%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP408-1 : 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 : n018.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 10:13:52 AM UTC 2026
% Result : Unsatisfiable 6.78s 3.04s
% Output : Refutation 16.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 2
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 247 ( 247 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(X1),multiply(inverse(X1),X1))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),multiply(inverse(X3),multiply(inverse(X3),X3)))) = multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),multiply(inverse(X2),X2))))),
inference(superposition,[],[f1,f1]) ).
fof(f8,plain,
! [X2,X3,X0,X1,X4] : multiply(X1,inverse(multiply(inverse(X4),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(X0),X4)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),multiply(inverse(X3),multiply(inverse(X3),X3))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),multiply(inverse(X3),multiply(inverse(X3),X3))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X0)),multiply(inverse(X3),multiply(inverse(X3),X3)))))))),
inference(superposition,[],[f4,f1]) ).
fof(f22,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X2)),multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(inverse(X2),X2)))))) = X1,
inference(superposition,[],[f1,f4]) ).
fof(f26,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),multiply(inverse(multiply(X0,X1)),X3))),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X3,
inference(superposition,[],[f1,f4]) ).
fof(f37,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(inverse(multiply(X0,X2)),X4)),X1) = multiply(inverse(multiply(X3,X4)),multiply(X3,multiply(X0,inverse(multiply(inverse(X1),multiply(inverse(X2),multiply(inverse(X2),X2))))))),
inference(superposition,[],[f22,f4]) ).
fof(f52,plain,
! [X0,X4,X5] : inverse(multiply(inverse(multiply(inverse(multiply(X0,X4)),multiply(X0,X5))),multiply(inverse(X4),multiply(inverse(X4),X4)))) = X5,
inference(superposition,[],[f26,f26]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(inverse(multiply(X3,X4)),X2)),multiply(inverse(multiply(X3,X4)),X0)) = multiply(inverse(multiply(X1,X2)),multiply(X1,X0)),
inference(superposition,[],[f22,f26]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X0),multiply(inverse(multiply(X1,X2)),X3)) = multiply(inverse(multiply(X4,multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),multiply(inverse(X2),X2))))))),multiply(X4,X3)),
inference(superposition,[],[f64,f22]) ).
fof(f96,plain,
! [X2,X0,X1,X5] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X5,X1)),multiply(X5,X2)),
inference(superposition,[],[f64,f64]) ).
fof(f182,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X0)),multiply(inverse(X4),multiply(inverse(X4),X4)))))) = multiply(inverse(multiply(X3,X2)),X0),
inference(superposition,[],[f96,f1]) ).
fof(f221,plain,
! [X2,X3,X0,X1] : multiply(inverse(X2),X1) = multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(X2),X2)))))),
inference(superposition,[],[f22,f96]) ).
fof(f230,plain,
! [X2,X3,X0,X1,X4,X5] : multiply(inverse(multiply(X5,X4)),multiply(X5,multiply(X3,X2))) = multiply(inverse(multiply(inverse(multiply(X3,X1)),X4)),multiply(inverse(multiply(X0,X1)),multiply(X0,X2))),
inference(superposition,[],[f64,f96]) ).
fof(f353,plain,
! [X2,X0,X1] : multiply(inverse(X2),multiply(inverse(X2),X2)) = multiply(inverse(multiply(X1,X2)),inverse(multiply(X0,multiply(inverse(multiply(X1,X0)),multiply(inverse(multiply(X1,X0)),multiply(X1,X0)))))),
inference(superposition,[],[f1,f52]) ).
fof(f539,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X4),multiply(inverse(X4),X4)) = multiply(inverse(multiply(X0,X4)),inverse(multiply(inverse(multiply(inverse(X3),multiply(inverse(X1),multiply(inverse(X1),X1)))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X3)),multiply(inverse(X2),multiply(inverse(X2),X2))))))))),
inference(superposition,[],[f353,f4]) ).
fof(f597,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(X2)))),multiply(inverse(X0),multiply(inverse(X0),X0))) = X2,
inference(superposition,[],[f22,f353]) ).
fof(f617,plain,
! [X0,X1,X4] : multiply(inverse(X4),multiply(inverse(X4),X4)) = multiply(inverse(multiply(X0,X4)),multiply(X0,inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(X1),X1))),multiply(inverse(X1),multiply(inverse(X1),X1)))))),
inference(forward_demodulation,[],[f539,f8]) ).
fof(f2247,plain,
! [X2,X3,X0,X1] : multiply(inverse(X2),multiply(inverse(X2),X2)) = multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(X0),multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),X1)),multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1)))))))))),
inference(superposition,[],[f617,f79]) ).
fof(f2445,plain,
! [X2,X3,X0] : multiply(inverse(X2),multiply(inverse(X2),X2)) = multiply(inverse(multiply(X3,X2)),multiply(X3,inverse(multiply(inverse(X0),X0)))),
inference(forward_demodulation,[],[f2247,f22]) ).
fof(f2628,plain,
! [X2,X0] : multiply(inverse(X2),X2) = multiply(inverse(multiply(inverse(X0),multiply(inverse(X0),X0))),multiply(inverse(X0),multiply(inverse(X0),X0))),
inference(superposition,[],[f597,f2445]) ).
fof(f2669,plain,
! [X2,X3,X0,X1] : multiply(inverse(inverse(multiply(inverse(X1),X1))),X2) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X1)))),multiply(X3,inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),X0)),X2)),multiply(inverse(X0),multiply(inverse(X0),X0)))))),
inference(superposition,[],[f221,f2445]) ).
fof(f2709,plain,
! [X2,X1] : multiply(inverse(inverse(multiply(inverse(X1),X1))),X2) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))),X2),
inference(forward_demodulation,[],[f2669,f182]) ).
fof(f2777,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f2628,f2628]) ).
fof(f3175,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X2),multiply(inverse(X0),X0)))))) = X3,
inference(superposition,[],[f22,f2777]) ).
fof(f3178,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(X2),multiply(inverse(X0),X0)))) = X3,
inference(superposition,[],[f52,f2777]) ).
fof(f3184,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(X1),X2) = multiply(inverse(multiply(X3,X1)),multiply(X3,inverse(multiply(inverse(multiply(X4,X2)),multiply(X4,multiply(inverse(X0),X0)))))),
inference(superposition,[],[f221,f2777]) ).
fof(f3220,plain,
! [X2,X0] : inverse(multiply(inverse(multiply(inverse(X0),X0)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = X2,
inference(superposition,[],[f52,f2777]) ).
fof(f3441,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X0),X0)) = multiply(inverse(X0),multiply(inverse(X1),X1)),
inference(superposition,[],[f2445,f3175]) ).
fof(f3697,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(X1),X1)),X2) = multiply(inverse(multiply(inverse(X0),multiply(inverse(X0),X0))),multiply(inverse(X0),inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1))))))),
inference(superposition,[],[f221,f3441]) ).
fof(f3710,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(X1),X1)),X2) = multiply(inverse(multiply(inverse(X0),X0)),X2),
inference(forward_demodulation,[],[f3697,f3184]) ).
fof(f4427,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(X1),X1)))) = X1,
inference(superposition,[],[f3220,f96]) ).
fof(f4441,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(multiply(X0,multiply(inverse(X0),multiply(inverse(X0),X0)))),
inference(superposition,[],[f52,f3220]) ).
fof(f4638,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,inverse(X0))),X2)),X0) = multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X1,multiply(inverse(inverse(X0)),inverse(X0))))),
inference(superposition,[],[f37,f4441]) ).
fof(f4747,plain,
! [X2,X0,X1] : multiply(inverse(X1),X1) = inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(X2),X2))))),multiply(inverse(X1),multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1))))),
inference(superposition,[],[f4427,f2445]) ).
fof(f4776,plain,
! [X2,X0,X1] : multiply(X2,inverse(multiply(inverse(X0),X0))) = inverse(multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(inverse(X0),X0))))),multiply(X1,multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0))))))),
inference(superposition,[],[f4427,f2445]) ).
fof(f4810,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(X0),multiply(inverse(X0),X0)))) = X1,
inference(superposition,[],[f4427,f3441]) ).
fof(f4840,plain,
! [X2,X3,X0,X1,X4] : multiply(inverse(multiply(X1,multiply(X2,multiply(inverse(X0),X0)))),multiply(X1,multiply(X2,X3))) = multiply(X0,multiply(inverse(multiply(X4,X0)),multiply(X4,X3))),
inference(superposition,[],[f230,f4427]) ).
fof(f4847,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X0)) = multiply(inverse(X2),X0),
inference(superposition,[],[f3175,f4427]) ).
fof(f4923,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,multiply(X2,multiply(inverse(X0),X0)))),multiply(X1,multiply(X2,X3))) = multiply(X0,multiply(inverse(X0),X3)),
inference(forward_demodulation,[],[f4840,f4847]) ).
fof(f4933,plain,
! [X0,X1] : inverse(multiply(inverse(X1),multiply(inverse(X0),X0))) = X1,
inference(forward_demodulation,[],[f4810,f4847]) ).
fof(f4950,plain,
! [X2,X0] : multiply(X2,inverse(multiply(inverse(X0),X0))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))),multiply(X2,inverse(multiply(inverse(X0),X0))))),multiply(inverse(X0),X0))),
inference(forward_demodulation,[],[f4776,f4638]) ).
fof(f4978,plain,
! [X2,X1] : multiply(inverse(X1),X1) = inverse(multiply(inverse(X2),X2)),
inference(forward_demodulation,[],[f4747,f3178]) ).
fof(f5005,plain,
! [X2,X3,X0] : multiply(inverse(multiply(X2,multiply(inverse(X0),X0))),multiply(X2,X3)) = multiply(X0,multiply(inverse(X0),X3)),
inference(forward_demodulation,[],[f4923,f4847]) ).
fof(f5017,plain,
! [X2,X0] : multiply(X2,inverse(multiply(inverse(X0),X0))) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0)))),multiply(X2,inverse(multiply(inverse(X0),X0)))),
inference(forward_demodulation,[],[f4950,f4933]) ).
fof(f5056,plain,
! [X3,X0] : multiply(inverse(multiply(inverse(X0),X0)),X3) = multiply(X0,multiply(inverse(X0),X3)),
inference(forward_demodulation,[],[f5005,f4847]) ).
fof(f5059,plain,
! [X2,X0] : multiply(X2,inverse(multiply(inverse(X0),X0))) = multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(X2,inverse(multiply(inverse(X0),X0)))),
inference(forward_demodulation,[],[f5017,f2709]) ).
fof(f5209,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,inverse(multiply(inverse(X3),inverse(multiply(inverse(X0),X0)))))) = X3,
inference(superposition,[],[f3175,f4978]) ).
fof(f5265,plain,
! [X0,X1] : inverse(multiply(inverse(inverse(multiply(inverse(X0),X0))),multiply(inverse(X1),inverse(multiply(inverse(X0),X0))))) = X1,
inference(superposition,[],[f4427,f4978]) ).
fof(f5325,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(multiply(inverse(X0),X0),multiply(inverse(X2),X3)),
inference(superposition,[],[f96,f4978]) ).
fof(f5422,plain,
! [X2,X3,X0] : multiply(inverse(X2),X3) = multiply(multiply(inverse(X0),X0),multiply(inverse(X2),X3)),
inference(forward_demodulation,[],[f5325,f4847]) ).
fof(f5453,plain,
! [X0,X1] : inverse(multiply(inverse(X1),inverse(multiply(inverse(X0),X0)))) = X1,
inference(forward_demodulation,[],[f5265,f5059]) ).
fof(f5486,plain,
! [X2,X3,X0] : multiply(inverse(multiply(inverse(X2),X2)),inverse(multiply(inverse(X3),inverse(multiply(inverse(X0),X0))))) = X3,
inference(forward_demodulation,[],[f5209,f4847]) ).
fof(f5590,plain,
! [X2,X3,X0] : multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),inverse(multiply(inverse(X0),X0)))))) = X3,
inference(forward_demodulation,[],[f5486,f5056]) ).
fof(f5629,plain,
! [X2,X3] : multiply(X2,multiply(inverse(X2),X3)) = X3,
inference(forward_demodulation,[],[f5590,f5453]) ).
fof(f5662,plain,
! [X0,X1] : multiply(X1,multiply(inverse(X0),X0)) = X1,
inference(superposition,[],[f5629,f2777]) ).
fof(f5665,plain,
! [X2,X0,X1] : multiply(multiply(inverse(X2),X2),multiply(inverse(multiply(inverse(X0),X0)),X1)) = X1,
inference(superposition,[],[f5629,f3710]) ).
fof(f5691,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f5629,f5629]) ).
fof(f5707,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),X2)),multiply(inverse(multiply(inverse(X1),X0)),multiply(inverse(multiply(inverse(X1),X0)),multiply(inverse(X1),X0)))))) = X2,
inference(superposition,[],[f1,f5629]) ).
fof(f5723,plain,
! [X2,X3,X0,X1] : multiply(inverse(X0),multiply(X2,X3)) = multiply(inverse(multiply(X1,multiply(inverse(X2),X0))),multiply(X1,X3)),
inference(superposition,[],[f96,f5629]) ).
fof(f5724,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X3,X2)),X0) = multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(inverse(X3),X0))),
inference(superposition,[],[f96,f5629]) ).
fof(f5744,plain,
! [X0,X1] : multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),multiply(X1,multiply(inverse(multiply(inverse(X1),X0)),multiply(inverse(X1),X0))))),
inference(superposition,[],[f4427,f5629]) ).
fof(f5755,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),multiply(inverse(X2),X2))))) = multiply(inverse(inverse(multiply(X1,X2))),X0),
inference(superposition,[],[f1,f5629]) ).
fof(f5787,plain,
! [X0,X1] : multiply(inverse(X1),X0) = inverse(multiply(inverse(X0),multiply(X1,multiply(inverse(X0),X0)))),
inference(forward_demodulation,[],[f5744,f4847]) ).
fof(f5805,plain,
! [X2,X3,X0] : multiply(inverse(multiply(X3,X2)),X0) = multiply(inverse(X2),multiply(inverse(X3),X0)),
inference(forward_demodulation,[],[f5724,f4847]) ).
fof(f5806,plain,
! [X2,X3,X0] : multiply(inverse(X0),multiply(X2,X3)) = multiply(inverse(multiply(inverse(X2),X0)),X3),
inference(forward_demodulation,[],[f5723,f4847]) ).
fof(f5817,plain,
! [X2,X0,X1] : multiply(inverse(inverse(multiply(X1,multiply(inverse(X1),X0)))),multiply(inverse(X0),X2)) = X2,
inference(forward_demodulation,[],[f5707,f5755]) ).
fof(f5853,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),X0)),X1) = X1,
inference(forward_demodulation,[],[f5665,f5422]) ).
fof(f5878,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(forward_demodulation,[],[f5787,f5662]) ).
fof(f5897,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,inverse(multiply(X1,multiply(inverse(X1),X0))))),X2) = X2,
inference(forward_demodulation,[],[f5817,f5805]) ).
fof(f5923,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f5853,f5806]) ).
fof(f5956,plain,
! [X2,X0] : multiply(inverse(multiply(X0,inverse(X0))),X2) = X2,
inference(forward_demodulation,[],[f5897,f5629]) ).
fof(f6079,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(X0))),multiply(inverse(X1),multiply(inverse(X1),X1)))) = X1,
inference(superposition,[],[f3220,f5956]) ).
fof(f6368,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X1),multiply(inverse(X1),X1))),multiply(X0,inverse(X0))) = X1,
inference(forward_demodulation,[],[f6079,f5878]) ).
fof(f6544,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X1),X1)),multiply(X1,multiply(X0,inverse(X0)))) = X1,
inference(forward_demodulation,[],[f6368,f5806]) ).
fof(f6673,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X1,multiply(X1,multiply(X0,inverse(X0))))) = X1,
inference(forward_demodulation,[],[f6544,f5806]) ).
fof(f6753,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(forward_demodulation,[],[f6673,f5923]) ).
fof(f7814,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),multiply(inverse(X1),multiply(inverse(X1),X1))) = X0,
inference(superposition,[],[f597,f6753]) ).
fof(f7932,plain,
! [X0,X1] : multiply(inverse(multiply(X1,inverse(multiply(X0,X1)))),multiply(inverse(X1),X1)) = X0,
inference(forward_demodulation,[],[f7814,f5805]) ).
fof(f8057,plain,
! [X0,X1] : inverse(multiply(X1,inverse(multiply(X0,X1)))) = X0,
inference(forward_demodulation,[],[f7932,f5662]) ).
fof(f8544,plain,
! [X2,X3,X0,X1] : multiply(X0,multiply(X2,X3)) = multiply(inverse(multiply(X1,inverse(multiply(X0,X2)))),multiply(X1,X3)),
inference(superposition,[],[f96,f8057]) ).
fof(f8691,plain,
! [X2,X3,X0] : multiply(X0,multiply(X2,X3)) = multiply(inverse(inverse(multiply(X0,X2))),X3),
inference(forward_demodulation,[],[f8544,f4847]) ).
fof(f8814,plain,
! [X2,X3,X0] : multiply(X0,multiply(X2,X3)) = multiply(multiply(X0,X2),X3),
inference(forward_demodulation,[],[f8691,f5691]) ).
fof(f9401,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(superposition,[],[f2,f8814]) ).
fof(f9473,plain,
$false,
inference(trivial_inequality_removal,[],[f9401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP408-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:05:53 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.78/3.04 % (2095475)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.78/3.04 % (2095486)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2380353095:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.78/3.04 % (2095485)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3658187968:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.78/3.04 % (2095482)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2641894236:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.78/3.04 % (2095480)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=3091220078:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.78/3.04 % (2095484)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3239180019:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.78/3.04 % (2095481)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=1986594995:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.78/3.04 % (2095483)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=727430702:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.78/3.04 % (2095483)Instruction limit reached!
% 6.78/3.04 % (2095483)------------------------------
% 6.78/3.04 % (2095483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095483)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095483)Termination reason: Instruction limit
% 6.78/3.04 % (2095483)Termination phase: Saturation
% 6.78/3.04 % (2095483)Time elapsed: 0.075 s
% 6.78/3.04 % (2095483)Peak memory usage: 89 MB
% 6.78/3.04 % (2095483)Instructions burned: 136 (million)
% 6.78/3.04 % (2095484)Instruction limit reached!
% 6.78/3.04 % (2095484)------------------------------
% 6.78/3.04 % (2095484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095484)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095484)Termination reason: Instruction limit
% 6.78/3.04 % (2095484)Termination phase: Saturation
% 6.78/3.04 % (2095484)Time elapsed: 0.098 s
% 6.78/3.04 % (2095484)Peak memory usage: 89 MB
% 6.78/3.04 % (2095484)Instructions burned: 181 (million)
% 6.78/3.04 % (2095485)Instruction limit reached!
% 6.78/3.04 % (2095485)------------------------------
% 6.78/3.04 % (2095485)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095485)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095485)Termination reason: Instruction limit
% 6.78/3.04 % (2095485)Termination phase: Saturation
% 6.78/3.04 % (2095485)Time elapsed: 0.152 s
% 6.78/3.04 % (2095485)Peak memory usage: 90 MB
% 6.78/3.04 % (2095485)Instructions burned: 259 (million)
% 6.78/3.04 % (2095494)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3355125025:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.78/3.04 % (2095495)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2291481793:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.78/3.04 % (2095486)Instruction limit reached!
% 6.78/3.04 % (2095486)------------------------------
% 6.78/3.04 % (2095486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095486)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095486)Termination reason: Instruction limit
% 6.78/3.04 % (2095486)Termination phase: Saturation
% 6.78/3.04 % (2095486)Time elapsed: 0.331 s
% 6.78/3.04 % (2095486)Peak memory usage: 98 MB
% 6.78/3.04 % (2095486)Instructions burned: 1190 (million)
% 6.78/3.04 % (2095496)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3607378168:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.78/3.04 % (2095499)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=3441664104:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 6.78/3.04 % (2095496)Instruction limit reached!
% 6.78/3.04 % (2095496)------------------------------
% 6.78/3.04 % (2095496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095496)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095496)Termination reason: Instruction limit
% 6.78/3.04 % (2095496)Termination phase: Saturation
% 6.78/3.04 % (2095496)Time elapsed: 0.121 s
% 6.78/3.04 % (2095496)Peak memory usage: 89 MB
% 6.78/3.04 % (2095496)Instructions burned: 215 (million)
% 6.78/3.04 % (2095499)Instruction limit reached!
% 6.78/3.04 % (2095499)------------------------------
% 6.78/3.04 % (2095499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095499)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095499)Termination reason: Instruction limit
% 6.78/3.04 % (2095499)Termination phase: Saturation
% 6.78/3.04 % (2095499)Time elapsed: 0.077 s
% 6.78/3.04 % (2095499)Peak memory usage: 89 MB
% 6.78/3.04 % (2095499)Instructions burned: 321 (million)
% 6.78/3.04 % (2095502)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=1491910786:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 6.78/3.04 % (2095503)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=129750718:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2993 on theBenchmark for (2993ds/2836Mi)
% 6.78/3.04 % (2095494)Instruction limit reached!
% 6.78/3.04 % (2095494)------------------------------
% 6.78/3.04 % (2095494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095494)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095494)Termination reason: Instruction limit
% 6.78/3.04 % (2095494)Termination phase: Saturation
% 6.78/3.04 % (2095494)Time elapsed: 1.251 s
% 6.78/3.04 % (2095494)Peak memory usage: 140 MB
% 6.78/3.04 % (2095494)Instructions burned: 2051 (million)
% 6.78/3.04 % (2095503)Instruction limit reached!
% 6.78/3.04 % (2095503)------------------------------
% 6.78/3.04 % (2095503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.78/3.04 % (2095503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.78/3.04 % (2095503)CaDiCaL version: 2.1.3
% 6.78/3.04 % (2095503)Termination reason: Instruction limit
% 6.78/3.04 % (2095503)Termination phase: Saturation
% 6.78/3.04 % (2095503)Time elapsed: 0.976 s
% 6.78/3.04 % (2095503)Peak memory usage: 118 MB
% 6.78/3.04 % (2095503)Instructions burned: 2840 (million)
% 6.78/3.04 % (2095506)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=375552018:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2983 on theBenchmark for (2983ds/14534Mi)
% 6.78/3.04 % (2095507)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=4125261297:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2982 on theBenchmark for (2982ds/11832Mi)
% 6.78/3.04 % (2095495)First to succeed.
% 6.78/3.04 % (2095495)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2095475"
% 6.78/3.04 % (2095495)Refutation found. Thanks to Tanya!
% 6.78/3.04 % SZS status Unsatisfiable for theBenchmark
% 6.78/3.04 % SZS output start Proof for theBenchmark
% See solution above
% 16.07/3.23 % (2095495)------------------------------
% 16.07/3.23 % (2095495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.07/3.23 % (2095495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.07/3.23 % (2095495)CaDiCaL version: 2.1.3
% 16.07/3.23 % (2095495)Termination reason: Refutation
% 16.07/3.23 % (2095495)Time elapsed: 1.510 s
% 16.07/3.23 % (2095495)Peak memory usage: 144 MB
% 16.07/3.23 % (2095495)Instructions burned: 2549 (million)
% 16.07/3.23 % (2095495)------------------------------
% 16.07/3.23 % (2095495)------------------------------
% 16.07/3.23 % (2095475)Success in time 2.186 s
% 16.07/3.23 % Vampire exiting
%------------------------------------------------------------------------------