%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP444-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:14:01 AM UTC 2026
% Result : Unsatisfiable 6.93s 1.84s
% Output : Refutation 8.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 2
% Syntax : Number of formulae : 94 ( 94 unt; 0 def)
% Number of atoms : 94 ( 93 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 12 ( 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 : 341 ( 341 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,X1))))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X0,multiply(X3,X1)))),multiply(multiply(X4,inverse(X4)),X0)))) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f8,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,multiply(X0,X4)))) = inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(multiply(multiply(X3,inverse(X3)),X0),multiply(multiply(X6,inverse(X6)),X4)))),
inference(superposition,[],[f4,f4]) ).
fof(f11,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X0,X3)))),multiply(multiply(multiply(X4,inverse(X4)),X2),multiply(multiply(X5,inverse(X5)),X0)))) = X3,
inference(superposition,[],[f1,f4]) ).
fof(f12,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(X0,X3)))),multiply(multiply(X6,inverse(X6)),X5))),X0),inverse(multiply(X7,multiply(X1,X2))))))) = X7,
inference(superposition,[],[f1,f4]) ).
fof(f244,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,inverse(X0)),inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X2)))) = X3,
inference(superposition,[],[f11,f8]) ).
fof(f288,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : multiply(multiply(X7,inverse(X7)),X3) = multiply(multiply(X4,inverse(X4)),inverse(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,multiply(X2,X3)))),multiply(multiply(multiply(X5,inverse(X5)),X1),multiply(multiply(X6,inverse(X6)),X2))))),
inference(superposition,[],[f244,f8]) ).
fof(f321,plain,
! [X3,X7,X4] : multiply(multiply(X4,inverse(X4)),X3) = multiply(multiply(X7,inverse(X7)),X3),
inference(forward_demodulation,[],[f288,f11]) ).
fof(f502,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : multiply(X8,inverse(X8)) = inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(X6,X3)))),multiply(multiply(X7,inverse(X7)),X5))),X6),inverse(multiply(multiply(X0,inverse(X0)),multiply(X1,X2))))))),
inference(superposition,[],[f12,f321]) ).
fof(f520,plain,
! [X0,X8] : multiply(X0,inverse(X0)) = multiply(X8,inverse(X8)),
inference(forward_demodulation,[],[f502,f12]) ).
fof(f544,plain,
! [X2,X3,X0,X1,X4] : multiply(X1,inverse(X1)) = multiply(multiply(X2,multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X0,multiply(X2,X3)))))),X0),
inference(superposition,[],[f520,f1]) ).
fof(f624,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X0,inverse(X0)))))))) = X3,
inference(superposition,[],[f1,f520]) ).
fof(f637,plain,
! [X2,X3,X0,X1] : inverse(X3) = multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X0,inverse(X0)))),multiply(X2,X3)))),
inference(superposition,[],[f244,f520]) ).
fof(f690,plain,
! [X3,X0,X1] : inverse(multiply(X3,multiply(inverse(X3),X0))) = inverse(multiply(X1,multiply(inverse(X1),X0))),
inference(superposition,[],[f624,f244]) ).
fof(f818,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(X2),multiply(X1,multiply(multiply(X3,inverse(X3)),inverse(multiply(X0,multiply(inverse(X0),X1))))))) = X2,
inference(superposition,[],[f1,f690]) ).
fof(f871,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X2,multiply(inverse(X2),X1)) = inverse(multiply(inverse(multiply(X0,multiply(inverse(X0),X1))),multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,multiply(inverse(X5),X3))))))),
inference(superposition,[],[f818,f690]) ).
fof(f961,plain,
! [X2,X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(forward_demodulation,[],[f871,f818]) ).
fof(f996,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,inverse(X0))) = multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))),
inference(superposition,[],[f961,f520]) ).
fof(f1257,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X4),inverse(inverse(X0))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(X0,multiply(X1,inverse(X1))))),multiply(X3,X4)))),
inference(superposition,[],[f244,f996]) ).
fof(f1963,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X0,inverse(X0)) = multiply(X5,multiply(inverse(X5),inverse(inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(multiply(X4,inverse(X4)),multiply(X1,X2)))))))))),
inference(superposition,[],[f996,f544]) ).
fof(f1965,plain,
! [X0,X4,X5] : multiply(X0,inverse(X0)) = multiply(X5,multiply(inverse(X5),inverse(multiply(X4,inverse(X4))))),
inference(forward_demodulation,[],[f1963,f1]) ).
fof(f2137,plain,
! [X2,X3,X0,X1,X4] : multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X0,inverse(X0)))),multiply(X2,X3)))) = multiply(inverse(X3),inverse(multiply(X4,inverse(X4)))),
inference(superposition,[],[f244,f1965]) ).
fof(f2155,plain,
! [X3,X4] : inverse(X3) = multiply(inverse(X3),inverse(multiply(X4,inverse(X4)))),
inference(forward_demodulation,[],[f2137,f637]) ).
fof(f2168,plain,
! [X0,X4] : multiply(X0,inverse(multiply(X4,inverse(X4)))) = X0,
inference(superposition,[],[f2155,f818]) ).
fof(f2291,plain,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X0)))))) = X3,
inference(superposition,[],[f1,f2168]) ).
fof(f2422,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(X2,X0))) = inverse(multiply(multiply(X1,X2),multiply(inverse(multiply(X3,inverse(X3))),X0))),
inference(superposition,[],[f2291,f244]) ).
fof(f2640,plain,
! [X2,X3,X0,X1,X4] : multiply(X0,X1) = inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,multiply(multiply(X4,inverse(X4)),inverse(multiply(X0,multiply(X1,X2))))))),
inference(superposition,[],[f1,f2422]) ).
fof(f2691,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(X0,X1),multiply(inverse(multiply(X3,inverse(X3))),X2)) = inverse(multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,multiply(inverse(X6),X4))))))),
inference(superposition,[],[f818,f2422]) ).
fof(f2714,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),multiply(inverse(multiply(X3,inverse(X3))),X2)),
inference(forward_demodulation,[],[f2691,f818]) ).
fof(f4194,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,multiply(X2,X0))),X1) = inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,X0))),
inference(superposition,[],[f2640,f244]) ).
fof(f4471,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X0,multiply(X1,X2))),X0) = multiply(inverse(multiply(X3,multiply(X1,X2))),X3),
inference(superposition,[],[f4194,f4194]) ).
fof(f4743,plain,
! [X3,X0,X1] : multiply(inverse(multiply(X1,X0)),X1) = multiply(inverse(multiply(X3,X0)),X3),
inference(superposition,[],[f4471,f2168]) ).
fof(f5014,plain,
! [X2,X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(X2))))),X1),
inference(superposition,[],[f4743,f2168]) ).
fof(f5218,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(forward_demodulation,[],[f5014,f2168]) ).
fof(f5368,plain,
! [X0,X1] : inverse(multiply(inverse(X1),multiply(inverse(X0),X0))) = X1,
inference(superposition,[],[f2291,f5218]) ).
fof(f5393,plain,
! [X2,X3,X0,X1] : multiply(inverse(X1),multiply(X1,X2)) = multiply(multiply(inverse(X0),X0),multiply(inverse(multiply(X3,inverse(X3))),X2)),
inference(superposition,[],[f2714,f5218]) ).
fof(f5425,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(X1,X2)) = multiply(inverse(X0),multiply(X0,X2)),
inference(forward_demodulation,[],[f5393,f2714]) ).
fof(f5521,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(inverse(X1),multiply(X1,X2)) = multiply(inverse(multiply(X3,multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,multiply(X3,X4))))))),multiply(X0,inverse(X0))),
inference(superposition,[],[f5425,f544]) ).
fof(f5766,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,inverse(X0))) = multiply(inverse(X1),multiply(X1,X2)),
inference(forward_demodulation,[],[f5521,f1]) ).
fof(f5832,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(inverse(X0),multiply(X0,X1))),
inference(superposition,[],[f5368,f5425]) ).
fof(f5840,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X0,multiply(X1,inverse(X1)))),
inference(superposition,[],[f5368,f996]) ).
fof(f5853,plain,
! [X2,X0,X1] : inverse(X0) = inverse(multiply(inverse(X1),multiply(X1,multiply(multiply(X2,inverse(X2)),X0)))),
inference(superposition,[],[f1,f5368]) ).
fof(f5856,plain,
! [X2,X3,X0,X1] : inverse(X1) = inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),X0),multiply(multiply(X3,inverse(X3)),inverse(X0))))),
inference(superposition,[],[f4,f5368]) ).
fof(f5868,plain,
! [X2,X3,X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(inverse(multiply(X2,inverse(X2))),multiply(X1,multiply(multiply(X3,inverse(X3)),X0)))),
inference(superposition,[],[f2640,f5368]) ).
fof(f6085,plain,
! [X2,X3,X0,X1] : inverse(multiply(X2,multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(X0),multiply(X0,X1))))))) = X1,
inference(superposition,[],[f1,f5766]) ).
fof(f6091,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(multiply(multiply(X4,inverse(X4)),X1),multiply(multiply(multiply(X5,inverse(X5)),X3),multiply(multiply(X6,inverse(X6)),inverse(X3))))) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(X0),multiply(X0,X1)))),
inference(superposition,[],[f8,f5766]) ).
fof(f6097,plain,
! [X2,X3,X0,X1] : inverse(X3) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(inverse(X0),multiply(X0,X1))),multiply(X1,X3)))),
inference(superposition,[],[f244,f5766]) ).
fof(f6100,plain,
! [X2,X3,X0,X1,X4] : multiply(X1,X2) = inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(inverse(X2),multiply(multiply(X4,inverse(X4)),inverse(multiply(inverse(X0),multiply(X0,X1))))))),
inference(superposition,[],[f2640,f5766]) ).
fof(f6205,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X3,inverse(X3)),multiply(inverse(multiply(X0,multiply(X1,inverse(X1)))),multiply(X2,inverse(X2))))) = X0,
inference(superposition,[],[f624,f5766]) ).
fof(f6229,plain,
! [X2,X3,X0,X1] : multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X0,multiply(X1,inverse(X1)))),multiply(inverse(X3),X3)))) = X0,
inference(superposition,[],[f244,f5766]) ).
fof(f6234,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,X0))) = multiply(inverse(multiply(X0,multiply(X1,inverse(X1)))),inverse(X2)),
inference(superposition,[],[f4194,f5766]) ).
fof(f6274,plain,
! [X2,X3,X0,X1,X4] : multiply(X4,X0) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(multiply(X3,multiply(X0,multiply(X1,inverse(X1))))),multiply(X3,inverse(X4))))),
inference(superposition,[],[f244,f5766]) ).
fof(f6287,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X0,multiply(X1,inverse(X1)))),inverse(X2)) = multiply(inverse(multiply(X3,multiply(X2,X0))),X3),
inference(superposition,[],[f4743,f5766]) ).
fof(f6290,plain,
! [X2,X3,X0] : multiply(inverse(X0),inverse(X2)) = multiply(inverse(multiply(X3,multiply(X2,X0))),X3),
inference(forward_demodulation,[],[f6287,f5840]) ).
fof(f6297,plain,
! [X0,X4] : multiply(X4,X0) = multiply(inverse(inverse(X4)),inverse(inverse(X0))),
inference(forward_demodulation,[],[f6274,f1257]) ).
fof(f6316,plain,
! [X2,X3,X0] : inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X2,X0))) = multiply(inverse(X0),inverse(X2)),
inference(forward_demodulation,[],[f6234,f5840]) ).
fof(f6321,plain,
! [X2,X0,X1] : multiply(multiply(X2,inverse(X2)),multiply(X0,multiply(X1,inverse(X1)))) = X0,
inference(forward_demodulation,[],[f6229,f5368]) ).
fof(f6334,plain,
! [X2,X3,X0] : inverse(multiply(multiply(X3,inverse(X3)),multiply(inverse(X0),multiply(X2,inverse(X2))))) = X0,
inference(forward_demodulation,[],[f6205,f5840]) ).
fof(f6363,plain,
! [X2,X0,X1] : multiply(X1,X2) = multiply(inverse(inverse(multiply(inverse(X0),multiply(X0,X1)))),inverse(inverse(X2))),
inference(forward_demodulation,[],[f6100,f5868]) ).
fof(f6366,plain,
! [X2,X3,X1] : inverse(X3) = multiply(multiply(X2,inverse(X2)),inverse(multiply(inverse(X1),multiply(X1,X3)))),
inference(forward_demodulation,[],[f6097,f5832]) ).
fof(f6372,plain,
! [X2,X3,X1,X6,X4,X5] : multiply(multiply(X2,inverse(X2)),inverse(X1)) = inverse(multiply(multiply(multiply(X4,inverse(X4)),X1),multiply(multiply(multiply(X5,inverse(X5)),X3),multiply(multiply(X6,inverse(X6)),inverse(X3))))),
inference(forward_demodulation,[],[f6091,f5832]) ).
fof(f6378,plain,
! [X2,X3,X1] : inverse(multiply(X2,multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),inverse(X1))))) = X1,
inference(forward_demodulation,[],[f6085,f5832]) ).
fof(f6399,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f6334,f6321]) ).
fof(f6409,plain,
! [X2,X0,X1] : multiply(X1,X2) = multiply(multiply(inverse(X0),multiply(X0,X1)),X2),
inference(forward_demodulation,[],[f6363,f6297]) ).
fof(f6410,plain,
! [X2,X3] : inverse(X3) = multiply(multiply(X2,inverse(X2)),inverse(X3)),
inference(forward_demodulation,[],[f6366,f5832]) ).
fof(f6411,plain,
! [X2,X1,X4] : multiply(multiply(X2,inverse(X2)),inverse(X1)) = inverse(multiply(multiply(X4,inverse(X4)),X1)),
inference(forward_demodulation,[],[f6372,f5856]) ).
fof(f6413,plain,
! [X1,X4] : inverse(X1) = inverse(multiply(multiply(X4,inverse(X4)),X1)),
inference(forward_demodulation,[],[f6411,f6410]) ).
fof(f6461,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(inverse(X0),X0))))))) = X3,
inference(superposition,[],[f624,f6399]) ).
fof(f6462,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(X0),multiply(X0,multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,inverse(X3)))))))) = X2,
inference(superposition,[],[f624,f6399]) ).
fof(f6492,plain,
! [X2,X3,X0,X1,X4] : multiply(X1,X2) = inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(X3,multiply(multiply(X4,inverse(X4)),inverse(multiply(X1,multiply(X2,X3))))))),
inference(superposition,[],[f2640,f6399]) ).
fof(f6499,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,multiply(X2,X3))),X1) = inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(X2,X3))),
inference(superposition,[],[f4194,f6399]) ).
fof(f6509,plain,
! [X2,X3,X0] : inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(X2,X3))) = multiply(inverse(X3),inverse(X2)),
inference(forward_demodulation,[],[f6499,f6290]) ).
fof(f6511,plain,
! [X2,X3,X0,X1] : multiply(X1,X2) = inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(X3,inverse(multiply(X1,multiply(X2,X3)))))),
inference(forward_demodulation,[],[f6492,f6410]) ).
fof(f6527,plain,
! [X2,X3] : inverse(inverse(multiply(X2,multiply(X3,inverse(X3))))) = X2,
inference(forward_demodulation,[],[f6462,f5853]) ).
fof(f6528,plain,
! [X3,X0] : multiply(X3,multiply(inverse(X0),X0)) = X3,
inference(forward_demodulation,[],[f6461,f6378]) ).
fof(f6560,plain,
! [X2,X3,X1] : multiply(X1,X2) = multiply(inverse(inverse(multiply(X1,multiply(X2,X3)))),inverse(X3)),
inference(forward_demodulation,[],[f6511,f6509]) ).
fof(f6561,plain,
! [X2,X3] : multiply(X2,multiply(X3,inverse(X3))) = X2,
inference(forward_demodulation,[],[f6527,f6399]) ).
fof(f6567,plain,
! [X2,X3,X1] : multiply(X1,X2) = multiply(multiply(X1,multiply(X2,X3)),inverse(X3)),
inference(forward_demodulation,[],[f6560,f6399]) ).
fof(f6699,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X0,inverse(X0)),multiply(X1,X2))) = inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X1,X2))),
inference(superposition,[],[f4194,f6561]) ).
fof(f6786,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X0,inverse(X0)),multiply(X1,X2))) = multiply(inverse(X2),inverse(X1)),
inference(forward_demodulation,[],[f6699,f6316]) ).
fof(f6887,plain,
! [X2,X1] : inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
inference(forward_demodulation,[],[f6786,f6413]) ).
fof(f7041,plain,
! [X2,X3,X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(inverse(multiply(X2,inverse(X2))),multiply(X1,multiply(multiply(X3,inverse(X3)),inverse(X0))))),
inference(superposition,[],[f2640,f6528]) ).
fof(f7087,plain,
! [X0,X1] : inverse(multiply(inverse(X1),inverse(multiply(inverse(X0),X0)))) = X1,
inference(superposition,[],[f5368,f6528]) ).
fof(f7154,plain,
! [X0,X1] : inverse(inverse(multiply(multiply(inverse(X0),X0),X1))) = X1,
inference(forward_demodulation,[],[f7087,f6887]) ).
fof(f7194,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = multiply(inverse(inverse(X0)),inverse(X1)),
inference(forward_demodulation,[],[f7041,f5868]) ).
fof(f7269,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(forward_demodulation,[],[f7154,f6399]) ).
fof(f7287,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(forward_demodulation,[],[f7194,f6887]) ).
fof(f7523,plain,
! [X2,X3,X0,X1,X4] : multiply(X2,multiply(X3,X4)) = multiply(multiply(X2,X3),multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),multiply(X1,X0))))),X4)),
inference(superposition,[],[f2714,f6409]) ).
fof(f7716,plain,
! [X2,X3,X0,X1,X4] : multiply(X2,multiply(X3,X4)) = multiply(multiply(X2,X3),multiply(multiply(multiply(inverse(X1),multiply(X1,X0)),inverse(X0)),X4)),
inference(forward_demodulation,[],[f7523,f7287]) ).
fof(f7882,plain,
! [X2,X3,X1,X4] : multiply(X2,multiply(X3,X4)) = multiply(multiply(X2,X3),multiply(multiply(inverse(X1),X1),X4)),
inference(forward_demodulation,[],[f7716,f6567]) ).
fof(f7965,plain,
! [X2,X3,X4] : multiply(X2,multiply(X3,X4)) = multiply(multiply(X2,X3),X4),
inference(forward_demodulation,[],[f7882,f7269]) ).
fof(f8200,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(superposition,[],[f2,f7965]) ).
fof(f8346,plain,
$false,
inference(trivial_inequality_removal,[],[f8200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP444-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n012.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:04:20 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.93/1.84 % (2137381)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.93/1.84 % (2137391)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2004498639:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.93/1.84 % (2137392)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=717552876:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.93/1.84 % (2137389)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1022338448:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.93/1.84 % (2137390)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3802749594:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.93/1.84 % (2137393)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1473630718:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.93/1.84 % (2137395)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3086818569:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.93/1.84 % (2137394)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1297081377:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.93/1.84 % (2137392)Instruction limit reached!
% 6.93/1.84 % (2137392)------------------------------
% 6.93/1.84 % (2137392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137392)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137392)Termination reason: Instruction limit
% 6.93/1.84 % (2137392)Termination phase: Saturation
% 6.93/1.84 % (2137392)Time elapsed: 0.041 s
% 6.93/1.84 % (2137392)Peak memory usage: 88 MB
% 6.93/1.84 % (2137392)Instructions burned: 138 (million)
% 6.93/1.84 % (2137393)Instruction limit reached!
% 6.93/1.84 % (2137393)------------------------------
% 6.93/1.84 % (2137393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137393)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137393)Termination reason: Instruction limit
% 6.93/1.84 % (2137393)Termination phase: Saturation
% 6.93/1.84 % (2137393)Time elapsed: 0.048 s
% 6.93/1.84 % (2137393)Peak memory usage: 89 MB
% 6.93/1.84 % (2137393)Instructions burned: 185 (million)
% 6.93/1.84 % (2137394)Instruction limit reached!
% 6.93/1.84 % (2137394)------------------------------
% 6.93/1.84 % (2137394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137394)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137394)Termination reason: Instruction limit
% 6.93/1.84 % (2137394)Termination phase: Saturation
% 6.93/1.84 % (2137394)Time elapsed: 0.079 s
% 6.93/1.84 % (2137394)Peak memory usage: 90 MB
% 6.93/1.84 % (2137394)Instructions burned: 257 (million)
% 6.93/1.84 % (2137404)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2917932954:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.93/1.84 % (2137405)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2859091545:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 6.93/1.84 % (2137413)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1361622969:i=215:ep=RSTC_2998 on theBenchmark for (2998ds/215Mi)
% 6.93/1.84 % (2137413)Instruction limit reached!
% 6.93/1.84 % (2137413)------------------------------
% 6.93/1.84 % (2137413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137413)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137413)Termination reason: Instruction limit
% 6.93/1.84 % (2137413)Termination phase: Saturation
% 6.93/1.84 % (2137413)Time elapsed: 0.069 s
% 6.93/1.84 % (2137413)Peak memory usage: 91 MB
% 6.93/1.84 % (2137413)Instructions burned: 215 (million)
% 6.93/1.84 % (2137395)Instruction limit reached!
% 6.93/1.84 % (2137395)------------------------------
% 6.93/1.84 % (2137395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137395)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137395)Termination reason: Instruction limit
% 6.93/1.84 % (2137395)Termination phase: Saturation
% 6.93/1.84 % (2137395)Time elapsed: 0.334 s
% 6.93/1.84 % (2137395)Peak memory usage: 98 MB
% 6.93/1.84 % (2137395)Instructions burned: 1190 (million)
% 6.93/1.84 % (2137450)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1536880293:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2996 on theBenchmark for (2996ds/317Mi)
% 6.93/1.84 % (2137451)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=905947298:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2995 on theBenchmark for (2995ds/12125Mi)
% 6.93/1.84 % (2137450)Instruction limit reached!
% 6.93/1.84 % (2137450)------------------------------
% 6.93/1.84 % (2137450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137450)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137450)Termination reason: Instruction limit
% 6.93/1.84 % (2137450)Termination phase: Saturation
% 6.93/1.84 % (2137450)Time elapsed: 0.107 s
% 6.93/1.84 % (2137450)Peak memory usage: 92 MB
% 6.93/1.84 % (2137450)Instructions burned: 321 (million)
% 6.93/1.84 % (2137474)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1318636103:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2994 on theBenchmark for (2994ds/2836Mi)
% 6.93/1.84 % (2137404)Instruction limit reached!
% 6.93/1.84 % (2137404)------------------------------
% 6.93/1.84 % (2137404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.93/1.84 % (2137404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.93/1.84 % (2137404)CaDiCaL version: 2.1.3
% 6.93/1.84 % (2137404)Termination reason: Instruction limit
% 6.93/1.84 % (2137404)Termination phase: Saturation
% 6.93/1.84 % (2137404)Time elapsed: 0.686 s
% 6.93/1.84 % (2137404)Peak memory usage: 140 MB
% 6.93/1.84 % (2137404)Instructions burned: 2052 (million)
% 6.93/1.84 % (2137511)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3300982828:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2990 on theBenchmark for (2990ds/14534Mi)
% 6.93/1.84 % (2137390)First to succeed.
% 6.93/1.84 % (2137390)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2137381"
% 6.93/1.84 % (2137390)Refutation found. Thanks to Tanya!
% 6.93/1.84 % SZS status Unsatisfiable for theBenchmark
% 6.93/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 8.95/1.94 % (2137390)------------------------------
% 8.95/1.94 % (2137390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.95/1.94 % (2137390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.95/1.94 % (2137390)CaDiCaL version: 2.1.3
% 8.95/1.94 % (2137390)Termination reason: Refutation
% 8.95/1.94 % (2137390)Time elapsed: 0.974 s
% 8.95/1.94 % (2137390)Peak memory usage: 149 MB
% 8.95/1.94 % (2137390)Instructions burned: 3097 (million)
% 8.95/1.94 % (2137390)------------------------------
% 8.95/1.94 % (2137390)------------------------------
% 8.95/1.94 % (2137381)Success in time 1.231 s
% 8.95/1.94 % Vampire exiting
%------------------------------------------------------------------------------