%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 11.96s 2.57s
% Output : Refutation 12.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 2
% Syntax : Number of formulae : 103 ( 103 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 12 ( 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 : 338 ( 338 !; 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/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
fof(f4,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X0,multiply(X3,X4)))))),X0),inverse(multiply(X6,multiply(X1,X2))))))) = X6,
inference(superposition,[],[f1,f1]) ).
fof(f5,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(f9,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,[],[f5,f5]) ).
fof(f12,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,f5]) ).
fof(f98,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,inverse(X0)),inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X2)))) = X3,
inference(superposition,[],[f12,f9]) ).
fof(f124,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,[],[f98,f9]) ).
fof(f145,plain,
! [X3,X7,X4] : multiply(multiply(X4,inverse(X4)),X3) = multiply(multiply(X7,inverse(X7)),X3),
inference(forward_demodulation,[],[f124,f12]) ).
fof(f256,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : multiply(X7,inverse(X7)) = inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,multiply(X3,X4)))))),X6),inverse(multiply(multiply(X0,inverse(X0)),multiply(X1,X2))))))),
inference(superposition,[],[f4,f145]) ).
fof(f268,plain,
! [X0,X7] : multiply(X0,inverse(X0)) = multiply(X7,inverse(X7)),
inference(forward_demodulation,[],[f256,f4]) ).
fof(f283,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,[],[f268,f1]) ).
fof(f337,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,f268]) ).
fof(f344,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,[],[f98,f268]) ).
fof(f353,plain,
! [X2,X0,X1] : multiply(X0,inverse(X0)) = multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),
inference(superposition,[],[f145,f268]) ).
fof(f570,plain,
! [X3,X0,X1] : inverse(multiply(X3,multiply(inverse(X3),X0))) = inverse(multiply(X1,multiply(inverse(X1),X0))),
inference(superposition,[],[f337,f98]) ).
fof(f681,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,f570]) ).
fof(f723,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,[],[f681,f570]) ).
fof(f810,plain,
! [X2,X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X2,multiply(inverse(X2),X1)),
inference(forward_demodulation,[],[f723,f681]) ).
fof(f845,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,inverse(X0))) = multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))),
inference(superposition,[],[f810,f268]) ).
fof(f1199,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,[],[f845,f283]) ).
fof(f1201,plain,
! [X0,X4,X5] : multiply(X0,inverse(X0)) = multiply(X5,multiply(inverse(X5),inverse(multiply(X4,inverse(X4))))),
inference(forward_demodulation,[],[f1199,f1]) ).
fof(f1333,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,[],[f98,f1201]) ).
fof(f1348,plain,
! [X3,X4] : inverse(X3) = multiply(inverse(X3),inverse(multiply(X4,inverse(X4)))),
inference(forward_demodulation,[],[f1333,f344]) ).
fof(f1358,plain,
! [X0,X4] : multiply(X0,inverse(multiply(X4,inverse(X4)))) = X0,
inference(superposition,[],[f1348,f681]) ).
fof(f1461,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,f1358]) ).
fof(f1569,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,[],[f1461,f98]) ).
fof(f1578,plain,
! [X2,X0,X1] : inverse(multiply(inverse(X1),multiply(inverse(multiply(X2,inverse(X2))),multiply(X0,inverse(X0))))) = X1,
inference(superposition,[],[f1461,f268]) ).
fof(f1797,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,[],[f681,f1569]) ).
fof(f1816,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),multiply(inverse(multiply(X3,inverse(X3))),X2)),
inference(forward_demodulation,[],[f1797,f681]) ).
fof(f1867,plain,
! [X2,X3,X0,X1,X4] : multiply(X2,multiply(multiply(inverse(X2),X1),X3)) = multiply(multiply(X0,multiply(inverse(X0),X1)),multiply(inverse(multiply(X4,inverse(X4))),X3)),
inference(superposition,[],[f1816,f810]) ).
fof(f1985,plain,
! [X2,X3,X0,X1] : multiply(X2,multiply(multiply(inverse(X2),X1),X3)) = multiply(X0,multiply(multiply(inverse(X0),X1),X3)),
inference(forward_demodulation,[],[f1867,f1816]) ).
fof(f2154,plain,
! [X2,X3,X0,X1] : inverse(multiply(X3,multiply(X0,multiply(multiply(inverse(X0),inverse(inverse(X1))),inverse(multiply(X2,multiply(X3,X1))))))) = X2,
inference(superposition,[],[f1,f1985]) ).
fof(f2494,plain,
! [X2,X3,X0,X1] : multiply(multiply(X3,inverse(X3)),multiply(inverse(multiply(X0,inverse(X0))),multiply(multiply(X1,inverse(X1)),X2))) = X2,
inference(superposition,[],[f98,f1578]) ).
fof(f2566,plain,
! [X2,X3,X1] : multiply(X3,multiply(inverse(X3),multiply(multiply(X1,inverse(X1)),X2))) = X2,
inference(forward_demodulation,[],[f2494,f1816]) ).
fof(f2660,plain,
! [X0,X1] : inverse(inverse(multiply(X0,multiply(X1,inverse(X1))))) = X0,
inference(superposition,[],[f2154,f2566]) ).
fof(f2664,plain,
! [X2,X3,X0,X1,X4] : inverse(X3) = inverse(multiply(multiply(multiply(X1,inverse(X1)),X0),multiply(multiply(multiply(X2,inverse(X2)),inverse(X0)),multiply(multiply(X4,inverse(X4)),X3)))),
inference(superposition,[],[f5,f2566]) ).
fof(f2794,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(multiply(X0,multiply(X4,inverse(X4)))),multiply(X0,X2))))))) = X1,
inference(superposition,[],[f681,f2660]) ).
fof(f2823,plain,
! [X2,X1] : inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = X1,
inference(forward_demodulation,[],[f2794,f344]) ).
fof(f2891,plain,
! [X2,X0,X1] : multiply(multiply(X2,inverse(X2)),multiply(X0,multiply(inverse(X0),X1))) = X1,
inference(superposition,[],[f98,f2823]) ).
fof(f2904,plain,
! [X0,X1] : inverse(multiply(X1,multiply(inverse(X1),inverse(inverse(inverse(X0)))))) = X0,
inference(superposition,[],[f570,f2823]) ).
fof(f3193,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(multiply(X1,inverse(X1)),X0) = inverse(multiply(multiply(multiply(X3,inverse(X3)),X2),multiply(multiply(multiply(X4,inverse(X4)),inverse(X2)),multiply(multiply(X5,inverse(X5)),inverse(inverse(inverse(X0))))))),
inference(superposition,[],[f9,f2904]) ).
fof(f3271,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X1)),X0) = inverse(inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[],[f3193,f2664]) ).
fof(f3345,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X1),inverse(inverse(inverse(inverse(X0)))))) = X0,
inference(superposition,[],[f2566,f3271]) ).
fof(f3347,plain,
! [X2,X0,X1] : multiply(X2,multiply(multiply(inverse(X2),inverse(inverse(X1))),X0)) = multiply(X1,inverse(inverse(inverse(inverse(X0))))),
inference(superposition,[],[f1985,f3271]) ).
fof(f4047,plain,
! [X2,X3,X0,X1] : multiply(inverse(inverse(X2)),multiply(multiply(X3,inverse(X3)),X0)) = multiply(multiply(X1,inverse(X1)),multiply(X2,X0)),
inference(superposition,[],[f2891,f2566]) ).
fof(f4157,plain,
! [X2,X3,X0] : multiply(inverse(inverse(X2)),multiply(multiply(X3,inverse(X3)),X0)) = inverse(inverse(inverse(inverse(multiply(X2,X0))))),
inference(forward_demodulation,[],[f4047,f3271]) ).
fof(f4237,plain,
! [X2,X0] : inverse(inverse(inverse(inverse(multiply(X2,X0))))) = multiply(inverse(inverse(X2)),inverse(inverse(inverse(inverse(X0))))),
inference(forward_demodulation,[],[f4157,f3271]) ).
fof(f4347,plain,
! [X2,X0,X1] : multiply(inverse(inverse(X2)),multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1))))) = X2,
inference(superposition,[],[f3345,f353]) ).
fof(f4383,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),inverse(inverse(inverse(inverse(X0))))) = multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,X0)),multiply(X2,X3)))),
inference(superposition,[],[f98,f3345]) ).
fof(f4387,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(inverse(multiply(X3,inverse(X3))),X2)) = multiply(X1,multiply(multiply(inverse(X1),inverse(inverse(inverse(inverse(X0))))),X2)),
inference(superposition,[],[f1816,f3345]) ).
fof(f4433,plain,
! [X2,X3,X0] : multiply(X0,multiply(inverse(multiply(X3,inverse(X3))),X2)) = multiply(inverse(inverse(X0)),inverse(inverse(inverse(inverse(X2))))),
inference(forward_demodulation,[],[f4387,f3347]) ).
fof(f4437,plain,
! [X2,X3,X0] : multiply(inverse(X3),inverse(inverse(inverse(inverse(X0))))) = inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(X2,X0)),multiply(X2,X3))))))),
inference(forward_demodulation,[],[f4383,f3271]) ).
fof(f4448,plain,
! [X2,X1] : multiply(inverse(inverse(X2)),inverse(inverse(inverse(inverse(inverse(multiply(X1,inverse(X1)))))))) = X2,
inference(forward_demodulation,[],[f4347,f3271]) ).
fof(f4486,plain,
! [X2,X3,X0] : multiply(X0,multiply(inverse(multiply(X3,inverse(X3))),X2)) = inverse(inverse(inverse(inverse(multiply(X0,X2))))),
inference(forward_demodulation,[],[f4433,f4237]) ).
fof(f4496,plain,
! [X2,X1] : inverse(inverse(inverse(inverse(multiply(X2,inverse(multiply(X1,inverse(X1)))))))) = X2,
inference(forward_demodulation,[],[f4448,f4237]) ).
fof(f4519,plain,
! [X2] : inverse(inverse(inverse(inverse(X2)))) = X2,
inference(forward_demodulation,[],[f4496,f1358]) ).
fof(f4577,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(inverse(multiply(X2,inverse(X2))),multiply(multiply(X3,inverse(X3)),inverse(multiply(X0,X1))))) = inverse(inverse(inverse(X0))),
inference(superposition,[],[f4519,f1461]) ).
fof(f4590,plain,
! [X0,X1] : inverse(X0) = multiply(X1,multiply(inverse(X1),inverse(X0))),
inference(superposition,[],[f3345,f4519]) ).
fof(f4707,plain,
! [X3,X0,X1] : inverse(inverse(inverse(X0))) = inverse(inverse(inverse(inverse(multiply(X1,multiply(multiply(X3,inverse(X3)),inverse(multiply(X0,X1)))))))),
inference(forward_demodulation,[],[f4577,f4486]) ).
fof(f4740,plain,
! [X3,X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,multiply(multiply(X3,inverse(X3)),inverse(multiply(X0,X1)))),
inference(forward_demodulation,[],[f4707,f4519]) ).
fof(f4758,plain,
! [X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,inverse(inverse(inverse(inverse(inverse(multiply(X0,X1))))))),
inference(forward_demodulation,[],[f4740,f3271]) ).
fof(f4769,plain,
! [X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f4758,f4519]) ).
fof(f4805,plain,
! [X0,X1] : inverse(inverse(inverse(X1))) = multiply(inverse(multiply(X0,X1)),inverse(inverse(inverse(inverse(X0))))),
inference(superposition,[],[f4769,f4769]) ).
fof(f4827,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0))))))) = multiply(multiply(multiply(multiply(X4,inverse(X4)),X2),multiply(multiply(X5,inverse(X5)),X3)),X0),
inference(superposition,[],[f4769,f12]) ).
fof(f4848,plain,
! [X2,X3,X0,X1] : inverse(multiply(X0,X3)) = multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,inverse(inverse(inverse(X0))))),multiply(X2,X3)))),
inference(superposition,[],[f98,f4769]) ).
fof(f4850,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(X2,inverse(X2))),multiply(multiply(X3,inverse(X3)),inverse(inverse(inverse(inverse(X0)))))))) = X1,
inference(superposition,[],[f1461,f4769]) ).
fof(f4877,plain,
! [X0] : inverse(X0) = inverse(inverse(inverse(X0))),
inference(superposition,[],[f1348,f4769]) ).
fof(f4883,plain,
! [X2,X0,X1] : multiply(X2,inverse(inverse(inverse(X0)))) = multiply(X1,multiply(inverse(X1),inverse(multiply(X0,inverse(X2))))),
inference(superposition,[],[f810,f4769]) ).
fof(f4887,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X2,inverse(multiply(X0,inverse(multiply(X3,inverse(X3))))))) = multiply(multiply(X1,X2),inverse(inverse(inverse(X0)))),
inference(superposition,[],[f1816,f4769]) ).
fof(f4890,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),inverse(inverse(inverse(X0)))) = multiply(X1,multiply(X2,inverse(X0))),
inference(forward_demodulation,[],[f4887,f1358]) ).
fof(f4892,plain,
! [X2,X0] : multiply(X2,inverse(inverse(inverse(X0)))) = inverse(multiply(X0,inverse(X2))),
inference(forward_demodulation,[],[f4883,f4590]) ).
fof(f4910,plain,
! [X3,X0,X1] : inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(X0,X1)),multiply(multiply(X3,inverse(X3)),inverse(inverse(inverse(inverse(X0))))))))))) = X1,
inference(forward_demodulation,[],[f4850,f4486]) ).
fof(f4912,plain,
! [X2,X3,X0] : inverse(multiply(X0,X3)) = inverse(inverse(inverse(inverse(inverse(multiply(inverse(multiply(X2,inverse(inverse(inverse(X0))))),multiply(X2,X3))))))),
inference(forward_demodulation,[],[f4848,f3271]) ).
fof(f4926,plain,
! [X2,X3,X0,X1,X4] : inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0))))))) = multiply(multiply(multiply(multiply(X4,inverse(X4)),X2),inverse(inverse(inverse(inverse(X3))))),X0),
inference(forward_demodulation,[],[f4827,f3271]) ).
fof(f4946,plain,
! [X0,X1] : inverse(inverse(inverse(X1))) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f4805,f4519]) ).
fof(f4965,plain,
! [X2,X0,X1] : multiply(X1,multiply(X2,inverse(X0))) = multiply(multiply(X1,X2),inverse(X0)),
inference(forward_demodulation,[],[f4890,f4877]) ).
fof(f4967,plain,
! [X2,X0] : multiply(X2,inverse(X0)) = inverse(multiply(X0,inverse(X2))),
inference(forward_demodulation,[],[f4892,f4877]) ).
fof(f4981,plain,
! [X3,X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),multiply(multiply(X3,inverse(X3)),inverse(inverse(inverse(inverse(X0))))))) = X1,
inference(forward_demodulation,[],[f4910,f4519]) ).
fof(f4983,plain,
! [X3,X0] : inverse(multiply(X0,X3)) = multiply(inverse(X3),inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))))),
inference(forward_demodulation,[],[f4912,f4437]) ).
fof(f4993,plain,
! [X2,X3,X0,X1,X4] : inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0))))))) = multiply(multiply(multiply(multiply(X4,inverse(X4)),X2),X3),X0),
inference(forward_demodulation,[],[f4926,f4519]) ).
fof(f5009,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f4946,f4877]) ).
fof(f5032,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),inverse(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0)))))))))) = X1,
inference(forward_demodulation,[],[f4981,f3271]) ).
fof(f5034,plain,
! [X3,X0] : inverse(multiply(X0,X3)) = multiply(inverse(X3),inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[],[f4983,f4519]) ).
fof(f5044,plain,
! [X2,X3,X0,X1] : inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0))))))) = multiply(multiply(inverse(inverse(inverse(inverse(X2)))),X3),X0),
inference(forward_demodulation,[],[f4993,f3271]) ).
fof(f5074,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(inverse(inverse(inverse(inverse(X0))))))),inverse(inverse(multiply(X0,X1)))) = X1,
inference(forward_demodulation,[],[f5032,f4967]) ).
fof(f5076,plain,
! [X3,X0] : inverse(multiply(X0,X3)) = multiply(inverse(X3),inverse(X0)),
inference(forward_demodulation,[],[f5034,f4877]) ).
fof(f5084,plain,
! [X2,X3,X0,X1] : inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0))))))) = multiply(multiply(X2,X3),X0),
inference(forward_demodulation,[],[f5044,f4519]) ).
fof(f5101,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),inverse(inverse(multiply(X0,X1)))) = X1,
inference(forward_demodulation,[],[f5074,f4519]) ).
fof(f5110,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X0))))) = multiply(multiply(X2,X3),X0),
inference(forward_demodulation,[],[f5084,f4877]) ).
fof(f5119,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),inverse(inverse(X0)))) = X1,
inference(forward_demodulation,[],[f5101,f5076]) ).
fof(f5127,plain,
! [X2,X3,X0,X1] : multiply(multiply(X2,X3),X0) = multiply(multiply(X2,multiply(X3,X0)),inverse(multiply(X1,inverse(X1)))),
inference(forward_demodulation,[],[f5110,f4967]) ).
fof(f5135,plain,
! [X0,X1] : multiply(inverse(X0),inverse(inverse(multiply(X0,X1)))) = X1,
inference(forward_demodulation,[],[f5119,f4967]) ).
fof(f5141,plain,
! [X2,X3,X0,X1] : multiply(multiply(X2,X3),X0) = multiply(X2,multiply(multiply(X3,X0),inverse(multiply(X1,inverse(X1))))),
inference(forward_demodulation,[],[f5127,f4965]) ).
fof(f5147,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(forward_demodulation,[],[f5135,f5076]) ).
fof(f5153,plain,
! [X2,X3,X0,X1] : multiply(multiply(X2,X3),X0) = multiply(X2,multiply(X3,multiply(X0,inverse(multiply(X1,inverse(X1)))))),
inference(forward_demodulation,[],[f5141,f4965]) ).
fof(f5157,plain,
! [X1] : inverse(inverse(X1)) = X1,
inference(forward_demodulation,[],[f5147,f5009]) ).
fof(f5162,plain,
! [X2,X3,X0] : multiply(X2,multiply(X3,X0)) = multiply(multiply(X2,X3),X0),
inference(forward_demodulation,[],[f5153,f1358]) ).
fof(f5283,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,inverse(inverse(inverse(inverse(X1)))))) = X1,
inference(superposition,[],[f3345,f5157]) ).
fof(f5285,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f5283,f4519]) ).
fof(f5683,plain,
a2 != multiply(inverse(b2),multiply(b2,a2)),
inference(superposition,[],[f3,f5162]) ).
fof(f5882,plain,
$false,
inference(forward_subsumption_resolution,[],[f5683,f5285]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n006.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 10:04:26 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.96/2.57 % (2750424)Detected a unit-equality problem, will run specialized UEQ schedule.
% 11.96/2.57 % (2750433)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1563304443:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 11.96/2.57 % (2750429)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=2113171993:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 11.96/2.57 % (2750430)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=1271339594:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 11.96/2.57 % (2750431)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1304691905:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 11.96/2.57 % (2750435)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=220241839:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 11.96/2.57 % (2750432)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=554509055:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 11.96/2.57 % (2750434)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=323467570:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 11.96/2.57 % (2750433)Instruction limit reached!
% 11.96/2.57 % (2750433)------------------------------
% 11.96/2.57 % (2750433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750433)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750433)Termination reason: Instruction limit
% 11.96/2.57 % (2750433)Termination phase: Saturation
% 11.96/2.57 % (2750433)Time elapsed: 0.051 s
% 11.96/2.57 % (2750433)Peak memory usage: 89 MB
% 11.96/2.57 % (2750433)Instructions burned: 181 (million)
% 11.96/2.57 % (2750432)Instruction limit reached!
% 11.96/2.57 % (2750432)------------------------------
% 11.96/2.57 % (2750432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750432)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750432)Termination reason: Instruction limit
% 11.96/2.57 % (2750432)Termination phase: Saturation
% 11.96/2.57 % (2750432)Time elapsed: 0.079 s
% 11.96/2.57 % (2750432)Peak memory usage: 89 MB
% 11.96/2.57 % (2750432)Instructions burned: 138 (million)
% 11.96/2.57 % (2750443)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=535652946:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 11.96/2.57 % (2750434)Instruction limit reached!
% 11.96/2.57 % (2750434)------------------------------
% 11.96/2.57 % (2750434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750434)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750434)Termination reason: Instruction limit
% 11.96/2.57 % (2750434)Termination phase: Saturation
% 11.96/2.57 % (2750434)Time elapsed: 0.150 s
% 11.96/2.57 % (2750434)Peak memory usage: 90 MB
% 11.96/2.57 % (2750434)Instructions burned: 257 (million)
% 11.96/2.57 % (2750444)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=512853321:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 11.96/2.57 % (2750446)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3085697353:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 11.96/2.57 % (2750446)Instruction limit reached!
% 11.96/2.57 % (2750446)------------------------------
% 11.96/2.57 % (2750446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750446)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750446)Termination reason: Instruction limit
% 11.96/2.57 % (2750446)Termination phase: Saturation
% 11.96/2.57 % (2750446)Time elapsed: 0.129 s
% 11.96/2.57 % (2750446)Peak memory usage: 91 MB
% 11.96/2.57 % (2750446)Instructions burned: 215 (million)
% 11.96/2.57 % (2750449)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=1486532508:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 11.96/2.57 % (2750435)Instruction limit reached!
% 11.96/2.57 % (2750435)------------------------------
% 11.96/2.57 % (2750435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750435)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750435)Termination reason: Instruction limit
% 11.96/2.57 % (2750435)Termination phase: Saturation
% 11.96/2.57 % (2750435)Time elapsed: 0.613 s
% 11.96/2.57 % (2750435)Peak memory usage: 98 MB
% 11.96/2.57 % (2750435)Instructions burned: 1187 (million)
% 11.96/2.57 % (2750449)Instruction limit reached!
% 11.96/2.57 % (2750449)------------------------------
% 11.96/2.57 % (2750449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750449)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750449)Termination reason: Instruction limit
% 11.96/2.57 % (2750449)Termination phase: Saturation
% 11.96/2.57 % (2750449)Time elapsed: 0.148 s
% 11.96/2.57 % (2750449)Peak memory usage: 91 MB
% 11.96/2.57 % (2750449)Instructions burned: 317 (million)
% 11.96/2.57 % (2750451)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=1418390687:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 11.96/2.57 % (2750443)Instruction limit reached!
% 11.96/2.57 % (2750443)------------------------------
% 11.96/2.57 % (2750443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.96/2.57 % (2750443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.96/2.57 % (2750443)CaDiCaL version: 2.1.3
% 11.96/2.57 % (2750443)Termination reason: Instruction limit
% 11.96/2.57 % (2750443)Termination phase: Saturation
% 11.96/2.57 % (2750443)Time elapsed: 0.683 s
% 11.96/2.57 % (2750443)Peak memory usage: 140 MB
% 11.96/2.57 % (2750443)Instructions burned: 2054 (million)
% 11.96/2.57 % (2750452)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=4290308905:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 11.96/2.57 % (2750454)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2900789:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2990 on theBenchmark for (2990ds/14534Mi)
% 11.96/2.57 % (2750430)First to succeed.
% 11.96/2.57 % (2750430)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2750424"
% 11.96/2.57 % (2750431)Also succeeded, but the first one will report.
% 11.96/2.57 % (2750454)Also succeeded, but the first one will report.
% 11.96/2.57 % (2750430)Refutation found. Thanks to Tanya!
% 11.96/2.57 % SZS status Unsatisfiable for theBenchmark
% 11.96/2.57 % SZS output start Proof for theBenchmark
% See solution above
% 12.68/2.77 % (2750430)------------------------------
% 12.68/2.77 % (2750430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.68/2.77 % (2750430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.68/2.77 % (2750430)CaDiCaL version: 2.1.3
% 12.68/2.77 % (2750430)Termination reason: Refutation
% 12.68/2.77 % (2750430)Time elapsed: 1.317 s
% 12.68/2.77 % (2750430)Peak memory usage: 141 MB
% 12.68/2.77 % (2750430)Instructions burned: 2226 (million)
% 12.68/2.77 % (2750430)------------------------------
% 12.68/2.77 % (2750430)------------------------------
% 12.68/2.77 % (2750424)Success in time 1.713 s
% 12.68/2.77 % Vampire exiting
%------------------------------------------------------------------------------