%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP120-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 10:12:38 AM UTC 2026
% Result : Unsatisfiable 4.78s 1.70s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 3
% Syntax : Number of formulae : 107 ( 107 unt; 0 def)
% Number of atoms : 107 ( 106 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 157 ( 157 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,X2))),multiply(X2,multiply(X2,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
multiply(identity,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom2) ).
fof(f3,plain,
identity = multiply(identity,identity),
inference(reorient_equations,[],[f2]) ).
fof(f4,negated_conjecture,
multiply(identity,a) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).
fof(f5,plain,
a != multiply(identity,a),
inference(reorient_equations,[],[f4]) ).
fof(f6,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),multiply(X1,multiply(X1,X1)))) = X0,
inference(superposition,[],[f1,f3]) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(identity,identity))),
inference(superposition,[],[f1,f3]) ).
fof(f8,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X1),X0)),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X0,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X0,X3))),multiply(X3,multiply(X3,X3))),multiply(multiply(X2,multiply(multiply(X2,X2),multiply(X0,X3))),multiply(X3,multiply(X3,X3))))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X2,X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),multiply(X0,X2))) = multiply(X1,multiply(multiply(X1,X0),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),multiply(identity,identity))) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),multiply(X1,identity))),identity)) = X1,
inference(forward_demodulation,[],[f10,f3]) ).
fof(f12,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity)),
inference(forward_demodulation,[],[f7,f3]) ).
fof(f21,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = X0,
inference(superposition,[],[f11,f3]) ).
fof(f30,plain,
! [X0] : multiply(identity,multiply(identity,multiply(X0,identity))) = multiply(identity,multiply(multiply(identity,X0),identity)),
inference(superposition,[],[f21,f21]) ).
fof(f38,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,identity))),identity)) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))),
inference(superposition,[],[f30,f30]) ).
fof(f45,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,identity)),identity))) = X0,
inference(superposition,[],[f21,f30]) ).
fof(f54,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))) = X0,
inference(forward_demodulation,[],[f45,f30]) ).
fof(f61,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(multiply(identity,X0),identity),identity))) = X0,
inference(forward_demodulation,[],[f38,f21]) ).
fof(f97,plain,
! [X0] : multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity))))) = X0,
inference(superposition,[],[f6,f12]) ).
fof(f115,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity))))) = X0,
inference(forward_demodulation,[],[f97,f3]) ).
fof(f121,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity),multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity))))) = X0,
inference(forward_demodulation,[],[f115,f3]) ).
fof(f135,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = multiply(multiply(identity,X0),identity),
inference(superposition,[],[f21,f61]) ).
fof(f219,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),multiply(identity,X0))) = multiply(identity,multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))))),
inference(superposition,[],[f9,f3]) ).
fof(f236,plain,
! [X2,X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))),multiply(X2,multiply(X2,X2)))) = X1,
inference(superposition,[],[f1,f9]) ).
fof(f237,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(identity,multiply(identity,identity)),multiply(identity,multiply(identity,identity)))))),identity)) = X1,
inference(superposition,[],[f11,f9]) ).
fof(f240,plain,
! [X0,X1] : multiply(multiply(identity,identity),multiply(multiply(multiply(identity,identity),multiply(identity,identity)),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(superposition,[],[f6,f9]) ).
fof(f254,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,identity),multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(forward_demodulation,[],[f240,f3]) ).
fof(f255,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(multiply(identity,identity),multiply(multiply(identity,identity),multiply(identity,identity))))),identity)) = X1,
inference(forward_demodulation,[],[f237,f3]) ).
fof(f263,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))))) = multiply(identity,multiply(identity,multiply(identity,X0))),
inference(forward_demodulation,[],[f219,f3]) ).
fof(f275,plain,
! [X0,X1] : multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1))) = X0,
inference(forward_demodulation,[],[f254,f3]) ).
fof(f276,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,multiply(identity,identity)))),identity)) = X1,
inference(forward_demodulation,[],[f255,f3]) ).
fof(f294,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity))),identity)) = X1,
inference(forward_demodulation,[],[f276,f3]) ).
fof(f305,plain,
! [X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),identity)),identity)) = X1,
inference(forward_demodulation,[],[f294,f3]) ).
fof(f325,plain,
! [X0] : multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity) = multiply(multiply(X0,X0),multiply(multiply(X0,multiply(identity,identity)),identity)),
inference(superposition,[],[f305,f12]) ).
fof(f347,plain,
! [X0] : multiply(multiply(X0,multiply(multiply(X0,X0),identity)),identity) = multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),
inference(forward_demodulation,[],[f325,f3]) ).
fof(f379,plain,
! [X0,X1] : multiply(X0,identity) = multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1)),identity)),
inference(superposition,[],[f135,f275]) ).
fof(f390,plain,
! [X0,X1] : multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),identity))),
inference(forward_demodulation,[],[f379,f30]) ).
fof(f407,plain,
! [X0] : identity = multiply(X0,multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))),
inference(superposition,[],[f12,f347]) ).
fof(f470,plain,
! [X0] : identity = multiply(multiply(identity,X0),multiply(multiply(multiply(identity,X0),multiply(identity,X0)),multiply(multiply(identity,multiply(X0,identity)),identity))),
inference(superposition,[],[f407,f135]) ).
fof(f496,plain,
! [X0] : identity = multiply(multiply(identity,X0),multiply(multiply(multiply(identity,X0),multiply(identity,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f470,f135]) ).
fof(f563,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(multiply(multiply(X1,multiply(multiply(X1,X1),identity)),multiply(identity,identity)),multiply(multiply(multiply(X1,multiply(multiply(X1,X1),identity)),multiply(identity,identity)),multiply(multiply(X1,multiply(multiply(X1,X1),identity)),multiply(identity,identity)))))) = X1,
inference(superposition,[],[f8,f3]) ).
fof(f622,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(multiply(multiply(X1,multiply(multiply(X1,X1),identity)),identity),multiply(multiply(multiply(X1,multiply(multiply(X1,X1),identity)),identity),multiply(multiply(X1,multiply(multiply(X1,X1),identity)),identity))))) = X1,
inference(forward_demodulation,[],[f563,f3]) ).
fof(f635,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(multiply(multiply(X1,X1),multiply(multiply(X1,identity),identity)),multiply(multiply(multiply(X1,X1),multiply(multiply(X1,identity),identity)),multiply(multiply(X1,X1),multiply(multiply(X1,identity),identity)))))) = X1,
inference(forward_demodulation,[],[f622,f347]) ).
fof(f1107,plain,
! [X0,X1] : multiply(identity,multiply(multiply(X0,identity),identity)) = multiply(multiply(identity,multiply(X0,multiply(X1,multiply(X1,X1)))),X1),
inference(superposition,[],[f21,f390]) ).
fof(f2714,plain,
! [X0] : multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0))))) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(identity,X0))),identity)),identity)),
inference(superposition,[],[f305,f263]) ).
fof(f2719,plain,
! [X0] : multiply(identity,multiply(identity,X0)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0))))),
inference(forward_demodulation,[],[f2714,f305]) ).
fof(f2789,plain,
! [X0] : multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,X0)),identity)),identity)),
inference(superposition,[],[f305,f2719]) ).
fof(f2794,plain,
! [X0] : multiply(identity,X0) = multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))),
inference(forward_demodulation,[],[f2789,f305]) ).
fof(f2829,plain,
! [X0] : multiply(identity,multiply(X0,multiply(X0,X0))) = multiply(multiply(identity,X0),multiply(multiply(identity,X0),multiply(identity,X0))),
inference(superposition,[],[f2794,f2794]) ).
fof(f2832,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X1,multiply(X0,multiply(X0,X0))))),multiply(identity,X0))) = X1,
inference(superposition,[],[f6,f2794]) ).
fof(f3076,plain,
! [X0,X1] : multiply(identity,multiply(identity,multiply(X0,X1))) = multiply(identity,multiply(multiply(identity,X0),multiply(identity,X1))),
inference(superposition,[],[f2832,f6]) ).
fof(f3367,plain,
! [X0,X1] : multiply(multiply(identity,X0),multiply(identity,X1)) = multiply(multiply(identity,identity),multiply(multiply(identity,multiply(multiply(identity,multiply(identity,multiply(X0,X1))),identity)),identity)),
inference(superposition,[],[f305,f3076]) ).
fof(f3372,plain,
! [X0,X1] : multiply(identity,multiply(X0,X1)) = multiply(multiply(identity,X0),multiply(identity,X1)),
inference(forward_demodulation,[],[f3367,f305]) ).
fof(f3567,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),X1)) = multiply(X0,multiply(identity,X1)),
inference(superposition,[],[f3372,f54]) ).
fof(f4703,plain,
! [X0,X1] : multiply(identity,multiply(multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),identity),identity)) = multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),
inference(superposition,[],[f1107,f3567]) ).
fof(f4726,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(multiply(identity,multiply(X0,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))))))),multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(superposition,[],[f1107,f3567]) ).
fof(f4747,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(multiply(X0,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))))),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4726,f3372]) ).
fof(f4754,plain,
! [X0,X1] : multiply(identity,multiply(multiply(identity,multiply(multiply(identity,multiply(multiply(X0,identity),identity)),identity)),identity)) = multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),
inference(forward_demodulation,[],[f4703,f135]) ).
fof(f4796,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(multiply(X0,multiply(X0,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,identity),identity)))))),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4747,f3567]) ).
fof(f4803,plain,
! [X0,X1] : multiply(identity,multiply(identity,multiply(multiply(multiply(identity,multiply(multiply(X0,identity),identity)),identity),identity))) = multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),
inference(forward_demodulation,[],[f4754,f30]) ).
fof(f4838,plain,
! [X0] : multiply(identity,multiply(multiply(identity,identity),identity)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4796,f54]) ).
fof(f4841,plain,
! [X0,X1] : multiply(multiply(X0,identity),identity) = multiply(multiply(X0,multiply(identity,multiply(X1,multiply(X1,X1)))),X1),
inference(forward_demodulation,[],[f4803,f61]) ).
fof(f4862,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,identity))) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4838,f30]) ).
fof(f4878,plain,
! [X0] : multiply(identity,multiply(identity,identity)) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4862,f3]) ).
fof(f4888,plain,
! [X0] : multiply(identity,identity) = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4878,f3]) ).
fof(f4896,plain,
! [X0] : identity = multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity)))),
inference(forward_demodulation,[],[f4888,f3]) ).
fof(f5218,plain,
! [X0] : identity = multiply(identity,multiply(multiply(identity,identity),multiply(identity,multiply(multiply(multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),identity),identity)))),
inference(superposition,[],[f496,f4896]) ).
fof(f5246,plain,
! [X0] : identity = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),identity),identity)))),
inference(forward_demodulation,[],[f5218,f3076]) ).
fof(f5276,plain,
! [X0] : identity = multiply(multiply(X0,multiply(X0,X0)),multiply(identity,multiply(multiply(X0,identity),identity))),
inference(forward_demodulation,[],[f5246,f54]) ).
fof(f5419,plain,
! [X0] : multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))) = X0,
inference(forward_demodulation,[],[f121,f347]) ).
fof(f5953,plain,
! [X2,X0,X1] : multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))),multiply(X2,multiply(X2,X2)))) = X1,
inference(forward_demodulation,[],[f236,f2794]) ).
fof(f6535,plain,
! [X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),X0)) = multiply(X1,multiply(multiply(X1,identity),multiply(multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))))),multiply(multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))),multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))))))))))),
inference(superposition,[],[f9,f5419]) ).
fof(f6548,plain,
! [X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),X0)) = multiply(X1,multiply(multiply(X1,identity),multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))))),
inference(forward_demodulation,[],[f6535,f2794]) ).
fof(f6584,plain,
! [X0,X1] : multiply(multiply(X1,X1),multiply(multiply(multiply(X1,X1),multiply(X1,X1)),X0)) = multiply(X1,multiply(multiply(X1,identity),X0)),
inference(forward_demodulation,[],[f6548,f5419]) ).
fof(f7189,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,X1),multiply(multiply(X2,multiply(X2,X2)),multiply(multiply(X2,multiply(X2,X2)),multiply(X2,multiply(X2,X2)))))) = multiply(X0,multiply(multiply(X0,identity),multiply(X1,X2))),
inference(superposition,[],[f9,f6584]) ).
fof(f7247,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))) = multiply(X0,multiply(multiply(X0,identity),multiply(X1,X2))),
inference(forward_demodulation,[],[f7189,f2794]) ).
fof(f9408,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,identity),multiply(X1,X2)) = multiply(multiply(X0,X0),multiply(multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),multiply(identity,X2))),multiply(identity,X3))),multiply(X3,multiply(X3,X3)))),
inference(superposition,[],[f5953,f7247]) ).
fof(f9426,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),multiply(identity,X2)) = multiply(multiply(X0,identity),multiply(X1,X2)),
inference(forward_demodulation,[],[f9408,f5953]) ).
fof(f10031,plain,
! [X0] : identity = multiply(multiply(X0,identity),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity))),
inference(superposition,[],[f9426,f5276]) ).
fof(f11387,plain,
! [X0] : multiply(X0,identity) = multiply(identity,multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))),
inference(superposition,[],[f6,f10031]) ).
fof(f11405,plain,
! [X0] : multiply(X0,identity) = multiply(identity,multiply(multiply(identity,identity),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))),
inference(forward_demodulation,[],[f11387,f3]) ).
fof(f11430,plain,
! [X0] : multiply(X0,identity) = multiply(identity,multiply(identity,multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)),multiply(multiply(X0,X0),multiply(multiply(X0,identity),identity)))))),
inference(forward_demodulation,[],[f11405,f3]) ).
fof(f11452,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f11430,f5419]) ).
fof(f11692,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,multiply(X0,identity)))) = X0,
inference(superposition,[],[f21,f11452]) ).
fof(f11727,plain,
! [X0] : multiply(identity,multiply(identity,multiply(identity,X0))) = X0,
inference(forward_demodulation,[],[f11692,f11452]) ).
fof(f12626,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(multiply(multiply(X1,X1),multiply(X1,identity)),multiply(multiply(multiply(X1,X1),multiply(X1,identity)),multiply(multiply(X1,X1),multiply(X1,identity)))))) = X1,
inference(forward_demodulation,[],[f635,f11452]) ).
fof(f12627,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X0),identity)),multiply(multiply(multiply(X1,X1),X1),multiply(multiply(multiply(X1,X1),X1),multiply(multiply(X1,X1),X1))))) = X1,
inference(forward_demodulation,[],[f12626,f11452]) ).
fof(f12628,plain,
! [X0,X1] : multiply(X0,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(multiply(X1,X1),X1),multiply(multiply(multiply(X1,X1),X1),multiply(multiply(X1,X1),X1))))) = X1,
inference(forward_demodulation,[],[f12627,f11452]) ).
fof(f12964,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = multiply(identity,multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0)))),multiply(multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0)))),multiply(multiply(identity,multiply(identity,identity)),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0))))))),
inference(superposition,[],[f2829,f12628]) ).
fof(f13030,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = multiply(identity,multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0)))),multiply(multiply(multiply(identity,identity),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0)))),multiply(multiply(identity,identity),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0))))))),
inference(forward_demodulation,[],[f12964,f3]) ).
fof(f13082,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = multiply(identity,multiply(multiply(identity,multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0)))),multiply(multiply(identity,multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0)))),multiply(identity,multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0))))))),
inference(forward_demodulation,[],[f13030,f3]) ).
fof(f13119,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0))),multiply(multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0))),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(multiply(X0,X0),X0),multiply(multiply(X0,X0),X0))))))),
inference(forward_demodulation,[],[f13082,f2829]) ).
fof(f13145,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = multiply(identity,multiply(identity,multiply(identity,multiply(multiply(X0,X0),X0)))),
inference(forward_demodulation,[],[f13119,f263]) ).
fof(f13165,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = multiply(multiply(X0,X0),X0),
inference(forward_demodulation,[],[f13145,f11727]) ).
fof(f15289,plain,
! [X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,X1)),multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0)))))) = X0,
inference(superposition,[],[f12628,f13165]) ).
fof(f15476,plain,
! [X0,X1] : multiply(X1,multiply(multiply(X1,multiply(X1,X1)),multiply(identity,X0))) = X0,
inference(forward_demodulation,[],[f15289,f2794]) ).
fof(f15559,plain,
! [X0,X1] : multiply(X1,multiply(multiply(X1,identity),multiply(multiply(X1,X1),X0))) = X0,
inference(forward_demodulation,[],[f15476,f7247]) ).
fof(f15626,plain,
! [X0,X1] : multiply(X1,multiply(X1,multiply(multiply(X1,X1),X0))) = X0,
inference(forward_demodulation,[],[f15559,f11452]) ).
fof(f15817,plain,
! [X0] : multiply(multiply(identity,multiply(X0,multiply(X0,X0))),multiply(multiply(identity,multiply(X0,multiply(X0,X0))),multiply(multiply(multiply(identity,multiply(X0,multiply(X0,X0))),identity),identity))) = X0,
inference(superposition,[],[f15626,f4841]) ).
fof(f16042,plain,
! [X0] : multiply(multiply(identity,multiply(X0,multiply(X0,X0))),multiply(multiply(identity,multiply(X0,multiply(X0,X0))),multiply(multiply(identity,multiply(X0,multiply(X0,X0))),identity))) = X0,
inference(forward_demodulation,[],[f15817,f11452]) ).
fof(f16136,plain,
! [X0] : multiply(multiply(identity,multiply(X0,multiply(X0,X0))),multiply(multiply(identity,multiply(X0,multiply(X0,X0))),multiply(identity,multiply(X0,multiply(X0,X0))))) = X0,
inference(forward_demodulation,[],[f16042,f11452]) ).
fof(f16199,plain,
! [X0] : multiply(identity,multiply(multiply(X0,multiply(X0,X0)),multiply(multiply(X0,multiply(X0,X0)),multiply(X0,multiply(X0,X0))))) = X0,
inference(forward_demodulation,[],[f16136,f2829]) ).
fof(f16235,plain,
! [X0] : multiply(identity,multiply(identity,X0)) = X0,
inference(forward_demodulation,[],[f16199,f2794]) ).
fof(f16429,plain,
! [X0] : multiply(multiply(identity,identity),X0) = X0,
inference(superposition,[],[f15626,f16235]) ).
fof(f16464,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[],[f16429,f3]) ).
fof(f16928,plain,
a != a,
inference(superposition,[],[f5,f16464]) ).
fof(f17124,plain,
$false,
inference(trivial_inequality_removal,[],[f16928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP120-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 09:23:01 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.78/1.70 % (1391647)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.78/1.70 % (1391699)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=2399688333:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 4.78/1.70 % (1391703)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3360826943:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 4.78/1.70 % (1391698)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=4008758785:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 4.78/1.70 % (1391702)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=61045702:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 4.78/1.70 % (1391700)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=761186144:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 4.78/1.70 % (1391704)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1814911859:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 4.78/1.70 % (1391701)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4128126764:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 4.78/1.70 % (1391701)Instruction limit reached!
% 4.78/1.70 % (1391701)------------------------------
% 4.78/1.70 % (1391701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.78/1.70 % (1391701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.78/1.70 % (1391701)CaDiCaL version: 2.1.3
% 4.78/1.70 % (1391701)Termination reason: Instruction limit
% 4.78/1.70 % (1391701)Termination phase: Saturation
% 4.78/1.70 % (1391701)Time elapsed: 0.079 s
% 4.78/1.70 % (1391701)Peak memory usage: 89 MB
% 4.78/1.70 % (1391701)Instructions burned: 136 (million)
% 4.78/1.70 % (1391702)Instruction limit reached!
% 4.78/1.70 % (1391702)------------------------------
% 4.78/1.70 % (1391702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.78/1.70 % (1391702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.78/1.70 % (1391702)CaDiCaL version: 2.1.3
% 4.78/1.70 % (1391702)Termination reason: Instruction limit
% 4.78/1.70 % (1391702)Termination phase: Saturation
% 4.78/1.70 % (1391702)Time elapsed: 0.097 s
% 4.78/1.70 % (1391702)Peak memory usage: 89 MB
% 4.78/1.70 % (1391702)Instructions burned: 182 (million)
% 4.78/1.70 % (1391703)Instruction limit reached!
% 4.78/1.70 % (1391703)------------------------------
% 4.78/1.70 % (1391703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.78/1.70 % (1391703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.78/1.70 % (1391703)CaDiCaL version: 2.1.3
% 4.78/1.70 % (1391703)Termination reason: Instruction limit
% 4.78/1.70 % (1391703)Termination phase: Saturation
% 4.78/1.70 % (1391703)Time elapsed: 0.145 s
% 4.78/1.70 % (1391703)Peak memory usage: 91 MB
% 4.78/1.70 % (1391703)Instructions burned: 257 (million)
% 4.78/1.70 % (1391740)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=246708082:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.78/1.70 % (1391739)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4036499467:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.78/1.70 % (1391741)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2826926992:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 4.78/1.70 % (1391704)First to succeed.
% 4.78/1.70 % (1391704)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1391647"
% 4.78/1.70 % (1391741)Instruction limit reached!
% 4.78/1.70 % (1391741)------------------------------
% 4.78/1.70 % (1391741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.78/1.70 % (1391741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.78/1.70 % (1391741)CaDiCaL version: 2.1.3
% 4.78/1.70 % (1391741)Termination reason: Instruction limit
% 4.78/1.70 % (1391741)Termination phase: Saturation
% 4.78/1.70 % (1391741)Time elapsed: 0.125 s
% 4.78/1.70 % (1391741)Peak memory usage: 89 MB
% 4.78/1.70 % (1391741)Instructions burned: 215 (million)
% 4.78/1.70 % (1391745)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=2857512804:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 4.78/1.70 % (1391704)Refutation found. Thanks to Tanya!
% 4.78/1.70 % SZS status Unsatisfiable for theBenchmark
% 4.78/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/1.90 % (1391704)------------------------------
% 0.23/1.90 % (1391704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.90 % (1391704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.90 % (1391704)CaDiCaL version: 2.1.3
% 0.23/1.90 % (1391704)Termination reason: Refutation
% 0.23/1.90 % (1391704)Time elapsed: 0.364 s
% 0.23/1.90 % (1391704)Peak memory usage: 94 MB
% 0.23/1.90 % (1391704)Instructions burned: 673 (million)
% 0.23/1.90 % (1391704)------------------------------
% 0.23/1.90 % (1391704)------------------------------
% 0.23/1.90 % (1391647)Success in time 0.785 s
% 0.23/1.90 % Vampire exiting
%------------------------------------------------------------------------------