%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:13:52 AM UTC 2026
% Result : Unsatisfiable 4.67s 1.38s
% Output : Refutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 5
% Syntax : Number of formulae : 108 ( 108 unt; 3 def)
% Number of atoms : 108 ( 107 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 170 ( 170 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
fof(f4,definition,
sF0 = inverse(b2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f5,plain,
inverse(b2) = sF0,
inference(reorient_equations,[],[f4]) ).
fof(f6,definition,
sF1 = multiply(sF0,b2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f7,plain,
multiply(sF0,b2) = sF1,
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
sF2 = multiply(sF1,a2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f9,plain,
multiply(sF1,a2) = sF2,
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
a2 != sF2,
inference(definition_folding,[],[f3,f9,f7,f5]) ).
fof(f13,plain,
! [X0] : multiply(sF0,inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(inverse(b2),multiply(inverse(b2),b2))))) = X0,
inference(superposition,[],[f1,f7]) ).
fof(f14,plain,
! [X0] : multiply(sF0,inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(sF0,multiply(sF0,b2))))) = X0,
inference(forward_demodulation,[],[f13,f5]) ).
fof(f15,plain,
! [X0] : multiply(sF0,inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(sF0,sF1)))) = X0,
inference(forward_demodulation,[],[f14,f7]) ).
fof(f17,plain,
! [X0,X1] : multiply(sF0,inverse(multiply(inverse(multiply(inverse(X0),X1)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(sF0,sF1)))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(sF0,sF1)))),inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(sF0,sF1)))))))) = X1,
inference(superposition,[],[f1,f15]) ).
fof(f18,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(sF0,multiply(sF0,b2))))) = X1,
inference(superposition,[],[f1,f5]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(sF0,sF1)))) = X1,
inference(forward_demodulation,[],[f18,f7]) ).
fof(f25,plain,
! [X0] : multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X0)),multiply(sF0,sF1))),
inference(superposition,[],[f15,f19]) ).
fof(f26,plain,
! [X2,X0,X1] : multiply(X1,inverse(multiply(inverse(X0),multiply(inverse(X2),multiply(inverse(X2),X2))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),b2)),X0)),multiply(sF0,sF1))),
inference(superposition,[],[f1,f19]) ).
fof(f28,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(sF0,inverse(multiply(inverse(multiply(inverse(sF1),X0)),multiply(sF0,sF1))))),b2)),multiply(inverse(X0),X1))),multiply(sF0,sF1))) = X1,
inference(backward_demodulation,[],[f17,f26]) ).
fof(f32,plain,
! [X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(X0),b2)),multiply(inverse(X0),X1))),multiply(sF0,sF1))) = X1,
inference(forward_demodulation,[],[f28,f15]) ).
fof(f38,plain,
! [X2,X0] : inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),multiply(X0,X2))),multiply(sF0,sF1))) = X2,
inference(superposition,[],[f32,f32]) ).
fof(f47,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(sF1),multiply(sF0,X0))),multiply(sF0,sF1))) = X0,
inference(superposition,[],[f38,f7]) ).
fof(f48,plain,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X0)),multiply(inverse(X2),multiply(inverse(X2),X2)))) = inverse(multiply(inverse(multiply(inverse(multiply(X1,b2)),X0)),multiply(sF0,sF1))),
inference(superposition,[],[f38,f1]) ).
fof(f65,plain,
! [X0] : multiply(inverse(sF1),multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1))))) = X0,
inference(superposition,[],[f19,f25]) ).
fof(f74,plain,
! [X0] : multiply(inverse(multiply(inverse(sF1),multiply(sF0,X0))),multiply(sF0,sF1)) = multiply(inverse(sF1),multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1))))),
inference(superposition,[],[f65,f47]) ).
fof(f76,plain,
! [X0,X1] : multiply(inverse(sF1),multiply(sF0,X0)) = multiply(inverse(multiply(X1,b2)),multiply(X1,X0)),
inference(superposition,[],[f65,f38]) ).
fof(f82,plain,
! [X0] : inverse(multiply(inverse(sF1),multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1)))))) = X0,
inference(backward_demodulation,[],[f47,f74]) ).
fof(f121,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),b2)),multiply(sF0,sF1))),multiply(sF0,sF1))) = inverse(multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0)))),
inference(superposition,[],[f48,f25]) ).
fof(f127,plain,
! [X0,X1] : multiply(inverse(X1),multiply(inverse(X1),X1)) = multiply(inverse(multiply(X0,X1)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),b2)),multiply(sF0,sF1))),multiply(sF0,sF1)))),
inference(superposition,[],[f19,f48]) ).
fof(f129,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,X2)),X1)),multiply(inverse(X2),multiply(inverse(X2),X2))) = multiply(inverse(sF1),multiply(sF0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(sF0,sF1))),multiply(sF0,sF1))))),
inference(superposition,[],[f65,f48]) ).
fof(f130,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(X0,X2)),X1)),multiply(inverse(X2),multiply(inverse(X2),X2))),
inference(forward_demodulation,[],[f129,f65]) ).
fof(f132,plain,
! [X0,X1] : multiply(inverse(X1),multiply(inverse(X1),X1)) = multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(inverse(b2),multiply(inverse(b2),b2)))))),
inference(forward_demodulation,[],[f127,f26]) ).
fof(f135,plain,
! [X0] : inverse(multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0)))) = multiply(inverse(sF1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(inverse(b2),multiply(inverse(b2),b2))))),
inference(forward_demodulation,[],[f121,f26]) ).
fof(f143,plain,
! [X0,X1] : multiply(inverse(X1),multiply(inverse(X1),X1)) = multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,multiply(sF0,b2)))))),
inference(forward_demodulation,[],[f132,f5]) ).
fof(f145,plain,
! [X0] : inverse(multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0)))) = multiply(inverse(sF1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,multiply(sF0,b2))))),
inference(forward_demodulation,[],[f135,f5]) ).
fof(f147,plain,
! [X0,X1] : multiply(inverse(X1),multiply(inverse(X1),X1)) = multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))))),
inference(forward_demodulation,[],[f143,f7]) ).
fof(f149,plain,
! [X0] : inverse(multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0)))) = multiply(inverse(sF1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),
inference(forward_demodulation,[],[f145,f7]) ).
fof(f167,plain,
! [X0] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),b2)),multiply(sF0,sF1))),multiply(sF0,sF1)) = multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0))),
inference(superposition,[],[f130,f25]) ).
fof(f175,plain,
! [X0] : multiply(multiply(sF0,inverse(multiply(inverse(b2),multiply(sF0,sF1)))),multiply(sF0,sF1)) = multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0))),
inference(forward_demodulation,[],[f167,f25]) ).
fof(f184,plain,
! [X0] : multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1)) = multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),multiply(inverse(X0),X0))),
inference(forward_demodulation,[],[f175,f5]) ).
fof(f187,plain,
inverse(multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1))) = multiply(inverse(sF1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),
inference(backward_demodulation,[],[f149,f184]) ).
fof(f195,plain,
! [X0,X1] : multiply(inverse(multiply(X1,X0)),multiply(inverse(multiply(X1,X0)),multiply(X1,X0))) = multiply(inverse(multiply(inverse(sF1),multiply(sF0,X0))),multiply(inverse(multiply(X1,b2)),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))))),
inference(superposition,[],[f147,f76]) ).
fof(f198,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1))) = multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),multiply(inverse(X1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))))),
inference(superposition,[],[f147,f147]) ).
fof(f206,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),X2)),multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1)))),
inference(superposition,[],[f130,f147]) ).
fof(f212,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X0),multiply(inverse(X0),X0))),multiply(inverse(X0),multiply(inverse(X0),X0))) = multiply(inverse(multiply(inverse(multiply(X1,b2)),multiply(X1,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),multiply(sF0,sF1)),
inference(superposition,[],[f130,f147]) ).
fof(f216,plain,
! [X0] : multiply(inverse(multiply(inverse(X0),multiply(inverse(X0),X0))),multiply(inverse(X0),multiply(inverse(X0),X0))) = multiply(inverse(multiply(inverse(sF1),multiply(sF0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),multiply(sF0,sF1)),
inference(forward_demodulation,[],[f212,f76]) ).
fof(f228,plain,
! [X0] : multiply(inverse(multiply(inverse(X0),multiply(inverse(X0),X0))),multiply(inverse(X0),multiply(inverse(X0),X0))) = multiply(inverse(sF1),multiply(sF0,inverse(multiply(inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),multiply(sF0,sF1))))),
inference(forward_demodulation,[],[f216,f74]) ).
fof(f238,plain,
! [X0] : multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(X0),multiply(inverse(X0),X0))),multiply(inverse(X0),multiply(inverse(X0),X0))),
inference(forward_demodulation,[],[f228,f65]) ).
fof(f265,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X1)),multiply(sF0,sF1)) = multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1))))),multiply(inverse(multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1))))),multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1))))))),
inference(superposition,[],[f130,f82]) ).
fof(f271,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X1)),multiply(sF0,sF1)) = multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(sF1),multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1)))))),multiply(inverse(multiply(sF0,b2)),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),
inference(forward_demodulation,[],[f265,f195]) ).
fof(f273,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X1)),multiply(sF0,sF1)) = multiply(inverse(multiply(X0,X1)),multiply(inverse(multiply(inverse(sF1),multiply(sF0,inverse(multiply(X0,multiply(sF0,sF1)))))),multiply(inverse(sF1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),
inference(forward_demodulation,[],[f271,f7]) ).
fof(f274,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X1)),multiply(sF0,sF1)) = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(sF1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),
inference(forward_demodulation,[],[f273,f82]) ).
fof(f457,plain,
! [X0,X1] : multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),X1)),b2)),X0)),multiply(sF0,sF1))))),multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),X1)),b2)),X0)),multiply(sF0,sF1))))),
inference(superposition,[],[f238,f26]) ).
fof(f463,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,[],[f19,f26]) ).
fof(f550,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(X0,X3)),X1) = multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X0,b2)),X1)),multiply(sF0,sF1))))),
inference(superposition,[],[f463,f130]) ).
fof(f571,plain,
! [X0,X1] : multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),X1)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(X0),multiply(inverse(X1),multiply(inverse(X1),X1))))),X1)),b2)),X0)),multiply(sF0,sF1))))),X0),
inference(backward_demodulation,[],[f457,f550]) ).
fof(f609,plain,
! [X0] : multiply(inverse(X0),X0) = multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)),
inference(forward_demodulation,[],[f571,f19]) ).
fof(f630,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),multiply(inverse(X1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))))) = multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),
inference(backward_demodulation,[],[f198,f609]) ).
fof(f631,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))))),X2)),multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),
inference(backward_demodulation,[],[f206,f609]) ).
fof(f651,plain,
! [X0,X1] : multiply(inverse(X1),X1) = multiply(inverse(X0),X0),
inference(superposition,[],[f609,f609]) ).
fof(f654,plain,
! [X0,X1] : multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))))) = multiply(inverse(X0),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),
inference(superposition,[],[f147,f609]) ).
fof(f703,plain,
! [X1] : multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))) = multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),multiply(inverse(X1),inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))))),
inference(backward_demodulation,[],[f630,f654]) ).
fof(f704,plain,
! [X2,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),X2)),multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),
inference(backward_demodulation,[],[f631,f654]) ).
fof(f745,plain,
! [X1] : multiply(inverse(multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))) = multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),
inference(forward_demodulation,[],[f703,f654]) ).
fof(f750,plain,
! [X1] : multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),
inference(forward_demodulation,[],[f745,f609]) ).
fof(f751,plain,
! [X2,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1)))),X2)),multiply(inverse(multiply(sF0,sF1)),multiply(sF0,sF1))),
inference(backward_demodulation,[],[f704,f750]) ).
fof(f766,plain,
! [X0] : multiply(sF0,b2) = multiply(inverse(X0),X0),
inference(superposition,[],[f651,f5]) ).
fof(f811,plain,
! [X2,X3,X0,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),b2)),X2)),multiply(sF0,sF1))) = multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(inverse(X0),X0))))),
inference(superposition,[],[f26,f651]) ).
fof(f813,plain,
! [X2,X3,X0,X1] : multiply(inverse(multiply(inverse(multiply(X1,b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),multiply(inverse(X3),multiply(inverse(X0),X0))),
inference(superposition,[],[f130,f651]) ).
fof(f827,plain,
! [X2,X0,X1] : multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(X1),multiply(inverse(X0),X0))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X0),X0)),b2)),X2)),multiply(sF0,sF1))),
inference(superposition,[],[f26,f651]) ).
fof(f829,plain,
! [X2,X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(X0),X0)),X2)),multiply(inverse(X1),multiply(inverse(X0),X0))),
inference(superposition,[],[f130,f651]) ).
fof(f860,plain,
! [X0] : sF1 = multiply(inverse(X0),X0),
inference(forward_demodulation,[],[f766,f7]) ).
fof(f889,plain,
! [X0] : multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1)) = multiply(multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))),multiply(inverse(X0),sF1)),
inference(backward_demodulation,[],[f184,f860]) ).
fof(f952,plain,
! [X2,X3,X1] : inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),b2)),X2)),multiply(sF0,sF1))) = multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),sF1)))),
inference(backward_demodulation,[],[f811,f860]) ).
fof(f954,plain,
! [X2,X3,X1] : multiply(inverse(multiply(inverse(multiply(X1,b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(X1,X3)),X2)),multiply(inverse(X3),sF1)),
inference(backward_demodulation,[],[f813,f860]) ).
fof(f955,plain,
! [X2,X1] : multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(X1),sF1)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X2)),multiply(sF0,sF1))),
inference(backward_demodulation,[],[f827,f860]) ).
fof(f957,plain,
! [X2,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(sF1),X2)),multiply(inverse(X1),sF1)),
inference(backward_demodulation,[],[f829,f860]) ).
fof(f969,plain,
inverse(multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1))) = multiply(inverse(sF1),inverse(sF1)),
inference(backward_demodulation,[],[f187,f860]) ).
fof(f973,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),X1)),multiply(sF0,sF1)) = multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(sF1),inverse(sF1)))),
inference(backward_demodulation,[],[f274,f860]) ).
fof(f990,plain,
! [X0,X1] : multiply(inverse(X0),sF1) = multiply(inverse(multiply(X1,X0)),multiply(X1,inverse(sF1))),
inference(backward_demodulation,[],[f654,f860]) ).
fof(f1005,plain,
! [X2,X1] : multiply(inverse(multiply(inverse(multiply(inverse(X1),b2)),X2)),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(X1),sF1)),X2)),sF1),
inference(backward_demodulation,[],[f751,f860]) ).
fof(f1041,plain,
! [X0] : multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(sF1),sF1)),X0)),sF1)),
inference(backward_demodulation,[],[f25,f1005]) ).
fof(f1066,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(sF1),inverse(sF1)))) = multiply(inverse(multiply(inverse(multiply(inverse(sF1),sF1)),X1)),sF1),
inference(forward_demodulation,[],[f973,f1005]) ).
fof(f1076,plain,
! [X2,X1] : multiply(inverse(multiply(inverse(sF1),X2)),multiply(inverse(X1),sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(X1),sF1)),X2)),sF1),
inference(backward_demodulation,[],[f1005,f957]) ).
fof(f1078,plain,
! [X2,X1] : multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(X1),sF1)))) = inverse(multiply(inverse(multiply(inverse(sF1),X2)),multiply(inverse(sF1),sF1))),
inference(forward_demodulation,[],[f955,f957]) ).
fof(f1080,plain,
! [X2,X3,X1] : multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),sF1)))) = inverse(multiply(inverse(multiply(inverse(sF1),X2)),multiply(inverse(multiply(X1,X3)),sF1))),
inference(forward_demodulation,[],[f952,f957]) ).
fof(f1150,plain,
! [X0] : multiply(sF0,inverse(multiply(inverse(X0),multiply(sF0,sF1)))) = inverse(multiply(inverse(multiply(inverse(sF1),X0)),sF1)),
inference(forward_demodulation,[],[f1041,f860]) ).
fof(f1158,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(inverse(sF1),inverse(sF1)))) = multiply(inverse(multiply(inverse(sF1),X1)),sF1),
inference(forward_demodulation,[],[f1066,f860]) ).
fof(f1174,plain,
! [X2,X1] : multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(X1),sF1)))) = inverse(multiply(inverse(multiply(inverse(sF1),X2)),sF1)),
inference(forward_demodulation,[],[f1078,f860]) ).
fof(f1230,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(sF1),multiply(inverse(sF1),X0))),sF1)) = X0,
inference(backward_demodulation,[],[f15,f1150]) ).
fof(f1233,plain,
! [X0] : multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(sF1),X0)),sF1)),multiply(inverse(X0),sF1)),
inference(backward_demodulation,[],[f889,f1150]) ).
fof(f1280,plain,
multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(multiply(inverse(sF1),b2)),sF1)),multiply(sF0,sF1)),
inference(forward_demodulation,[],[f1233,f954]) ).
fof(f1305,plain,
multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1)) = multiply(inverse(multiply(inverse(sF1),sF1)),multiply(inverse(sF1),sF1)),
inference(forward_demodulation,[],[f1280,f957]) ).
fof(f1312,plain,
sF1 = multiply(multiply(sF0,inverse(multiply(sF0,multiply(sF0,sF1)))),multiply(sF0,sF1)),
inference(forward_demodulation,[],[f1305,f860]) ).
fof(f1316,plain,
inverse(sF1) = multiply(inverse(sF1),inverse(sF1)),
inference(backward_demodulation,[],[f969,f1312]) ).
fof(f1317,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(sF1))) = multiply(inverse(multiply(inverse(sF1),X1)),sF1),
inference(backward_demodulation,[],[f1158,f1316]) ).
fof(f1325,plain,
! [X1] : multiply(inverse(X1),sF1) = multiply(inverse(multiply(inverse(sF1),X1)),sF1),
inference(forward_demodulation,[],[f1317,f990]) ).
fof(f1328,plain,
! [X2,X1] : inverse(multiply(inverse(X2),sF1)) = multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(X1),sF1)))),
inference(backward_demodulation,[],[f1174,f1325]) ).
fof(f1337,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(sF1),X0)),sF1)) = X0,
inference(backward_demodulation,[],[f1230,f1325]) ).
fof(f1338,plain,
! [X0] : inverse(multiply(inverse(X0),sF1)) = X0,
inference(forward_demodulation,[],[f1337,f1325]) ).
fof(f1340,plain,
! [X2,X1] : multiply(inverse(multiply(inverse(sF1),X2)),multiply(inverse(X1),sF1)) = multiply(inverse(multiply(X1,X2)),sF1),
inference(backward_demodulation,[],[f1076,f1338]) ).
fof(f1349,plain,
! [X2,X1] : multiply(inverse(X1),inverse(multiply(inverse(X2),multiply(inverse(X1),sF1)))) = X2,
inference(backward_demodulation,[],[f1328,f1338]) ).
fof(f1371,plain,
! [X2,X3,X1] : multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),sF1)))) = inverse(multiply(inverse(multiply(multiply(X1,X3),X2)),sF1)),
inference(backward_demodulation,[],[f1080,f1340]) ).
fof(f1389,plain,
! [X2,X3,X1] : multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),sF1)))) = multiply(multiply(X1,X3),X2),
inference(forward_demodulation,[],[f1371,f1338]) ).
fof(f1406,plain,
! [X2,X1] : multiply(multiply(inverse(X1),X1),X2) = X2,
inference(backward_demodulation,[],[f1349,f1389]) ).
fof(f1411,plain,
! [X2] : multiply(sF1,X2) = X2,
inference(forward_demodulation,[],[f1406,f860]) ).
fof(f1419,plain,
a2 = sF2,
inference(backward_demodulation,[],[f9,f1411]) ).
fof(f1420,plain,
$false,
inference(forward_subsumption_resolution,[],[f1419,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP407-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n012.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:03:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.67/1.38 % (2133890)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.67/1.38 % (2133950)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2287491901:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.67/1.38 % (2133946)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=3765350211:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.67/1.38 % (2133947)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1044760604:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.67/1.38 % (2133952)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3296155387:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.67/1.38 % (2133951)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3188531009:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.67/1.38 % (2133944)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=1142318779:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.67/1.38 % (2133948)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2557480190:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.67/1.38 % (2133948)Instruction limit reached!
% 4.67/1.38 % (2133948)------------------------------
% 4.67/1.38 % (2133948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.38 % (2133948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.38 % (2133948)CaDiCaL version: 2.1.3
% 4.67/1.38 % (2133948)Termination reason: Instruction limit
% 4.67/1.38 % (2133948)Termination phase: Saturation
% 4.67/1.38 % (2133948)Time elapsed: 0.040 s
% 4.67/1.38 % (2133948)Peak memory usage: 89 MB
% 4.67/1.38 % (2133948)Instructions burned: 138 (million)
% 4.67/1.38 % (2133950)Instruction limit reached!
% 4.67/1.38 % (2133950)------------------------------
% 4.67/1.38 % (2133950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.38 % (2133950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.38 % (2133950)CaDiCaL version: 2.1.3
% 4.67/1.38 % (2133950)Termination reason: Instruction limit
% 4.67/1.38 % (2133950)Termination phase: Saturation
% 4.67/1.38 % (2133950)Time elapsed: 0.053 s
% 4.67/1.38 % (2133950)Peak memory usage: 89 MB
% 4.67/1.38 % (2133950)Instructions burned: 183 (million)
% 4.67/1.38 % (2133951)Instruction limit reached!
% 4.67/1.38 % (2133951)------------------------------
% 4.67/1.38 % (2133951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.38 % (2133951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.38 % (2133951)CaDiCaL version: 2.1.3
% 4.67/1.38 % (2133951)Termination reason: Instruction limit
% 4.67/1.38 % (2133951)Termination phase: Saturation
% 4.67/1.38 % (2133951)Time elapsed: 0.083 s
% 4.67/1.38 % (2133951)Peak memory usage: 91 MB
% 4.67/1.38 % (2133951)Instructions burned: 258 (million)
% 4.67/1.38 % (2134003)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3383268158:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 4.67/1.38 % (2134007)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3818804125:i=4948:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/4948Mi)
% 4.67/1.38 % (2134018)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1052276875:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 4.67/1.38 % (2134018)Instruction limit reached!
% 4.67/1.38 % (2134018)------------------------------
% 4.67/1.38 % (2134018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.38 % (2134018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.38 % (2134018)CaDiCaL version: 2.1.3
% 4.67/1.38 % (2134018)Termination reason: Instruction limit
% 4.67/1.38 % (2134018)Termination phase: Saturation
% 4.67/1.38 % (2134018)Time elapsed: 0.071 s
% 4.67/1.38 % (2134018)Peak memory usage: 90 MB
% 4.67/1.38 % (2134018)Instructions burned: 217 (million)
% 4.67/1.38 % (2133952)Instruction limit reached!
% 4.67/1.38 % (2133952)------------------------------
% 4.67/1.38 % (2133952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.38 % (2133952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.38 % (2133952)CaDiCaL version: 2.1.3
% 4.67/1.38 % (2133952)Termination reason: Instruction limit
% 4.67/1.38 % (2133952)Termination phase: Saturation
% 4.67/1.38 % (2133952)Time elapsed: 0.328 s
% 4.67/1.38 % (2133952)Peak memory usage: 96 MB
% 4.67/1.38 % (2133952)Instructions burned: 1189 (million)
% 4.67/1.38 % (2134067)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=2792748252: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)
% 4.67/1.38 % (2134068)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=434185155:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2995 on theBenchmark for (2995ds/12125Mi)
% 4.67/1.38 % (2133947)First to succeed.
% 4.67/1.38 % (2133947)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2133890"
% 4.67/1.38 % (2134067)Instruction limit reached!
% 4.67/1.38 % (2134067)------------------------------
% 4.67/1.38 % (2134067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.38 % (2134067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.38 % (2134067)CaDiCaL version: 2.1.3
% 4.67/1.38 % (2134067)Termination reason: Instruction limit
% 4.67/1.38 % (2134067)Termination phase: Saturation
% 4.67/1.38 % (2134067)Time elapsed: 0.099 s
% 4.67/1.38 % (2134067)Peak memory usage: 92 MB
% 4.67/1.38 % (2134067)Instructions burned: 317 (million)
% 4.67/1.38 % (2134071)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=4263417437:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2993 on theBenchmark for (2993ds/2836Mi)
% 4.67/1.38 % (2133947)Refutation found. Thanks to Tanya!
% 4.67/1.38 % SZS status Unsatisfiable for theBenchmark
% 4.67/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 5.61/1.48 % (2133947)------------------------------
% 5.61/1.48 % (2133947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.61/1.48 % (2133947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.61/1.48 % (2133947)CaDiCaL version: 2.1.3
% 5.61/1.48 % (2133947)Termination reason: Refutation
% 5.61/1.48 % (2133947)Time elapsed: 0.466 s
% 5.61/1.48 % (2133947)Peak memory usage: 129 MB
% 5.61/1.48 % (2133947)Instructions burned: 1305 (million)
% 5.61/1.48 % (2133947)------------------------------
% 5.61/1.48 % (2133947)------------------------------
% 5.61/1.48 % (2133890)Success in time 0.766 s
% 5.61/1.48 % Vampire exiting
%------------------------------------------------------------------------------