%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP427-1 : 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 : n013.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 10:13:58 AM UTC 2026
% Result : Unsatisfiable 16.74s 3.19s
% Output : Refutation 17.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 2
% Syntax : Number of formulae : 109 ( 109 unt; 0 def)
% Number of atoms : 109 ( 108 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 390 ( 390 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(X0),X2))),X3),inverse(multiply(X1,X3))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X3),multiply(inverse(inverse(X1)),X0))),X4),inverse(multiply(X3,X4)))) = multiply(X1,inverse(multiply(multiply(inverse(multiply(inverse(X2),X0)),X5),inverse(multiply(X2,X5))))),
inference(superposition,[],[f1,f1]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : multiply(inverse(X0),multiply(X0,inverse(multiply(multiply(inverse(multiply(inverse(X1),X2)),X3),inverse(multiply(X1,X3)))))) = X2,
inference(superposition,[],[f1,f3]) ).
fof(f53,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X0)),X3),inverse(multiply(X2,X3)))) = multiply(X1,inverse(multiply(multiply(inverse(X0),X4),inverse(multiply(inverse(X1),X4))))),
inference(superposition,[],[f1,f29]) ).
fof(f101,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(multiply(inverse(multiply(inverse(X1),X2)),X3),inverse(multiply(inverse(X0),X3)))))) = X2,
inference(superposition,[],[f1,f53]) ).
fof(f103,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X3,multiply(X0,inverse(multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X0),X2))))))) = X1,
inference(superposition,[],[f29,f53]) ).
fof(f149,plain,
! [X2,X0,X1] : multiply(inverse(inverse(X2)),multiply(inverse(X2),X0)) = multiply(inverse(X1),multiply(X1,X0)),
inference(superposition,[],[f103,f1]) ).
fof(f181,plain,
! [X3,X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(inverse(X3),multiply(X3,X1)),
inference(superposition,[],[f149,f149]) ).
fof(f198,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(X3,inverse(multiply(multiply(inverse(multiply(inverse(X5),multiply(inverse(X3),X1))),X6),inverse(multiply(X5,X6))))) = inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X0),multiply(X0,X1)))),X4),inverse(multiply(X2,X4)))),
inference(superposition,[],[f3,f149]) ).
fof(f199,plain,
! [X2,X3,X0,X1] : multiply(X2,inverse(multiply(multiply(inverse(multiply(inverse(X0),multiply(X0,X1))),X3),inverse(multiply(inverse(X2),X3))))) = X1,
inference(superposition,[],[f1,f149]) ).
fof(f203,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X2),X1) = multiply(inverse(X2),inverse(multiply(multiply(inverse(multiply(inverse(X3),multiply(inverse(X0),multiply(X0,X1)))),X4),inverse(multiply(X3,X4))))),
inference(superposition,[],[f1,f149]) ).
fof(f205,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X3),X1) = multiply(inverse(X2),multiply(X2,inverse(multiply(multiply(inverse(multiply(inverse(X0),multiply(X0,X1))),X4),inverse(multiply(inverse(X3),X4)))))),
inference(superposition,[],[f29,f149]) ).
fof(f242,plain,
! [X2,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(inverse(X0),multiply(X0,X1)))),X4),inverse(multiply(X2,X4)))) = X1,
inference(forward_demodulation,[],[f198,f1]) ).
fof(f314,plain,
! [X2,X3,X0,X1,X4] : multiply(X3,X1) = multiply(inverse(X2),multiply(X2,inverse(multiply(multiply(inverse(multiply(inverse(X0),multiply(X0,X1))),X4),inverse(multiply(X3,X4)))))),
inference(superposition,[],[f29,f181]) ).
fof(f318,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(multiply(inverse(X4),multiply(X3,X1)),inverse(multiply(inverse(X0),multiply(X0,X1)))))))) = X4,
inference(superposition,[],[f103,f181]) ).
fof(f320,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X3,multiply(X2,X1))) = multiply(inverse(inverse(X2)),multiply(inverse(X0),multiply(X0,X1))),
inference(superposition,[],[f149,f181]) ).
fof(f810,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X4,multiply(X0,X2)) = multiply(inverse(X3),multiply(X3,inverse(multiply(multiply(inverse(multiply(inverse(inverse(X0)),multiply(inverse(X1),multiply(X1,X2)))),X5),inverse(multiply(X4,X5)))))),
inference(superposition,[],[f29,f320]) ).
fof(f1766,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(X0,inverse(multiply(inverse(X6),multiply(X6,multiply(X3,inverse(multiply(multiply(inverse(X0),multiply(X3,X4)),inverse(multiply(inverse(X5),multiply(X5,X4)))))))))))))) = X2,
inference(superposition,[],[f318,f318]) ).
fof(f1917,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(X0,inverse(X0)))))) = X2,
inference(forward_demodulation,[],[f1766,f318]) ).
fof(f1957,plain,
! [X2,X0,X1] : inverse(multiply(X1,inverse(X1))) = inverse(multiply(multiply(inverse(X0),X2),inverse(multiply(inverse(X0),X2)))),
inference(superposition,[],[f242,f1917]) ).
fof(f2153,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X0,inverse(X0))))) = X2,
inference(superposition,[],[f101,f1957]) ).
fof(f2154,plain,
! [X2,X0,X1] : multiply(multiply(inverse(X1),multiply(X1,X2)),inverse(multiply(X0,inverse(X0)))) = X2,
inference(superposition,[],[f199,f1957]) ).
fof(f2211,plain,
! [X2,X3,X0,X1,X6,X4,X5] : multiply(multiply(inverse(X3),X4),inverse(multiply(inverse(X3),X4))) = multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(multiply(inverse(multiply(X0,inverse(X0))),multiply(X2,X5)),inverse(multiply(inverse(X6),multiply(X6,X5)))))))),
inference(superposition,[],[f318,f1957]) ).
fof(f2220,plain,
! [X3,X0,X4] : multiply(X0,inverse(X0)) = multiply(multiply(inverse(X3),X4),inverse(multiply(inverse(X3),X4))),
inference(forward_demodulation,[],[f2211,f318]) ).
fof(f2353,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[],[f2220,f2220]) ).
fof(f2608,plain,
! [X2,X0,X1] : multiply(inverse(X2),multiply(X0,inverse(X0))) = multiply(inverse(X1),multiply(X1,inverse(X2))),
inference(superposition,[],[f181,f2353]) ).
fof(f2659,plain,
! [X0,X4,X5] : multiply(inverse(X5),multiply(X5,X0)) = multiply(X0,multiply(X4,inverse(X4))),
inference(superposition,[],[f2608,f242]) ).
fof(f2755,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X2,multiply(X3,inverse(X3))) = multiply(inverse(X4),multiply(X4,inverse(multiply(multiply(inverse(multiply(inverse(inverse(X1)),multiply(inverse(X0),multiply(X0,inverse(X1))))),X5),inverse(multiply(X2,X5)))))),
inference(superposition,[],[f314,f2608]) ).
fof(f2851,plain,
! [X2,X3,X1] : multiply(X2,multiply(X3,inverse(X3))) = multiply(X2,multiply(X1,inverse(X1))),
inference(forward_demodulation,[],[f2755,f810]) ).
fof(f3470,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(X0,multiply(X1,inverse(X1))),
inference(superposition,[],[f2851,f2153]) ).
fof(f3471,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(X1),multiply(X1,X0)),
inference(superposition,[],[f2659,f2153]) ).
fof(f3557,plain,
! [X2,X0,X1] : inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X0),X1)),X2),inverse(multiply(X0,X2)))))) = X1,
inference(superposition,[],[f29,f3470]) ).
fof(f3570,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(X1,multiply(X2,inverse(X0)))) = multiply(inverse(inverse(X2)),inverse(inverse(inverse(X0)))),
inference(superposition,[],[f320,f3470]) ).
fof(f3686,plain,
! [X2,X0] : multiply(inverse(inverse(X2)),inverse(inverse(inverse(X0)))) = inverse(inverse(multiply(X2,inverse(X0)))),
inference(forward_demodulation,[],[f3570,f3471]) ).
fof(f3766,plain,
! [X0,X1] : inverse(inverse(multiply(X1,X0))) = multiply(inverse(inverse(X1)),inverse(inverse(X0))),
inference(superposition,[],[f3471,f3471]) ).
fof(f3818,plain,
! [X0,X1] : inverse(inverse(multiply(X0,inverse(multiply(X1,inverse(X1)))))) = X0,
inference(superposition,[],[f1917,f3471]) ).
fof(f3833,plain,
! [X2,X0] : multiply(inverse(inverse(X0)),inverse(multiply(X2,inverse(X2)))) = X0,
inference(superposition,[],[f2154,f3471]) ).
fof(f4035,plain,
! [X2,X3,X0,X1] : multiply(inverse(X0),inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(X1,X2))),inverse(multiply(X3,inverse(X3)))),inverse(X0)))) = X2,
inference(superposition,[],[f199,f3833]) ).
fof(f4096,plain,
! [X2,X3,X0] : multiply(inverse(X0),inverse(multiply(multiply(inverse(inverse(inverse(X2))),inverse(multiply(X3,inverse(X3)))),inverse(X0)))) = X2,
inference(forward_demodulation,[],[f4035,f3471]) ).
fof(f4114,plain,
! [X2,X0] : multiply(inverse(X0),inverse(multiply(inverse(X2),inverse(X0)))) = X2,
inference(forward_demodulation,[],[f4096,f3833]) ).
fof(f4125,plain,
! [X0,X4] : multiply(X0,inverse(multiply(inverse(X4),X0))) = X4,
inference(superposition,[],[f4114,f242]) ).
fof(f4142,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(inverse(X2)),inverse(multiply(inverse(X0),inverse(X3)))))),X4),inverse(multiply(X1,X4)))) = multiply(X2,inverse(multiply(multiply(inverse(X0),X5),inverse(multiply(X3,X5))))),
inference(superposition,[],[f3,f4114]) ).
fof(f4145,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(X0),inverse(X2))) = multiply(inverse(X1),multiply(X1,inverse(multiply(multiply(inverse(X0),X3),inverse(multiply(X2,X3)))))),
inference(superposition,[],[f29,f4114]) ).
fof(f4166,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X1),X2) = multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(X3,inverse(multiply(inverse(X0),inverse(multiply(inverse(X3),multiply(inverse(X4),multiply(X4,X2))))))))))),
inference(superposition,[],[f203,f4114]) ).
fof(f4173,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(inverse(X2)),X3))),X4),inverse(multiply(X1,X4)))) = multiply(X2,inverse(multiply(X0,inverse(multiply(X5,inverse(multiply(inverse(X0),inverse(multiply(inverse(X5),X3))))))))),
inference(superposition,[],[f3,f4114]) ).
fof(f4189,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(inverse(X2)),X0))),X3),inverse(multiply(X1,X3)))) = inverse(multiply(inverse(X0),inverse(X2))),
inference(superposition,[],[f242,f4114]) ).
fof(f4220,plain,
! [X2,X3,X0,X5] : multiply(X2,inverse(multiply(X0,inverse(multiply(X5,inverse(multiply(inverse(X0),inverse(multiply(inverse(X5),X3))))))))) = inverse(multiply(inverse(X3),inverse(X2))),
inference(forward_demodulation,[],[f4173,f4189]) ).
fof(f4225,plain,
! [X2,X3,X0,X1] : multiply(inverse(X1),X2) = multiply(inverse(X1),inverse(multiply(X0,inverse(multiply(X3,inverse(multiply(inverse(X0),inverse(multiply(inverse(X3),inverse(inverse(X2))))))))))),
inference(forward_demodulation,[],[f4166,f3471]) ).
fof(f4234,plain,
! [X2,X3,X0] : inverse(multiply(inverse(X0),inverse(X2))) = inverse(inverse(inverse(multiply(multiply(inverse(X0),X3),inverse(multiply(X2,X3)))))),
inference(forward_demodulation,[],[f4145,f3471]) ).
fof(f4235,plain,
! [X2,X3,X0,X5] : multiply(X2,inverse(multiply(multiply(inverse(X0),X5),inverse(multiply(X3,X5))))) = inverse(multiply(inverse(inverse(multiply(inverse(X0),inverse(X3)))),inverse(X2))),
inference(forward_demodulation,[],[f4142,f4189]) ).
fof(f4253,plain,
! [X2,X1] : multiply(inverse(X1),X2) = inverse(multiply(inverse(inverse(inverse(X2))),inverse(inverse(X1)))),
inference(forward_demodulation,[],[f4225,f4220]) ).
fof(f4260,plain,
! [X2,X1] : multiply(inverse(X1),X2) = inverse(inverse(inverse(multiply(inverse(X2),X1)))),
inference(forward_demodulation,[],[f4253,f3766]) ).
fof(f4353,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(X0),X2)) = inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(X2),X0))),X3),inverse(multiply(X1,X3)))),
inference(superposition,[],[f242,f4125]) ).
fof(f4465,plain,
! [X2,X0,X1] : multiply(inverse(X2),inverse(inverse(multiply(inverse(X1),X0)))) = inverse(inverse(inverse(multiply(multiply(inverse(X0),X1),X2)))),
inference(superposition,[],[f4260,f4260]) ).
fof(f4470,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X4),X2)),X5),inverse(multiply(X4,X5))))),X1) = inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X0),multiply(inverse(inverse(inverse(X1))),X2))),X3),inverse(multiply(X0,X3))))))),
inference(superposition,[],[f4260,f3]) ).
fof(f4490,plain,
! [X2,X0,X1] : inverse(inverse(inverse(multiply(inverse(X0),multiply(X0,X1))))) = multiply(inverse(multiply(X2,X1)),X2),
inference(superposition,[],[f4260,f181]) ).
fof(f4519,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))) = multiply(inverse(inverse(multiply(inverse(X1),X0))),inverse(multiply(multiply(inverse(X3),X5),inverse(multiply(multiply(inverse(X0),X1),X5))))),
inference(superposition,[],[f53,f4260]) ).
fof(f4535,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(inverse(multiply(inverse(X1),X0))),inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),X4),inverse(multiply(multiply(inverse(X0),X1),X4))))) = X3,
inference(superposition,[],[f199,f4260]) ).
fof(f4544,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X2,X3) = multiply(inverse(X4),multiply(X4,inverse(multiply(multiply(inverse(multiply(multiply(inverse(X0),X1),multiply(inverse(inverse(multiply(inverse(X1),X0))),X3))),X5),inverse(multiply(X2,X5)))))),
inference(superposition,[],[f314,f4260]) ).
fof(f4575,plain,
! [X2,X0,X1] : inverse(inverse(X2)) = multiply(multiply(inverse(X0),X1),multiply(inverse(inverse(multiply(inverse(X1),X0))),X2)),
inference(superposition,[],[f3471,f4260]) ).
fof(f4601,plain,
! [X2,X3,X0,X1,X5] : multiply(X2,X3) = inverse(inverse(inverse(multiply(multiply(inverse(multiply(multiply(inverse(X0),X1),multiply(inverse(inverse(multiply(inverse(X1),X0))),X3))),X5),inverse(multiply(X2,X5)))))),
inference(forward_demodulation,[],[f4544,f3471]) ).
fof(f4609,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),inverse(multiply(inverse(X0),X1))))),inverse(inverse(inverse(multiply(inverse(X1),X0)))))) = X3,
inference(forward_demodulation,[],[f4535,f4235]) ).
fof(f4624,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))) = inverse(multiply(inverse(inverse(multiply(inverse(X3),inverse(multiply(inverse(X0),X1))))),inverse(inverse(inverse(multiply(inverse(X1),X0)))))),
inference(forward_demodulation,[],[f4519,f4235]) ).
fof(f4649,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X2,X1)),X2) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f4490,f4260]) ).
fof(f4664,plain,
! [X2,X1,X4,X5] : inverse(multiply(inverse(inverse(inverse(X1))),X2)) = multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X4),X2)),X5),inverse(multiply(X4,X5))))),X1),
inference(forward_demodulation,[],[f4470,f3557]) ).
fof(f4681,plain,
! [X2,X3,X0,X1] : multiply(X2,X3) = inverse(multiply(inverse(multiply(multiply(inverse(X0),X1),multiply(inverse(inverse(multiply(inverse(X1),X0))),X3))),inverse(X2))),
inference(forward_demodulation,[],[f4601,f4234]) ).
fof(f4687,plain,
! [X2,X3,X0,X1] : inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X2,X3))),inverse(multiply(inverse(X0),X1))),inverse(multiply(inverse(X1),X0)))))) = X3,
inference(forward_demodulation,[],[f4609,f3686]) ).
fof(f4695,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))) = inverse(inverse(inverse(multiply(multiply(inverse(X3),inverse(multiply(inverse(X0),X1))),inverse(multiply(inverse(X1),X0)))))),
inference(forward_demodulation,[],[f4624,f3686]) ).
fof(f4721,plain,
! [X2,X3] : multiply(X2,X3) = inverse(multiply(inverse(inverse(inverse(X3))),inverse(X2))),
inference(forward_demodulation,[],[f4681,f4575]) ).
fof(f4726,plain,
! [X2,X3,X0,X1] : multiply(inverse(inverse(multiply(inverse(X1),X0))),inverse(inverse(multiply(inverse(inverse(multiply(inverse(X0),X1))),multiply(inverse(X2),multiply(X2,X3)))))) = X3,
inference(forward_demodulation,[],[f4687,f4465]) ).
fof(f4732,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))) = multiply(inverse(inverse(multiply(inverse(X1),X0))),inverse(inverse(multiply(inverse(inverse(multiply(inverse(X0),X1))),X3)))),
inference(forward_demodulation,[],[f4695,f4465]) ).
fof(f4745,plain,
! [X2,X3,X0,X1] : inverse(inverse(multiply(multiply(inverse(X1),X0),multiply(inverse(inverse(multiply(inverse(X0),X1))),multiply(inverse(X2),multiply(X2,X3)))))) = X3,
inference(forward_demodulation,[],[f4726,f3766]) ).
fof(f4749,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))) = inverse(inverse(multiply(multiply(inverse(X1),X0),multiply(inverse(inverse(multiply(inverse(X0),X1))),X3)))),
inference(forward_demodulation,[],[f4732,f3766]) ).
fof(f4757,plain,
! [X2,X3] : inverse(inverse(inverse(inverse(multiply(inverse(X2),multiply(X2,X3)))))) = X3,
inference(forward_demodulation,[],[f4745,f4575]) ).
fof(f4759,plain,
! [X2,X3,X4] : inverse(multiply(multiply(inverse(multiply(inverse(X2),X3)),X4),inverse(multiply(X2,X4)))) = inverse(inverse(inverse(inverse(X3)))),
inference(forward_demodulation,[],[f4749,f4575]) ).
fof(f4765,plain,
! [X2,X3] : inverse(multiply(inverse(multiply(X2,X3)),X2)) = X3,
inference(forward_demodulation,[],[f4757,f4260]) ).
fof(f4773,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(inverse(X1),X4),inverse(multiply(inverse(X3),X4)))) = inverse(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(X0),X1)),X2),inverse(multiply(X0,X2))))),X3)),
inference(superposition,[],[f4765,f53]) ).
fof(f4810,plain,
! [X0,X1] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(superposition,[],[f4765,f4765]) ).
fof(f4860,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(X2,X0)),X2))),X3),inverse(multiply(X1,X3)))) = multiply(X4,inverse(multiply(multiply(X0,X5),inverse(multiply(inverse(X4),X5))))),
inference(superposition,[],[f53,f4765]) ).
fof(f4964,plain,
! [X2,X0,X4,X5] : inverse(multiply(inverse(X2),multiply(X2,X0))) = multiply(X4,inverse(multiply(multiply(X0,X5),inverse(multiply(inverse(X4),X5))))),
inference(forward_demodulation,[],[f4860,f4353]) ).
fof(f5029,plain,
! [X3,X1,X4] : inverse(multiply(multiply(inverse(X1),X4),inverse(multiply(inverse(X3),X4)))) = inverse(inverse(multiply(inverse(inverse(inverse(X3))),X1))),
inference(forward_demodulation,[],[f4773,f4664]) ).
fof(f5056,plain,
! [X0,X4,X5] : inverse(inverse(inverse(X0))) = multiply(X4,inverse(multiply(multiply(X0,X5),inverse(multiply(inverse(X4),X5))))),
inference(forward_demodulation,[],[f4964,f3471]) ).
fof(f5181,plain,
! [X2,X3,X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,multiply(X2,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(X2),X3)))))),
inference(superposition,[],[f101,f4810]) ).
fof(f5189,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
inference(superposition,[],[f4125,f4810]) ).
fof(f5340,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[],[f5181,f5056]) ).
fof(f5499,plain,
! [X2,X0,X1] : multiply(X2,multiply(inverse(X0),X1)) = inverse(multiply(multiply(inverse(X1),X0),inverse(X2))),
inference(superposition,[],[f5340,f4260]) ).
fof(f6002,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X3,X1))),X4),inverse(multiply(X2,X4)))) = multiply(X5,inverse(multiply(multiply(inverse(multiply(X0,X1)),X0),inverse(multiply(inverse(X5),X3))))),
inference(superposition,[],[f53,f4649]) ).
fof(f6138,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X3,X1))),X4),inverse(multiply(X2,X4)))) = multiply(X5,multiply(multiply(inverse(X5),X3),multiply(inverse(X0),multiply(X0,X1)))),
inference(forward_demodulation,[],[f6002,f5499]) ).
fof(f6389,plain,
! [X2,X3,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(inverse(X2),multiply(X3,X1))),X4),inverse(multiply(X2,X4)))) = multiply(X5,multiply(multiply(inverse(X5),X3),inverse(inverse(X1)))),
inference(forward_demodulation,[],[f6138,f3471]) ).
fof(f6567,plain,
! [X3,X1,X5] : multiply(X5,multiply(multiply(inverse(X5),X3),inverse(inverse(X1)))) = inverse(inverse(inverse(inverse(multiply(X3,X1))))),
inference(forward_demodulation,[],[f6389,f4759]) ).
fof(f6799,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X0))),X1) = X1,
inference(superposition,[],[f5189,f2353]) ).
fof(f7089,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(X1,inverse(X1)),X0),
inference(superposition,[],[f4721,f3833]) ).
fof(f8671,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X2),X1) = multiply(inverse(X3),multiply(X3,inverse(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X4),inverse(multiply(inverse(X2),X4)))))),
inference(superposition,[],[f205,f6799]) ).
fof(f8721,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(inverse(inverse(multiply(X0,inverse(X0))))))) = X2,
inference(superposition,[],[f2153,f6799]) ).
fof(f8793,plain,
! [X2,X0] : inverse(inverse(inverse(inverse(multiply(X2,inverse(multiply(X0,inverse(X0)))))))) = X2,
inference(forward_demodulation,[],[f8721,f6567]) ).
fof(f8833,plain,
! [X2,X0,X1,X4] : multiply(inverse(X2),X1) = inverse(inverse(inverse(multiply(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X4),inverse(multiply(inverse(X2),X4)))))),
inference(forward_demodulation,[],[f8671,f3471]) ).
fof(f8933,plain,
! [X2] : inverse(inverse(X2)) = X2,
inference(forward_demodulation,[],[f8793,f3818]) ).
fof(f8955,plain,
! [X2,X0,X1] : multiply(inverse(X2),X1) = inverse(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),inverse(inverse(X2)))),
inference(forward_demodulation,[],[f8833,f4234]) ).
fof(f9021,plain,
! [X2,X0,X1] : multiply(inverse(X2),X1) = inverse(multiply(inverse(multiply(multiply(X0,inverse(X0)),X1)),X2)),
inference(forward_demodulation,[],[f8955,f8933]) ).
fof(f9069,plain,
! [X2,X1] : multiply(inverse(X2),X1) = inverse(multiply(inverse(inverse(inverse(X1))),X2)),
inference(forward_demodulation,[],[f9021,f7089]) ).
fof(f9107,plain,
! [X2,X1] : inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(forward_demodulation,[],[f9069,f8933]) ).
fof(f9226,plain,
! [X2,X0,X1] : inverse(multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X1),X2)))) = inverse(multiply(inverse(X0),X0)),
inference(superposition,[],[f1957,f8933]) ).
fof(f9278,plain,
! [X2,X0,X1] : inverse(multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X1),X2)))) = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f9226,f9107]) ).
fof(f9345,plain,
! [X0,X1] : inverse(inverse(multiply(inverse(inverse(inverse(X1))),X1))) = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f9278,f5029]) ).
fof(f9394,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X1))),X1) = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f9345,f8933]) ).
fof(f9436,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(forward_demodulation,[],[f9394,f8933]) ).
fof(f9744,plain,
! [X0] : multiply(inverse(a1),a1) != multiply(inverse(X0),X0),
inference(superposition,[],[f2,f9436]) ).
fof(f9842,plain,
$false,
inference(forward_subsumption_resolution,[],[f9744,f9436]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP427-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 10:03:36 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 16.74/3.19 % (4170673)Detected a unit-equality problem, will run specialized UEQ schedule.
% 16.74/3.19 % (4170682)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=506769347:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 16.74/3.19 % (4170684)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=873625270:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 16.74/3.19 % (4170681)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3827061277:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 16.74/3.19 % (4170678)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=3598520672:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 16.74/3.19 % (4170679)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=1241452304:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 16.74/3.19 % (4170680)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2279217269:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 16.74/3.19 % (4170683)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2194868065:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 16.74/3.19 % (4170682)Instruction limit reached!
% 16.74/3.19 % (4170682)------------------------------
% 16.74/3.19 % (4170682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170682)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170682)Termination reason: Instruction limit
% 16.74/3.19 % (4170682)Termination phase: Saturation
% 16.74/3.19 % (4170682)Time elapsed: 0.051 s
% 16.74/3.19 % (4170682)Peak memory usage: 90 MB
% 16.74/3.19 % (4170682)Instructions burned: 182 (million)
% 16.74/3.19 % (4170681)Instruction limit reached!
% 16.74/3.19 % (4170681)------------------------------
% 16.74/3.19 % (4170681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170681)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170681)Termination reason: Instruction limit
% 16.74/3.19 % (4170681)Termination phase: Saturation
% 16.74/3.19 % (4170681)Time elapsed: 0.078 s
% 16.74/3.19 % (4170681)Peak memory usage: 89 MB
% 16.74/3.19 % (4170681)Instructions burned: 137 (million)
% 16.74/3.19 % (4170692)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3096681795:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 16.74/3.19 % (4170683)Instruction limit reached!
% 16.74/3.19 % (4170683)------------------------------
% 16.74/3.19 % (4170683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170683)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170683)Termination reason: Instruction limit
% 16.74/3.19 % (4170683)Termination phase: Saturation
% 16.74/3.19 % (4170683)Time elapsed: 0.163 s
% 16.74/3.19 % (4170683)Peak memory usage: 91 MB
% 16.74/3.19 % (4170683)Instructions burned: 257 (million)
% 16.74/3.19 % (4170693)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=245524506:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 16.74/3.19 % (4170695)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3213564765:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 16.74/3.19 % (4170695)Instruction limit reached!
% 16.74/3.19 % (4170695)------------------------------
% 16.74/3.19 % (4170695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170695)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170695)Termination reason: Instruction limit
% 16.74/3.19 % (4170695)Termination phase: Saturation
% 16.74/3.19 % (4170695)Time elapsed: 0.126 s
% 16.74/3.19 % (4170695)Peak memory usage: 90 MB
% 16.74/3.19 % (4170695)Instructions burned: 216 (million)
% 16.74/3.19 % (4170684)Instruction limit reached!
% 16.74/3.19 % (4170684)------------------------------
% 16.74/3.19 % (4170684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170684)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170684)Termination reason: Instruction limit
% 16.74/3.19 % (4170684)Termination phase: Saturation
% 16.74/3.19 % (4170684)Time elapsed: 0.612 s
% 16.74/3.19 % (4170684)Peak memory usage: 97 MB
% 16.74/3.19 % (4170684)Instructions burned: 1189 (million)
% 16.74/3.19 % (4170698)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=1843421267:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 16.74/3.19 % (4170699)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=291222623:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 16.74/3.19 % (4170698)Instruction limit reached!
% 16.74/3.19 % (4170698)------------------------------
% 16.74/3.19 % (4170698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170698)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170698)Termination reason: Instruction limit
% 16.74/3.19 % (4170698)Termination phase: Saturation
% 16.74/3.19 % (4170698)Time elapsed: 0.169 s
% 16.74/3.19 % (4170698)Peak memory usage: 92 MB
% 16.74/3.19 % (4170698)Instructions burned: 318 (million)
% 16.74/3.19 % (4170702)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1061105566:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 16.74/3.19 % (4170692)Instruction limit reached!
% 16.74/3.19 % (4170692)------------------------------
% 16.74/3.19 % (4170692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.74/3.19 % (4170692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.74/3.19 % (4170692)CaDiCaL version: 2.1.3
% 16.74/3.19 % (4170692)Termination reason: Instruction limit
% 16.74/3.19 % (4170692)Termination phase: Saturation
% 16.74/3.19 % (4170692)Time elapsed: 0.976 s
% 16.74/3.19 % (4170692)Peak memory usage: 140 MB
% 16.74/3.19 % (4170692)Instructions burned: 2051 (million)
% 16.74/3.19 % (4170704)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=1605795091:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2987 on theBenchmark for (2987ds/14534Mi)
% 16.74/3.19 % (4170693)First to succeed.
% 16.74/3.19 % (4170693)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4170673"
% 16.74/3.19 % (4170693)Refutation found. Thanks to Tanya!
% 16.74/3.19 % SZS status Unsatisfiable for theBenchmark
% 16.74/3.19 % SZS output start Proof for theBenchmark
% See solution above
% 17.23/3.38 % (4170693)------------------------------
% 17.23/3.38 % (4170693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.23/3.38 % (4170693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.23/3.38 % (4170693)CaDiCaL version: 2.1.3
% 17.23/3.38 % (4170693)Termination reason: Refutation
% 17.23/3.38 % (4170693)Time elapsed: 1.668 s
% 17.23/3.38 % (4170693)Peak memory usage: 148 MB
% 17.23/3.38 % (4170693)Instructions burned: 2890 (million)
% 17.23/3.38 % (4170693)------------------------------
% 17.23/3.38 % (4170693)------------------------------
% 17.23/3.38 % (4170673)Success in time 2.36 s
% 17.23/3.38 % Vampire exiting
%------------------------------------------------------------------------------