%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP667-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 28.39s 4.95s
% Output : Refutation 29.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 11
% Syntax : Number of formulae : 126 ( 126 unt; 1 def)
% Number of atoms : 126 ( 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/sandbox2/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
fof(f6,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',c07) ).
fof(f8,axiom,
! [X0,X1] : mult(mult(X0,X1),X0) = mult(X0,mult(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
fof(f9,axiom,
! [X0] : mult(f(X0),f(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
fof(f10,negated_conjecture,
mult(mult(a,b),mult(c,a)) != mult(mult(a,mult(b,c)),a),
file('/export/starexec/sandbox2/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(mult(a,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,
sP0(mult(a,mult(mult(b,c),a))),
inference(forward_demodulation,[],[f12,f8]) ).
fof(f15,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(f22,plain,
! [X0,X1] : mult(X0,mult(mult(X1,mult(X0,X1)),X0)) = mult(mult(X0,X1),mult(X0,mult(X1,X0))),
inference(superposition,[],[f8,f15]) ).
fof(f26,plain,
! [X0,X1] : mult(mult(X1,unit),mult(X0,mult(unit,X0))) = mult(mult(X1,mult(X0,unit)),X0),
inference(superposition,[],[f15,f6]) ).
fof(f27,plain,
! [X0,X1] : mult(mult(X0,mult(X1,X0)),X1) = mult(mult(unit,X0),mult(X1,mult(X0,X1))),
inference(superposition,[],[f15,f6]) ).
fof(f28,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X0,X1))) = mult(mult(X0,mult(X1,X0)),X1),
inference(forward_demodulation,[],[f27,f6]) ).
fof(f29,plain,
! [X0,X1] : mult(mult(X1,unit),mult(X0,mult(unit,X0))) = mult(mult(X1,X0),X0),
inference(forward_demodulation,[],[f26,f5]) ).
fof(f31,plain,
! [X0,X1] : mult(mult(X0,X1),mult(X0,mult(X1,X0))) = mult(X0,mult(X1,mult(X0,mult(X1,X0)))),
inference(backward_demodulation,[],[f22,f28]) ).
fof(f32,plain,
! [X0,X1] : mult(mult(X1,X0),X0) = mult(mult(X1,unit),mult(X0,X0)),
inference(forward_demodulation,[],[f29,f6]) ).
fof(f34,plain,
! [X0,X1] : mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
inference(forward_demodulation,[],[f32,f5]) ).
fof(f37,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,[],[f15,f1]) ).
fof(f38,plain,
! [X0,X1] : mult(X0,X1) = mult(X1,mult(ld(X1,X0),X1)),
inference(superposition,[],[f8,f1]) ).
fof(f39,plain,
! [X0] : ld(unit,X0) = X0,
inference(superposition,[],[f6,f1]) ).
fof(f40,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,[],[f37,f38]) ).
fof(f45,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,[],[f31,f1]) ).
fof(f65,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(X1,mult(ld(X1,X0),mult(X0,X1))),
inference(forward_demodulation,[],[f45,f38]) ).
fof(f71,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,[],[f15,f38]) ).
fof(f82,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,[],[f71,f1]) ).
fof(f100,plain,
! [X0,X1] : mult(mult(unit,ld(X0,X1)),mult(X1,X0)) = mult(mult(ld(X0,X1),X1),X0),
inference(superposition,[],[f40,f6]) ).
fof(f113,plain,
! [X0,X1] : mult(ld(X0,X1),mult(X1,X0)) = mult(mult(ld(X0,X1),X1),X0),
inference(forward_demodulation,[],[f100,f6]) ).
fof(f149,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[],[f2,f3]) ).
fof(f152,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,[],[f15,f3]) ).
fof(f153,plain,
! [X0,X1] : mult(rd(X0,X1),mult(X1,rd(X0,X1))) = mult(X0,rd(X0,X1)),
inference(superposition,[],[f8,f3]) ).
fof(f154,plain,
! [X2,X0,X1] : mult(X0,X2) = mult(mult(rd(X0,mult(X1,mult(X2,X1))),X1),mult(X2,mult(X1,X2))),
inference(superposition,[],[f15,f3]) ).
fof(f157,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,[],[f152,f153]) ).
fof(f187,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,f154]) ).
fof(f289,plain,
! [X0,X1] : mult(X0,X1) = rd(mult(X0,mult(X1,X0)),X0),
inference(superposition,[],[f4,f8]) ).
fof(f291,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,f15]) ).
fof(f293,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,f157]) ).
fof(f294,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,f154]) ).
fof(f313,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,mult(X2,X1))) = rd(mult(X0,mult(X2,mult(X1,X2))),X2),
inference(superposition,[],[f291,f3]) ).
fof(f314,plain,
! [X0,X1] : mult(unit,mult(X0,mult(X1,X0))) = rd(mult(X0,mult(X1,mult(X0,X1))),X1),
inference(superposition,[],[f291,f6]) ).
fof(f350,plain,
! [X0,X1] : mult(X0,mult(X1,X0)) = rd(mult(X0,mult(X1,mult(X0,X1))),X1),
inference(forward_demodulation,[],[f314,f6]) ).
fof(f400,plain,
! [X2,X0,X1] : rd(X0,X1) = mult(rd(rd(X0,mult(X1,mult(X2,X1))),X2),mult(X2,mult(X1,X2))),
inference(superposition,[],[f313,f3]) ).
fof(f401,plain,
! [X0,X1] : rd(mult(X0,mult(X1,X0)),X0) = mult(rd(unit,X1),mult(X1,mult(X0,X1))),
inference(superposition,[],[f313,f6]) ).
fof(f423,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(unit,X1),mult(X1,mult(X0,X1))),
inference(forward_demodulation,[],[f401,f289]) ).
fof(f473,plain,
! [X0,X1] : mult(X1,mult(ld(X1,X0),mult(X1,ld(X1,X0)))) = mult(mult(X0,X1),ld(X1,X0)),
inference(superposition,[],[f28,f38]) ).
fof(f505,plain,
! [X0,X1] : mult(X1,mult(ld(X1,X0),X0)) = mult(mult(X0,X1),ld(X1,X0)),
inference(forward_demodulation,[],[f473,f1]) ).
fof(f535,plain,
! [X0,X1] : mult(rd(X0,X1),mult(X1,rd(X0,X1))) = rd(mult(rd(X0,X1),mult(X1,X0)),X1),
inference(superposition,[],[f350,f3]) ).
fof(f558,plain,
! [X0,X1] : mult(X0,rd(X0,X1)) = rd(mult(rd(X0,X1),mult(X1,X0)),X1),
inference(forward_demodulation,[],[f535,f153]) ).
fof(f739,plain,
! [X0,X1] : mult(rd(unit,X1),mult(X1,X0)) = X0,
inference(superposition,[],[f423,f3]) ).
fof(f816,plain,
! [X0,X1] : ld(X1,X0) = mult(rd(unit,X1),X0),
inference(superposition,[],[f739,f1]) ).
fof(f852,plain,
! [X0,X1] : mult(X0,rd(unit,X1)) = mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))),
inference(superposition,[],[f8,f739]) ).
fof(f865,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,[],[f350,f739]) ).
fof(f867,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,[],[f865,f34]) ).
fof(f899,plain,
! [X0,X1] : mult(X0,rd(unit,X1)) = ld(X1,mult(mult(X1,X0),rd(unit,X1))),
inference(backward_demodulation,[],[f852,f816]) ).
fof(f913,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,[],[f867,f816]) ).
fof(f934,plain,
! [X0,X1] : mult(rd(unit,X1),mult(mult(X1,X0),rd(unit,X1))) = rd(mult(X0,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f913,f2]) ).
fof(f945,plain,
! [X0,X1] : ld(X1,mult(mult(X1,X0),rd(unit,X1))) = rd(mult(X0,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f934,f816]) ).
fof(f947,plain,
! [X0,X1] : mult(X0,rd(unit,X1)) = rd(mult(X0,X0),mult(X1,X0)),
inference(forward_demodulation,[],[f945,f899]) ).
fof(f958,plain,
! [X0,X1] : rd(unit,X0) = rd(ld(X0,X1),X1),
inference(superposition,[],[f4,f816]) ).
fof(f992,plain,
! [X0] : ld(X0,unit) = rd(unit,X0),
inference(superposition,[],[f5,f816]) ).
fof(f996,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(X1,unit),X0),
inference(backward_demodulation,[],[f816,f992]) ).
fof(f1011,plain,
! [X0,X1] : rd(mult(X0,X0),mult(X1,X0)) = mult(X0,ld(X1,unit)),
inference(backward_demodulation,[],[f947,f992]) ).
fof(f1045,plain,
! [X0,X1] : ld(X0,unit) = rd(ld(X0,X1),X1),
inference(forward_demodulation,[],[f958,f992]) ).
fof(f1375,plain,
! [X0,X1] : mult(rd(X1,mult(unit,mult(X0,unit))),unit) = rd(mult(X1,X0),mult(X0,X0)),
inference(superposition,[],[f294,f6]) ).
fof(f1415,plain,
! [X0,X1] : rd(X1,mult(unit,mult(X0,unit))) = rd(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f1375,f5]) ).
fof(f1442,plain,
! [X0,X1] : rd(X1,mult(X0,unit)) = rd(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f1415,f6]) ).
fof(f1457,plain,
! [X0,X1] : rd(X1,X0) = rd(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f1442,f5]) ).
fof(f1707,plain,
! [X0,X1] : mult(ld(X0,X1),X1) = mult(ld(X0,unit),mult(X1,X1)),
inference(superposition,[],[f34,f996]) ).
fof(f1764,plain,
! [X0,X1] : mult(ld(X0,X1),X1) = ld(X0,mult(X1,X1)),
inference(forward_demodulation,[],[f1707,f996]) ).
fof(f1777,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(X1,f(X0)),f(X0)),
inference(superposition,[],[f1764,f9]) ).
fof(f1782,plain,
! [X0,X1] : mult(X0,mult(mult(ld(X0,X1),X1),X0)) = mult(mult(X1,X1),X0),
inference(superposition,[],[f38,f1764]) ).
fof(f1783,plain,
! [X0,X1] : mult(X1,X1) = mult(X0,mult(ld(X0,X1),X1)),
inference(superposition,[],[f1,f1764]) ).
fof(f1784,plain,
! [X0,X1] : mult(X0,X0) = mult(mult(X0,X1),ld(X1,X0)),
inference(backward_demodulation,[],[f505,f1783]) ).
fof(f1787,plain,
! [X0,X1] : mult(X0,mult(ld(X0,X1),mult(X1,X0))) = mult(mult(X1,X1),X0),
inference(forward_demodulation,[],[f1782,f113]) ).
fof(f1794,plain,
! [X0,X1] : mult(X1,mult(X1,X0)) = mult(mult(X1,X1),X0),
inference(forward_demodulation,[],[f1787,f65]) ).
fof(f1827,plain,
! [X0,X1] : mult(X0,X1) = mult(f(X0),mult(f(X0),X1)),
inference(superposition,[],[f1794,f9]) ).
fof(f2013,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = rd(ld(X0,X1),mult(X1,X1)),
inference(superposition,[],[f1457,f996]) ).
fof(f2258,plain,
! [X0,X1] : ld(X1,X0) = ld(mult(X0,X1),mult(X0,X0)),
inference(superposition,[],[f2,f1784]) ).
fof(f2289,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(mult(X0,X1),X0),X0),
inference(forward_demodulation,[],[f2258,f1764]) ).
fof(f2407,plain,
! [X0,X1] : rd(ld(X0,X1),X1) = ld(mult(X1,X0),X1),
inference(superposition,[],[f4,f2289]) ).
fof(f2425,plain,
! [X0,X1] : rd(ld(X0,X1),mult(X1,X1)) = rd(ld(mult(X1,X0),X1),X1),
inference(superposition,[],[f1457,f2289]) ).
fof(f2441,plain,
! [X0,X1] : rd(ld(X0,X1),mult(X1,X1)) = ld(mult(X1,X0),unit),
inference(forward_demodulation,[],[f2425,f1045]) ).
fof(f2453,plain,
! [X0,X1] : ld(X0,unit) = ld(mult(X1,X0),X1),
inference(forward_demodulation,[],[f2407,f1045]) ).
fof(f2471,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = ld(mult(X1,X0),unit),
inference(backward_demodulation,[],[f2013,f2441]) ).
fof(f2596,plain,
! [X0,X1] : ld(X0,X1) = ld(ld(X1,X0),unit),
inference(superposition,[],[f2453,f1]) ).
fof(f2612,plain,
! [X0,X1] : ld(X1,unit) = ld(X0,rd(X0,X1)),
inference(superposition,[],[f2453,f3]) ).
fof(f2709,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,[],[f82,f1827]) ).
fof(f2742,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,[],[f2709,f2453]) ).
fof(f2783,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,[],[f2742,f996]) ).
fof(f2805,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,[],[f2783,f82]) ).
fof(f2813,plain,
! [X2,X0,X1] : mult(mult(X2,mult(X0,X1)),ld(X1,unit)) = mult(mult(X2,X1),ld(X1,X0)),
inference(forward_demodulation,[],[f2805,f1777]) ).
fof(f3820,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,X2)) = rd(mult(X0,mult(X2,rd(X2,X1))),rd(X2,X1)),
inference(superposition,[],[f293,f3]) ).
fof(f4232,plain,
! [X0,X1] : mult(X1,ld(X0,unit)) = rd(X1,X0),
inference(superposition,[],[f1,f2612]) ).
fof(f4255,plain,
! [X0,X1] : rd(X0,X1) = rd(mult(X0,X0),mult(X1,X0)),
inference(backward_demodulation,[],[f1011,f4232]) ).
fof(f4299,plain,
! [X2,X0,X1] : mult(mult(X2,X1),ld(X1,X0)) = rd(mult(X2,mult(X0,X1)),X1),
inference(backward_demodulation,[],[f2813,f4232]) ).
fof(f4376,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,[],[f3820,f4299]) ).
fof(f4471,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,X2)) = mult(mult(X0,rd(X2,X1)),X1),
inference(forward_demodulation,[],[f4376,f149]) ).
fof(f4987,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = rd(ld(X0,ld(X0,unit)),mult(X1,ld(X0,unit))),
inference(superposition,[],[f4255,f996]) ).
fof(f5028,plain,
! [X0,X1] : mult(X0,X0) = mult(rd(X0,X1),mult(X1,X0)),
inference(superposition,[],[f3,f4255]) ).
fof(f5041,plain,
! [X0,X1] : mult(X0,rd(X0,X1)) = rd(mult(X0,X0),X1),
inference(backward_demodulation,[],[f558,f5028]) ).
fof(f5096,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = rd(ld(X0,ld(X0,unit)),rd(X1,X0)),
inference(forward_demodulation,[],[f4987,f4232]) ).
fof(f5122,plain,
! [X0,X1] : ld(mult(X1,X0),unit) = rd(ld(X0,ld(X0,unit)),rd(X1,X0)),
inference(forward_demodulation,[],[f5096,f2471]) ).
fof(f5451,plain,
! [X0,X1] : mult(ld(X0,unit),rd(ld(X0,unit),X1)) = rd(ld(X0,ld(X0,unit)),X1),
inference(superposition,[],[f5041,f996]) ).
fof(f5506,plain,
! [X0,X1] : ld(X0,rd(ld(X0,unit),X1)) = rd(ld(X0,ld(X0,unit)),X1),
inference(forward_demodulation,[],[f5451,f996]) ).
fof(f5514,plain,
! [X0,X1] : ld(X0,ld(mult(X1,X0),unit)) = rd(ld(X0,ld(X0,unit)),X1),
inference(forward_demodulation,[],[f5506,f2471]) ).
fof(f5521,plain,
! [X0,X1] : ld(mult(X1,X0),unit) = ld(X0,ld(mult(rd(X1,X0),X0),unit)),
inference(backward_demodulation,[],[f5122,f5514]) ).
fof(f5523,plain,
! [X0,X1] : ld(X0,ld(X1,unit)) = ld(mult(X1,X0),unit),
inference(forward_demodulation,[],[f5521,f3]) ).
fof(f5525,plain,
! [X0,X1] : rd(ld(X0,unit),X1) = ld(X0,ld(X1,unit)),
inference(backward_demodulation,[],[f2471,f5523]) ).
fof(f5762,plain,
! [X2,X0,X1] : mult(mult(X1,X0),X2) = mult(rd(X1,X2),mult(X2,mult(X0,X2))),
inference(superposition,[],[f4471,f4]) ).
fof(f5880,plain,
! [X2,X0,X1] : rd(X0,X1) = mult(mult(rd(X0,mult(X1,mult(X2,X1))),X1),X2),
inference(backward_demodulation,[],[f400,f5762]) ).
fof(f7434,plain,
! [X2,X0,X1] : mult(rd(X0,mult(X1,mult(X2,X1))),X1) = rd(rd(X0,X1),X2),
inference(superposition,[],[f4,f5880]) ).
fof(f7484,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(rd(rd(X0,X2),X1),mult(X0,X1)),
inference(backward_demodulation,[],[f187,f7434]) ).
fof(f7877,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(rd(ld(X0,unit),X1),mult(ld(X0,X2),X1)),
inference(superposition,[],[f7484,f1045]) ).
fof(f7951,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = ld(ld(X0,ld(X1,unit)),mult(ld(X0,X2),X1)),
inference(forward_demodulation,[],[f7877,f5525]) ).
fof(f12503,plain,
! [X2,X0,X1] : mult(ld(X0,X1),X2) = ld(ld(X1,X0),X2),
inference(superposition,[],[f996,f2596]) ).
fof(f12573,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(ld(ld(X1,unit),X0),mult(ld(X0,X2),X1)),
inference(backward_demodulation,[],[f7951,f12503]) ).
fof(f12614,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(mult(ld(unit,X1),X0),mult(ld(X0,X2),X1)),
inference(forward_demodulation,[],[f12573,f12503]) ).
fof(f12663,plain,
! [X2,X0,X1] : mult(X1,mult(X2,X1)) = mult(mult(X1,X0),mult(ld(X0,X2),X1)),
inference(forward_demodulation,[],[f12614,f39]) ).
fof(f12800,plain,
! [X2,X0,X1] : mult(X1,mult(mult(X2,X0),X1)) = mult(mult(X1,X2),mult(X0,X1)),
inference(superposition,[],[f12663,f2]) ).
fof(f12942,plain,
~ sP0(mult(a,mult(mult(b,c),a))),
inference(backward_demodulation,[],[f11,f12800]) ).
fof(f13122,plain,
$false,
inference(forward_subsumption_resolution,[],[f12942,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP667-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:29:50 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 28.39/4.95 % (2347367)Detected a unit-equality problem, will run specialized UEQ schedule.
% 28.39/4.95 % (2347431)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=117731286:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 28.39/4.95 % (2347427)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=3564348161:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 28.39/4.95 % (2347430)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1016446721:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 28.39/4.95 % (2347429)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1413139324:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 28.39/4.95 % (2347433)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2046041617:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 28.39/4.95 % (2347431)Instruction limit reached!
% 28.39/4.95 % (2347431)------------------------------
% 28.39/4.95 % (2347431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347431)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347431)Termination reason: Instruction limit
% 28.39/4.95 % (2347431)Termination phase: Saturation
% 28.39/4.95 % (2347431)Time elapsed: 0.058 s
% 28.39/4.95 % (2347431)Peak memory usage: 89 MB
% 28.39/4.95 % (2347431)Instructions burned: 184 (million)
% 28.39/4.95 % (2347432)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=441808356:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 28.39/4.95 % (2347428)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=820408902:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 28.39/4.95 % (2347430)Instruction limit reached!
% 28.39/4.95 % (2347430)------------------------------
% 28.39/4.95 % (2347430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347430)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347430)Termination reason: Instruction limit
% 28.39/4.95 % (2347430)Termination phase: Saturation
% 28.39/4.95 % (2347430)Time elapsed: 0.083 s
% 28.39/4.95 % (2347430)Peak memory usage: 89 MB
% 28.39/4.95 % (2347430)Instructions burned: 137 (million)
% 28.39/4.95 % (2347440)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3474585662:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 28.39/4.95 % (2347432)Instruction limit reached!
% 28.39/4.95 % (2347432)------------------------------
% 28.39/4.95 % (2347432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347432)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347432)Termination reason: Instruction limit
% 28.39/4.95 % (2347432)Termination phase: Saturation
% 28.39/4.95 % (2347432)Time elapsed: 0.160 s
% 28.39/4.95 % (2347432)Peak memory usage: 90 MB
% 28.39/4.95 % (2347432)Instructions burned: 257 (million)
% 28.39/4.95 % (2347442)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=329102963:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 28.39/4.95 % (2347444)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1900489989:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 28.39/4.95 % (2347444)Instruction limit reached!
% 28.39/4.95 % (2347444)------------------------------
% 28.39/4.95 % (2347444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347444)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347444)Termination reason: Instruction limit
% 28.39/4.95 % (2347444)Termination phase: Saturation
% 28.39/4.95 % (2347444)Time elapsed: 0.160 s
% 28.39/4.95 % (2347444)Peak memory usage: 90 MB
% 28.39/4.95 % (2347444)Instructions burned: 215 (million)
% 28.39/4.95 % (2347456)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=307108594: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)
% 28.39/4.95 % (2347433)Instruction limit reached!
% 28.39/4.95 % (2347433)------------------------------
% 28.39/4.95 % (2347433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347433)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347433)Termination reason: Instruction limit
% 28.39/4.95 % (2347433)Termination phase: Saturation
% 28.39/4.95 % (2347433)Time elapsed: 0.832 s
% 28.39/4.95 % (2347433)Peak memory usage: 101 MB
% 28.39/4.95 % (2347433)Instructions burned: 1188 (million)
% 28.39/4.95 % (2347456)Instruction limit reached!
% 28.39/4.95 % (2347456)------------------------------
% 28.39/4.95 % (2347456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347456)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347456)Termination reason: Instruction limit
% 28.39/4.95 % (2347456)Termination phase: Saturation
% 28.39/4.95 % (2347456)Time elapsed: 0.320 s
% 28.39/4.95 % (2347456)Peak memory usage: 94 MB
% 28.39/4.95 % (2347456)Instructions burned: 317 (million)
% 28.39/4.95 % (2347440)Instruction limit reached!
% 28.39/4.95 % (2347440)------------------------------
% 28.39/4.95 % (2347440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347440)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347440)Termination reason: Instruction limit
% 28.39/4.95 % (2347440)Termination phase: Saturation
% 28.39/4.95 % (2347440)Time elapsed: 0.963 s
% 28.39/4.95 % (2347440)Peak memory usage: 140 MB
% 28.39/4.95 % (2347440)Instructions burned: 2052 (million)
% 28.39/4.95 % (2347468)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=3192905202:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2989 on theBenchmark for (2989ds/12125Mi)
% 28.39/4.95 % (2347472)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=144002045:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2987 on theBenchmark for (2987ds/14534Mi)
% 28.39/4.95 % (2347471)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1298761814:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2987 on theBenchmark for (2987ds/2836Mi)
% 28.39/4.95 % (2347471)Instruction limit reached!
% 28.39/4.95 % (2347471)------------------------------
% 28.39/4.95 % (2347471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347471)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347471)Termination reason: Instruction limit
% 28.39/4.95 % (2347471)Termination phase: Saturation
% 28.39/4.95 % (2347471)Time elapsed: 2.098 s
% 28.39/4.95 % (2347471)Peak memory usage: 132 MB
% 28.39/4.95 % (2347471)Instructions burned: 2837 (million)
% 28.39/4.95 % (2347632)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=3558719901:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2963 on theBenchmark for (2963ds/11832Mi)
% 28.39/4.95 % (2347472)First to succeed.
% 28.39/4.95 % (2347472)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2347367"
% 28.39/4.95 % (2347468)Also succeeded, but the first one will report.
% 28.39/4.95 % (2347428)Also succeeded, but the first one will report.
% 28.39/4.95 % (2347442)Instruction limit reached!
% 28.39/4.95 % (2347442)------------------------------
% 28.39/4.95 % (2347442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 28.39/4.95 % (2347442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 28.39/4.95 % (2347442)CaDiCaL version: 2.1.3
% 28.39/4.95 % (2347442)Termination reason: Instruction limit
% 28.39/4.95 % (2347442)Termination phase: Saturation
% 28.39/4.95 % (2347442)Time elapsed: 3.468 s
% 28.39/4.95 % (2347442)Peak memory usage: 170 MB
% 28.39/4.95 % (2347442)Instructions burned: 4949 (million)
% 28.39/4.95 % (2347634)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=463879659:i=2279:fgj=on:bd=all_2961 on theBenchmark for (2961ds/2279Mi)
% 28.39/4.95 % (2347472)Refutation found. Thanks to Tanya!
% 28.39/4.95 % SZS status Unsatisfiable for theBenchmark
% 28.39/4.95 % SZS output start Proof for theBenchmark
% See solution above
% 29.39/5.05 % (2347472)------------------------------
% 29.39/5.05 % (2347472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 29.39/5.05 % (2347472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.39/5.05 % (2347472)CaDiCaL version: 2.1.3
% 29.39/5.05 % (2347472)Termination reason: Refutation
% 29.39/5.05 % (2347472)Time elapsed: 2.307 s
% 29.39/5.05 % (2347472)Peak memory usage: 154 MB
% 29.39/5.05 % (2347472)Instructions burned: 3911 (million)
% 29.39/5.05 % (2347472)------------------------------
% 29.39/5.05 % (2347472)------------------------------
% 29.39/5.05 % (2347367)Success in time 4.086 s
% 29.39/5.05 % Vampire exiting
%------------------------------------------------------------------------------