%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP667-5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 10:15:32 AM UTC 2026
% Result : Unsatisfiable 31.67s 5.46s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 125 ( 125 unt; 1 def)
% Number of atoms : 125 ( 121 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 271 ( 271 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
fof(f6,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
fof(f7,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),mult(mult(X2,X1),X2)) = mult(mult(X0,mult(mult(X1,X2),X1)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
fof(f8,axiom,
! [X0,X1] : mult(mult(X0,X1),X0) = mult(X0,mult(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
fof(f9,axiom,
! [X0] : mult(f(X0),f(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
fof(f10,negated_conjecture,
mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f11,definition,
~ sP0(mult(mult(a,b),mult(c,a))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f12,plain,
sP0(mult(a,mult(mult(b,c),a))),
inference(inequality_splitting,[],[f10,f11]) ).
fof(f13,plain,
! [X2,X0,X1] : mult(mult(X0,mult(mult(X1,X2),X1)),X2) = mult(mult(X0,X1),mult(X2,mult(X1,X2))),
inference(backward_demodulation,[],[f7,f8]) ).
fof(f14,plain,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X2,mult(X1,X2))) = mult(mult(X0,mult(X1,mult(X2,X1))),X2),
inference(forward_demodulation,[],[f13,f8]) ).
fof(f21,plain,
! [X0,X1] : mult(X0,mult(mult(X1,mult(X0,X1)),X0)) = mult(mult(X0,X1),mult(X0,mult(X1,X0))),
inference(superposition,[],[f8,f14]) ).
fof(f25,plain,
! [X0,X1] : mult(mult(X1,unit),mult(X0,mult(unit,X0))) = mult(mult(X1,mult(X0,unit)),X0),
inference(superposition,[],[f14,f6]) ).
fof(f26,plain,
! [X0,X1] : mult(mult(X0,mult(X1,X0)),X1) = mult(mult(unit,X0),mult(X1,mult(X0,X1))),
inference(superposition,[],[f14,f6]) ).
fof(f27,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X0,X1))) = mult(mult(X0,mult(X1,X0)),X1),
inference(forward_demodulation,[],[f26,f6]) ).
fof(f28,plain,
! [X0,X1] : mult(mult(X1,unit),mult(X0,mult(unit,X0))) = mult(mult(X1,X0),X0),
inference(forward_demodulation,[],[f25,f5]) ).
fof(f30,plain,
! [X0,X1] : mult(mult(X0,X1),mult(X0,mult(X1,X0))) = mult(X0,mult(X1,mult(X0,mult(X1,X0)))),
inference(backward_demodulation,[],[f21,f27]) ).
fof(f31,plain,
! [X0,X1] : mult(mult(X1,X0),X0) = mult(mult(X1,unit),mult(X0,X0)),
inference(forward_demodulation,[],[f28,f6]) ).
fof(f33,plain,
! [X0,X1] : mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
inference(forward_demodulation,[],[f31,f5]) ).
fof(f36,plain,
! [X2,X0,X1] : mult(mult(X1,ld(X2,X0)),mult(X2,mult(ld(X2,X0),X2))) = mult(mult(X1,mult(ld(X2,X0),X0)),X2),
inference(superposition,[],[f14,f1]) ).
fof(f37,plain,
! [X0,X1] : mult(X0,X1) = mult(X1,mult(ld(X1,X0),X1)),
inference(superposition,[],[f8,f1]) ).
fof(f38,plain,
! [X0] : ld(unit,X0) = X0,
inference(superposition,[],[f6,f1]) ).
fof(f39,plain,
! [X2,X0,X1] : mult(mult(X1,mult(ld(X2,X0),X0)),X2) = mult(mult(X1,ld(X2,X0)),mult(X0,X2)),
inference(forward_demodulation,[],[f36,f37]) ).
fof(f44,plain,
! [X0,X1] : mult(X1,mult(ld(X1,X0),mult(X1,mult(ld(X1,X0),X1)))) = mult(X0,mult(X1,mult(ld(X1,X0),X1))),
inference(superposition,[],[f30,f1]) ).
fof(f64,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(X1,mult(ld(X1,X0),mult(X0,X1))),
inference(forward_demodulation,[],[f44,f37]) ).
fof(f70,plain,
! [X2,X0,X1] : mult(mult(X2,X1),mult(ld(X1,X0),mult(X1,ld(X1,X0)))) = mult(mult(X2,mult(X0,X1)),ld(X1,X0)),
inference(superposition,[],[f14,f37]) ).
fof(f81,plain,
! [X2,X0,X1] : mult(mult(X2,mult(X0,X1)),ld(X1,X0)) = mult(mult(X2,X1),mult(ld(X1,X0),X0)),
inference(forward_demodulation,[],[f70,f1]) ).
fof(f99,plain,
! [X0,X1] : mult(mult(unit,ld(X0,X1)),mult(X1,X0)) = mult(mult(ld(X0,X1),X1),X0),
inference(superposition,[],[f39,f6]) ).
fof(f112,plain,
! [X0,X1] : mult(ld(X0,X1),mult(X1,X0)) = mult(mult(ld(X0,X1),X1),X0),
inference(forward_demodulation,[],[f99,f6]) ).
fof(f148,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[],[f2,f3]) ).
fof(f151,plain,
! [X2,X0,X1] : mult(mult(X1,X2),mult(rd(X0,X2),mult(X2,rd(X0,X2)))) = mult(mult(X1,mult(X2,X0)),rd(X0,X2)),
inference(superposition,[],[f14,f3]) ).
fof(f152,plain,
! [X0,X1] : mult(rd(X0,X1),mult(X1,rd(X0,X1))) = mult(X0,rd(X0,X1)),
inference(superposition,[],[f8,f3]) ).
fof(f153,plain,
! [X2,X0,X1] : mult(X0,X2) = mult(mult(rd(X0,mult(X1,mult(X2,X1))),X1),mult(X2,mult(X1,X2))),
inference(superposition,[],[f14,f3]) ).
fof(f156,plain,
! [X2,X0,X1] : mult(mult(X1,mult(X2,X0)),rd(X0,X2)) = mult(mult(X1,X2),mult(X0,rd(X0,X2))),
inference(forward_demodulation,[],[f151,f152]) ).
fof(f186,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(mult(rd(X0,mult(X2,mult(X1,X2))),X2),mult(X0,X1)),
inference(superposition,[],[f2,f153]) ).
fof(f288,plain,
! [X0,X1] : mult(X0,X1) = rd(mult(X0,mult(X1,X0)),X0),
inference(superposition,[],[f4,f8]) ).
fof(f290,plain,
! [X2,X0,X1] : mult(X0,mult(X1,mult(X2,X1))) = rd(mult(mult(X0,X1),mult(X2,mult(X1,X2))),X2),
inference(superposition,[],[f4,f14]) ).
fof(f292,plain,
! [X2,X0,X1] : mult(X0,mult(X1,X2)) = rd(mult(mult(X0,X1),mult(X2,rd(X2,X1))),rd(X2,X1)),
inference(superposition,[],[f4,f156]) ).
fof(f293,plain,
! [X2,X0,X1] : mult(rd(X0,mult(X2,mult(X1,X2))),X2) = rd(mult(X0,X1),mult(X1,mult(X2,X1))),
inference(superposition,[],[f4,f153]) ).
fof(f312,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,mult(X2,X1))) = rd(mult(X0,mult(X2,mult(X1,X2))),X2),
inference(superposition,[],[f290,f3]) ).
fof(f313,plain,
! [X0,X1] : mult(unit,mult(X0,mult(X1,X0))) = rd(mult(X0,mult(X1,mult(X0,X1))),X1),
inference(superposition,[],[f290,f6]) ).
fof(f349,plain,
! [X0,X1] : mult(X0,mult(X1,X0)) = rd(mult(X0,mult(X1,mult(X0,X1))),X1),
inference(forward_demodulation,[],[f313,f6]) ).
fof(f399,plain,
! [X2,X0,X1] : rd(X0,X1) = mult(rd(rd(X0,mult(X1,mult(X2,X1))),X2),mult(X2,mult(X1,X2))),
inference(superposition,[],[f312,f3]) ).
fof(f400,plain,
! [X0,X1] : rd(mult(X0,mult(X1,X0)),X0) = mult(rd(unit,X1),mult(X1,mult(X0,X1))),
inference(superposition,[],[f312,f6]) ).
fof(f422,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(unit,X1),mult(X1,mult(X0,X1))),
inference(forward_demodulation,[],[f400,f288]) ).
fof(f472,plain,
! [X0,X1] : mult(X1,mult(ld(X1,X0),mult(X1,ld(X1,X0)))) = mult(mult(X0,X1),ld(X1,X0)),
inference(superposition,[],[f27,f37]) ).
fof(f504,plain,
! [X0,X1] : mult(X1,mult(ld(X1,X0),X0)) = mult(mult(X0,X1),ld(X1,X0)),
inference(forward_demodulation,[],[f472,f1]) ).
fof(f534,plain,
! [X0,X1] : mult(rd(X0,X1),mult(X1,rd(X0,X1))) = rd(mult(rd(X0,X1),mult(X1,X0)),X1),
inference(superposition,[],[f349,f3]) ).
fof(f557,plain,
! [X0,X1] : mult(X0,rd(X0,X1)) = rd(mult(rd(X0,X1),mult(X1,X0)),X1),
inference(forward_demodulation,[],[f534,f152]) ).
fof(f738,plain,
! [X0,X1] : mult(rd(unit,X1),mult(X1,X0)) = X0,
inference(superposition,[],[f422,f3]) ).
fof(f815,plain,
! [X0,X1] : ld(X1,X0) = mult(rd(unit,X1),X0),
inference(superposition,[],[f738,f1]) ).
fof(f851,plain,
! [X0,X1] : mult(X0,rd(unit,X1)) = mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))),
inference(superposition,[],[f8,f738]) ).
fof(f864,plain,
! [X0,X1] : mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))) = rd(mult(rd(unit,X1),mult(mult(X1,X0),X0)),mult(X1,X0)),
inference(superposition,[],[f349,f738]) ).
fof(f866,plain,
! [X0,X1] : mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))) = rd(mult(rd(unit,X1),mult(X1,mult(X0,X0))),mult(X1,X0)),
inference(forward_demodulation,[],[f864,f33]) ).
fof(f898,plain,
! [X0,X1] : mult(X0,rd(unit,X1)) = ld(X1,mult(mult(X1,X0),rd(unit,X1))),
inference(backward_demodulation,[],[f851,f815]) ).
fof(f912,plain,
! [X0,X1] : mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))) = rd(ld(X1,mult(X1,mult(X0,X0))),mult(X1,X0)),
inference(forward_demodulation,[],[f866,f815]) ).
fof(f933,plain,
! [X0,X1] : mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))) = rd(mult(X0,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f912,f2]) ).
fof(f944,plain,
! [X0,X1] : ld(X1,mult(mult(X1,X0),rd(unit,X1))) = rd(mult(X0,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f933,f815]) ).
fof(f946,plain,
! [X0,X1] : mult(X0,rd(unit,X1)) = rd(mult(X0,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f944,f898]) ).
fof(f957,plain,
! [X0,X1] : rd(unit,X0) = rd(ld(X0,X1),X1),
inference(superposition,[],[f4,f815]) ).
fof(f991,plain,
! [X0] : ld(X0,unit) = rd(unit,X0),
inference(superposition,[],[f5,f815]) ).
fof(f995,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(X1,unit),X0),
inference(backward_demodulation,[],[f815,f991]) ).
fof(f1010,plain,
! [X0,X1] : rd(mult(X0,X0),mult(X1,X0)) = mult(X0,ld(X1,unit)),
inference(backward_demodulation,[],[f946,f991]) ).
fof(f1044,plain,
! [X0,X1] : ld(X0,unit) = rd(ld(X0,X1),X1),
inference(forward_demodulation,[],[f957,f991]) ).
fof(f1374,plain,
! [X0,X1] : mult(rd(X1,mult(unit,mult(X0,unit))),unit) = rd(mult(X1,X0),mult(X0,X0)),
inference(superposition,[],[f293,f6]) ).
fof(f1414,plain,
! [X0,X1] : rd(X1,mult(unit,mult(X0,unit))) = rd(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f1374,f5]) ).
fof(f1441,plain,
! [X0,X1] : rd(X1,mult(X0,unit)) = rd(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f1414,f6]) ).
fof(f1456,plain,
! [X0,X1] : rd(X1,X0) = rd(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f1441,f5]) ).
fof(f1706,plain,
! [X0,X1] : mult(ld(X0,X1),X1) = mult(ld(X0,unit),mult(X1,X1)),
inference(superposition,[],[f33,f995]) ).
fof(f1763,plain,
! [X0,X1] : mult(ld(X0,X1),X1) = ld(X0,mult(X1,X1)),
inference(forward_demodulation,[],[f1706,f995]) ).
fof(f1776,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(X1,f(X0)),f(X0)),
inference(superposition,[],[f1763,f9]) ).
fof(f1781,plain,
! [X0,X1] : mult(X0,mult(mult(ld(X0,X1),X1),X0)) = mult(mult(X1,X1),X0),
inference(superposition,[],[f37,f1763]) ).
fof(f1782,plain,
! [X0,X1] : mult(X1,X1) = mult(X0,mult(ld(X0,X1),X1)),
inference(superposition,[],[f1,f1763]) ).
fof(f1783,plain,
! [X0,X1] : mult(X0,X0) = mult(mult(X0,X1),ld(X1,X0)),
inference(backward_demodulation,[],[f504,f1782]) ).
fof(f1786,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),mult(X1,X0))) = mult(mult(X1,X1),X0),
inference(forward_demodulation,[],[f1781,f112]) ).
fof(f1793,plain,
! [X0,X1] : mult(X1,mult(X1,X0)) = mult(mult(X1,X1),X0),
inference(forward_demodulation,[],[f1786,f64]) ).
fof(f1826,plain,
! [X0,X1] : mult(X0,X1) = mult(f(X0),mult(f(X0),X1)),
inference(superposition,[],[f1793,f9]) ).
fof(f2012,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = rd(ld(X0,X1),mult(X1,X1)),
inference(superposition,[],[f1456,f995]) ).
fof(f2257,plain,
! [X0,X1] : ld(X1,X0) = ld(mult(X0,X1),mult(X0,X0)),
inference(superposition,[],[f2,f1783]) ).
fof(f2288,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(mult(X0,X1),X0),X0),
inference(forward_demodulation,[],[f2257,f1763]) ).
fof(f2406,plain,
! [X0,X1] : rd(ld(X0,X1),X1) = ld(mult(X1,X0),X1),
inference(superposition,[],[f4,f2288]) ).
fof(f2424,plain,
! [X0,X1] : rd(ld(X0,X1),mult(X1,X1)) = rd(ld(mult(X1,X0),X1),X1),
inference(superposition,[],[f1456,f2288]) ).
fof(f2440,plain,
! [X0,X1] : rd(ld(X0,X1),mult(X1,X1)) = ld(mult(X1,X0),unit),
inference(forward_demodulation,[],[f2424,f1044]) ).
fof(f2452,plain,
! [X0,X1] : ld(X0,unit) = ld(mult(X1,X0),X1),
inference(forward_demodulation,[],[f2406,f1044]) ).
fof(f2470,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = ld(mult(X1,X0),unit),
inference(backward_demodulation,[],[f2012,f2440]) ).
fof(f2595,plain,
! [X0,X1] : ld(X0,X1) = ld(ld(X1,X0),unit),
inference(superposition,[],[f2452,f1]) ).
fof(f2611,plain,
! [X0,X1] : ld(X1,unit) = ld(X0,rd(X0,X1)),
inference(superposition,[],[f2452,f3]) ).
fof(f2708,plain,
! [X2,X0,X1] : mult(mult(X2,mult(f(X0),X1)),mult(ld(mult(f(X0),X1),f(X0)),f(X0))) = mult(mult(X2,mult(X0,X1)),ld(mult(f(X0),X1),f(X0))),
inference(superposition,[],[f81,f1826]) ).
fof(f2741,plain,
! [X2,X0,X1] : mult(mult(X2,mult(f(X0),X1)),mult(ld(X1,unit),f(X0))) = mult(mult(X2,mult(X0,X1)),ld(X1,unit)),
inference(forward_demodulation,[],[f2708,f2452]) ).
fof(f2782,plain,
! [X2,X0,X1] : mult(mult(X2,mult(X0,X1)),ld(X1,unit)) = mult(mult(X2,mult(f(X0),X1)),ld(X1,f(X0))),
inference(forward_demodulation,[],[f2741,f995]) ).
fof(f2804,plain,
! [X2,X0,X1] : mult(mult(X2,mult(X0,X1)),ld(X1,unit)) = mult(mult(X2,X1),mult(ld(X1,f(X0)),f(X0))),
inference(forward_demodulation,[],[f2782,f81]) ).
fof(f2812,plain,
! [X2,X0,X1] : mult(mult(X2,mult(X0,X1)),ld(X1,unit)) = mult(mult(X2,X1),ld(X1,X0)),
inference(forward_demodulation,[],[f2804,f1776]) ).
fof(f3819,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,X2)) = rd(mult(X0,mult(X2,rd(X2,X1))),rd(X2,X1)),
inference(superposition,[],[f292,f3]) ).
fof(f4231,plain,
! [X0,X1] : mult(X1,ld(X0,unit)) = rd(X1,X0),
inference(superposition,[],[f1,f2611]) ).
fof(f4254,plain,
! [X0,X1] : rd(X0,X1) = rd(mult(X0,X0),mult(X1,X0)),
inference(backward_demodulation,[],[f1010,f4231]) ).
fof(f4298,plain,
! [X2,X0,X1] : mult(mult(X2,X1),ld(X1,X0)) = rd(mult(X2,mult(X0,X1)),X1),
inference(backward_demodulation,[],[f2812,f4231]) ).
fof(f4375,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,X2)) = mult(mult(X0,rd(X2,X1)),ld(rd(X2,X1),X2)),
inference(backward_demodulation,[],[f3819,f4298]) ).
fof(f4470,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,X2)) = mult(mult(X0,rd(X2,X1)),X1),
inference(forward_demodulation,[],[f4375,f148]) ).
fof(f4986,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = rd(ld(X0,ld(X0,unit)),mult(X1,ld(X0,unit))),
inference(superposition,[],[f4254,f995]) ).
fof(f5027,plain,
! [X0,X1] : mult(X0,X0) = mult(rd(X0,X1),mult(X1,X0)),
inference(superposition,[],[f3,f4254]) ).
fof(f5040,plain,
! [X0,X1] : mult(X0,rd(X0,X1)) = rd(mult(X0,X0),X1),
inference(backward_demodulation,[],[f557,f5027]) ).
fof(f5095,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = rd(ld(X0,ld(X0,unit)),rd(X1,X0)),
inference(forward_demodulation,[],[f4986,f4231]) ).
fof(f5121,plain,
! [X0,X1] : ld(mult(X1,X0),unit) = rd(ld(X0,ld(X0,unit)),rd(X1,X0)),
inference(forward_demodulation,[],[f5095,f2470]) ).
fof(f5450,plain,
! [X0,X1] : mult(ld(X0,unit),rd(ld(X0,unit),X1)) = rd(ld(X0,ld(X0,unit)),X1),
inference(superposition,[],[f5040,f995]) ).
fof(f5505,plain,
! [X0,X1] : ld(X0,rd(ld(X0,unit),X1)) = rd(ld(X0,ld(X0,unit)),X1),
inference(forward_demodulation,[],[f5450,f995]) ).
fof(f5513,plain,
! [X0,X1] : ld(X0,ld(mult(X1,X0),unit)) = rd(ld(X0,ld(X0,unit)),X1),
inference(forward_demodulation,[],[f5505,f2470]) ).
fof(f5520,plain,
! [X0,X1] : ld(mult(X1,X0),unit) = ld(X0,ld(mult(rd(X1,X0),X0),unit)),
inference(backward_demodulation,[],[f5121,f5513]) ).
fof(f5522,plain,
! [X0,X1] : ld(X0,ld(X1,unit)) = ld(mult(X1,X0),unit),
inference(forward_demodulation,[],[f5520,f3]) ).
fof(f5524,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = ld(X0,ld(X1,unit)),
inference(backward_demodulation,[],[f2470,f5522]) ).
fof(f5761,plain,
! [X2,X0,X1] : mult(mult(X1,X0),X2) = mult(rd(X1,X2),mult(X2,mult(X0,X2))),
inference(superposition,[],[f4470,f4]) ).
fof(f5879,plain,
! [X2,X0,X1] : rd(X0,X1) = mult(mult(rd(X0,mult(X1,mult(X2,X1))),X1),X2),
inference(backward_demodulation,[],[f399,f5761]) ).
fof(f7433,plain,
! [X2,X0,X1] : mult(rd(X0,mult(X1,mult(X2,X1))),X1) = rd(rd(X0,X1),X2),
inference(superposition,[],[f4,f5879]) ).
fof(f7483,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(rd(rd(X0,X2),X1),mult(X0,X1)),
inference(backward_demodulation,[],[f186,f7433]) ).
fof(f7876,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(rd(ld(X0,unit),X1),mult(ld(X0,X2),X1)),
inference(superposition,[],[f7483,f1044]) ).
fof(f7950,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(ld(X0,ld(X1,unit)),mult(ld(X0,X2),X1)),
inference(forward_demodulation,[],[f7876,f5524]) ).
fof(f12502,plain,
! [X2,X0,X1] : mult(ld(X0,X1),X2) = ld(ld(X1,X0),X2),
inference(superposition,[],[f995,f2595]) ).
fof(f12572,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(ld(ld(X1,unit),X0),mult(ld(X0,X2),X1)),
inference(backward_demodulation,[],[f7950,f12502]) ).
fof(f12613,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(mult(ld(unit,X1),X0),mult(ld(X0,X2),X1)),
inference(forward_demodulation,[],[f12572,f12502]) ).
fof(f12662,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(mult(X1,X0),mult(ld(X0,X2),X1)),
inference(forward_demodulation,[],[f12613,f38]) ).
fof(f12799,plain,
! [X2,X0,X1] : mult(X1,mult(mult(X2,X0),X1)) = mult(mult(X1,X2),mult(X0,X1)),
inference(superposition,[],[f12662,f2]) ).
fof(f12941,plain,
~ sP0(mult(a,mult(mult(b,c),a))),
inference(backward_demodulation,[],[f11,f12799]) ).
fof(f13121,plain,
$false,
inference(forward_subsumption_resolution,[],[f12941,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP667-5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 10:29:34 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.50 Running first-order theorem proving
% 0.23/0.51 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
% 31.67/5.46 % (2346608)Detected a unit-equality problem, will run specialized UEQ schedule.
% 31.67/5.46 % (2346617)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3890256652:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 31.67/5.46 % (2346616)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=396811909:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 31.67/5.46 % (2346619)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3279242827:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 31.67/5.46 % (2346613)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=151410584:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 31.67/5.46 % (2346615)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=981036175:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 31.67/5.46 % (2346614)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=325479881:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 31.67/5.46 % (2346618)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=845372840:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 31.67/5.46 % (2346617)Instruction limit reached!
% 31.67/5.46 % (2346617)------------------------------
% 31.67/5.46 % (2346617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346617)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346617)Termination reason: Instruction limit
% 31.67/5.46 % (2346617)Termination phase: Saturation
% 31.67/5.46 % (2346617)Time elapsed: 0.093 s
% 31.67/5.46 % (2346617)Peak memory usage: 89 MB
% 31.67/5.46 % (2346617)Instructions burned: 182 (million)
% 31.67/5.46 % (2346616)Instruction limit reached!
% 31.67/5.46 % (2346616)------------------------------
% 31.67/5.46 % (2346616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346616)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346616)Termination reason: Instruction limit
% 31.67/5.46 % (2346616)Termination phase: Saturation
% 31.67/5.46 % (2346616)Time elapsed: 0.135 s
% 31.67/5.46 % (2346616)Peak memory usage: 89 MB
% 31.67/5.46 % (2346616)Instructions burned: 137 (million)
% 31.67/5.46 % (2346627)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2063643691:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 31.67/5.46 % (2346618)Instruction limit reached!
% 31.67/5.46 % (2346618)------------------------------
% 31.67/5.46 % (2346618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346618)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346618)Termination reason: Instruction limit
% 31.67/5.46 % (2346618)Termination phase: Saturation
% 31.67/5.46 % (2346618)Time elapsed: 0.266 s
% 31.67/5.46 % (2346618)Peak memory usage: 90 MB
% 31.67/5.46 % (2346618)Instructions burned: 257 (million)
% 31.67/5.46 % (2346628)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=343270702:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 31.67/5.46 % (2346630)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1848892561:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 31.67/5.46 % (2346630)Instruction limit reached!
% 31.67/5.46 % (2346630)------------------------------
% 31.67/5.46 % (2346630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346630)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346630)Termination reason: Instruction limit
% 31.67/5.46 % (2346630)Termination phase: Saturation
% 31.67/5.46 % (2346630)Time elapsed: 0.199 s
% 31.67/5.46 % (2346630)Peak memory usage: 90 MB
% 31.67/5.46 % (2346630)Instructions burned: 215 (million)
% 31.67/5.46 % (2346633)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=2471685702:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 31.67/5.46 % (2346619)Instruction limit reached!
% 31.67/5.46 % (2346619)------------------------------
% 31.67/5.46 % (2346619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346619)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346619)Termination reason: Instruction limit
% 31.67/5.46 % (2346619)Termination phase: Saturation
% 31.67/5.46 % (2346619)Time elapsed: 1.108 s
% 31.67/5.46 % (2346619)Peak memory usage: 101 MB
% 31.67/5.46 % (2346619)Instructions burned: 1187 (million)
% 31.67/5.46 % (2346635)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=525338090:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 31.67/5.46 % (2346633)Instruction limit reached!
% 31.67/5.46 % (2346633)------------------------------
% 31.67/5.46 % (2346633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346633)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346633)Termination reason: Instruction limit
% 31.67/5.46 % (2346633)Termination phase: Saturation
% 31.67/5.46 % (2346633)Time elapsed: 0.310 s
% 31.67/5.46 % (2346633)Peak memory usage: 95 MB
% 31.67/5.46 % (2346633)Instructions burned: 317 (million)
% 31.67/5.46 % (2346627)Instruction limit reached!
% 31.67/5.46 % (2346627)------------------------------
% 31.67/5.46 % (2346627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 31.67/5.46 % (2346627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 31.67/5.46 % (2346627)CaDiCaL version: 2.1.3
% 31.67/5.46 % (2346627)Termination reason: Instruction limit
% 31.67/5.46 % (2346627)Termination phase: Saturation
% 31.67/5.46 % (2346627)Time elapsed: 1.189 s
% 31.67/5.46 % (2346627)Peak memory usage: 141 MB
% 31.67/5.46 % (2346627)Instructions burned: 2052 (million)
% 31.67/5.46 % (2346637)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1987375653:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2983 on theBenchmark for (2983ds/2836Mi)
% 31.67/5.46 % (2346638)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=603573675:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2982 on theBenchmark for (2982ds/14534Mi)
% 31.67/5.46 % (2346638)First to succeed.
% 31.67/5.46 % (2346638)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2346608"
% 31.67/5.46 % (2346638)Refutation found. Thanks to Tanya!
% 31.67/5.46 % SZS status Unsatisfiable for theBenchmark
% 31.67/5.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/5.71 % (2346638)------------------------------
% 0.27/5.71 % (2346638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/5.71 % (2346638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/5.71 % (2346638)CaDiCaL version: 2.1.3
% 0.27/5.71 % (2346638)Termination reason: Refutation
% 0.27/5.71 % (2346638)Time elapsed: 2.225 s
% 0.27/5.71 % (2346638)Peak memory usage: 154 MB
% 0.27/5.71 % (2346638)Instructions burned: 3910 (million)
% 0.27/5.71 % (2346638)------------------------------
% 0.27/5.71 % (2346638)------------------------------
% 0.27/5.71 % (2346608)Success in time 4.426 s
% 0.27/5.71 % Vampire exiting
%------------------------------------------------------------------------------