%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP441-1 : 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 : n008.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 20.70s 3.65s
% Output : Refutation 21.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 2
% Syntax : Number of formulae : 112 ( 112 unt; 0 def)
% Number of atoms : 112 ( 111 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 : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 402 ( 402 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(X3,multiply(X0,X2))))))) = 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(f3,plain,
! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(X1,multiply(multiply(X2,multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(X0,multiply(X2,X4)))))),multiply(multiply(X0,X5),inverse(multiply(X6,multiply(X1,X5))))))) = X6,
inference(superposition,[],[f1,f1]) ).
fof(f4,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X0,multiply(X4,X3))))),X0)))) = X4,
inference(superposition,[],[f1,f1]) ).
fof(f11,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X0,X4))))),X5)),X0)))) = X3,
inference(superposition,[],[f1,f4]) ).
fof(f22,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : multiply(X6,multiply(X7,multiply(multiply(inverse(X7),X8),inverse(multiply(X3,multiply(X6,X8)))))) = inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(X3,X4),inverse(multiply(X0,multiply(X5,X4))))),X0)),X5)))),
inference(superposition,[],[f4,f3]) ).
fof(f257,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(X3),multiply(X0,X2)))))) = X3,
inference(superposition,[],[f11,f22]) ).
fof(f306,plain,
! [X2,X3,X0,X1,X4] : multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X0,multiply(inverse(X4),X3))))),X0))) = X4,
inference(superposition,[],[f257,f1]) ).
fof(f331,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(inverse(X0),multiply(X1,X4)))))),inverse(multiply(X5,X0)))))) = X5,
inference(superposition,[],[f1,f257]) ).
fof(f484,plain,
! [X0,X1,X4] : inverse(multiply(inverse(X1),multiply(X1,multiply(X0,inverse(multiply(X4,X0)))))) = X4,
inference(superposition,[],[f331,f257]) ).
fof(f561,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,multiply(multiply(inverse(X3),multiply(X4,inverse(multiply(X0,X4)))),X0))),inverse(multiply(X5,X1)))))) = X5,
inference(superposition,[],[f331,f484]) ).
fof(f562,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X0,X3)))),X0))) = X1,
inference(superposition,[],[f257,f484]) ).
fof(f563,plain,
! [X2,X3,X0,X1] : inverse(X1) = inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X0,X3)))),X0)))),
inference(superposition,[],[f1,f484]) ).
fof(f603,plain,
! [X2,X1,X5] : inverse(multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(X5,X1)))))) = X5,
inference(forward_demodulation,[],[f561,f562]) ).
fof(f726,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X1),inverse(multiply(X0,X3)))),X0)))) = X3,
inference(superposition,[],[f1,f603]) ).
fof(f802,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X4,multiply(multiply(inverse(X4),X5),inverse(multiply(X0,multiply(X3,X5))))) = inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(inverse(X1),X0)),X3)))),
inference(superposition,[],[f726,f1]) ).
fof(f961,plain,
! [X2,X3,X0,X1] : inverse(multiply(X3,inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),multiply(inverse(X0),X2)),X3)))))) = X2,
inference(superposition,[],[f1,f802]) ).
fof(f1025,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(multiply(inverse(X0),X1),inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X1))))) = X3,
inference(superposition,[],[f726,f802]) ).
fof(f1136,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,multiply(X1,multiply(inverse(X1),X2)))),X0)) = X2,
inference(superposition,[],[f961,f1]) ).
fof(f1469,plain,
! [X3,X0,X1] : multiply(inverse(X1),multiply(X1,multiply(X0,inverse(multiply(inverse(X3),X0))))) = X3,
inference(superposition,[],[f306,f1025]) ).
fof(f1556,plain,
! [X2,X3,X0,X1] : multiply(X2,multiply(X3,multiply(inverse(X3),X0))) = multiply(inverse(X1),multiply(X1,multiply(X2,X0))),
inference(superposition,[],[f1469,f1136]) ).
fof(f1583,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,multiply(X2,X0))),X1)) = multiply(X2,multiply(X3,inverse(multiply(inverse(X0),X3)))),
inference(superposition,[],[f1136,f1469]) ).
fof(f1697,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(inverse(X5),multiply(X5,X0)) = multiply(X1,multiply(X2,multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(inverse(multiply(X4,X0)),multiply(X4,X3))))))),
inference(superposition,[],[f1556,f1025]) ).
fof(f1701,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X4),X0) = multiply(X1,multiply(X2,multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(inverse(X0),multiply(X4,X3))))))),
inference(superposition,[],[f1556,f257]) ).
fof(f1715,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(inverse(X0),multiply(X0,multiply(X1,X2)))),X1)) = X2,
inference(superposition,[],[f1136,f1556]) ).
fof(f1909,plain,
! [X0,X4,X5] : multiply(inverse(X5),multiply(X5,X0)) = multiply(inverse(X4),multiply(X4,X0)),
inference(forward_demodulation,[],[f1697,f1701]) ).
fof(f2253,plain,
! [X2,X3,X0,X1] : multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X0),multiply(X1,X3)))) = inverse(multiply(inverse(multiply(inverse(X1),X0)),X2)),
inference(superposition,[],[f1715,f257]) ).
fof(f2363,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(inverse(multiply(X1,X0)),X1)) = multiply(X2,multiply(X5,inverse(multiply(inverse(multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(multiply(X4,X0)),multiply(X4,X3))))),X5)))),
inference(superposition,[],[f1583,f1025]) ).
fof(f2380,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(X0,X1)) = multiply(X2,multiply(X4,inverse(multiply(inverse(multiply(multiply(inverse(X2),X3),inverse(multiply(X0,multiply(X1,X3))))),X4)))),
inference(superposition,[],[f1583,f1]) ).
fof(f2674,plain,
! [X0,X1,X4] : inverse(multiply(inverse(multiply(X1,X0)),X1)) = inverse(multiply(inverse(multiply(X4,X0)),X4)),
inference(forward_demodulation,[],[f2363,f2380]) ).
fof(f2745,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X4,X3)))),X4)))),X1)),
inference(superposition,[],[f2674,f563]) ).
fof(f2946,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X0)) = inverse(multiply(inverse(X1),X1)),
inference(forward_demodulation,[],[f2745,f563]) ).
fof(f3118,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(inverse(X0),X0)),inverse(multiply(X1,multiply(inverse(X1),X2))))) = X2,
inference(superposition,[],[f1136,f2946]) ).
fof(f3159,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),X3) = multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(inverse(multiply(inverse(X0),X0)),X2))))),
inference(superposition,[],[f1469,f2946]) ).
fof(f3166,plain,
! [X3,X0] : multiply(inverse(X0),X0) = multiply(inverse(X3),X3),
inference(forward_demodulation,[],[f3159,f1469]) ).
fof(f3377,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X1,multiply(X2,multiply(inverse(X0),X0)))),X1)) = X2,
inference(superposition,[],[f1136,f3166]) ).
fof(f3903,plain,
! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(multiply(X1,multiply(X2,multiply(inverse(X3),X3)))),X1)) = multiply(X2,multiply(inverse(multiply(X4,multiply(inverse(X4),X0))),X0)),
inference(superposition,[],[f1583,f3118]) ).
fof(f3969,plain,
! [X2,X0,X4] : multiply(X2,multiply(inverse(multiply(X4,multiply(inverse(X4),X0))),X0)) = X2,
inference(forward_demodulation,[],[f3903,f3377]) ).
fof(f4038,plain,
! [X2,X3,X0,X1] : multiply(X3,inverse(multiply(X0,multiply(inverse(X0),multiply(inverse(multiply(X1,multiply(inverse(X1),X2))),X2))))) = X3,
inference(superposition,[],[f3969,f3969]) ).
fof(f4214,plain,
! [X3,X0] : multiply(X3,inverse(multiply(X0,inverse(X0)))) = X3,
inference(forward_demodulation,[],[f4038,f3969]) ).
fof(f4256,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X1,multiply(X2,X0))),X1)) = multiply(X2,inverse(inverse(X0))),
inference(superposition,[],[f1583,f4214]) ).
fof(f4294,plain,
! [X2,X0,X1] : inverse(X2) = inverse(multiply(X0,multiply(X1,multiply(multiply(inverse(X1),inverse(X0)),X2)))),
inference(superposition,[],[f726,f4214]) ).
fof(f4295,plain,
! [X0,X1] : inverse(multiply(inverse(X1),multiply(X0,inverse(X0)))) = X1,
inference(superposition,[],[f603,f4214]) ).
fof(f4315,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(multiply(X3,inverse(X3))),multiply(X4,X2))))) = inverse(multiply(X0,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))),
inference(superposition,[],[f802,f4214]) ).
fof(f4361,plain,
! [X3,X0,X1,X4,X5] : inverse(multiply(X0,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))) = multiply(X1,inverse(multiply(inverse(multiply(inverse(X4),multiply(X3,inverse(X3)))),X1))),
inference(forward_demodulation,[],[f4315,f2253]) ).
fof(f4411,plain,
! [X0,X1,X4,X5] : inverse(multiply(X0,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))) = multiply(X1,inverse(multiply(X4,X1))),
inference(forward_demodulation,[],[f4361,f4295]) ).
fof(f4413,plain,
! [X1,X4] : inverse(X4) = multiply(X1,inverse(multiply(X4,X1))),
inference(forward_demodulation,[],[f4411,f4294]) ).
fof(f4433,plain,
! [X2,X3,X0,X1] : inverse(inverse(multiply(X3,multiply(X0,X2)))) = multiply(X3,multiply(X0,multiply(X1,inverse(multiply(inverse(X2),X1))))),
inference(superposition,[],[f4413,f1583]) ).
fof(f4437,plain,
! [X0,X1] : inverse(inverse(X1)) = multiply(X1,inverse(multiply(inverse(X0),X0))),
inference(superposition,[],[f4413,f2946]) ).
fof(f4485,plain,
! [X2,X3,X0,X1] : inverse(multiply(X0,X3)) = multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(inverse(X0)),multiply(X3,X2))))),
inference(superposition,[],[f1025,f4413]) ).
fof(f4512,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(multiply(X0,inverse(X3))),multiply(X4,X2))))) = inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))),
inference(superposition,[],[f802,f4413]) ).
fof(f4515,plain,
! [X2,X0,X1] : inverse(multiply(X0,inverse(X2))) = inverse(multiply(inverse(multiply(X1,multiply(X2,inverse(X0)))),X1)),
inference(superposition,[],[f1136,f4413]) ).
fof(f4540,plain,
! [X0,X1] : multiply(X0,inverse(inverse(multiply(inverse(X0),X1)))) = X1,
inference(superposition,[],[f1025,f4413]) ).
fof(f4546,plain,
! [X2,X0] : inverse(multiply(X0,inverse(X2))) = multiply(X2,inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[],[f4515,f4256]) ).
fof(f4547,plain,
! [X3,X0,X1,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))) = multiply(X1,inverse(multiply(inverse(multiply(inverse(X4),multiply(X0,inverse(X3)))),X1))),
inference(forward_demodulation,[],[f4512,f2253]) ).
fof(f4549,plain,
! [X3,X0,X1] : inverse(multiply(X0,X3)) = multiply(X1,inverse(multiply(inverse(multiply(inverse(X3),inverse(X0))),X1))),
inference(forward_demodulation,[],[f4485,f2253]) ).
fof(f4555,plain,
! [X2,X3,X0] : inverse(inverse(multiply(X3,multiply(X0,X2)))) = multiply(X3,multiply(X0,inverse(inverse(X2)))),
inference(forward_demodulation,[],[f4433,f4413]) ).
fof(f4560,plain,
! [X3,X0,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))) = inverse(inverse(multiply(inverse(X4),multiply(X0,inverse(X3))))),
inference(forward_demodulation,[],[f4547,f4413]) ).
fof(f4562,plain,
! [X3,X0] : inverse(multiply(X0,X3)) = inverse(inverse(multiply(inverse(X3),inverse(X0)))),
inference(forward_demodulation,[],[f4549,f4413]) ).
fof(f4567,plain,
! [X3,X0,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))) = multiply(inverse(X4),multiply(X0,inverse(inverse(inverse(X3))))),
inference(forward_demodulation,[],[f4560,f4555]) ).
fof(f4570,plain,
! [X3,X0,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),inverse(X0)),X4)))) = multiply(inverse(X4),inverse(multiply(X3,inverse(X0)))),
inference(forward_demodulation,[],[f4567,f4546]) ).
fof(f4619,plain,
! [X0,X1] : multiply(X1,inverse(inverse(multiply(inverse(X0),X0)))) = X1,
inference(superposition,[],[f4540,f2946]) ).
fof(f4637,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(inverse(multiply(inverse(X1),X0)))),inverse(multiply(X3,X0)))))) = X3,
inference(superposition,[],[f1,f4540]) ).
fof(f4656,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,multiply(multiply(inverse(X3),X4),inverse(multiply(inverse(inverse(inverse(multiply(inverse(X5),X0)))),multiply(X1,X4)))))),inverse(X0))))) = X5,
inference(superposition,[],[f331,f4540]) ).
fof(f4688,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(multiply(inverse(inverse(multiply(inverse(inverse(X3)),X0))),multiply(X4,X2))))) = inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),X0),X4)))),
inference(superposition,[],[f802,f4540]) ).
fof(f4703,plain,
! [X3,X0,X1,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),X0),X4)))) = multiply(X1,inverse(multiply(inverse(multiply(inverse(X4),inverse(multiply(inverse(inverse(X3)),X0)))),X1))),
inference(forward_demodulation,[],[f4688,f2253]) ).
fof(f4708,plain,
! [X2,X3,X0,X1,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(inverse(multiply(inverse(X1),inverse(inverse(multiply(inverse(X5),X0))))),X3)))),inverse(X0))))) = X5,
inference(forward_demodulation,[],[f4656,f2253]) ).
fof(f4709,plain,
! [X3,X0,X1] : multiply(inverse(inverse(multiply(X3,X0))),inverse(multiply(X1,inverse(inverse(multiply(inverse(X1),X0)))))) = X3,
inference(forward_demodulation,[],[f4637,f4570]) ).
fof(f4727,plain,
! [X3,X0,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),X0),X4)))) = inverse(inverse(multiply(inverse(X4),inverse(multiply(inverse(inverse(X3)),X0))))),
inference(forward_demodulation,[],[f4703,f4413]) ).
fof(f4729,plain,
! [X2,X0,X1,X5] : inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),inverse(inverse(multiply(inverse(X1),inverse(inverse(multiply(inverse(X5),X0))))))),inverse(X0))))) = X5,
inference(forward_demodulation,[],[f4708,f4413]) ).
fof(f4730,plain,
! [X3,X0] : multiply(inverse(inverse(multiply(X3,X0))),inverse(X0)) = X3,
inference(forward_demodulation,[],[f4709,f4540]) ).
fof(f4738,plain,
! [X3,X0,X4,X5] : inverse(multiply(X3,multiply(X5,multiply(multiply(inverse(X5),X0),X4)))) = inverse(multiply(multiply(inverse(inverse(X3)),X0),X4)),
inference(forward_demodulation,[],[f4727,f4562]) ).
fof(f4739,plain,
! [X0,X1,X5] : multiply(inverse(inverse(X0)),inverse(multiply(X1,inverse(inverse(multiply(inverse(X1),inverse(inverse(multiply(inverse(X5),X0))))))))) = X5,
inference(forward_demodulation,[],[f4729,f4570]) ).
fof(f4742,plain,
! [X0,X5] : multiply(inverse(inverse(X0)),inverse(inverse(inverse(multiply(inverse(X5),X0))))) = X5,
inference(forward_demodulation,[],[f4739,f4540]) ).
fof(f4744,plain,
! [X0,X5] : inverse(multiply(multiply(inverse(X5),X0),inverse(inverse(inverse(X0))))) = X5,
inference(forward_demodulation,[],[f4742,f4546]) ).
fof(f4745,plain,
! [X0,X5] : inverse(inverse(multiply(X0,inverse(multiply(inverse(X5),X0))))) = X5,
inference(forward_demodulation,[],[f4744,f4546]) ).
fof(f4746,plain,
! [X5] : inverse(inverse(inverse(inverse(X5)))) = X5,
inference(forward_demodulation,[],[f4745,f4413]) ).
fof(f4767,plain,
! [X2,X0,X1] : inverse(multiply(X1,multiply(X2,multiply(inverse(X2),X0)))) = multiply(inverse(X0),inverse(X1)),
inference(superposition,[],[f4730,f1136]) ).
fof(f4796,plain,
! [X2,X0,X1] : multiply(inverse(inverse(multiply(X1,multiply(inverse(X2),X2)))),inverse(multiply(inverse(X0),X0))) = X1,
inference(superposition,[],[f4730,f2946]) ).
fof(f4840,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(X0,X3))))),X1)) = multiply(X2,multiply(inverse(X3),inverse(X0))),
inference(superposition,[],[f1583,f4730]) ).
fof(f4905,plain,
! [X2,X3,X0] : multiply(X2,multiply(inverse(X3),inverse(X0))) = multiply(X2,inverse(inverse(inverse(multiply(X0,X3))))),
inference(forward_demodulation,[],[f4840,f4256]) ).
fof(f4936,plain,
! [X2,X1] : inverse(inverse(inverse(inverse(multiply(X1,multiply(inverse(X2),X2)))))) = X1,
inference(forward_demodulation,[],[f4796,f4437]) ).
fof(f4975,plain,
! [X2,X3,X0] : multiply(X2,multiply(inverse(X3),inverse(X0))) = inverse(multiply(multiply(X0,X3),inverse(X2))),
inference(forward_demodulation,[],[f4905,f4546]) ).
fof(f5001,plain,
! [X2,X1] : multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(forward_demodulation,[],[f4936,f4746]) ).
fof(f5105,plain,
! [X2,X0,X1] : multiply(X1,X0) = multiply(inverse(X2),multiply(X2,multiply(X1,X0))),
inference(superposition,[],[f1556,f5001]) ).
fof(f5108,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X1,X0)),X1)) = X0,
inference(superposition,[],[f1136,f5001]) ).
fof(f5122,plain,
! [X2,X3,X0,X1,X4] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(X0))) = inverse(multiply(X3,multiply(X4,multiply(multiply(inverse(X4),multiply(inverse(X3),X0)),inverse(X2))))),
inference(superposition,[],[f802,f5001]) ).
fof(f5170,plain,
! [X2,X0,X1] : inverse(inverse(multiply(X0,X1))) = multiply(X0,multiply(X2,multiply(inverse(X2),X1))),
inference(superposition,[],[f1556,f5001]) ).
fof(f5172,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(X1),multiply(X1,X0)),
inference(superposition,[],[f1909,f5001]) ).
fof(f5180,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,multiply(X0,multiply(inverse(X0),inverse(multiply(X3,multiply(X1,multiply(inverse(X2),X2)))))))) = X3,
inference(superposition,[],[f1,f5001]) ).
fof(f5266,plain,
! [X2,X3,X1] : multiply(inverse(inverse(multiply(X3,multiply(X1,multiply(inverse(X2),X2))))),inverse(X1)) = X3,
inference(forward_demodulation,[],[f5180,f4767]) ).
fof(f5314,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(X0))) = inverse(multiply(multiply(inverse(inverse(X3)),multiply(inverse(X3),X0)),inverse(X2))),
inference(forward_demodulation,[],[f5122,f4738]) ).
fof(f5324,plain,
! [X0,X1] : multiply(X1,X0) = inverse(inverse(multiply(X1,X0))),
inference(forward_demodulation,[],[f5105,f5172]) ).
fof(f5357,plain,
! [X2,X3,X1] : multiply(multiply(X3,multiply(X1,inverse(inverse(multiply(inverse(X2),X2))))),inverse(X1)) = X3,
inference(forward_demodulation,[],[f5266,f4555]) ).
fof(f5379,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(X0))) = multiply(X2,multiply(inverse(multiply(inverse(X3),X0)),inverse(inverse(inverse(X3))))),
inference(forward_demodulation,[],[f5314,f4975]) ).
fof(f5406,plain,
! [X3,X1] : multiply(multiply(X3,X1),inverse(X1)) = X3,
inference(forward_demodulation,[],[f5357,f4619]) ).
fof(f5421,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(inverse(X1),X2),inverse(X0))) = multiply(X2,inverse(multiply(X3,inverse(inverse(multiply(inverse(X3),X0)))))),
inference(forward_demodulation,[],[f5379,f4546]) ).
fof(f5454,plain,
! [X2,X0,X1] : multiply(X2,inverse(X0)) = multiply(X1,multiply(multiply(inverse(X1),X2),inverse(X0))),
inference(forward_demodulation,[],[f5421,f4540]) ).
fof(f5577,plain,
! [X2,X3,X0,X1] : multiply(inverse(X3),multiply(X3,X0)) = multiply(multiply(X0,X1),multiply(X2,multiply(inverse(X2),inverse(X1)))),
inference(superposition,[],[f1556,f5406]) ).
fof(f5597,plain,
! [X3,X0,X1] : multiply(inverse(X3),multiply(X3,X0)) = inverse(inverse(multiply(multiply(X0,X1),inverse(X1)))),
inference(forward_demodulation,[],[f5577,f5170]) ).
fof(f5667,plain,
! [X3,X0,X1] : multiply(inverse(X3),multiply(X3,X0)) = multiply(multiply(X0,X1),inverse(X1)),
inference(forward_demodulation,[],[f5597,f5324]) ).
fof(f5724,plain,
! [X3,X0] : multiply(inverse(X3),multiply(X3,X0)) = X0,
inference(forward_demodulation,[],[f5667,f5406]) ).
fof(f6001,plain,
! [X2,X3,X0,X1,X4,X5] : inverse(multiply(X4,multiply(X5,multiply(multiply(inverse(X5),multiply(inverse(X4),X3)),inverse(X2))))) = multiply(X1,multiply(multiply(inverse(X1),multiply(X2,X0)),inverse(multiply(X3,X0)))),
inference(superposition,[],[f802,f5724]) ).
fof(f6029,plain,
! [X2,X3,X0,X4,X5] : inverse(multiply(X4,multiply(X5,multiply(multiply(inverse(X5),multiply(inverse(X4),X3)),inverse(X2))))) = multiply(multiply(X2,X0),inverse(multiply(X3,X0))),
inference(forward_demodulation,[],[f6001,f5454]) ).
fof(f6174,plain,
! [X2,X3,X0,X4] : multiply(multiply(X2,X0),inverse(multiply(X3,X0))) = inverse(multiply(multiply(inverse(inverse(X4)),multiply(inverse(X4),X3)),inverse(X2))),
inference(forward_demodulation,[],[f6029,f4738]) ).
fof(f6280,plain,
! [X2,X3,X0,X4] : multiply(multiply(X2,X0),inverse(multiply(X3,X0))) = multiply(X2,multiply(inverse(multiply(inverse(X4),X3)),inverse(inverse(inverse(X4))))),
inference(forward_demodulation,[],[f6174,f4975]) ).
fof(f6354,plain,
! [X2,X3,X0,X4] : multiply(multiply(X2,X0),inverse(multiply(X3,X0))) = multiply(X2,inverse(multiply(X4,inverse(inverse(multiply(inverse(X4),X3)))))),
inference(forward_demodulation,[],[f6280,f4546]) ).
fof(f6397,plain,
! [X2,X3,X0] : multiply(X2,inverse(X3)) = multiply(multiply(X2,X0),inverse(multiply(X3,X0))),
inference(forward_demodulation,[],[f6354,f4540]) ).
fof(f21814,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = multiply(X1,inverse(inverse(multiply(X2,X0)))),
inference(superposition,[],[f6397,f5108]) ).
fof(f21976,plain,
! [X2,X0,X1] : multiply(X1,multiply(X2,X0)) = multiply(multiply(X1,X2),X0),
inference(forward_demodulation,[],[f21814,f5324]) ).
fof(f22788,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(superposition,[],[f2,f21976]) ).
fof(f22929,plain,
$false,
inference(trivial_inequality_removal,[],[f22788]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP441-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.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 10:05:40 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 20.70/3.65 % (995441)Detected a unit-equality problem, will run specialized UEQ schedule.
% 20.70/3.65 % (995451)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2192354550:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 20.70/3.65 % (995449)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1605689078:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 20.70/3.65 % (995452)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1054983740:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 20.70/3.65 % (995447)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=1348277087:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 20.70/3.65 % (995450)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4076573885:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 20.70/3.65 % (995448)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2977078747:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 20.70/3.65 % (995446)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=2406199492:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 20.70/3.65 % (995449)Instruction limit reached!
% 20.70/3.65 % (995449)------------------------------
% 20.70/3.65 % (995449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995449)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995449)Termination reason: Instruction limit
% 20.70/3.65 % (995449)Termination phase: Saturation
% 20.70/3.65 % (995449)Time elapsed: 0.073 s
% 20.70/3.65 % (995449)Peak memory usage: 89 MB
% 20.70/3.65 % (995449)Instructions burned: 136 (million)
% 20.70/3.65 % (995450)Instruction limit reached!
% 20.70/3.65 % (995450)------------------------------
% 20.70/3.65 % (995450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995450)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995450)Termination reason: Instruction limit
% 20.70/3.65 % (995450)Termination phase: Saturation
% 20.70/3.65 % (995450)Time elapsed: 0.089 s
% 20.70/3.65 % (995450)Peak memory usage: 89 MB
% 20.70/3.65 % (995450)Instructions burned: 181 (million)
% 20.70/3.65 % (995451)Instruction limit reached!
% 20.70/3.65 % (995451)------------------------------
% 20.70/3.65 % (995451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995451)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995451)Termination reason: Instruction limit
% 20.70/3.65 % (995451)Termination phase: Saturation
% 20.70/3.65 % (995451)Time elapsed: 0.091 s
% 20.70/3.65 % (995451)Peak memory usage: 90 MB
% 20.70/3.65 % (995451)Instructions burned: 258 (million)
% 20.70/3.65 % (995462)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3038069656:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 20.70/3.65 % (995460)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3885404434:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 20.70/3.65 % (995461)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3310977206:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 20.70/3.65 % (995462)Instruction limit reached!
% 20.70/3.65 % (995462)------------------------------
% 20.70/3.65 % (995462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995462)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995462)Termination reason: Instruction limit
% 20.70/3.65 % (995462)Termination phase: Saturation
% 20.70/3.65 % (995462)Time elapsed: 0.069 s
% 20.70/3.65 % (995462)Peak memory usage: 91 MB
% 20.70/3.65 % (995462)Instructions burned: 217 (million)
% 20.70/3.65 % (995466)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=2081052025: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)
% 20.70/3.65 % (995466)Instruction limit reached!
% 20.70/3.65 % (995466)------------------------------
% 20.70/3.65 % (995466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995466)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995466)Termination reason: Instruction limit
% 20.70/3.65 % (995466)Termination phase: Saturation
% 20.70/3.65 % (995466)Time elapsed: 0.100 s
% 20.70/3.65 % (995466)Peak memory usage: 91 MB
% 20.70/3.65 % (995466)Instructions burned: 320 (million)
% 20.70/3.65 % (995468)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=3870212340:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 20.70/3.65 % (995452)Instruction limit reached!
% 20.70/3.65 % (995452)------------------------------
% 20.70/3.65 % (995452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995452)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995452)Termination reason: Instruction limit
% 20.70/3.65 % (995452)Termination phase: Saturation
% 20.70/3.65 % (995452)Time elapsed: 0.610 s
% 20.70/3.65 % (995452)Peak memory usage: 98 MB
% 20.70/3.65 % (995452)Instructions burned: 1188 (million)
% 20.70/3.65 % (995470)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3008936448:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2992 on theBenchmark for (2992ds/2836Mi)
% 20.70/3.65 % (995460)Instruction limit reached!
% 20.70/3.65 % (995460)------------------------------
% 20.70/3.65 % (995460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995460)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995460)Termination reason: Instruction limit
% 20.70/3.65 % (995460)Termination phase: Saturation
% 20.70/3.65 % (995460)Time elapsed: 1.203 s
% 20.70/3.65 % (995460)Peak memory usage: 140 MB
% 20.70/3.65 % (995460)Instructions burned: 2051 (million)
% 20.70/3.65 % (995472)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3983518590:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2984 on theBenchmark for (2984ds/14534Mi)
% 20.70/3.65 % (995470)Instruction limit reached!
% 20.70/3.65 % (995470)------------------------------
% 20.70/3.65 % (995470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.70/3.65 % (995470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.70/3.65 % (995470)CaDiCaL version: 2.1.3
% 20.70/3.65 % (995470)Termination reason: Instruction limit
% 20.70/3.65 % (995470)Termination phase: Saturation
% 20.70/3.65 % (995470)Time elapsed: 1.564 s
% 20.70/3.65 % (995470)Peak memory usage: 124 MB
% 20.70/3.65 % (995470)Instructions burned: 2838 (million)
% 20.70/3.65 % (995474)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=1838203974:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2975 on theBenchmark for (2975ds/11832Mi)
% 20.70/3.65 % (995461)First to succeed.
% 20.70/3.65 % (995461)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-995441"
% 20.70/3.65 % (995461)Refutation found. Thanks to Tanya!
% 20.70/3.65 % SZS status Unsatisfiable for theBenchmark
% 20.70/3.65 % SZS output start Proof for theBenchmark
% See solution above
% 21.76/3.84 % (995461)------------------------------
% 21.76/3.84 % (995461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.76/3.84 % (995461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.76/3.84 % (995461)CaDiCaL version: 2.1.3
% 21.76/3.84 % (995461)Termination reason: Refutation
% 21.76/3.84 % (995461)Time elapsed: 2.393 s
% 21.76/3.84 % (995461)Peak memory usage: 161 MB
% 21.76/3.84 % (995461)Instructions burned: 4179 (million)
% 21.76/3.84 % (995461)------------------------------
% 21.76/3.84 % (995461)------------------------------
% 21.76/3.84 % (995441)Success in time 3.019 s
% 21.76/3.84 % Vampire exiting
%------------------------------------------------------------------------------