%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG029-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:35:12 PM UTC 2026
% Result : Unsatisfiable 8.72s 3.93s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 82 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 26 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 153 ( 153 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f4,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f5,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_inverse) ).
fof(f7,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_of_inverses) ).
fof(f9,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f10,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_over_add1) ).
fof(f12,axiom,
! [X0,X1] : multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
fof(f13,axiom,
! [X0,X1] : multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_alternative) ).
fof(f19,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f20,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f21,axiom,
! [X2,X0,X1] :
( add(X0,X1) != add(X2,X1)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation_for_addition) ).
fof(f23,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = add(multiply(multiply(X0,X1),X2),additive_inverse(multiply(X0,multiply(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
fof(f25,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X1,X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
fof(f26,axiom,
! [X2,X0,X1] : associator(X0,X1,X2) = additive_inverse(associator(X2,X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
fof(f27,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_middle_law) ).
fof(f28,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(forward_demodulation,[],[f7,f19]) ).
fof(f29,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = add(additive_inverse(multiply(X0,multiply(X1,X2))),multiply(multiply(X0,X1),X2)),
inference(forward_demodulation,[],[f23,f19]) ).
fof(f81,plain,
! [X0] : add(multiply(multiply(cx,cy),multiply(cz,cx)),X0) != add(multiply(cx,multiply(multiply(cy,cz),cx)),X0),
inference(unit_resulting_resolution,[],[f21,f27]) ).
fof(f93,plain,
! [X0,X1] :
( additive_identity != add(X1,additive_inverse(X0))
| X0 = X1 ),
inference(superposition,[],[f21,f28]) ).
fof(f119,plain,
additive_identity != add(multiply(multiply(cx,cy),multiply(cz,cx)),additive_inverse(multiply(cx,multiply(multiply(cy,cz),cx)))),
inference(superposition,[],[f81,f28]) ).
fof(f144,plain,
! [X2,X0,X1] : associator(X0,X1,X2) = associator(X1,X2,X0),
inference(superposition,[],[f25,f26]) ).
fof(f214,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(additive_inverse(X0),X1)),
inference(superposition,[],[f20,f28]) ).
fof(f224,plain,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(X1,add(X2,X0)),
inference(superposition,[],[f19,f20]) ).
fof(f234,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f214,f1]) ).
fof(f468,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),multiply(multiply(multiply(X0,X0),X1),X2)),
inference(superposition,[],[f29,f13]) ).
fof(f471,plain,
! [X2,X0,X1] : associator(multiply(X0,X1),X1,X2) = add(additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))),multiply(multiply(X0,multiply(X1,X1)),X2)),
inference(superposition,[],[f29,f12]) ).
fof(f474,plain,
! [X0,X1] : associator(X0,X0,X1) = add(additive_inverse(multiply(X0,multiply(X0,X1))),multiply(X0,multiply(X0,X1))),
inference(superposition,[],[f29,f13]) ).
fof(f488,plain,
! [X0,X1] : associator(X0,X0,X1) = add(multiply(X0,multiply(X0,X1)),additive_inverse(multiply(X0,multiply(X0,X1)))),
inference(forward_demodulation,[],[f474,f19]) ).
fof(f491,plain,
! [X2,X0,X1] : add(additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))),multiply(multiply(X0,multiply(X1,X1)),X2)) = associator(X1,X2,multiply(X0,X1)),
inference(forward_demodulation,[],[f471,f144]) ).
fof(f494,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),multiply(multiply(X0,multiply(X0,X1)),X2)),
inference(forward_demodulation,[],[f468,f13]) ).
fof(f506,plain,
! [X0,X1] : additive_identity = associator(X0,X0,X1),
inference(forward_demodulation,[],[f488,f28]) ).
fof(f784,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = add(multiply(X1,multiply(X2,X0)),associator(X1,X2,X0)),
inference(superposition,[],[f234,f29]) ).
fof(f786,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[],[f234,f19]) ).
fof(f813,plain,
! [X2,X0,X1] : multiply(multiply(X1,X2),X0) = add(associator(X1,X2,X0),multiply(X1,multiply(X2,X0))),
inference(forward_demodulation,[],[f784,f19]) ).
fof(f845,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))),add(associator(X0,multiply(X1,X1),X2),multiply(X0,multiply(multiply(X1,X1),X2)))),
inference(backward_demodulation,[],[f491,f813]) ).
fof(f849,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(associator(X0,multiply(X0,X1),X2),multiply(X0,multiply(multiply(X0,X1),X2)))),
inference(backward_demodulation,[],[f494,f813]) ).
fof(f854,plain,
additive_identity != add(add(associator(cx,cy,multiply(cz,cx)),multiply(cx,multiply(cy,multiply(cz,cx)))),additive_inverse(multiply(cx,multiply(multiply(cy,cz),cx)))),
inference(backward_demodulation,[],[f119,f813]) ).
fof(f929,plain,
additive_identity != add(associator(cx,cy,multiply(cz,cx)),add(multiply(cx,multiply(cy,multiply(cz,cx))),additive_inverse(multiply(cx,multiply(multiply(cy,cz),cx))))),
inference(forward_demodulation,[],[f854,f20]) ).
fof(f934,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(associator(X0,multiply(X0,X1),X2),multiply(X0,add(associator(X0,X1,X2),multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f849,f813]) ).
fof(f938,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))),add(associator(X0,multiply(X1,X1),X2),multiply(X0,add(associator(X1,X1,X2),multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f845,f813]) ).
fof(f999,plain,
additive_identity != add(associator(cx,cy,multiply(cz,cx)),add(multiply(cx,multiply(cy,multiply(cz,cx))),additive_inverse(multiply(cx,add(associator(cy,cz,cx),multiply(cy,multiply(cz,cx))))))),
inference(forward_demodulation,[],[f929,f813]) ).
fof(f1004,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))),add(associator(X0,multiply(X0,X1),X2),add(multiply(X0,associator(X0,X1,X2)),multiply(X0,multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f934,f10]) ).
fof(f1008,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(add(associator(X0,multiply(X1,X1),X2),multiply(X0,add(associator(X1,X1,X2),multiply(X1,multiply(X1,X2))))),additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2)))),
inference(forward_demodulation,[],[f938,f19]) ).
fof(f1065,plain,
additive_identity != add(associator(cx,cy,multiply(cz,cx)),add(multiply(cx,multiply(cy,multiply(cz,cx))),additive_inverse(add(multiply(cx,associator(cy,cz,cx)),multiply(cx,multiply(cy,multiply(cz,cx))))))),
inference(forward_demodulation,[],[f999,f10]) ).
fof(f1070,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(add(associator(X0,multiply(X0,X1),X2),add(multiply(X0,associator(X0,X1,X2)),multiply(X0,multiply(X0,multiply(X1,X2))))),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2))))),
inference(forward_demodulation,[],[f1004,f19]) ).
fof(f1074,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,add(associator(X1,X1,X2),multiply(X1,multiply(X1,X2)))),additive_inverse(multiply(multiply(X0,X1),multiply(X1,X2))))),
inference(forward_demodulation,[],[f1008,f20]) ).
fof(f1119,plain,
additive_identity != add(associator(cx,cy,multiply(cz,cx)),add(multiply(cx,multiply(cy,multiply(cz,cx))),add(additive_inverse(multiply(cx,associator(cy,cz,cx))),additive_inverse(multiply(cx,multiply(cy,multiply(cz,cx))))))),
inference(forward_demodulation,[],[f1065,f8]) ).
fof(f1122,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(associator(X0,multiply(X0,X1),X2),add(add(multiply(X0,associator(X0,X1,X2)),multiply(X0,multiply(X0,multiply(X1,X2)))),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1070,f20]) ).
fof(f1126,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,add(associator(X1,X1,X2),multiply(X1,multiply(X1,X2)))),additive_inverse(add(associator(X0,X1,multiply(X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2))))))),
inference(forward_demodulation,[],[f1074,f813]) ).
fof(f1157,plain,
additive_identity != add(associator(cx,cy,multiply(cz,cx)),additive_inverse(multiply(cx,associator(cy,cz,cx)))),
inference(forward_demodulation,[],[f1119,f786]) ).
fof(f1160,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(associator(X0,multiply(X0,X1),X2),add(multiply(X0,associator(X0,X1,X2)),add(multiply(X0,multiply(X0,multiply(X1,X2))),additive_inverse(multiply(X0,multiply(X0,multiply(X1,X2))))))),
inference(forward_demodulation,[],[f1122,f20]) ).
fof(f1164,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(additive_inverse(add(associator(X0,X1,multiply(X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2))))),add(associator(X0,multiply(X1,X1),X2),multiply(X0,add(associator(X1,X1,X2),multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1126,f224]) ).
fof(f1180,plain,
additive_identity != add(additive_inverse(multiply(cx,associator(cy,cz,cx))),associator(cx,cy,multiply(cz,cx))),
inference(forward_demodulation,[],[f1157,f19]) ).
fof(f1181,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(associator(X0,multiply(X0,X1),X2),add(multiply(X0,associator(X0,X1,X2)),additive_identity)),
inference(forward_demodulation,[],[f1160,f28]) ).
fof(f1185,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(additive_inverse(add(associator(X0,X1,multiply(X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2))))),add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1164,f10]) ).
fof(f1195,plain,
additive_identity != add(additive_inverse(multiply(cx,associator(cx,cy,cz))),associator(cx,cy,multiply(cz,cx))),
inference(forward_demodulation,[],[f1180,f144]) ).
fof(f1196,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(additive_identity,add(associator(X0,multiply(X0,X1),X2),multiply(X0,associator(X0,X1,X2)))),
inference(forward_demodulation,[],[f1181,f224]) ).
fof(f1200,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2))))),additive_inverse(add(associator(X0,X1,multiply(X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1185,f19]) ).
fof(f1207,plain,
! [X2,X0,X1] : associator(multiply(X0,X0),X1,X2) = add(associator(X0,multiply(X0,X1),X2),multiply(X0,associator(X0,X1,X2))),
inference(forward_demodulation,[],[f1196,f1]) ).
fof(f1211,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(add(multiply(X0,associator(X1,X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2)))),additive_inverse(add(associator(X0,X1,multiply(X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2))))))),
inference(forward_demodulation,[],[f1200,f20]) ).
fof(f1220,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),add(multiply(X0,multiply(X1,multiply(X1,X2))),additive_inverse(add(associator(X0,X1,multiply(X1,X2)),multiply(X0,multiply(X1,multiply(X1,X2)))))))),
inference(forward_demodulation,[],[f1211,f20]) ).
fof(f1228,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),add(multiply(X0,multiply(X1,multiply(X1,X2))),add(additive_inverse(associator(X0,X1,multiply(X1,X2))),additive_inverse(multiply(X0,multiply(X1,multiply(X1,X2)))))))),
inference(forward_demodulation,[],[f1220,f8]) ).
fof(f1233,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),additive_inverse(associator(X0,X1,multiply(X1,X2))))),
inference(forward_demodulation,[],[f1228,f786]) ).
fof(f1237,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),associator(multiply(X1,X2),X1,X0))),
inference(forward_demodulation,[],[f1233,f26]) ).
fof(f1241,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,associator(X1,X1,X2)),associator(X1,X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f1237,f144]) ).
fof(f1245,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(multiply(X0,additive_identity),associator(X1,X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f1241,f506]) ).
fof(f1248,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),add(additive_identity,associator(X1,X0,multiply(X1,X2)))),
inference(forward_demodulation,[],[f1245,f5]) ).
fof(f1251,plain,
! [X2,X0,X1] : associator(X1,X2,multiply(X0,X1)) = add(associator(X0,multiply(X1,X1),X2),associator(X1,X0,multiply(X1,X2))),
inference(forward_demodulation,[],[f1248,f1]) ).
fof(f1291,plain,
additive_identity != add(additive_inverse(multiply(cx,associator(cx,cy,cz))),add(associator(cz,multiply(cx,cx),cy),associator(cx,cz,multiply(cx,cy)))),
inference(backward_demodulation,[],[f1195,f1251]) ).
fof(f1294,plain,
additive_identity != add(add(associator(cz,multiply(cx,cx),cy),associator(cx,cz,multiply(cx,cy))),additive_inverse(multiply(cx,associator(cx,cy,cz)))),
inference(forward_demodulation,[],[f1291,f19]) ).
fof(f1334,plain,
additive_identity != add(associator(cz,multiply(cx,cx),cy),add(associator(cx,cz,multiply(cx,cy)),additive_inverse(multiply(cx,associator(cx,cy,cz))))),
inference(forward_demodulation,[],[f1294,f20]) ).
fof(f1372,plain,
additive_identity != add(associator(multiply(cx,cx),cy,cz),add(associator(cx,cz,multiply(cx,cy)),additive_inverse(multiply(cx,associator(cx,cy,cz))))),
inference(forward_demodulation,[],[f1334,f144]) ).
fof(f1479,plain,
additive_identity != add(additive_identity,additive_inverse(add(associator(multiply(cx,cx),cy,cz),add(associator(cx,cz,multiply(cx,cy)),additive_inverse(multiply(cx,associator(cx,cy,cz))))))),
inference(unit_resulting_resolution,[],[f93,f1372]) ).
fof(f1500,plain,
additive_identity != additive_inverse(add(associator(multiply(cx,cx),cy,cz),add(associator(cx,cz,multiply(cx,cy)),additive_inverse(multiply(cx,associator(cx,cy,cz)))))),
inference(forward_demodulation,[],[f1479,f1]) ).
fof(f1511,plain,
additive_identity != add(additive_inverse(associator(multiply(cx,cx),cy,cz)),additive_inverse(add(associator(cx,cz,multiply(cx,cy)),additive_inverse(multiply(cx,associator(cx,cy,cz)))))),
inference(forward_demodulation,[],[f1500,f8]) ).
fof(f1522,plain,
additive_identity != add(additive_inverse(associator(multiply(cx,cx),cy,cz)),add(additive_inverse(associator(cx,cz,multiply(cx,cy))),additive_inverse(additive_inverse(multiply(cx,associator(cx,cy,cz)))))),
inference(forward_demodulation,[],[f1511,f8]) ).
fof(f1532,plain,
additive_identity != add(additive_inverse(associator(multiply(cx,cx),cy,cz)),add(additive_inverse(associator(cx,cz,multiply(cx,cy))),multiply(cx,associator(cx,cy,cz)))),
inference(forward_demodulation,[],[f1522,f9]) ).
fof(f1540,plain,
additive_identity != add(additive_inverse(associator(multiply(cx,cx),cy,cz)),add(associator(multiply(cx,cy),cz,cx),multiply(cx,associator(cx,cy,cz)))),
inference(forward_demodulation,[],[f1532,f26]) ).
fof(f1546,plain,
additive_identity != add(additive_inverse(associator(multiply(cx,cx),cy,cz)),add(associator(cx,multiply(cx,cy),cz),multiply(cx,associator(cx,cy,cz)))),
inference(forward_demodulation,[],[f1540,f144]) ).
fof(f1552,plain,
additive_identity != add(additive_inverse(associator(multiply(cx,cx),cy,cz)),associator(multiply(cx,cx),cy,cz)),
inference(forward_demodulation,[],[f1546,f1207]) ).
fof(f1558,plain,
additive_identity != add(associator(multiply(cx,cx),cy,cz),additive_inverse(associator(multiply(cx,cx),cy,cz))),
inference(forward_demodulation,[],[f1552,f19]) ).
fof(f1562,plain,
$false,
inference(forward_subsumption_resolution,[],[f1558,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG029-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 23:03:36 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 8.72/3.93 % (3992813)Input is clausal, will run a generic CNF schedule.
% 8.72/3.93 % (3992820)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2028065378:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.72/3.93 % (3992818)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=864302734:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.72/3.93 % (3992819)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2627854214:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.72/3.93 % (3992823)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2518403762:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.72/3.93 % (3992821)lrs+10_1_sil=8000:sp=occurrence:random_seed=811394271:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.72/3.93 % (3992824)dis-21_1_sil=8000:lcm=predicate:random_seed=3999854767:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 8.72/3.93 % (3992822)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2479490067:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.72/3.93 % (3992824)Refutation not found, incomplete strategy
% 8.72/3.93 % (3992824)------------------------------
% 8.72/3.93 % (3992824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992824)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992824)Termination reason: Refutation not found, incomplete strategy
% 8.72/3.93 % (3992824)Time elapsed: 0.003 s
% 8.72/3.93 % (3992824)Peak memory usage: 88 MB
% 8.72/3.93 % (3992824)Instructions burned: 1 (million)
% 8.72/3.93 % (3992821)Instruction limit reached!
% 8.72/3.93 % (3992821)------------------------------
% 8.72/3.93 % (3992821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992821)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992821)Termination reason: Instruction limit
% 8.72/3.93 % (3992821)Termination phase: Saturation
% 8.72/3.93 % (3992821)Time elapsed: 0.096 s
% 8.72/3.93 % (3992821)Peak memory usage: 88 MB
% 8.72/3.93 % (3992821)Instructions burned: 107 (million)
% 8.72/3.93 % (3992822)Instruction limit reached!
% 8.72/3.93 % (3992822)------------------------------
% 8.72/3.93 % (3992822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992822)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992822)Termination reason: Instruction limit
% 8.72/3.93 % (3992822)Termination phase: Saturation
% 8.72/3.93 % (3992822)Time elapsed: 0.112 s
% 8.72/3.93 % (3992822)Peak memory usage: 88 MB
% 8.72/3.93 % (3992822)Instructions burned: 114 (million)
% 8.72/3.93 % (3992823)Instruction limit reached!
% 8.72/3.93 % (3992823)------------------------------
% 8.72/3.93 % (3992823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992823)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992823)Termination reason: Instruction limit
% 8.72/3.93 % (3992823)Termination phase: Saturation
% 8.72/3.93 % (3992823)Time elapsed: 0.172 s
% 8.72/3.93 % (3992823)Peak memory usage: 89 MB
% 8.72/3.93 % (3992823)Instructions burned: 180 (million)
% 8.72/3.93 % (3992832)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1858978415:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 8.72/3.93 % (3992832)Refutation not found, incomplete strategy
% 8.72/3.93 % (3992832)------------------------------
% 8.72/3.93 % (3992832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992832)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992832)Termination reason: Refutation not found, incomplete strategy
% 8.72/3.93 % (3992832)Time elapsed: 0.003 s
% 8.72/3.93 % (3992832)Peak memory usage: 88 MB
% 8.72/3.93 % (3992832)Instructions burned: 1 (million)
% 8.72/3.93 % (3992824)------------------------------
% 8.72/3.93 % (3992824)------------------------------
% 8.72/3.93 % (3992833)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=397928532:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 8.72/3.93 % (3992834)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=930968095:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 8.72/3.93 % (3992834)Refutation not found, incomplete strategy
% 8.72/3.93 % (3992834)------------------------------
% 8.72/3.93 % (3992834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992834)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992834)Termination reason: Refutation not found, incomplete strategy
% 8.72/3.93 % (3992834)Time elapsed: 0.002 s
% 8.72/3.93 % (3992834)Peak memory usage: 87 MB
% 8.72/3.93 % (3992834)Instructions burned: 1 (million)
% 8.72/3.93 % (3992833)Instruction limit reached!
% 8.72/3.93 % (3992833)------------------------------
% 8.72/3.93 % (3992833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992833)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992833)Termination reason: Instruction limit
% 8.72/3.93 % (3992833)Termination phase: Saturation
% 8.72/3.93 % (3992833)Time elapsed: 0.188 s
% 8.72/3.93 % (3992833)Peak memory usage: 89 MB
% 8.72/3.93 % (3992833)Instructions burned: 189 (million)
% 8.72/3.93 % (3992837)lrs+10_64_to=lpo:sil=8000:random_seed=2115414161:i=126:bd=preordered_2992 on theBenchmark for (2992ds/126Mi)
% 8.72/3.93 % (3992832)------------------------------
% 8.72/3.93 % (3992832)------------------------------
% 8.72/3.93 % (3992837)Instruction limit reached!
% 8.72/3.93 % (3992837)------------------------------
% 8.72/3.93 % (3992837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992837)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992837)Termination reason: Instruction limit
% 8.72/3.93 % (3992837)Termination phase: Saturation
% 8.72/3.93 % (3992837)Time elapsed: 0.127 s
% 8.72/3.93 % (3992837)Peak memory usage: 88 MB
% 8.72/3.93 % (3992837)Instructions burned: 126 (million)
% 8.72/3.93 % (3992839)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3713340979:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 8.72/3.93 % (3992834)------------------------------
% 8.72/3.93 % (3992834)------------------------------
% 8.72/3.93 % (3992839)Instruction limit reached!
% 8.72/3.93 % (3992839)------------------------------
% 8.72/3.93 % (3992839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992839)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992839)Termination reason: Instruction limit
% 8.72/3.93 % (3992839)Termination phase: Saturation
% 8.72/3.93 % (3992839)Time elapsed: 0.102 s
% 8.72/3.93 % (3992839)Peak memory usage: 89 MB
% 8.72/3.93 % (3992839)Instructions burned: 196 (million)
% 8.72/3.93 % (3992841)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4108608937:i=157:gtg=all_2989 on theBenchmark for (2989ds/157Mi)
% 8.72/3.93 % (3992843)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1310707353:i=3394:sd=4:ss=included:sgt=64_2988 on theBenchmark for (2988ds/3394Mi)
% 8.72/3.93 % (3992844)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=1248631993:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2988 on theBenchmark for (2988ds/106Mi)
% 8.72/3.93 % (3992845)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2972037050:i=107_2987 on theBenchmark for (2987ds/107Mi)
% 8.72/3.93 % (3992845)Refutation not found, incomplete strategy
% 8.72/3.93 % (3992845)------------------------------
% 8.72/3.93 % (3992845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992845)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992845)Termination reason: Refutation not found, incomplete strategy
% 8.72/3.93 % (3992845)Time elapsed: 0.001 s
% 8.72/3.93 % (3992845)Peak memory usage: 88 MB
% 8.72/3.93 % (3992845)Instructions burned: 1 (million)
% 8.72/3.93 % (3992841)Instruction limit reached!
% 8.72/3.93 % (3992841)------------------------------
% 8.72/3.93 % (3992841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992841)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992841)Termination reason: Instruction limit
% 8.72/3.93 % (3992841)Termination phase: Saturation
% 8.72/3.93 % (3992841)Time elapsed: 0.162 s
% 8.72/3.93 % (3992841)Peak memory usage: 90 MB
% 8.72/3.93 % (3992841)Instructions burned: 158 (million)
% 8.72/3.93 % (3992844)Instruction limit reached!
% 8.72/3.93 % (3992844)------------------------------
% 8.72/3.93 % (3992844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992844)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992844)Termination reason: Instruction limit
% 8.72/3.93 % (3992844)Termination phase: Saturation
% 8.72/3.93 % (3992844)Time elapsed: 0.102 s
% 8.72/3.93 % (3992844)Peak memory usage: 88 MB
% 8.72/3.93 % (3992844)Instructions burned: 106 (million)
% 8.72/3.93 % (3992845)------------------------------
% 8.72/3.93 % (3992845)------------------------------
% 8.72/3.93 % (3992851)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=2327863110:cond=fast:i=5208:av=off_2984 on theBenchmark for (2984ds/5208Mi)
% 8.72/3.93 % (3992850)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3941926394:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2984 on theBenchmark for (2984ds/242Mi)
% 8.72/3.93 % (3992852)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=835592343:i=134:sd=2:doe=on:ss=axioms:sgt=14_2982 on theBenchmark for (2982ds/134Mi)
% 8.72/3.93 % (3992852)Instruction limit reached!
% 8.72/3.93 % (3992852)------------------------------
% 8.72/3.93 % (3992852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992852)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992852)Termination reason: Instruction limit
% 8.72/3.93 % (3992852)Termination phase: Saturation
% 8.72/3.93 % (3992852)Time elapsed: 0.067 s
% 8.72/3.93 % (3992852)Peak memory usage: 88 MB
% 8.72/3.93 % (3992852)Instructions burned: 135 (million)
% 8.72/3.93 % (3992850)Instruction limit reached!
% 8.72/3.93 % (3992850)------------------------------
% 8.72/3.93 % (3992850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992850)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992850)Termination reason: Instruction limit
% 8.72/3.93 % (3992850)Termination phase: Saturation
% 8.72/3.93 % (3992850)Time elapsed: 0.230 s
% 8.72/3.93 % (3992850)Peak memory usage: 90 MB
% 8.72/3.93 % (3992850)Instructions burned: 243 (million)
% 8.72/3.93 % (3992856)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2582595542:i=499:bd=all_2979 on theBenchmark for (2979ds/499Mi)
% 8.72/3.93 % (3992857)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=918369307:i=191:fgj=on:bd=all_2979 on theBenchmark for (2979ds/191Mi)
% 8.72/3.93 % (3992856)First to succeed.
% 8.72/3.93 % (3992856)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3992813"
% 8.72/3.93 % (3992857)Instruction limit reached!
% 8.72/3.93 % (3992857)------------------------------
% 8.72/3.93 % (3992857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.72/3.93 % (3992857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.72/3.93 % (3992857)CaDiCaL version: 2.1.3
% 8.72/3.93 % (3992857)Termination reason: Instruction limit
% 8.72/3.93 % (3992857)Termination phase: Saturation
% 8.72/3.93 % (3992857)Time elapsed: 0.105 s
% 8.72/3.93 % (3992857)Peak memory usage: 89 MB
% 8.72/3.93 % (3992857)Instructions burned: 191 (million)
% 8.72/3.93 % (3992856)Refutation found. Thanks to Tanya!
% 8.72/3.93 % SZS status Unsatisfiable for theBenchmark
% 8.72/3.93 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/4.31 % (3992856)------------------------------
% 0.17/4.31 % (3992856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/4.31 % (3992856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/4.31 % (3992856)CaDiCaL version: 2.1.3
% 0.17/4.31 % (3992856)Termination reason: Refutation
% 0.17/4.31 % (3992856)Time elapsed: 0.110 s
% 0.17/4.31 % (3992856)Peak memory usage: 89 MB
% 0.17/4.31 % (3992856)Instructions burned: 109 (million)
% 0.17/4.31 % (3992856)------------------------------
% 0.17/4.31 % (3992856)------------------------------
% 0.17/4.31 % (3992813)Success in time 2.859 s
% 0.17/4.31 % Vampire exiting
%------------------------------------------------------------------------------