) = multiply(Z,multiply(multiply(inverse(Z),U),inverse(multiply(X,multiply(Y,U))))),
inference('REWRITE',[status(thm)],[1626,4702,5213,theory(equality)]) ).
cnf(5525,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)],[1712,4702,4735,5228,5457,5213,theory(equality)]) ).
cnf(5589,plain,
inverse(multiply(X,multiply(inverse(Y),multiply(multiply(Y,Z),U)))) = inverse(multiply(multiply(X,Z),U)),
inference('REWRITE',[status(thm)],[5006,4735,5228,5457,5213,theory(equality)]) ).
cnf(5599,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)],[685,4763,4735,5228,5457,5213,theory(equality)]) ).
cnf(5630,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference('REWRITE',[status(thm)],[4555,4736,theory(equality)]) ).
cnf(5670,plain,
multiply(X,inverse(Y)) = multiply(Z,multiply(multiply(inverse(Z),multiply(X,inverse(multiply(U,Y)))),U)),
inference('REWRITE',[status(thm)],[3379,5335,5340,4711,theory(equality)]) ).
cnf(5673,plain,
inverse(multiply(X,inverse(Y))) = multiply(multiply(Y,Z),inverse(multiply(X,Z))),
inference('REWRITE',[status(thm)],[5525,5670,theory(equality)]) ).
cnf(5727,plain,
multiply(X,multiply(multiply(inverse(X),Y),inverse(Z))) = multiply(Y,inverse(Z)),
inference('REWRITE',[status(thm)],[3971,5670,4702,theory(equality)]) ).
cnf(5729,plain,
inverse(multiply(X,Y)) = inverse(multiply(multiply(X,multiply(Y,Z)),inverse(Z))),
inference('REWRITE',[status(thm)],[5457,5340,5727,theory(equality)]) ).
cnf(5760,plain,
multiply(inverse(X),multiply(multiply(X,Y),Z)) = multiply(Y,Z),
inference('REWRITE',[status(thm)],[2425,5007,5228,5729,5589,4763,5335,5340,4711,5673,5670,4702,theory(equality)]) ).
cnf(5763,plain,
multiply(multiply(inverse(X),Y),multiply(multiply(inverse(Y),X),Z)) = Z,
inference('REWRITE',[status(thm)],[5599,4711,5213,5228,4763,5760,theory(equality)]) ).
cnf(5910,plain,
multiply(X,Y) = multiply(Z,multiply(multiply(inverse(Z),X),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5760,5763,theory(equality)]),4711,theory(equality)]) ).
cnf(5945,plain,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[5213,5910,theory(equality)]) ).
cnf(5946,plain,
$false,
inference('REWRITE',[status(thm)],[5630,5945,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP061-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 02:16:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T02:16:53
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n009.cluster.edu at 2022-06-14T02:16:53
% 7.66/7.90
% 7.66/7.90
% 7.66/7.90 #||
% 7.66/7.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.66/7.90 % SZS output start Refutation
% See solution above
% 7.75/7.94 ||#
% 7.75/7.94
% 7.75/7.94 ; Summary of computation:
% 7.75/7.94 ; 15054 formulas have been input or derived (from 62 formulas).
% 7.75/7.94 ; 5946 (39%) were retained. Of these,
% 7.75/7.94 ; 5757 (97%) were simplified or subsumed later,
% 7.75/7.94 ; 189 ( 3%) are still being kept.
% 7.75/7.94 ;
% 7.75/7.94 ; Run time in seconds excluding printing time:
% 7.75/7.94 ; 0.001 0% Read assertion file (1 call)
% 7.75/7.94 ; 0.001 0% Assert (2 calls)
% 7.75/7.94 ; 1.759 24% Process new row (14,949 calls)
% 7.75/7.94 ; 0.033 0% Resolution (122 calls)
% 7.75/7.94 ; 0.557 7% Paramodulation (61 calls)
% 7.75/7.94 ; 0.000 0% Condensing (3 calls)
% 7.75/7.94 ; 0.000 0% Forward subsumption (3 calls)
% 7.75/7.94 ; 0.001 0% Backward subsumption (3 calls)
% 7.75/7.94 ; 0.000 0% Clause clause subsumption (1 call)
% 7.75/7.94 ; 2.767 37% Forward simplification (13,501 calls)
% 7.75/7.94 ; 1.832 25% Backward simplification (5,946 calls)
% 7.75/7.94 ; 0.412 6% Ordering (77,525 calls)
% 7.75/7.94 ; 0.000 0% Sortal reasoning (32 calls)
% 7.75/7.94 ; 0.000 0% Purity testing (1 call)
% 7.75/7.94 ; 0.074 1% Other
% 7.75/7.94 ; 7.437 Total
% 7.75/7.94 ; 7.480 Real time
% 7.75/7.94 ;
% 7.75/7.94 ; Term-hash-array has 38,404 terms in all.
% 7.75/7.94 ; Feature-vector-row-index has 0 entries (1 at peak, 3 added, 3 deleted).
% 7.75/7.94 ; Feature-vector-row-index has 1 node (30 at peak, 71 added, 70 deleted).
% 7.75/7.94 ; Retrieved 0 possibly forward subsuming rows in 3 calls.
% 7.75/7.94 ; Retrieved 1 possibly backward subsumed row in 3 calls.
% 7.75/7.94 ; Path-index has 1,074 entries (30,962 at peak, 39,755 added, 38,681 deleted).
% 7.75/7.94 ; Path-index has 39,533 nodes (46,390 at peak, 61,022 added, 21,489 deleted).
% 7.75/7.94 ; Trie-index has 1,074 entries (30,962 at peak, 39,755 added, 38,681 deleted).
% 7.75/7.94 ; Trie-index has 6,346 nodes (233,138 at peak, 295,240 added, 288,894 deleted).
% 7.75/7.94 ; Retrieved 140,827 generalization terms in 309,349 calls.
% 7.75/7.94 ; Retrieved 27,847 instance terms in 5,979 calls.
% 7.75/7.94 ; Retrieved 305,494 unifiable terms in 799 calls.
% 7.75/7.94 ;
% 7.75/7.94 ; The agenda of backward simplifiable rows to process has 58 entries:
% 7.75/7.94 ; 58 with value 0
% 7.75/7.94 ; The agenda of rows to process has 17 entries:
% 7.75/7.94 ; 1 with value 29 3 with value 31 5 with value 33
% 7.75/7.94 ; 2 with value 30 1 with value 32 5 with value 34
% 7.75/7.94 ; The agenda of rows to give has 179 entries:
% 7.75/7.94 ; 1 with value (4 25) 9 with value (4 38) 5 with value (4 51)
% 7.75/7.94 ; 1 with value (4 26) 5 with value (4 39) 3 with value (4 53)
% 7.75/7.94 ; 9 with value (4 27) 6 with value (4 40) 3 with value (4 54)
% 7.75/7.94 ; 6 with value (4 28) 12 with value (4 41) 3 with value (4 55)
% 7.75/7.94 ; 9 with value (4 29) 6 with value (4 42) 1 with value (4 56)
% 7.75/7.94 ; 6 with value (4 30) 5 with value (4 43) 1 with value (4 58)
% 7.75/7.94 ; 3 with value (4 31) 7 with value (4 44) 1 with value (4 59)
% 7.75/7.94 ; 8 with value (4 32) 3 with value (4 45) 1 with value (4 60)
% 7.75/7.94 ; 4 with value (4 33) 6 with value (4 46) 2 with value (4 61)
% 7.75/7.94 ; 7 with value (4 34) 3 with value (4 47) 1 with value (4 62)
% 7.75/7.94 ; 11 with value (4 35) 5 with value (4 48) 1 with value (4 64)
% 7.75/7.94 ; 11 with value (4 36) 1 with value (4 49) 1 with value (4 66)
% 7.75/7.94 ; 9 with value (4 37) 3 with value (4 50)
% 7.75/7.94 Evaluation took:
% 7.75/7.94 7.482 seconds of real time
% 7.75/7.94 6.978306 seconds of user run time
% 7.75/7.94 0.503163 seconds of system run time
% 7.75/7.94 [Run times include 1.693 seconds GC run time.]
% 7.75/7.94 0 calls to %EVAL
% 7.75/7.94 0 page faults and
% 7.75/7.94 455,015,688 bytes consed.
% 7.75/7.94 :PROOF-FOUND
% 7.75/7.94 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T02:17:00
% 7.75/7.94 :PROOF-FOUND
% 7.75/7.94 *
%------------------------------------------------------------------------------