TSTP Solution File: GRP440-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP440-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n016.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 5.92s 6.18s
% Output   : Refutation 6.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :    2
% Syntax   : Number of clauses     :   93 (  93 unt;   0 nHn;   6 RR)
%            Number of literals    :   93 (  92 equ;   5 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   15 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  352 (   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_2,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).

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(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(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(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(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(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(2068,plain,
    inverse(multiply(inverse(X),multiply(X,multiply(Y,inverse(multiply(Z,Y)))))) = Z,
    inference('PARAMODULATE',[status(thm)],[1030,1113,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(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(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(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(4134,plain,
    multiply(X,inverse(X)) = multiply(Y,inverse(Y)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4086,1017,theory(equality)]),1017,theory(equality)]) ).

cnf(4266,plain,
    multiply(inverse(multiply(X,multiply(Y,multiply(Z,inverse(Z))))),X) = inverse(Y),
    inference('PARAMODULATE',[status(thm)],[3742,4134,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(4526,plain,
    multiply(multiply(inverse(X),X),a2) != a2,
    inference('PARAMODULATE',[status(thm)],[prove_these_axioms_2,4417,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(4676,plain,
    multiply(multiply(inverse(multiply(X,inverse(multiply(Y,X)))),multiply(Z,inverse(multiply(Y,Z)))),a2) != a2,
    inference('PARAMODULATE',[status(thm)],[4526,2999,theory(equality)]) ).

cnf(4713,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(4714,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(4719,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(4721,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(4722,plain,
    multiply(X,multiply(inverse(X),Y)) = Y,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4527,4527,theory(equality)]),4534,theory(equality)]) ).

cnf(4723,plain,
    inverse(multiply(multiply(inverse(X),X),Y)) = multiply(inverse(multiply(Z,Y)),Z),
    inference('REWRITE',[status(thm)],[4721,4722,theory(equality)]) ).

cnf(4724,plain,
    inverse(inverse(inverse(multiply(X,inverse(multiply(Y,X)))))) = Y,
    inference('REWRITE',[status(thm)],[4714,4722,theory(equality)]) ).

cnf(4725,plain,
    inverse(inverse(multiply(X,inverse(multiply(inverse(Y),X))))) = Y,
    inference('REWRITE',[status(thm)],[4713,4722,theory(equality)]) ).

cnf(4727,plain,
    multiply(X,multiply(inverse(Y),Y)) = X,
    inference('REWRITE',[status(thm)],[4541,4725,theory(equality)]) ).

cnf(4728,plain,
    multiply(multiply(inverse(inverse(X)),multiply(Y,inverse(multiply(Z,Y)))),Z) = X,
    inference('REWRITE',[status(thm)],[4719,4727,theory(equality)]) ).

cnf(4730,plain,
    multiply(multiply(X,multiply(Y,inverse(multiply(Z,Y)))),Z) = X,
    inference('REWRITE',[status(thm)],[1022,4728,theory(equality)]) ).

cnf(4731,plain,
    inverse(inverse(X)) = X,
    inference('REWRITE',[status(thm)],[4728,4730,theory(equality)]) ).

cnf(4732,plain,
    inverse(multiply(X,inverse(multiply(Y,X)))) = Y,
    inference('REWRITE',[status(thm)],[4724,4731,theory(equality)]) ).

cnf(4734,plain,
    multiply(multiply(X,multiply(Y,inverse(multiply(X,Y)))),a2) != a2,
    inference('REWRITE',[status(thm)],[4676,4732,theory(equality)]) ).

cnf(4739,plain,
    multiply(inverse(X),multiply(X,multiply(inverse(multiply(Y,inverse(Z))),Y))) = Z,
    inference('REWRITE',[status(thm)],[3668,4732,theory(equality)]) ).

cnf(4742,plain,
    multiply(inverse(X),multiply(X,multiply(multiply(inverse(Y),Y),Z))) = Z,
    inference('REWRITE',[status(thm)],[4552,4732,theory(equality)]) ).

cnf(4744,plain,
    multiply(X,multiply(Y,inverse(multiply(Z,Y)))) = inverse(multiply(Z,inverse(X))),
    inference('REWRITE',[status(thm)],[3672,4732,theory(equality)]) ).

cnf(4746,plain,
    multiply(inverse(multiply(X,inverse(X))),a2) != a2,
    inference('REWRITE',[status(thm)],[4734,4744,theory(equality)]) ).

cnf(4747,plain,
    inverse(multiply(inverse(multiply(inverse(X),Y)),inverse(X))) = Y,
    inference('REWRITE',[status(thm)],[2998,4744,theory(equality)]) ).

cnf(4748,plain,
    multiply(multiply(X,multiply(multiply(inverse(X),Y),inverse(multiply(Z,multiply(inverse(U),Y))))),Z) = U,
    inference('REWRITE',[status(thm)],[3405,4747,theory(equality)]) ).

cnf(4749,plain,
    multiply(inverse(X),inverse(Y)) = multiply(inverse(multiply(Z,multiply(Y,X))),Z),
    inference('REWRITE',[status(thm)],[4458,4748,theory(equality)]) ).

cnf(4753,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)],[4475,4749,theory(equality)]) ).

cnf(4754,plain,
    multiply(inverse(multiply(X,inverse(X))),inverse(Y)) = inverse(Y),
    inference('REWRITE',[status(thm)],[4266,4749,theory(equality)]) ).

cnf(4756,plain,
    multiply(inverse(multiply(X,inverse(Y))),X) = Y,
    inference('REWRITE',[status(thm)],[4084,11,4749,theory(equality)]) ).

cnf(4757,plain,
    multiply(inverse(X),multiply(X,Y)) = Y,
    inference('REWRITE',[status(thm)],[4739,4756,theory(equality)]) ).

cnf(4758,plain,
    multiply(multiply(inverse(X),X),Y) = Y,
    inference('REWRITE',[status(thm)],[4742,4757,theory(equality)]) ).

cnf(4784,plain,
    inverse(X) = multiply(inverse(multiply(Y,X)),Y),
    inference('REWRITE',[status(thm)],[4723,4758,theory(equality)]) ).

cnf(4785,plain,
    multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
    inference('REWRITE',[status(thm)],[4749,4784,theory(equality)]) ).

cnf(5005,plain,
    inverse(multiply(X,multiply(Y,inverse(Y)))) = inverse(X),
    inference('REWRITE',[status(thm)],[4754,4785,theory(equality)]) ).

cnf(5011,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)],[4753,4785,theory(equality)]) ).

cnf(5017,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)],[1665,4785,theory(equality)]) ).

cnf(5018,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)],[3393,4785,theory(equality)]) ).

cnf(5198,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)],[4474,4731,4785,4784,theory(equality)]) ).

cnf(5236,plain,
    multiply(X,multiply(Y,multiply(multiply(inverse(Y),Z),U))) = multiply(multiply(X,Z),U),
    inference('REWRITE',[status(thm)],[4387,4731,4784,theory(equality)]) ).

cnf(5247,plain,
    multiply(X,inverse(multiply(inverse(Y),X))) = Y,
    inference('REWRITE',[status(thm)],[5198,4757,4784,5236,theory(equality)]) ).

cnf(5249,plain,
    inverse(multiply(X,multiply(Y,multiply(inverse(multiply(multiply(Z,X),Y)),U)))) = multiply(inverse(U),Z),
    inference('REWRITE',[status(thm)],[5018,5247,theory(equality)]) ).

cnf(5250,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)],[5017,5249,theory(equality)]) ).

cnf(5251,plain,
    multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
    inference('REWRITE',[status(thm)],[5011,5250,theory(equality)]) ).

cnf(5254,plain,
    $false,
    inference('REWRITE',[status(thm)],[4746,4731,5005,5251,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP440-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12  % Command  : run-snark %s %d
% 0.12/0.33  % Computer : n016.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 : Mon Jun 13 11:02:14 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p 2022-06-13T11:02:14
% 0.18/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n016.cluster.edu at 2022-06-13T11:02:14
% 5.92/6.18  
% 5.92/6.18  
% 5.92/6.18  #||
% 5.92/6.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.92/6.18  % SZS output start Refutation
% See solution above
% 6.02/6.22  ||#
% 6.02/6.22  
% 6.02/6.22  ; Summary of computation:
% 6.02/6.22  ;     14297 formulas have been input or derived (from 54 formulas).
% 6.02/6.22  ;      5254 (37%) were retained.  Of these,
% 6.02/6.22  ;         5111 (97%) were simplified or subsumed later,
% 6.02/6.22  ;          143 ( 3%) are still being kept.
% 6.02/6.22  ; 
% 6.02/6.22  ; Run time in seconds excluding printing time:
% 6.02/6.22  ;     0.001   0%   Read assertion file          (1 call)
% 6.02/6.22  ;     0.000   0%   Assert                       (2 calls)
% 6.02/6.22  ;     1.869  33%   Process new row              (9,558 calls)
% 6.02/6.22  ;     0.067   1%   Resolution                   (106 calls)
% 6.02/6.22  ;     0.467   8%   Paramodulation               (53 calls)
% 6.02/6.22  ;     1.657  29%   Forward simplification       (8,492 calls)
% 6.02/6.22  ;     1.537  27%   Backward simplification      (5,254 calls)
% 6.02/6.22  ;     0.056   1%   Ordering                     (19,785 calls)
% 6.02/6.22  ;     0.000   0%   Sortal reasoning             (32 calls)
% 6.02/6.22  ;     0.000   0%   Purity testing               (1 call)
% 6.02/6.22  ;     0.061   1%   Other
% 6.02/6.22  ;     5.715        Total
% 6.02/6.22  ;     5.758        Real time
% 6.02/6.22  ; 
% 6.02/6.22  ; Term-hash-array has 35,022 terms in all.
% 6.02/6.22  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 6.02/6.22  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 6.02/6.22  ; Path-index has 998 entries (31,005 at peak, 35,329 added, 34,331 deleted).
% 6.02/6.22  ; Path-index has 37,234 nodes (46,521 at peak, 54,742 added, 17,508 deleted).
% 6.02/6.22  ; Trie-index has 998 entries (31,005 at peak, 35,329 added, 34,331 deleted).
% 6.02/6.22  ; Trie-index has 6,574 nodes (233,600 at peak, 265,413 added, 258,839 deleted).
% 6.02/6.22  ; Retrieved 17,208 generalization terms in 159,511 calls.
% 6.02/6.22  ; Retrieved 22,908 instance terms in 5,265 calls.
% 6.02/6.22  ; Retrieved 301,891 unifiable terms in 722 calls.
% 6.02/6.22  ; 
% 6.02/6.22  ; The agenda of backward simplifiable rows to process has 4351 entries:
% 6.02/6.22  ;  4351 with value 0
% 6.02/6.22  ; The agenda of rows to process has 361 entries:
% 6.02/6.22  ;     7 with value 43              8 with value 55               3 with value 67
% 6.02/6.22  ;    12 with value 44             11 with value 56               4 with value 69
% 6.02/6.22  ;    26 with value 45             14 with value 57              23 with value 70
% 6.02/6.22  ;    20 with value 46              5 with value 58              17 with value 71
% 6.02/6.22  ;    16 with value 47              4 with value 59              12 with value 72
% 6.02/6.22  ;     7 with value 48              2 with value 60               2 with value 73
% 6.02/6.22  ;    13 with value 49              2 with value 61               1 with value 74
% 6.02/6.22  ;    17 with value 50              7 with value 62              13 with value 75
% 6.02/6.22  ;     7 with value 51             10 with value 63               7 with value 76
% 6.02/6.22  ;    12 with value 52             12 with value 64              13 with value 77
% 6.02/6.22  ;    18 with value 53             14 with value 65               4 with value 78
% 6.02/6.22  ;    12 with value 54              6 with value 66
% 6.02/6.22  ; The agenda of rows to give has 138 entries:
% 6.02/6.22  ;     1 with value (4 23)          6 with value (4 39)           2 with value (4 53)
% 6.02/6.22  ;     1 with value (4 24)          3 with value (4 40)           3 with value (4 54)
% 6.02/6.22  ;     1 with value (4 26)          6 with value (4 41)           2 with value (4 55)
% 6.02/6.22  ;     4 with value (4 27)          3 with value (4 42)           5 with value (4 56)
% 6.02/6.22  ;     6 with value (4 28)          6 with value (4 43)           2 with value (4 57)
% 6.02/6.22  ;     2 with value (4 29)          2 with value (4 44)           2 with value (4 58)
% 6.02/6.22  ;     6 with value (4 30)          5 with value (4 45)           2 with value (4 59)
% 6.02/6.22  ;     1 with value (4 31)          8 with value (4 46)           4 with value (4 60)
% 6.02/6.22  ;     2 with value (4 33)          5 with value (4 47)           4 with value (4 61)
% 6.02/6.22  ;     2 with value (4 34)          4 with value (4 48)           3 with value (4 62)
% 6.02/6.22  ;     5 with value (4 35)          5 with value (4 49)           1 with value (4 63)
% 6.02/6.22  ;     2 with value (4 36)          5 with value (4 50)           2 with value (4 65)
% 6.02/6.22  ;     2 with value (4 37)          2 with value (4 51)           5 with value (4 66)
% 6.02/6.22  ;     2 with value (4 38)          3 with value (4 52)           1 with value (4 67)
% 6.02/6.22  Evaluation took:
% 6.02/6.22    5.76 seconds of real time
% 6.02/6.22    5.3857 seconds of user run time
% 6.02/6.22    0.374048 seconds of system run time
% 6.02/6.22    [Run times include 1.46 seconds GC run time.]
% 6.02/6.22    0 calls to %EVAL
% 6.02/6.22    0 page faults and
% 6.02/6.22    361,809,216 bytes consed.
% 6.02/6.22  :PROOF-FOUND
% 6.02/6.22  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T11:02:20
% 6.02/6.22  :PROOF-FOUND
% 6.02/6.22  * 
%------------------------------------------------------------------------------