TSTP Solution File: GRP408-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP408-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n021.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 11:38:08 EDT 2022
% Result : Unsatisfiable 1.36s 1.54s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 2 RR)
% Number of literals : 77 ( 76 equ; 1 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 353 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),multiply(inverse(Y),Y))))) = Z,
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,
multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),multiply(inverse(U),multiply(inverse(U),U)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,single_axiom,theory(equality)]) ).
cnf(5,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),multiply(inverse(Y),multiply(inverse(Y),Y)))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(6,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(X,Y)),U))),multiply(inverse(Z),multiply(inverse(Z),Z)))) = U,
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(11,plain,
multiply(X,inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),U)),V)),multiply(inverse(U),multiply(inverse(U),U))))),multiply(inverse(Y),multiply(inverse(Y),Y))))) = inverse(multiply(inverse(V),multiply(inverse(Z),multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[single_axiom,3,theory(equality)]) ).
cnf(25,plain,
multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,inverse(multiply(inverse(U),multiply(inverse(V),multiply(inverse(V),V))))))) = multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),U),
inference('PARAMODULATE',[status(thm)],[5,3,theory(equality)]) ).
cnf(31,plain,
multiply(inverse(X),multiply(Y,inverse(multiply(inverse(Z),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(Y,U)),X)),multiply(inverse(U),multiply(inverse(U),U))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(Y,U)),X)),multiply(inverse(U),multiply(inverse(U),U))))),inverse(multiply(inverse(multiply(inverse(multiply(Y,U)),X)),multiply(inverse(U),multiply(inverse(U),U)))))))))) = Z,
inference('PARAMODULATE',[status(thm)],[5,single_axiom,theory(equality)]) ).
cnf(35,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(Y),multiply(inverse(Y),Y)))) = Z,
inference('PARAMODULATE',[status(thm)],[6,6,theory(equality)]) ).
cnf(36,plain,
multiply(inverse(multiply(X,Y)),multiply(X,Z)) = multiply(inverse(multiply(U,Y)),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[5,35,theory(equality)]) ).
cnf(59,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(multiply(Z,U)),multiply(Z,multiply(inverse(Y),Y)))))) = multiply(inverse(Y),U),
inference('PARAMODULATE',[status(thm)],[5,36,theory(equality)]) ).
cnf(60,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)) = multiply(inverse(multiply(W,multiply(U,Z))),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[36,36,theory(equality)]) ).
cnf(61,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(multiply(U,Y)),multiply(U,V))) = multiply(inverse(multiply(W,Z)),multiply(W,multiply(X,V))),
inference('PARAMODULATE',[status(thm)],[36,36,theory(equality)]) ).
cnf(62,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(inverse(multiply(V,multiply(inverse(Z),multiply(inverse(Z),Z)))),multiply(V,U)),
inference('PARAMODULATE',[status(thm)],[36,35,theory(equality)]) ).
cnf(75,plain,
multiply(multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),U)),Y)),V)) = multiply(inverse(multiply(W,multiply(inverse(U),multiply(inverse(U),U)))),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[36,3,theory(equality)]) ).
cnf(80,plain,
inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(X),multiply(inverse(X),X)))) = inverse(multiply(inverse(multiply(Z,Y)),multiply(Z,multiply(inverse(X),X)))),
inference('PARAMODULATE',[status(thm)],[35,59,theory(equality)]) ).
cnf(85,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Z,U)),multiply(Z,V))),multiply(inverse(multiply(W,U)),multiply(inverse(Y),Y)))))) = multiply(inverse(Y),multiply(W,V)),
inference('PARAMODULATE',[status(thm)],[59,36,theory(equality)]) ).
cnf(140,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(Z,inverse(multiply(inverse(U),multiply(inverse(V),multiply(inverse(V),V)))))))),multiply(inverse(multiply(inverse(multiply(Z,V)),Y)),W)) = multiply(inverse(multiply(X1,U)),multiply(X1,W)),
inference('PARAMODULATE',[status(thm)],[60,5,theory(equality)]) ).
cnf(195,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U))) = multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,U))),
inference('PARAMODULATE',[status(thm)],[60,61,theory(equality)]) ).
cnf(226,plain,
multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),multiply(inverse(multiply(U,V)),V))),Y)),multiply(inverse(multiply(W,V)),multiply(W,multiply(U,V))))),
inference('PARAMODULATE',[status(thm)],[3,61,theory(equality)]) ).
cnf(241,plain,
multiply(inverse(X),multiply(inverse(multiply(Y,Z)),multiply(Y,U))) = multiply(inverse(X),multiply(inverse(multiply(V,Z)),multiply(V,U))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[59,61,theory(equality)]),85,theory(equality)]) ).
cnf(277,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(Z,U)))),multiply(X,inverse(multiply(inverse(multiply(V,W)),multiply(V,multiply(inverse(multiply(inverse(multiply(Z,X1)),multiply(Z,U))),multiply(inverse(multiply(Y1,X1)),multiply(Y1,U)))))))) = multiply(inverse(multiply(Y,multiply(Z,U))),W),
inference('PARAMODULATE',[status(thm)],[59,61,theory(equality)]) ).
cnf(303,plain,
multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U))) = multiply(X,multiply(inverse(multiply(V,Z)),multiply(V,U))),
inference('PARAMODULATE',[status(thm)],[241,35,theory(equality)]) ).
cnf(338,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U)))),multiply(X,inverse(multiply(inverse(multiply(V,W)),multiply(V,multiply(inverse(multiply(inverse(multiply(X1,Z)),multiply(X1,U))),multiply(inverse(multiply(X1,Z)),multiply(X1,U)))))))) = multiply(inverse(multiply(inverse(multiply(X1,Z)),multiply(X1,U))),W),
inference('PARAMODULATE',[status(thm)],[59,303,theory(equality)]) ).
cnf(347,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U)))),multiply(X,multiply(inverse(multiply(V,Z)),W))) = multiply(inverse(multiply(X1,multiply(Y1,multiply(V,U)))),multiply(X1,multiply(Y1,W))),
inference('PARAMODULATE',[status(thm)],[195,36,theory(equality)]) ).
cnf(368,plain,
multiply(inverse(multiply(X,multiply(Y,multiply(Z,U)))),multiply(X,inverse(multiply(inverse(multiply(V,W)),multiply(V,multiply(inverse(multiply(X1,multiply(Y1,U))),multiply(X1,multiply(Y1,U)))))))) = multiply(inverse(multiply(Y,multiply(Z,U))),W),
inference('PARAMODULATE',[status(thm)],[59,195,theory(equality)]) ).
cnf(369,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U) = multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,Z))),U),
inference('REWRITE',[status(thm)],[338,368,theory(equality)]) ).
cnf(376,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),V)),multiply(inverse(multiply(W,multiply(X1,U))),multiply(W,multiply(X1,Z))))))) = multiply(inverse(multiply(Y,Z)),V),
inference('PARAMODULATE',[status(thm)],[59,195,theory(equality)]) ).
cnf(399,plain,
multiply(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U)))),multiply(inverse(multiply(V,multiply(W,Z))),inverse(multiply(inverse(multiply(X1,Y1)),multiply(X1,multiply(inverse(multiply(V,multiply(W,U))),multiply(V,multiply(W,U)))))))) = multiply(inverse(multiply(V,multiply(W,U))),Y1),
inference('PARAMODULATE',[status(thm)],[59,195,theory(equality)]) ).
cnf(453,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(X,multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[80,80,theory(equality)]) ).
cnf(467,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U)),multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,Y))))) = inverse(multiply(inverse(multiply(X1,U)),multiply(X1,multiply(inverse(multiply(X,Y)),multiply(X,Y))))),
inference('PARAMODULATE',[status(thm)],[453,195,theory(equality)]) ).
cnf(491,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(inverse(multiply(inverse(multiply(V,multiply(W,X1))),multiply(V,multiply(W,Z)))),multiply(inverse(multiply(inverse(Z),multiply(inverse(Z),X1))),U)),
inference('PARAMODULATE',[status(thm)],[62,195,theory(equality)]) ).
cnf(499,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(multiply(V,inverse(multiply(inverse(W),multiply(inverse(X1),multiply(inverse(X1),X1))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(V,X1)),Z)),W)),U)),
inference('PARAMODULATE',[status(thm)],[62,3,theory(equality)]) ).
cnf(500,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),inverse(multiply(inverse(multiply(inverse(multiply(U,V)),W)),multiply(inverse(V),multiply(inverse(V),V)))))) = multiply(inverse(multiply(U,multiply(inverse(Z),multiply(inverse(Z),Z)))),W),
inference('PARAMODULATE',[status(thm)],[62,single_axiom,theory(equality)]) ).
cnf(587,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,inverse(Z)))),multiply(inverse(Y),multiply(inverse(Y),Y))) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,62,theory(equality)]),277,theory(equality)]) ).
cnf(592,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U)))),multiply(X,inverse(multiply(inverse(multiply(U,V)),multiply(inverse(multiply(W,multiply(inverse(Z),multiply(inverse(Z),Z)))),multiply(W,multiply(inverse(multiply(Y,Z)),multiply(Y,U)))))))) = multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),V),
inference('PARAMODULATE',[status(thm)],[59,62,theory(equality)]) ).
cnf(594,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,multiply(inverse(U),multiply(inverse(U),U)))),multiply(Z,multiply(inverse(multiply(V,U)),multiply(V,X)))))) = inverse(multiply(inverse(multiply(W,Y)),multiply(W,multiply(inverse(multiply(inverse(multiply(V,U)),multiply(V,X))),multiply(inverse(multiply(V,U)),multiply(V,X)))))),
inference('PARAMODULATE',[status(thm)],[453,62,theory(equality)]) ).
cnf(619,plain,
multiply(inverse(multiply(inverse(multiply(X,multiply(inverse(Y),multiply(inverse(Y),Y)))),multiply(X,Z))),multiply(U,inverse(multiply(inverse(multiply(V,W)),multiply(V,multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,Y)),multiply(X1,U))),Z)),multiply(inverse(multiply(inverse(multiply(X1,Y)),multiply(X1,U))),Z))))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,Y)),multiply(X1,U))),Z)),W),
inference('PARAMODULATE',[status(thm)],[59,62,theory(equality)]) ).
cnf(629,plain,
multiply(inverse(X),X) = multiply(inverse(multiply(Y,multiply(inverse(Z),multiply(inverse(Z),Z)))),multiply(Y,multiply(inverse(Z),multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[62,587,theory(equality)]) ).
cnf(677,plain,
multiply(inverse(X),X) = multiply(inverse(Y),Y),
inference('PARAMODULATE',[status(thm)],[629,629,theory(equality)]) ).
cnf(678,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Y),Y)))) = Y,
inference('PARAMODULATE',[status(thm)],[35,677,theory(equality)]) ).
cnf(687,plain,
multiply(inverse(multiply(X,Y)),multiply(X,inverse(multiply(inverse(Z),multiply(inverse(Y),multiply(inverse(U),U)))))) = Z,
inference('PARAMODULATE',[status(thm)],[5,677,theory(equality)]) ).
cnf(688,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),Z)),multiply(inverse(Y),multiply(inverse(U),U))))) = Z,
inference('PARAMODULATE',[status(thm)],[single_axiom,677,theory(equality)]) ).
cnf(693,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(inverse(multiply(U,multiply(inverse(X),multiply(inverse(X),X)))),multiply(U,Z)),
inference('PARAMODULATE',[status(thm)],[62,677,theory(equality)]) ).
cnf(705,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),Y)),multiply(inverse(Z),Z))),U) = multiply(inverse(multiply(inverse(multiply(V,Y)),multiply(V,X))),U),
inference('PARAMODULATE',[status(thm)],[369,677,theory(equality)]) ).
cnf(707,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = inverse(multiply(inverse(multiply(U,Y)),multiply(U,multiply(inverse(Z),Z)))),
inference('PARAMODULATE',[status(thm)],[453,677,theory(equality)]) ).
cnf(710,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(inverse(multiply(V,multiply(inverse(Z),multiply(inverse(W),W)))),multiply(V,U)),
inference('PARAMODULATE',[status(thm)],[62,677,theory(equality)]) ).
cnf(727,plain,
inverse(multiply(inverse(multiply(inverse(X),X)),multiply(inverse(Y),multiply(inverse(Z),Z)))) = Y,
inference('PARAMODULATE',[status(thm)],[678,677,theory(equality)]) ).
cnf(728,plain,
X = inverse(multiply(inverse(multiply(Y,X)),multiply(Y,multiply(inverse(Z),Z)))),
inference('REWRITE',[status(thm)],[707,727,theory(equality)]) ).
cnf(734,plain,
inverse(multiply(inverse(multiply(X,Y)),multiply(inverse(multiply(Z,multiply(inverse(U),multiply(inverse(U),U)))),multiply(Z,multiply(inverse(multiply(V,U)),multiply(V,X)))))) = Y,
inference('REWRITE',[status(thm)],[594,728,theory(equality)]) ).
cnf(735,plain,
multiply(inverse(multiply(X,multiply(inverse(multiply(Y,Z)),multiply(Y,U)))),multiply(X,V)) = multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,U))),V),
inference('REWRITE',[status(thm)],[592,734,theory(equality)]) ).
cnf(753,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)) = multiply(inverse(multiply(W,multiply(X1,multiply(U,Z)))),multiply(W,multiply(X1,V))),
inference('REWRITE',[status(thm)],[347,735,theory(equality)]) ).
cnf(768,plain,
multiply(inverse(multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,multiply(Y,U)))),multiply(inverse(multiply(V,multiply(W,Z))),X1)) = multiply(inverse(multiply(V,multiply(W,U))),X1),
inference('REWRITE',[status(thm)],[399,728,theory(equality)]) ).
cnf(769,plain,
multiply(X,multiply(inverse(multiply(inverse(multiply(Y,Z)),multiply(Y,X))),U)) = multiply(inverse(multiply(inverse(Z),multiply(inverse(Z),Z))),U),
inference('REWRITE',[status(thm)],[491,768,theory(equality)]) ).
cnf(819,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),U)),multiply(inverse(Z),multiply(inverse(Z),Z))))) = multiply(inverse(multiply(Y,multiply(inverse(X),multiply(inverse(X),X)))),U),
inference('REWRITE',[status(thm)],[500,769,theory(equality)]) ).
cnf(895,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Y) = multiply(multiply(Z,inverse(multiply(inverse(U),multiply(inverse(V),multiply(inverse(V),V))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z,V)),X)),U)),Y)),
inference('REWRITE',[status(thm)],[499,769,theory(equality)]) ).
cnf(896,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Y) = multiply(inverse(multiply(Z,multiply(inverse(X),multiply(inverse(X),X)))),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[75,895,theory(equality)]) ).
cnf(911,plain,
multiply(X,multiply(inverse(multiply(inverse(Y),Y)),Z)) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Z),
inference('REWRITE',[status(thm)],[693,896,theory(equality)]) ).
cnf(940,plain,
multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Y) = multiply(inverse(multiply(Z,multiply(inverse(X),multiply(inverse(U),U)))),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[710,769,theory(equality)]) ).
cnf(944,plain,
multiply(inverse(multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Y)),multiply(Z,U)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(V,X)),multiply(V,Z))),Y)),U),
inference('REWRITE',[status(thm)],[619,940,728,theory(equality)]) ).
cnf(949,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),U)),multiply(inverse(multiply(V,multiply(W,Z))),multiply(V,multiply(W,Y))))) = U,
inference('REWRITE',[status(thm)],[467,728,theory(equality)]) ).
cnf(950,plain,
multiply(inverse(multiply(X,multiply(Y,Z))),multiply(X,U)) = multiply(inverse(multiply(Y,Z)),U),
inference('REWRITE',[status(thm)],[376,949,theory(equality)]) ).
cnf(960,plain,
multiply(inverse(multiply(inverse(multiply(X,Y)),multiply(X,Z))),multiply(inverse(multiply(U,Y)),V)) = multiply(inverse(multiply(U,Z)),V),
inference('REWRITE',[status(thm)],[753,950,theory(equality)]) ).
cnf(961,plain,
multiply(inverse(X),Y) = multiply(inverse(multiply(Z,X)),multiply(Z,Y)),
inference('REWRITE',[status(thm)],[140,687,960,theory(equality)]) ).
cnf(968,plain,
multiply(inverse(X),multiply(Y,inverse(multiply(inverse(Z),multiply(inverse(U),multiply(inverse(U),U)))))) = multiply(inverse(multiply(inverse(multiply(Y,U)),X)),Z),
inference('REWRITE',[status(thm)],[25,961,theory(equality)]) ).
cnf(969,plain,
multiply(inverse(multiply(inverse(X),X)),Y) = Y,
inference('REWRITE',[status(thm)],[31,688,968,theory(equality)]) ).
cnf(970,plain,
multiply(X,Y) = multiply(inverse(multiply(inverse(X),multiply(inverse(X),X))),Y),
inference('REWRITE',[status(thm)],[911,969,theory(equality)]) ).
cnf(980,plain,
multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(Y,Z)),U)),multiply(inverse(Z),multiply(inverse(Z),Z))))) = multiply(inverse(multiply(Y,multiply(inverse(X),multiply(inverse(X),X)))),U),
inference('REWRITE',[status(thm)],[819,970,theory(equality)]) ).
cnf(988,plain,
inverse(multiply(inverse(X),multiply(inverse(Y),Y))) = X,
inference('REWRITE',[status(thm)],[727,969,theory(equality)]) ).
cnf(1011,plain,
multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X,Z)),multiply(inverse(multiply(U,V)),V))),Y)),multiply(inverse(V),multiply(U,V)))),
inference('REWRITE',[status(thm)],[226,961,theory(equality)]) ).
cnf(1065,plain,
multiply(inverse(multiply(X,Y)),multiply(Z,U)) = multiply(inverse(multiply(inverse(multiply(inverse(X),Z)),Y)),U),
inference('REWRITE',[status(thm)],[944,988,961,theory(equality)]) ).
cnf(1066,plain,
multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))) = inverse(multiply(inverse(multiply(multiply(X,Z),Y)),multiply(multiply(inverse(multiply(U,V)),V),multiply(inverse(V),multiply(U,V))))),
inference('REWRITE',[status(thm)],[1011,1065,theory(equality)]) ).
cnf(1092,plain,
multiply(multiply(inverse(X),Y),Z) = multiply(inverse(multiply(inverse(Y),X)),Z),
inference('REWRITE',[status(thm)],[705,988,961,theory(equality)]) ).
cnf(1093,plain,
multiply(X,inverse(multiply(inverse(Y),multiply(inverse(Z),multiply(inverse(Z),Z))))) = multiply(multiply(X,Z),Y),
inference('REWRITE',[status(thm)],[1066,988,961,1092,theory(equality)]) ).
cnf(1094,plain,
multiply(X,Y) = inverse(multiply(inverse(Y),multiply(inverse(X),multiply(inverse(X),X)))),
inference('REWRITE',[status(thm)],[11,988,961,980,1093,theory(equality)]) ).
cnf(1146,plain,
multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z),
inference('REWRITE',[status(thm)],[1093,1094,theory(equality)]) ).
cnf(1147,plain,
$false,
inference('REWRITE',[status(thm)],[prove_these_axioms_3,1146,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP408-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 08:27:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:27:28
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n021.cluster.edu at 2022-06-14T08:27:28
% 1.36/1.54
% 1.36/1.54
% 1.36/1.54 #||
% 1.36/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.36/1.54 % SZS output start Refutation
% See solution above
% 1.36/1.55 ||#
% 1.36/1.55
% 1.36/1.55 ; Summary of computation:
% 1.36/1.55 ; 3636 formulas have been input or derived (from 22 formulas).
% 1.36/1.55 ; 1147 (32%) were retained. Of these,
% 1.36/1.55 ; 1035 (90%) were simplified or subsumed later,
% 1.36/1.55 ; 112 (10%) are still being kept.
% 1.36/1.55 ;
% 1.36/1.55 ; Run time in seconds excluding printing time:
% 1.36/1.55 ; 0.001 0% Read assertion file (1 call)
% 1.36/1.55 ; 0.000 0% Assert (2 calls)
% 1.36/1.55 ; 0.254 24% Process new row (3,033 calls)
% 1.36/1.55 ; 0.003 0% Resolution (42 calls)
% 1.36/1.55 ; 0.086 8% Paramodulation (21 calls)
% 1.36/1.55 ; 0.318 30% Forward simplification (2,373 calls)
% 1.36/1.55 ; 0.269 25% Backward simplification (1,147 calls)
% 1.36/1.55 ; 0.096 9% Ordering (9,409 calls)
% 1.36/1.55 ; 0.000 0% Sortal reasoning (32 calls)
% 1.36/1.55 ; 0.000 0% Purity testing (1 call)
% 1.36/1.55 ; 0.040 4% Other
% 1.36/1.55 ; 1.067 Total
% 1.36/1.55 ; 1.084 Real time
% 1.36/1.55 ;
% 1.36/1.55 ; Term-hash-array has 7,665 terms in all.
% 1.36/1.55 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 1.36/1.55 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 1.36/1.55 ; Path-index has 746 entries (5,621 at peak, 8,586 added, 7,840 deleted).
% 1.36/1.55 ; Path-index has 4,980 nodes (6,524 at peak, 7,950 added, 2,970 deleted).
% 1.36/1.55 ; Trie-index has 746 entries (5,621 at peak, 8,586 added, 7,840 deleted).
% 1.36/1.55 ; Trie-index has 3,480 nodes (38,432 at peak, 58,212 added, 54,732 deleted).
% 1.36/1.55 ; Retrieved 7,766 generalization terms in 34,778 calls.
% 1.36/1.55 ; Retrieved 13,670 instance terms in 1,415 calls.
% 1.36/1.55 ; Retrieved 41,810 unifiable terms in 290 calls.
% 1.36/1.55 ;
% 1.36/1.55 ; The agenda of backward simplifiable rows to process has 507 entries:
% 1.36/1.55 ; 507 with value 0
% 1.36/1.55 ; The agenda of rows to process has 67 entries:
% 1.36/1.55 ; 1 with value 32 4 with value 42 2 with value 53
% 1.36/1.55 ; 2 with value 35 6 with value 45 4 with value 56
% 1.36/1.55 ; 2 with value 36 3 with value 46 3 with value 57
% 1.36/1.55 ; 4 with value 37 1 with value 47 1 with value 62
% 1.36/1.55 ; 1 with value 38 8 with value 49 6 with value 63
% 1.36/1.55 ; 2 with value 39 4 with value 50 1 with value 66
% 1.36/1.55 ; 1 with value 40 1 with value 51 2 with value 76
% 1.36/1.55 ; 6 with value 41 2 with value 52
% 1.36/1.55 ; The agenda of rows to give has 110 entries:
% 1.36/1.55 ; 1 with value (4 20) 5 with value (4 34) 2 with value (4 44)
% 1.36/1.55 ; 1 with value (4 21) 5 with value (4 35) 3 with value (4 45)
% 1.36/1.55 ; 3 with value (4 23) 7 with value (4 36) 3 with value (4 46)
% 1.36/1.55 ; 1 with value (4 25) 8 with value (4 37) 5 with value (4 47)
% 1.36/1.55 ; 2 with value (4 26) 8 with value (4 38) 3 with value (4 48)
% 1.36/1.55 ; 1 with value (4 27) 7 with value (4 39) 5 with value (4 49)
% 1.36/1.55 ; 2 with value (4 28) 3 with value (4 40) 3 with value (4 50)
% 1.36/1.55 ; 5 with value (4 29) 6 with value (4 41) 1 with value (4 51)
% 1.36/1.55 ; 2 with value (4 30) 4 with value (4 42) 1 with value (4 52)
% 1.36/1.55 ; 4 with value (4 32) 6 with value (4 43) 1 with value (4 55)
% 1.36/1.55 ; 2 with value (4 33)
% 1.36/1.55 Evaluation took:
% 1.36/1.55 1.084 seconds of real time
% 1.36/1.55 1.024845 seconds of user run time
% 1.36/1.55 0.0591 seconds of system run time
% 1.36/1.55 [Run times include 0.109 seconds GC run time.]
% 1.36/1.55 0 calls to %EVAL
% 1.36/1.55 0 page faults and
% 1.36/1.55 90,617,968 bytes consed.
% 1.36/1.55 :PROOF-FOUND
% 1.36/1.55 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:27:29
% 1.36/1.55 :PROOF-FOUND
% 1.36/1.55 *
%------------------------------------------------------------------------------