%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP654+3 : 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 : n026.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 10:15:22 AM UTC 2026
% Result : Theorem 15.80s 3.13s
% Output : Refutation 16.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 11
% Syntax : Number of formulae : 192 ( 180 unt; 5 def)
% Number of atoms : 204 ( 189 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 8 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 225 ( 0 sgn 223 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X0,X1,X2] : mult(X2,mult(X1,mult(X2,X0))) = mult(mult(mult(X2,X1),X2),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,conjecture,
! [X0,X1] :
( mult(X0,ld(X1,X1)) = X0
& mult(ld(X1,X1),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( mult(X0,ld(X1,X1)) = X0
& mult(ld(X1,X1),X0) = X0 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( mult(X0,ld(X1,X1)) != X0
| mult(ld(X1,X1),X0) != X0 ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( sK0 != mult(sK0,ld(sK1,sK1))
| sK0 != mult(ld(sK1,sK1),sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
fof(f10,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f14,plain,
! [X2,X0,X1] : mult(X2,mult(X1,mult(X2,X0))) = mult(mult(mult(X2,X1),X2),X0),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
( sK0 != mult(sK0,ld(sK1,sK1))
| sK0 != mult(ld(sK1,sK1),sK0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f16,definition,
sF2 = ld(sK1,sK1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f17,plain,
ld(sK1,sK1) = sF2,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF3 = mult(sK0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f19,plain,
mult(sK0,sF2) = sF3,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF4 = mult(sF2,sK0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f21,plain,
mult(sF2,sK0) = sF4,
inference(reorient_equations,[],[f20]) ).
fof(f22,plain,
( sK0 != sF3
| sK0 != sF4 ),
inference(definition_folding,[],[f15,f21,f17,f19,f17]) ).
fof(f24,definition,
( spl5_1
<=> sK0 = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f26,plain,
( sK0 != sF4
| spl5_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl5_2
<=> sK0 = sF3 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f31,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f22,f28,f24]) ).
fof(f32,plain,
sK1 = mult(sK1,sF2),
inference(superposition,[],[f10,f17]) ).
fof(f33,plain,
sF2 = ld(sK0,sF3),
inference(superposition,[],[f11,f19]) ).
fof(f34,plain,
sK0 = ld(sF2,sF4),
inference(superposition,[],[f11,f21]) ).
fof(f35,plain,
! [X2,X0,X1] : mult(X1,mult(ld(X1,X0),mult(X1,X2))) = mult(mult(X0,X1),X2),
inference(superposition,[],[f14,f10]) ).
fof(f46,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[],[f11,f12]) ).
fof(f47,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[],[f13,f10]) ).
fof(f48,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X0) = rd(mult(X0,mult(X1,mult(X0,X2))),X2),
inference(superposition,[],[f13,f14]) ).
fof(f49,plain,
sK0 = rd(sF3,sF2),
inference(superposition,[],[f13,f19]) ).
fof(f56,plain,
! [X2,X0,X1] : mult(mult(X2,X1),ld(X1,X0)) = mult(X1,mult(ld(X1,X2),X0)),
inference(superposition,[],[f35,f10]) ).
fof(f65,plain,
! [X2,X0,X1] : mult(ld(X1,X0),mult(X1,X2)) = ld(X1,mult(mult(X0,X1),X2)),
inference(superposition,[],[f11,f35]) ).
fof(f73,plain,
! [X2,X0,X1] : mult(ld(X1,rd(X0,X1)),mult(X1,X2)) = ld(X1,mult(X0,X2)),
inference(superposition,[],[f65,f12]) ).
fof(f77,plain,
! [X2,X0,X1] : ld(X1,X0) = mult(ld(X1,X2),mult(X1,ld(mult(X2,X1),X0))),
inference(superposition,[],[f65,f10]) ).
fof(f87,plain,
! [X2,X0,X1] : mult(X1,mult(ld(X1,rd(X0,X1)),X2)) = mult(X0,ld(X1,X2)),
inference(superposition,[],[f56,f12]) ).
fof(f99,plain,
! [X2,X0,X1] : mult(X1,X0) = rd(mult(X0,mult(ld(X0,X1),X2)),ld(X0,X2)),
inference(superposition,[],[f13,f56]) ).
fof(f107,plain,
! [X2,X0,X1] : ld(X1,mult(X2,ld(X1,X0))) = mult(ld(X1,rd(X2,X1)),X0),
inference(superposition,[],[f73,f10]) ).
fof(f117,plain,
! [X2,X0,X1] : ld(X0,rd(X1,X0)) = rd(ld(X0,mult(X1,X2)),mult(X0,X2)),
inference(superposition,[],[f13,f73]) ).
fof(f133,plain,
! [X0,X1] : ld(X0,X1) = mult(ld(X0,rd(X0,X0)),X1),
inference(superposition,[],[f11,f107]) ).
fof(f148,plain,
! [X0,X1] : ld(X0,rd(X0,X0)) = rd(ld(X0,X1),X1),
inference(superposition,[],[f13,f133]) ).
fof(f169,plain,
! [X0,X1] : ld(X1,rd(X1,X1)) = rd(X0,mult(X1,X0)),
inference(superposition,[],[f148,f11]) ).
fof(f174,plain,
! [X2,X0,X1] : ld(X0,X2) = mult(rd(ld(X0,X1),X1),X2),
inference(superposition,[],[f133,f148]) ).
fof(f184,plain,
! [X2,X0,X1] : rd(X0,mult(X1,X0)) = rd(X2,mult(X1,X2)),
inference(superposition,[],[f169,f169]) ).
fof(f194,plain,
! [X2,X0,X1] : ld(X1,X2) = mult(rd(X0,mult(X1,X0)),X2),
inference(superposition,[],[f133,f169]) ).
fof(f200,plain,
! [X0,X1] : rd(X1,X1) = mult(X1,rd(X0,mult(X1,X0))),
inference(superposition,[],[f10,f169]) ).
fof(f244,plain,
! [X2,X0,X1] : ld(rd(X0,X1),X2) = mult(rd(X1,X0),X2),
inference(superposition,[],[f194,f12]) ).
fof(f246,plain,
! [X0] : ld(sK0,X0) = mult(rd(sF2,sF3),X0),
inference(superposition,[],[f194,f19]) ).
fof(f353,plain,
! [X2,X0,X1] : mult(ld(rd(X1,mult(X0,X1)),X0),mult(rd(X1,mult(X0,X1)),X2)) = ld(rd(X1,mult(X0,X1)),mult(rd(X0,X0),X2)),
inference(superposition,[],[f65,f200]) ).
fof(f366,plain,
! [X2,X0,X1] : mult(ld(rd(X1,mult(X0,X1)),X0),mult(rd(X1,mult(X0,X1)),X2)) = mult(rd(mult(X0,X1),X1),mult(rd(X0,X0),X2)),
inference(forward_demodulation,[],[f353,f244]) ).
fof(f380,plain,
! [X2,X0,X1] : mult(ld(rd(X1,mult(X0,X1)),X0),mult(rd(X1,mult(X0,X1)),X2)) = mult(X0,mult(rd(X0,X0),X2)),
inference(forward_demodulation,[],[f366,f13]) ).
fof(f387,plain,
! [X2,X0,X1] : mult(X0,mult(rd(X0,X0),X2)) = mult(ld(rd(X1,mult(X0,X1)),X0),ld(X0,X2)),
inference(forward_demodulation,[],[f380,f194]) ).
fof(f389,plain,
! [X2,X0,X1] : mult(X0,mult(rd(X0,X0),X2)) = mult(mult(rd(mult(X0,X1),X1),X0),ld(X0,X2)),
inference(forward_demodulation,[],[f387,f244]) ).
fof(f391,plain,
! [X2,X0,X1] : mult(X0,mult(rd(X0,X0),X2)) = mult(X0,mult(ld(X0,rd(mult(X0,X1),X1)),X2)),
inference(forward_demodulation,[],[f389,f56]) ).
fof(f393,plain,
! [X2,X0] : mult(X0,mult(rd(X0,X0),X2)) = mult(X0,mult(ld(X0,X0),X2)),
inference(forward_demodulation,[],[f391,f13]) ).
fof(f407,plain,
! [X0,X1] : mult(ld(X0,X0),X1) = ld(X0,mult(X0,mult(rd(X0,X0),X1))),
inference(superposition,[],[f11,f393]) ).
fof(f428,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(ld(X0,X0),X1),
inference(forward_demodulation,[],[f407,f11]) ).
fof(f459,plain,
! [X0,X1] : ld(X0,X0) = rd(mult(rd(X0,X0),X1),X1),
inference(superposition,[],[f13,f428]) ).
fof(f485,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(forward_demodulation,[],[f459,f13]) ).
fof(f499,plain,
sF2 = rd(sK1,sK1),
inference(superposition,[],[f17,f485]) ).
fof(f500,plain,
! [X0] : mult(X0,rd(X0,X0)) = X0,
inference(superposition,[],[f10,f485]) ).
fof(f512,plain,
! [X0] : mult(sF2,X0) = ld(sF2,X0),
inference(superposition,[],[f244,f499]) ).
fof(f514,plain,
sK1 = mult(sF2,sK1),
inference(superposition,[],[f12,f499]) ).
fof(f523,plain,
rd(sF2,sF2) = mult(sF2,sF2),
inference(superposition,[],[f485,f512]) ).
fof(f528,plain,
! [X0] : sF2 = rd(X0,mult(sF2,X0)),
inference(superposition,[],[f47,f512]) ).
fof(f533,plain,
! [X0] : mult(sF2,mult(sF2,X0)) = X0,
inference(superposition,[],[f11,f512]) ).
fof(f572,plain,
! [X0] : ld(X0,rd(X0,X0)) = rd(rd(X0,X0),X0),
inference(superposition,[],[f169,f500]) ).
fof(f766,plain,
sK0 = mult(sF2,sF4),
inference(superposition,[],[f533,f21]) ).
fof(f1012,plain,
! [X2,X0,X1] : mult(mult(X1,X2),X1) = rd(mult(X1,mult(X2,X0)),ld(X1,X0)),
inference(superposition,[],[f48,f10]) ).
fof(f1137,plain,
! [X2,X0,X1] : mult(mult(X1,X2),X1) = rd(mult(X1,X0),ld(X1,ld(X2,X0))),
inference(superposition,[],[f1012,f10]) ).
fof(f1148,plain,
! [X2,X0,X1] : mult(mult(X1,rd(X0,X2)),X1) = rd(mult(X1,X0),ld(X1,X2)),
inference(superposition,[],[f1012,f12]) ).
fof(f1253,plain,
! [X2,X0,X1] : mult(mult(X1,X2),X1) = rd(X0,ld(X1,ld(X2,ld(X1,X0)))),
inference(superposition,[],[f1137,f10]) ).
fof(f1268,plain,
! [X0] : mult(mult(sK0,X0),sK0) = rd(sF3,ld(sK0,ld(X0,sF2))),
inference(superposition,[],[f1137,f19]) ).
fof(f1337,plain,
! [X0,X1] : mult(mult(X0,ld(X0,X1)),X0) = rd(X1,ld(X0,rd(ld(X0,X1),ld(X0,X1)))),
inference(superposition,[],[f1253,f485]) ).
fof(f1351,plain,
! [X0,X1] : mult(X1,X0) = rd(X1,ld(X0,rd(ld(X0,X1),ld(X0,X1)))),
inference(forward_demodulation,[],[f1337,f10]) ).
fof(f1849,plain,
! [X2,X3,X0,X1] : mult(X0,mult(rd(X1,X2),mult(X0,X3))) = mult(rd(mult(X0,X1),ld(X0,X2)),X3),
inference(superposition,[],[f14,f1148]) ).
fof(f1969,plain,
! [X2,X0,X1] : mult(X0,ld(mult(X2,X0),X1)) = ld(ld(X0,X2),ld(X0,X1)),
inference(superposition,[],[f11,f77]) ).
fof(f1970,plain,
! [X2,X0,X1] : ld(X0,X2) = rd(ld(X0,X1),mult(X0,ld(mult(X2,X0),X1))),
inference(superposition,[],[f13,f77]) ).
fof(f1979,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X2),X3) = mult(rd(mult(X0,ld(mult(X2,X0),X1)),ld(X0,X1)),X3),
inference(superposition,[],[f194,f77]) ).
fof(f1984,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X2),X3) = mult(X0,mult(rd(ld(mult(X2,X0),X1),X1),mult(X0,X3))),
inference(forward_demodulation,[],[f1979,f1849]) ).
fof(f2038,plain,
! [X2,X3,X0] : ld(ld(X0,X2),X3) = mult(X0,ld(mult(X2,X0),mult(X0,X3))),
inference(forward_demodulation,[],[f1984,f174]) ).
fof(f2087,plain,
! [X0,X1] : mult(X0,ld(mult(X0,X0),X1)) = ld(rd(X0,X0),ld(X0,X1)),
inference(superposition,[],[f1969,f485]) ).
fof(f2115,plain,
! [X0,X1] : rd(ld(X0,X1),ld(X0,X1)) = mult(X0,ld(mult(X1,X0),X1)),
inference(superposition,[],[f485,f1969]) ).
fof(f2150,plain,
! [X0,X1] : mult(X0,ld(mult(X0,X0),X1)) = mult(rd(X0,X0),ld(X0,X1)),
inference(forward_demodulation,[],[f2087,f244]) ).
fof(f2214,plain,
! [X0] : mult(rd(X0,X0),ld(X0,X0)) = rd(ld(rd(X0,X0),X0),ld(rd(X0,X0),X0)),
inference(superposition,[],[f2115,f500]) ).
fof(f2228,plain,
rd(ld(sF2,sK0),ld(sF2,sK0)) = mult(sF2,ld(sF3,sK0)),
inference(superposition,[],[f2115,f19]) ).
fof(f2229,plain,
rd(ld(sF2,sK1),ld(sF2,sK1)) = mult(sF2,ld(sK1,sK1)),
inference(superposition,[],[f2115,f32]) ).
fof(f2246,plain,
! [X0,X1] : ld(X0,rd(ld(X0,X1),ld(X0,X1))) = ld(mult(X1,X0),X1),
inference(superposition,[],[f11,f2115]) ).
fof(f2298,plain,
mult(sF2,rd(sK1,sK1)) = rd(ld(sF2,sK1),ld(sF2,sK1)),
inference(forward_demodulation,[],[f2229,f485]) ).
fof(f2299,plain,
mult(sF2,ld(sF3,sK0)) = rd(mult(sF2,sK0),mult(sF2,sK0)),
inference(forward_demodulation,[],[f2228,f512]) ).
fof(f2308,plain,
! [X0] : rd(X0,X0) = mult(rd(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[],[f2214,f46]) ).
fof(f2328,plain,
mult(sF2,rd(sK1,sK1)) = rd(mult(sF2,sK1),mult(sF2,sK1)),
inference(forward_demodulation,[],[f2298,f512]) ).
fof(f2329,plain,
mult(sF2,ld(sF3,sK0)) = rd(sF4,sF4),
inference(forward_demodulation,[],[f2299,f21]) ).
fof(f2332,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(mult(X0,X0),X0)),
inference(forward_demodulation,[],[f2308,f2150]) ).
fof(f2340,plain,
rd(sK1,sK1) = mult(sF2,rd(sK1,sK1)),
inference(forward_demodulation,[],[f2328,f514]) ).
fof(f2341,plain,
! [X0] : rd(X0,X0) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[],[f2332,f2115]) ).
fof(f2346,plain,
sF2 = mult(sF2,sF2),
inference(forward_demodulation,[],[f2340,f499]) ).
fof(f2347,plain,
! [X0] : rd(X0,X0) = rd(rd(X0,X0),rd(X0,X0)),
inference(forward_demodulation,[],[f2341,f485]) ).
fof(f2350,plain,
sF2 = rd(sF2,sF2),
inference(forward_demodulation,[],[f2346,f523]) ).
fof(f2355,plain,
ld(sF3,sK0) = mult(sF2,rd(sF4,sF4)),
inference(superposition,[],[f533,f2329]) ).
fof(f3452,plain,
! [X0,X1] : mult(X1,rd(X1,X0)) = rd(X1,ld(rd(X1,X0),rd(X0,X0))),
inference(superposition,[],[f1351,f46]) ).
fof(f3474,plain,
! [X0,X1] : mult(X1,rd(X1,X0)) = rd(X1,mult(rd(X0,X1),rd(X0,X0))),
inference(forward_demodulation,[],[f3452,f244]) ).
fof(f3607,plain,
! [X0] : ld(ld(sF2,sK0),X0) = mult(sF2,ld(sF3,mult(sF2,X0))),
inference(superposition,[],[f2038,f19]) ).
fof(f3670,plain,
! [X2,X0,X1] : ld(mult(X1,X0),mult(X0,X2)) = ld(X0,ld(ld(X0,X1),X2)),
inference(superposition,[],[f11,f2038]) ).
fof(f3761,plain,
! [X0] : ld(mult(sF2,sK0),X0) = mult(sF2,ld(sF3,mult(sF2,X0))),
inference(forward_demodulation,[],[f3607,f512]) ).
fof(f3818,plain,
! [X0] : ld(sF4,X0) = mult(sF2,ld(sF3,mult(sF2,X0))),
inference(forward_demodulation,[],[f3761,f21]) ).
fof(f3917,plain,
ld(sF4,rd(sF2,sF2)) = mult(sF2,ld(sF3,sF2)),
inference(superposition,[],[f3818,f500]) ).
fof(f3961,plain,
ld(sF4,sF2) = mult(sF2,ld(sF3,sF2)),
inference(forward_demodulation,[],[f3917,f2350]) ).
fof(f4535,plain,
rd(mult(sF2,sF4),ld(sF2,sF4)) = mult(ld(sF3,sK0),sF2),
inference(superposition,[],[f1148,f2355]) ).
fof(f4571,plain,
mult(ld(sF3,sK0),sF2) = rd(mult(sF2,sF4),sK0),
inference(forward_demodulation,[],[f4535,f34]) ).
fof(f4580,plain,
rd(sK0,sK0) = mult(ld(sF3,sK0),sF2),
inference(forward_demodulation,[],[f4571,f766]) ).
fof(f4587,plain,
ld(sF3,sK0) = rd(rd(sK0,sK0),sF2),
inference(superposition,[],[f13,f4580]) ).
fof(f5321,plain,
! [X2,X0,X1] : ld(mult(X2,X0),rd(ld(X0,X1),ld(X0,X1))) = ld(X0,ld(ld(X0,X2),ld(mult(X1,X0),X1))),
inference(superposition,[],[f3670,f2115]) ).
fof(f5902,plain,
! [X2,X0,X1] : ld(X1,rd(X2,X1)) = rd(ld(X1,X0),mult(X1,ld(X2,X0))),
inference(superposition,[],[f117,f10]) ).
fof(f6408,plain,
! [X2,X3,X0,X1] : mult(X2,rd(X1,mult(X0,X1))) = rd(ld(X0,mult(ld(rd(X1,mult(X0,X1)),X2),X3)),ld(rd(X1,mult(X0,X1)),X3)),
inference(superposition,[],[f99,f194]) ).
fof(f6461,plain,
! [X2,X3,X0,X1] : mult(X2,rd(X1,mult(X0,X1))) = rd(ld(X0,mult(ld(rd(X1,mult(X0,X1)),X2),X3)),mult(rd(mult(X0,X1),X1),X3)),
inference(forward_demodulation,[],[f6408,f244]) ).
fof(f6515,plain,
! [X2,X3,X0,X1] : mult(X2,rd(X1,mult(X0,X1))) = rd(ld(X0,mult(ld(rd(X1,mult(X0,X1)),X2),X3)),mult(X0,X3)),
inference(forward_demodulation,[],[f6461,f13]) ).
fof(f6540,plain,
! [X2,X0,X1] : mult(X2,rd(X1,mult(X0,X1))) = ld(X0,rd(ld(rd(X1,mult(X0,X1)),X2),X0)),
inference(forward_demodulation,[],[f6515,f117]) ).
fof(f6560,plain,
! [X2,X0,X1] : mult(X2,rd(X1,mult(X0,X1))) = ld(X0,rd(mult(rd(mult(X0,X1),X1),X2),X0)),
inference(forward_demodulation,[],[f6540,f244]) ).
fof(f6570,plain,
! [X2,X0,X1] : mult(X2,rd(X1,mult(X0,X1))) = ld(X0,rd(mult(X0,X2),X0)),
inference(forward_demodulation,[],[f6560,f13]) ).
fof(f6636,plain,
! [X2,X0,X1] : ld(X1,rd(X0,X1)) = mult(ld(X1,X0),rd(X2,mult(X1,X2))),
inference(superposition,[],[f6570,f10]) ).
fof(f6681,plain,
! [X0] : mult(sK0,rd(X0,mult(sF2,X0))) = ld(sF2,rd(sF4,sF2)),
inference(superposition,[],[f6570,f21]) ).
fof(f6866,plain,
! [X0] : mult(sK0,rd(X0,mult(sF2,X0))) = mult(sF2,rd(sF4,sF2)),
inference(forward_demodulation,[],[f6681,f512]) ).
fof(f7013,plain,
mult(sK0,sF2) = mult(sF2,rd(sF4,sF2)),
inference(forward_demodulation,[],[f6866,f528]) ).
fof(f7100,plain,
sF3 = mult(sF2,rd(sF4,sF2)),
inference(forward_demodulation,[],[f7013,f19]) ).
fof(f7232,plain,
rd(mult(sF2,sF4),ld(sF2,sF2)) = mult(sF3,sF2),
inference(superposition,[],[f1148,f7100]) ).
fof(f7280,plain,
mult(sF3,sF2) = rd(mult(sF2,sF4),rd(sF2,sF2)),
inference(forward_demodulation,[],[f7232,f485]) ).
fof(f7296,plain,
rd(mult(sF2,sF4),sF2) = mult(sF3,sF2),
inference(forward_demodulation,[],[f7280,f2350]) ).
fof(f7303,plain,
rd(sK0,sF2) = mult(sF3,sF2),
inference(forward_demodulation,[],[f7296,f766]) ).
fof(f7501,plain,
! [X2,X0,X1] : mult(X1,ld(X0,rd(X2,mult(X0,X2)))) = mult(X0,ld(X0,rd(rd(X1,X0),X0))),
inference(superposition,[],[f87,f6636]) ).
fof(f7547,plain,
! [X2,X0,X1] : rd(rd(X1,X0),X0) = mult(X1,ld(X0,rd(X2,mult(X0,X2)))),
inference(forward_demodulation,[],[f7501,f10]) ).
fof(f8469,plain,
! [X0] : rd(sF2,rd(sK0,sK0)) = rd(X0,mult(ld(sF3,sK0),X0)),
inference(superposition,[],[f184,f4580]) ).
fof(f9300,plain,
ld(sF3,sF2) = mult(sF2,ld(sF4,sF2)),
inference(superposition,[],[f533,f3961]) ).
fof(f14363,plain,
! [X0,X1] : rd(rd(X1,sF2),sF2) = mult(X1,mult(sF2,rd(X0,mult(sF2,X0)))),
inference(superposition,[],[f7547,f512]) ).
fof(f14569,plain,
! [X1] : rd(rd(X1,sF2),sF2) = mult(X1,rd(sF2,sF2)),
inference(forward_demodulation,[],[f14363,f200]) ).
fof(f14683,plain,
! [X1] : mult(X1,sF2) = rd(rd(X1,sF2),sF2),
inference(forward_demodulation,[],[f14569,f2350]) ).
fof(f16951,plain,
mult(sF3,rd(sF3,sF2)) = rd(sF3,ld(sK0,rd(sF2,sF2))),
inference(superposition,[],[f3474,f246]) ).
fof(f17109,plain,
mult(sF3,rd(sF3,sF2)) = rd(sF3,ld(sK0,sF2)),
inference(forward_demodulation,[],[f16951,f2350]) ).
fof(f17185,plain,
mult(sF3,sK0) = rd(sF3,ld(sK0,sF2)),
inference(forward_demodulation,[],[f17109,f49]) ).
fof(f17361,plain,
ld(sK0,sF2) = ld(mult(sF3,sK0),sF3),
inference(superposition,[],[f46,f17185]) ).
fof(f17406,plain,
mult(sF3,mult(sF3,sK0)) = rd(sF3,ld(mult(sF3,sK0),rd(ld(sK0,sF2),ld(sK0,sF2)))),
inference(superposition,[],[f1351,f17361]) ).
fof(f17417,plain,
mult(sF3,mult(sF3,sK0)) = rd(sF3,ld(sK0,ld(ld(sK0,sF3),ld(mult(sF2,sK0),sF2)))),
inference(forward_demodulation,[],[f17406,f5321]) ).
fof(f17426,plain,
mult(sF3,mult(sF3,sK0)) = rd(sF3,ld(sK0,ld(ld(sK0,sF3),ld(sF4,sF2)))),
inference(forward_demodulation,[],[f17417,f21]) ).
fof(f17432,plain,
mult(sF3,mult(sF3,sK0)) = rd(sF3,ld(sK0,ld(sF2,ld(sF4,sF2)))),
inference(forward_demodulation,[],[f17426,f33]) ).
fof(f17437,plain,
mult(sF3,mult(sF3,sK0)) = rd(sF3,ld(sK0,mult(sF2,ld(sF4,sF2)))),
inference(forward_demodulation,[],[f17432,f512]) ).
fof(f17441,plain,
mult(sF3,mult(sF3,sK0)) = rd(sF3,ld(sK0,ld(sF3,sF2))),
inference(forward_demodulation,[],[f17437,f9300]) ).
fof(f17444,plain,
mult(sF3,mult(sF3,sK0)) = mult(mult(sK0,sF3),sK0),
inference(forward_demodulation,[],[f17441,f1268]) ).
fof(f17448,plain,
mult(ld(sF3,sK0),mult(sF3,sK0)) = ld(sF3,mult(sF3,mult(sF3,sK0))),
inference(superposition,[],[f65,f17444]) ).
fof(f17494,plain,
mult(sF3,sK0) = mult(ld(sF3,sK0),mult(sF3,sK0)),
inference(forward_demodulation,[],[f17448,f11]) ).
fof(f17515,plain,
ld(sF3,sK0) = rd(mult(sF3,sK0),mult(sF3,sK0)),
inference(superposition,[],[f13,f17494]) ).
fof(f17529,plain,
! [X0] : rd(X0,mult(ld(sF3,sK0),X0)) = rd(mult(sF3,sK0),mult(sF3,sK0)),
inference(superposition,[],[f184,f17494]) ).
fof(f17553,plain,
rd(sF2,rd(sK0,sK0)) = rd(mult(sF3,sK0),mult(sF3,sK0)),
inference(forward_demodulation,[],[f17529,f8469]) ).
fof(f17566,plain,
ld(sF3,sK0) = rd(sF2,rd(sK0,sK0)),
inference(forward_demodulation,[],[f17553,f17515]) ).
fof(f17575,plain,
sF2 = mult(ld(sF3,sK0),rd(sK0,sK0)),
inference(superposition,[],[f12,f17566]) ).
fof(f17576,plain,
rd(sK0,sK0) = ld(ld(sF3,sK0),sF2),
inference(superposition,[],[f46,f17566]) ).
fof(f17580,plain,
! [X0] : ld(ld(sF3,sK0),X0) = mult(rd(rd(sK0,sK0),sF2),X0),
inference(superposition,[],[f244,f17566]) ).
fof(f17589,plain,
! [X0] : ld(ld(sF3,sK0),X0) = mult(ld(sF3,sK0),X0),
inference(forward_demodulation,[],[f17580,f4587]) ).
fof(f19970,plain,
ld(mult(sF2,ld(sF3,sK0)),sF2) = ld(ld(sF3,sK0),rd(rd(sK0,sK0),rd(sK0,sK0))),
inference(superposition,[],[f2246,f17576]) ).
fof(f20087,plain,
ld(mult(sF2,ld(sF3,sK0)),sF2) = mult(ld(sF3,sK0),rd(rd(sK0,sK0),rd(sK0,sK0))),
inference(forward_demodulation,[],[f19970,f17589]) ).
fof(f20128,plain,
ld(mult(sF2,ld(sF3,sK0)),sF2) = mult(ld(sF3,sK0),rd(sK0,sK0)),
inference(forward_demodulation,[],[f20087,f2347]) ).
fof(f20155,plain,
sF2 = ld(mult(sF2,ld(sF3,sK0)),sF2),
inference(forward_demodulation,[],[f20128,f17575]) ).
fof(f20175,plain,
sF2 = ld(rd(sF4,sF4),sF2),
inference(forward_demodulation,[],[f20155,f2329]) ).
fof(f20190,plain,
sF2 = mult(rd(sF4,sF4),sF2),
inference(forward_demodulation,[],[f20175,f244]) ).
fof(f20234,plain,
! [X0] : rd(ld(sF2,X0),mult(sF2,ld(sF2,X0))) = ld(sF2,rd(sF4,sF4)),
inference(superposition,[],[f1970,f20190]) ).
fof(f20255,plain,
! [X0] : rd(ld(sF2,X0),mult(sF2,ld(sF2,X0))) = mult(sF2,rd(sF4,sF4)),
inference(forward_demodulation,[],[f20234,f512]) ).
fof(f20293,plain,
! [X0] : rd(ld(sF2,X0),mult(sF2,ld(sF2,X0))) = ld(sF3,sK0),
inference(forward_demodulation,[],[f20255,f2355]) ).
fof(f20322,plain,
ld(sF2,rd(sF2,sF2)) = ld(sF3,sK0),
inference(forward_demodulation,[],[f20293,f5902]) ).
fof(f20344,plain,
rd(rd(sF2,sF2),sF2) = ld(sF3,sK0),
inference(forward_demodulation,[],[f20322,f572]) ).
fof(f20355,plain,
mult(sF2,sF2) = ld(sF3,sK0),
inference(forward_demodulation,[],[f20344,f14683]) ).
fof(f20362,plain,
rd(sF2,sF2) = ld(sF3,sK0),
inference(forward_demodulation,[],[f20355,f523]) ).
fof(f20365,plain,
sF2 = ld(sF3,sK0),
inference(forward_demodulation,[],[f20362,f2350]) ).
fof(f20369,plain,
rd(sK0,sK0) = mult(sF2,sF2),
inference(superposition,[],[f4580,f20365]) ).
fof(f20372,plain,
sK0 = mult(sF3,sF2),
inference(superposition,[],[f10,f20365]) ).
fof(f20374,plain,
sF3 = rd(sK0,sF2),
inference(superposition,[],[f47,f20365]) ).
fof(f20417,plain,
sK0 = rd(sK0,sF2),
inference(forward_demodulation,[],[f20372,f7303]) ).
fof(f20420,plain,
rd(sK0,sK0) = rd(sF2,sF2),
inference(forward_demodulation,[],[f20369,f523]) ).
fof(f20430,plain,
sK0 = sF3,
inference(forward_demodulation,[],[f20417,f20374]) ).
fof(f20433,plain,
sF2 = rd(sK0,sK0),
inference(forward_demodulation,[],[f20420,f2350]) ).
fof(f20440,plain,
spl5_2,
inference(avatar_split_clause,[],[f20430,f28]) ).
fof(f20547,plain,
sK0 = ld(sF2,sK0),
inference(superposition,[],[f46,f20433]) ).
fof(f20563,plain,
sK0 = mult(sF2,sK0),
inference(forward_demodulation,[],[f20547,f512]) ).
fof(f20583,plain,
sK0 = sF4,
inference(forward_demodulation,[],[f20563,f21]) ).
fof(f20597,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f20583,f26]) ).
fof(f20598,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f20597]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f20440]) ).
cnf(s4,plain,
spl5_1,
inference(sat_conversion,[],[f20598]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
fof(f20610,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP654+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n026.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 10:33:56 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 10.26/2.36 % (2634723)Detected formulas, will run a generic FOF schedule.
% 10.26/2.36 % (2634731)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4226828307:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.26/2.36 % (2634731)Refutation not found, incomplete strategy
% 10.26/2.36 % (2634731)------------------------------
% 10.26/2.36 % (2634731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.36 % (2634731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.36 % (2634731)CaDiCaL version: 2.1.3
% 10.26/2.36 % (2634731)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.36 % (2634731)Time elapsed: 0.001 s
% 10.26/2.36 % (2634731)Peak memory usage: 88 MB
% 10.26/2.36 % (2634733)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3753879632:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.26/2.36 % (2634734)dis-21_1_sil=8000:lcm=predicate:random_seed=885504062:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.26/2.36 % (2634732)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=389626086:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.26/2.36 % (2634730)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4279371466:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.26/2.36 % (2634729)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=149630912:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.26/2.36 % (2634728)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=608175535:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.26/2.36 % (2634734)Refutation not found, incomplete strategy
% 10.26/2.36 % (2634734)------------------------------
% 10.26/2.36 % (2634734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.36 % (2634734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.36 % (2634734)CaDiCaL version: 2.1.3
% 10.26/2.36 % (2634734)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.36 % (2634734)Time elapsed: 0.001 s
% 10.26/2.36 % (2634734)Peak memory usage: 88 MB
% 10.26/2.36 % (2634732)Instruction limit reached!
% 10.26/2.36 % (2634732)------------------------------
% 10.26/2.36 % (2634732)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.36 % (2634732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.36 % (2634732)CaDiCaL version: 2.1.3
% 10.26/2.36 % (2634732)Termination reason: Instruction limit
% 10.26/2.36 % (2634732)Termination phase: Saturation
% 10.26/2.36 % (2634732)Time elapsed: 0.066 s
% 10.26/2.36 % (2634732)Peak memory usage: 89 MB
% 10.26/2.36 % (2634732)Instructions burned: 121 (million)
% 10.26/2.36 % (2634733)Instruction limit reached!
% 10.26/2.36 % (2634733)------------------------------
% 10.26/2.36 % (2634733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.36 % (2634733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.36 % (2634733)CaDiCaL version: 2.1.3
% 10.26/2.36 % (2634733)Termination reason: Instruction limit
% 10.26/2.36 % (2634733)Termination phase: Saturation
% 10.26/2.36 % (2634733)Time elapsed: 0.079 s
% 10.26/2.36 % (2634733)Peak memory usage: 89 MB
% 10.26/2.36 % (2634733)Instructions burned: 139 (million)
% 10.26/2.36 % (2634731)------------------------------
% 10.26/2.36 % (2634731)------------------------------
% 10.26/2.36 % (2634742)lrs+10_1_sil=8000:sp=occurrence:random_seed=3295505815:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 10.26/2.36 % (2634743)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1276006411:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.26/2.36 % (2634744)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2431322531:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.26/2.36 % (2634734)------------------------------
% 10.26/2.36 % (2634734)------------------------------
% 10.26/2.36 % (2634743)Instruction limit reached!
% 10.26/2.36 % (2634743)------------------------------
% 10.26/2.36 % (2634743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634743)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634743)Termination reason: Instruction limit
% 12.67/2.75 % (2634743)Termination phase: Saturation
% 12.67/2.75 % (2634743)Time elapsed: 0.100 s
% 12.67/2.75 % (2634743)Peak memory usage: 90 MB
% 12.67/2.75 % (2634743)Instructions burned: 159 (million)
% 12.67/2.75 % (2634744)Instruction limit reached!
% 12.67/2.75 % (2634744)------------------------------
% 12.67/2.75 % (2634744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634744)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634744)Termination reason: Instruction limit
% 12.67/2.75 % (2634744)Termination phase: Saturation
% 12.67/2.75 % (2634744)Time elapsed: 0.106 s
% 12.67/2.75 % (2634744)Peak memory usage: 92 MB
% 12.67/2.75 % (2634744)Instructions burned: 328 (million)
% 12.67/2.75 % (2634742)Instruction limit reached!
% 12.67/2.75 % (2634742)------------------------------
% 12.67/2.75 % (2634742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634742)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634742)Termination reason: Instruction limit
% 12.67/2.75 % (2634742)Termination phase: Saturation
% 12.67/2.75 % (2634742)Time elapsed: 0.176 s
% 12.67/2.75 % (2634742)Peak memory usage: 92 MB
% 12.67/2.75 % (2634742)Instructions burned: 285 (million)
% 12.67/2.75 % (2634748)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3044422505:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 12.67/2.75 % (2634750)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2607247637:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 12.67/2.75 % (2634749)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4104450592:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 12.67/2.75 % (2634749)Refutation not found, incomplete strategy
% 12.67/2.75 % (2634749)------------------------------
% 12.67/2.75 % (2634749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634749)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634749)Termination reason: Refutation not found, incomplete strategy
% 12.67/2.75 % (2634749)Time elapsed: 0.001 s
% 12.67/2.75 % (2634749)Peak memory usage: 88 MB
% 12.67/2.75 % (2634751)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1761202013:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 12.67/2.75 % (2634751)Refutation not found, incomplete strategy
% 12.67/2.75 % (2634751)------------------------------
% 12.67/2.75 % (2634751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634751)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634751)Termination reason: Refutation not found, incomplete strategy
% 12.67/2.75 % (2634751)Time elapsed: 0.001 s
% 12.67/2.75 % (2634751)Peak memory usage: 88 MB
% 12.67/2.75 % (2634748)Instruction limit reached!
% 12.67/2.75 % (2634748)------------------------------
% 12.67/2.75 % (2634748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634748)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634748)Termination reason: Instruction limit
% 12.67/2.75 % (2634748)Termination phase: Saturation
% 12.67/2.75 % (2634748)Time elapsed: 0.160 s
% 12.67/2.75 % (2634748)Peak memory usage: 92 MB
% 12.67/2.75 % (2634748)Instructions burned: 249 (million)
% 12.67/2.75 % (2634730)Refutation not found, incomplete strategy
% 12.67/2.75 % (2634730)------------------------------
% 12.67/2.75 % (2634730)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.67/2.75 % (2634730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.67/2.75 % (2634730)CaDiCaL version: 2.1.3
% 12.67/2.75 % (2634730)Termination reason: Refutation not found, incomplete strategy
% 12.67/2.75 % (2634730)Time elapsed: 0.598 s
% 12.67/2.75 % (2634730)Peak memory usage: 126 MB
% 12.67/2.75 % (2634730)Instructions burned: 887 (million)
% 12.67/2.75 % (2634749)------------------------------
% 12.67/2.75 % (2634749)------------------------------
% 15.80/3.12 % (2634756)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2448995240:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 15.80/3.12 % (2634756)Refutation not found, incomplete strategy
% 15.80/3.12 % (2634756)------------------------------
% 15.80/3.12 % (2634756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.12 % (2634756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.12 % (2634756)CaDiCaL version: 2.1.3
% 15.80/3.12 % (2634756)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.12 % (2634756)Time elapsed: 0.001 s
% 15.80/3.12 % (2634756)Peak memory usage: 87 MB
% 15.80/3.12 % (2634751)------------------------------
% 15.80/3.12 % (2634751)------------------------------
% 15.80/3.12 % (2634758)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=212373776:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 15.80/3.12 % (2634758)Refutation not found, incomplete strategy
% 15.80/3.12 % (2634758)------------------------------
% 15.80/3.12 % (2634758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.12 % (2634758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.12 % (2634758)CaDiCaL version: 2.1.3
% 15.80/3.12 % (2634758)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.12 % (2634758)Time elapsed: 0.001 s
% 15.80/3.12 % (2634758)Peak memory usage: 88 MB
% 15.80/3.12 % (2634730)------------------------------
% 15.80/3.12 % (2634730)------------------------------
% 15.80/3.12 % (2634759)lrs+10_1_sil=8000:sp=occurrence:random_seed=1413768629:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 15.80/3.12 % (2634756)------------------------------
% 15.80/3.12 % (2634756)------------------------------
% 15.80/3.12 % (2634761)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4009845720:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 15.80/3.12 % (2634761)Refutation not found, incomplete strategy
% 15.80/3.12 % (2634761)------------------------------
% 15.80/3.12 % (2634761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.12 % (2634761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.12 % (2634761)CaDiCaL version: 2.1.3
% 15.80/3.12 % (2634761)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.12 % (2634761)Time elapsed: 0.001 s
% 15.80/3.12 % (2634761)Peak memory usage: 88 MB
% 15.80/3.12 % (2634758)------------------------------
% 15.80/3.12 % (2634758)------------------------------
% 15.80/3.12 % (2634763)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3639492554:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 15.80/3.12 % (2634765)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3066326513:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 15.80/3.12 % (2634765)Refutation not found, incomplete strategy
% 15.80/3.12 % (2634765)------------------------------
% 15.80/3.12 % (2634765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.12 % (2634765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.12 % (2634765)CaDiCaL version: 2.1.3
% 15.80/3.12 % (2634765)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.12 % (2634765)Time elapsed: 0.001 s
% 15.80/3.12 % (2634765)Peak memory usage: 88 MB
% 15.80/3.12 % (2634750)Instruction limit reached!
% 15.80/3.12 % (2634750)------------------------------
% 15.80/3.12 % (2634750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.12 % (2634750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.12 % (2634750)CaDiCaL version: 2.1.3
% 15.80/3.12 % (2634750)Termination reason: Instruction limit
% 15.80/3.12 % (2634750)Termination phase: Saturation
% 15.80/3.12 % (2634750)Time elapsed: 0.797 s
% 15.80/3.12 % (2634750)Peak memory usage: 143 MB
% 15.80/3.12 % (2634750)Instructions burned: 2353 (million)
% 15.80/3.12 % (2634761)------------------------------
% 15.80/3.12 % (2634761)------------------------------
% 15.80/3.12 % (2634768)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2108441632:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 15.80/3.12 % (2634769)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=496902006:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 15.80/3.13 % (2634765)------------------------------
% 15.80/3.13 % (2634765)------------------------------
% 15.80/3.13 % (2634759)Instruction limit reached!
% 15.80/3.13 % (2634759)------------------------------
% 15.80/3.13 % (2634759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634759)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634759)Termination reason: Instruction limit
% 15.80/3.13 % (2634759)Termination phase: Saturation
% 15.80/3.13 % (2634759)Time elapsed: 0.557 s
% 15.80/3.13 % (2634759)Peak memory usage: 99 MB
% 15.80/3.13 % (2634759)Instructions burned: 909 (million)
% 15.80/3.13 % (2634768)Instruction limit reached!
% 15.80/3.13 % (2634768)------------------------------
% 15.80/3.13 % (2634768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634768)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634768)Termination reason: Instruction limit
% 15.80/3.13 % (2634768)Termination phase: Saturation
% 15.80/3.13 % (2634768)Time elapsed: 0.173 s
% 15.80/3.13 % (2634768)Peak memory usage: 93 MB
% 15.80/3.13 % (2634768)Instructions burned: 593 (million)
% 15.80/3.13 % (2634772)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2579855840:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/125Mi)
% 15.80/3.13 % (2634773)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=192090935:i=134:gtgl=5:slsql=off:gtg=exists_sym_2984 on theBenchmark for (2984ds/134Mi)
% 15.80/3.13 % (2634774)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=483600875:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/141Mi)
% 15.80/3.13 % (2634774)Refutation not found, incomplete strategy
% 15.80/3.13 % (2634774)------------------------------
% 15.80/3.13 % (2634774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634774)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634774)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.13 % (2634774)Time elapsed: 0.0000 s
% 15.80/3.13 % (2634774)Peak memory usage: 88 MB
% 15.80/3.13 % (2634773)Instruction limit reached!
% 15.80/3.13 % (2634773)------------------------------
% 15.80/3.13 % (2634773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634773)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634773)Termination reason: Instruction limit
% 15.80/3.13 % (2634773)Termination phase: Saturation
% 15.80/3.13 % (2634773)Time elapsed: 0.060 s
% 15.80/3.13 % (2634773)Peak memory usage: 90 MB
% 15.80/3.13 % (2634773)Instructions burned: 134 (million)
% 15.80/3.13 % (2634772)Instruction limit reached!
% 15.80/3.13 % (2634772)------------------------------
% 15.80/3.13 % (2634772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634772)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634772)Termination reason: Instruction limit
% 15.80/3.13 % (2634772)Termination phase: Saturation
% 15.80/3.13 % (2634772)Time elapsed: 0.082 s
% 15.80/3.13 % (2634772)Peak memory usage: 90 MB
% 15.80/3.13 % (2634772)Instructions burned: 126 (million)
% 15.80/3.13 % (2634774)------------------------------
% 15.80/3.13 % (2634774)------------------------------
% 15.80/3.13 % (2634778)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=663415730:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2982 on theBenchmark for (2982ds/431Mi)
% 15.80/3.13 % (2634779)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2792661761:i=6060:aac=none:ins=25_2982 on theBenchmark for (2982ds/6060Mi)
% 15.80/3.13 % (2634778)Refutation not found, incomplete strategy
% 15.80/3.13 % (2634778)------------------------------
% 15.80/3.13 % (2634778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634778)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634778)Termination reason: Refutation not found, incomplete strategy
% 15.80/3.13 % (2634778)Time elapsed: 0.001 s
% 15.80/3.13 % (2634778)Peak memory usage: 88 MB
% 15.80/3.13 % (2634780)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=3003806958:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2981 on theBenchmark for (2981ds/150Mi)
% 15.80/3.13 % (2634728)First to succeed.
% 15.80/3.13 % (2634728)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2634723"
% 15.80/3.13 % (2634780)Instruction limit reached!
% 15.80/3.13 % (2634780)------------------------------
% 15.80/3.13 % (2634780)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.80/3.13 % (2634780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.80/3.13 % (2634780)CaDiCaL version: 2.1.3
% 15.80/3.13 % (2634780)Termination reason: Instruction limit
% 15.80/3.13 % (2634780)Termination phase: Saturation
% 15.80/3.13 % (2634780)Time elapsed: 0.050 s
% 15.80/3.13 % (2634780)Peak memory usage: 91 MB
% 15.80/3.13 % (2634780)Instructions burned: 151 (million)
% 15.80/3.13 % (2634778)------------------------------
% 15.80/3.13 % (2634778)------------------------------
% 15.80/3.13 % (2634784)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=2649816002:i=14155:bd=all_2979 on theBenchmark for (2979ds/14155Mi)
% 15.80/3.13 % (2634728)Refutation found. Thanks to Tanya!
% 15.80/3.13 % SZS status Theorem for theBenchmark
% 15.80/3.13 % SZS output start Proof for theBenchmark
% See solution above
% 16.67/3.32 % (2634728)------------------------------
% 16.67/3.32 % (2634728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.67/3.32 % (2634728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.67/3.32 % (2634728)CaDiCaL version: 2.1.3
% 16.67/3.32 % (2634728)Termination reason: Refutation
% 16.67/3.32 % (2634728)Time elapsed: 1.848 s
% 16.67/3.32 % (2634728)Peak memory usage: 149 MB
% 16.67/3.32 % (2634728)Instructions burned: 2965 (million)
% 16.67/3.32 % (2634728)------------------------------
% 16.67/3.32 % (2634728)------------------------------
% 16.67/3.32 % (2634723)Success in time 2.272 s
% 16.67/3.32 % Vampire exiting
%------------------------------------------------------------------------------