%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC225+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:03:01 PM UTC 2026
% Result : Theorem 4.67s 1.60s
% Output : Refutation 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 111 ( 23 unt; 8 def)
% Number of atoms : 433 ( 118 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 530 ( 208 ~; 236 |; 62 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 142 ( 0 sgn 117 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) )
| ! [X8] :
( ssList(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(app(X8,X2),X9) != X3
| ~ equalelemsP(X2)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X10,nil)) = X8
& ? [X12] :
( ssList(X12)
& app(cons(X10,nil),X12) = X2 ) ) )
| ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(cons(X13,nil),X14) = X9
& ? [X15] :
( ssList(X15)
& app(X15,cons(X13,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| nil = X0
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ! [X7] :
( ~ ssItem(X7)
| ~ memberP(X5,X7)
| ~ memberP(X6,X7)
| ~ leq(X4,X7)
| leq(X7,X4) ) ) ) )
| ! [X8] :
( ssList(X8)
=> ! [X9] :
( ~ ssList(X9)
| app(app(X8,X2),X9) != X3
| ~ equalelemsP(X2)
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(X11,cons(X10,nil)) = X8
& ? [X12] :
( ssList(X12)
& app(cons(X10,nil),X12) = X2 ) ) )
| ? [X13] :
( ssItem(X13)
& ? [X14] :
( ssList(X14)
& app(cons(X13,nil),X14) = X9
& ? [X15] :
( ssList(X15)
& app(X15,cons(X13,nil)) = X2 ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f192,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& nil != X0
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ? [X7] :
( ssItem(X7)
& memberP(X5,X7)
& memberP(X6,X7)
& leq(X4,X7)
& ~ leq(X7,X4) ) ) ) )
& ? [X8] :
( ? [X9] :
( ssList(X9)
& app(app(X8,X2),X9) = X3
& equalelemsP(X2)
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != X8
| ! [X12] :
( ~ ssList(X12)
| app(cons(X10,nil),X12) != X2 ) ) )
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| app(cons(X13,nil),X14) != X9
| ! [X15] :
( ~ ssList(X15)
| app(X15,cons(X13,nil)) != X2 ) ) ) )
& ssList(X8) )
& ( nil = X3
| nil != X2 ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& nil != sK53
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ( ssItem(sK57(X4,X5,X6))
& memberP(X5,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& leq(X4,sK57(X4,X5,X6))
& ~ leq(sK57(X4,X5,X6),X4) ) ) ) )
& ssList(sK59)
& sK56 = app(app(sK58,sK55),sK59)
& equalelemsP(sK55)
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X10,nil)) != sK58
| ! [X12] :
( ~ ssList(X12)
| app(cons(X10,nil),X12) != sK55 ) ) )
& ! [X13] :
( ~ ssItem(X13)
| ! [X14] :
( ~ ssList(X14)
| app(cons(X13,nil),X14) != sK59
| ! [X15] :
( ~ ssList(X15)
| app(X15,cons(X13,nil)) != sK55 ) ) )
& ssList(sK58)
& ( nil = sK56
| nil != sK55 )
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58),skolemize(X9,sK59)],[f221]) ).
fof(f387,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f396,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f398,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f418,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f473,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f476,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| memberP(X5,sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK53
| ssItem(sK57(X4,X5,X6)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
nil != sK53,
inference(cnf_transformation,[],[f295]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
nil != sK55,
inference(definition_unfolding,[],[f510,f511]) ).
fof(f515,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f516,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_unfolding,[],[f508,f511]) ).
fof(f521,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f511]) ).
fof(f549,definition,
! [X4] : sF60(X4) = cons(X4,nil),
introduced(definition,[new_symbols(definition,[sF60])],[function_definition]) ).
fof(f550,plain,
! [X4] : cons(X4,nil) = sF60(X4),
inference(reorient_equations,[],[f549]) ).
fof(f551,definition,
! [X4,X5] : sF61(X5,X4) = app(X5,sF60(X4)),
introduced(definition,[new_symbols(definition,[sF61])],[function_definition]) ).
fof(f552,plain,
! [X4,X5] : app(X5,sF60(X4)) = sF61(X5,X4),
inference(reorient_equations,[],[f551]) ).
fof(f553,definition,
! [X6,X4,X5] : sF62(X5,X4,X6) = app(sF61(X5,X4),X6),
introduced(definition,[new_symbols(definition,[sF62])],[function_definition]) ).
fof(f554,plain,
! [X6,X4,X5] : app(sF61(X5,X4),X6) = sF62(X5,X4,X6),
inference(reorient_equations,[],[f553]) ).
fof(f555,plain,
! [X6,X4,X5] :
( sK55 != sF62(X5,X4,X6)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| ssItem(sK57(X4,X5,X6)) ),
inference(definition_folding,[],[f515,f554,f552,f550]) ).
fof(f556,plain,
! [X6,X4,X5] :
( sK55 != sF62(X5,X4,X6)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ ssItem(X4)
| memberP(X5,sK57(X4,X5,X6)) ),
inference(definition_folding,[],[f516,f554,f552,f550]) ).
fof(f565,definition,
! [X10,X12] : sF65(X10,X12) = app(sF60(X10),X12),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f566,plain,
! [X10,X12] : app(sF60(X10),X12) = sF65(X10,X12),
inference(reorient_equations,[],[f565]) ).
fof(f577,definition,
( spl66_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl66_1])],[avatar_definition]) ).
fof(f579,plain,
( nil != sK55
| spl66_1 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f585,plain,
~ spl66_1,
inference(avatar_split_clause,[],[f514,f577]) ).
fof(f587,definition,
( spl66_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl66_3])],[avatar_definition]) ).
fof(f588,plain,
( ssList(nil)
| ~ spl66_3 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f615,plain,
spl66_3,
inference(avatar_split_clause,[],[f388,f587]) ).
fof(f626,plain,
! [X0] :
( ssList(sF60(X0))
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f387,f550]) ).
fof(f627,plain,
( ! [X0] :
( ssList(sF60(X0))
| ~ ssItem(X0) )
| ~ spl66_3 ),
inference(forward_subsumption_resolution,[],[f626,f588]) ).
fof(f630,plain,
( nil = sK55
| sK55 = cons(hd(sK55),tl(sK55)) ),
inference(resolution,[],[f473,f521]) ).
fof(f651,plain,
( sK55 = cons(hd(sK55),tl(sK55))
| spl66_1 ),
inference(forward_subsumption_resolution,[],[f630,f579]) ).
fof(f657,plain,
! [X0,X1] :
( ~ ssItem(X0)
| cons(X0,tl(X1)) = app(cons(X0,nil),tl(X1))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f476,f398]) ).
fof(f664,plain,
! [X0,X1] :
( cons(X0,tl(X1)) = app(sF60(X0),tl(X1))
| ~ ssItem(X0)
| nil = X1
| ~ ssList(X1) ),
inference(forward_demodulation,[],[f657,f550]) ).
fof(f670,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| nil = X1
| cons(X0,tl(X1)) = sF65(X0,tl(X1)) ),
inference(forward_demodulation,[],[f664,f566]) ).
fof(f680,plain,
( ! [X0] :
( ~ ssItem(X0)
| sF60(X0) = app(nil,sF60(X0)) )
| ~ spl66_3 ),
inference(resolution,[],[f627,f402]) ).
fof(f681,plain,
( ! [X0] :
( ~ ssItem(X0)
| sF60(X0) = sF61(nil,X0) )
| ~ spl66_3 ),
inference(forward_demodulation,[],[f680,f552]) ).
fof(f832,plain,
! [X0] :
( ~ ssItem(X0)
| nil = sK55
| cons(X0,tl(sK55)) = sF65(X0,tl(sK55)) ),
inference(resolution,[],[f670,f521]) ).
fof(f840,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,tl(sK55)) = sF65(X0,tl(sK55)) )
| spl66_1 ),
inference(forward_subsumption_resolution,[],[f832,f579]) ).
fof(f947,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(sK55)) = sF65(hd(X0),tl(sK55)) )
| spl66_1 ),
inference(resolution,[],[f840,f396]) ).
fof(f1004,plain,
( nil = sK55
| cons(hd(sK55),tl(sK55)) = sF65(hd(sK55),tl(sK55))
| spl66_1 ),
inference(resolution,[],[f947,f521]) ).
fof(f1013,plain,
( cons(hd(sK55),tl(sK55)) = sF65(hd(sK55),tl(sK55))
| spl66_1 ),
inference(forward_subsumption_resolution,[],[f1004,f579]) ).
fof(f1016,plain,
( sK55 = sF65(hd(sK55),tl(sK55))
| spl66_1 ),
inference(forward_demodulation,[],[f1013,f651]) ).
fof(f1154,definition,
( spl66_31
<=> ssList(tl(sK55)) ),
introduced(definition,[new_symbols(definition,[spl66_31])],[avatar_definition]) ).
fof(f1155,plain,
( ssList(tl(sK55))
| ~ spl66_31 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1156,plain,
( ~ ssList(tl(sK55))
| spl66_31 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1158,definition,
( spl66_32
<=> ssItem(hd(sK55)) ),
introduced(definition,[new_symbols(definition,[spl66_32])],[avatar_definition]) ).
fof(f1159,plain,
( ssItem(hd(sK55))
| ~ spl66_32 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1160,plain,
( ~ ssItem(hd(sK55))
| spl66_32 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1222,plain,
( nil = sK55
| ~ ssList(sK55)
| spl66_31 ),
inference(resolution,[],[f1156,f398]) ).
fof(f1223,plain,
( ~ ssList(sK55)
| spl66_1
| spl66_31 ),
inference(forward_subsumption_resolution,[],[f1222,f579]) ).
fof(f1224,plain,
( $false
| spl66_1
| spl66_31 ),
inference(forward_subsumption_resolution,[],[f1223,f521]) ).
fof(f1225,plain,
( spl66_1
| spl66_31 ),
inference(avatar_contradiction_clause,[],[f1224]) ).
fof(f1274,plain,
( nil = sK55
| ~ ssList(sK55)
| spl66_32 ),
inference(resolution,[],[f1160,f396]) ).
fof(f1275,plain,
( ~ ssList(sK55)
| spl66_1
| spl66_32 ),
inference(forward_subsumption_resolution,[],[f1274,f579]) ).
fof(f1276,plain,
( $false
| spl66_1
| spl66_32 ),
inference(forward_subsumption_resolution,[],[f1275,f521]) ).
fof(f1277,plain,
( spl66_1
| spl66_32 ),
inference(avatar_contradiction_clause,[],[f1276]) ).
fof(f1283,plain,
( sF60(hd(sK55)) = sF61(nil,hd(sK55))
| ~ spl66_3
| ~ spl66_32 ),
inference(resolution,[],[f1159,f681]) ).
fof(f1301,plain,
( ! [X0] : sF62(nil,hd(sK55),X0) = app(sF60(hd(sK55)),X0)
| ~ spl66_3
| ~ spl66_32 ),
inference(superposition,[],[f554,f1283]) ).
fof(f1302,plain,
( ! [X0] : sF65(hd(sK55),X0) = sF62(nil,hd(sK55),X0)
| ~ spl66_3
| ~ spl66_32 ),
inference(forward_demodulation,[],[f1301,f566]) ).
fof(f1386,plain,
( ! [X0] :
( sK55 != sF65(hd(sK55),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| ssItem(sK57(hd(sK55),nil,X0)) )
| ~ spl66_3
| ~ spl66_32 ),
inference(superposition,[],[f555,f1302]) ).
fof(f1388,plain,
( ! [X0] :
( sK55 != sF65(hd(sK55),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| memberP(nil,sK57(hd(sK55),nil,X0)) )
| ~ spl66_3
| ~ spl66_32 ),
inference(superposition,[],[f556,f1302]) ).
fof(f1391,plain,
( ! [X0] :
( sK55 != sF65(hd(sK55),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| memberP(nil,sK57(hd(sK55),nil,X0)) )
| ~ spl66_3
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1388,f588]) ).
fof(f1393,plain,
( ! [X0] :
( sK55 != sF65(hd(sK55),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sK55))
| ssItem(sK57(hd(sK55),nil,X0)) )
| ~ spl66_3
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1386,f588]) ).
fof(f1397,plain,
( ! [X0] :
( sK55 != sF65(hd(sK55),X0)
| ~ ssList(X0)
| memberP(nil,sK57(hd(sK55),nil,X0)) )
| ~ spl66_3
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1391,f1159]) ).
fof(f1399,plain,
( ! [X0] :
( sK55 != sF65(hd(sK55),X0)
| ~ ssList(X0)
| ssItem(sK57(hd(sK55),nil,X0)) )
| ~ spl66_3
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1393,f1159]) ).
fof(f1402,plain,
( sK55 != sK55
| ~ ssList(tl(sK55))
| memberP(nil,sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_32 ),
inference(superposition,[],[f1397,f1016]) ).
fof(f1404,plain,
( ~ ssList(tl(sK55))
| memberP(nil,sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_32 ),
inference(trivial_inequality_removal,[],[f1402]) ).
fof(f1405,plain,
( memberP(nil,sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_31
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1404,f1155]) ).
fof(f1412,plain,
( sK55 != sK55
| ~ ssList(tl(sK55))
| ssItem(sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_32 ),
inference(superposition,[],[f1399,f1016]) ).
fof(f1414,plain,
( ~ ssList(tl(sK55))
| ssItem(sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_32 ),
inference(trivial_inequality_removal,[],[f1412]) ).
fof(f1415,plain,
( ssItem(sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_31
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1414,f1155]) ).
fof(f1425,plain,
( ~ ssItem(sK57(hd(sK55),nil,tl(sK55)))
| spl66_1
| ~ spl66_3
| ~ spl66_31
| ~ spl66_32 ),
inference(resolution,[],[f1405,f418]) ).
fof(f1430,plain,
( $false
| spl66_1
| ~ spl66_3
| ~ spl66_31
| ~ spl66_32 ),
inference(forward_subsumption_resolution,[],[f1425,f1415]) ).
fof(f1431,plain,
( spl66_1
| ~ spl66_3
| ~ spl66_31
| ~ spl66_32 ),
inference(avatar_contradiction_clause,[],[f1430]) ).
cnf(s2,plain,
~ spl66_1,
inference(sat_conversion,[],[f585]) ).
cnf(s10,plain,
spl66_3,
inference(sat_conversion,[],[f615]) ).
cnf(s32,plain,
( spl66_1
| spl66_31 ),
inference(sat_conversion,[],[f1225]) ).
cnf(s40,plain,
( spl66_1
| spl66_32 ),
inference(sat_conversion,[],[f1277]) ).
cnf(s53,plain,
( spl66_1
| ~ spl66_3
| ~ spl66_31
| ~ spl66_32 ),
inference(sat_conversion,[],[f1431]) ).
cnf(s58,plain,
spl66_32,
inference(rat,[],[s40,s2]) ).
cnf(s59,plain,
spl66_31,
inference(rat,[],[s32,s2]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s53,s2,s10,s58,s59]) ).
fof(f1434,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC225+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n016.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 08:37:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.67/1.60 % (3478990)Detected formulas, will run a generic FOF schedule.
% 4.67/1.60 % (3479001)dis-21_1_sil=8000:lcm=predicate:random_seed=3022165840: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)
% 4.67/1.60 % (3479000)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=717176847:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.67/1.60 % (3478999)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=472924737:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.67/1.60 % (3478998)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1864417601:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.67/1.60 % (3478997)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=3166896702:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.67/1.60 % (3478995)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=3745206072:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.67/1.60 % (3478996)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=3459908713:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.67/1.60 % (3479001)Instruction limit reached!
% 4.67/1.60 % (3479001)------------------------------
% 4.67/1.60 % (3479001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479001)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479001)Termination reason: Instruction limit
% 4.67/1.60 % (3479001)Termination phase: Saturation
% 4.67/1.60 % (3479001)Time elapsed: 0.039 s
% 4.67/1.60 % (3479001)Peak memory usage: 91 MB
% 4.67/1.60 % (3479001)Instructions burned: 132 (million)
% 4.67/1.60 % (3478999)Instruction limit reached!
% 4.67/1.60 % (3478999)------------------------------
% 4.67/1.60 % (3478999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3478999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3478999)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3478999)Termination reason: Instruction limit
% 4.67/1.60 % (3478999)Termination phase: Saturation
% 4.67/1.60 % (3478999)Time elapsed: 0.070 s
% 4.67/1.60 % (3478999)Peak memory usage: 88 MB
% 4.67/1.60 % (3478999)Instructions burned: 119 (million)
% 4.67/1.60 % (3478998)Instruction limit reached!
% 4.67/1.60 % (3478998)------------------------------
% 4.67/1.60 % (3478998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3478998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3478998)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3478998)Termination reason: Instruction limit
% 4.67/1.60 % (3478998)Termination phase: Saturation
% 4.67/1.60 % (3478998)Time elapsed: 0.070 s
% 4.67/1.60 % (3478998)Peak memory usage: 89 MB
% 4.67/1.60 % (3478998)Instructions burned: 111 (million)
% 4.67/1.60 % (3479000)Instruction limit reached!
% 4.67/1.60 % (3479000)------------------------------
% 4.67/1.60 % (3479000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479000)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479000)Termination reason: Instruction limit
% 4.67/1.60 % (3479000)Termination phase: Saturation
% 4.67/1.60 % (3479000)Time elapsed: 0.094 s
% 4.67/1.60 % (3479000)Peak memory usage: 90 MB
% 4.67/1.60 % (3479000)Instructions burned: 139 (million)
% 4.67/1.60 % (3479009)lrs+10_1_sil=8000:sp=occurrence:random_seed=2777233591:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.67/1.60 % (3479010)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1017695067:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.67/1.60 % (3479011)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3377838632:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.67/1.60 % (3479009)Instruction limit reached!
% 4.67/1.60 % (3479009)------------------------------
% 4.67/1.60 % (3479009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479009)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479009)Termination reason: Instruction limit
% 4.67/1.60 % (3479009)Termination phase: Saturation
% 4.67/1.60 % (3479009)Time elapsed: 0.092 s
% 4.67/1.60 % (3479009)Peak memory usage: 92 MB
% 4.67/1.60 % (3479009)Instructions burned: 286 (million)
% 4.67/1.60 % (3479012)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=3752166178:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.67/1.60 % (3479010)Instruction limit reached!
% 4.67/1.60 % (3479010)------------------------------
% 4.67/1.60 % (3479010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479010)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479010)Termination reason: Instruction limit
% 4.67/1.60 % (3479010)Termination phase: Saturation
% 4.67/1.60 % (3479010)Time elapsed: 0.088 s
% 4.67/1.60 % (3479010)Peak memory usage: 95 MB
% 4.67/1.60 % (3479010)Instructions burned: 158 (million)
% 4.67/1.60 % (3479016)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3474481304:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.67/1.60 % (3479012)Instruction limit reached!
% 4.67/1.60 % (3479012)------------------------------
% 4.67/1.60 % (3479012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479012)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479012)Termination reason: Instruction limit
% 4.67/1.60 % (3479012)Termination phase: Saturation
% 4.67/1.60 % (3479012)Time elapsed: 0.124 s
% 4.67/1.60 % (3479012)Peak memory usage: 95 MB
% 4.67/1.60 % (3479012)Instructions burned: 250 (million)
% 4.67/1.60 % (3479011)Instruction limit reached!
% 4.67/1.60 % (3479011)------------------------------
% 4.67/1.60 % (3479011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479011)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479011)Termination reason: Instruction limit
% 4.67/1.60 % (3479011)Termination phase: Saturation
% 4.67/1.60 % (3479011)Time elapsed: 0.203 s
% 4.67/1.60 % (3479011)Peak memory usage: 92 MB
% 4.67/1.60 % (3479011)Instructions burned: 327 (million)
% 4.67/1.60 % (3479016)Instruction limit reached!
% 4.67/1.60 % (3479016)------------------------------
% 4.67/1.60 % (3479016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479016)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479016)Termination reason: Instruction limit
% 4.67/1.60 % (3479016)Termination phase: Saturation
% 4.67/1.60 % (3479016)Time elapsed: 0.093 s
% 4.67/1.60 % (3479016)Peak memory usage: 90 MB
% 4.67/1.60 % (3479016)Instructions burned: 299 (million)
% 4.67/1.60 % (3479018)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2438985913:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.67/1.60 % (3479020)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1469134522:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.67/1.60 % (3479021)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1127818890:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.67/1.60 % (3479022)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2474698127:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 4.67/1.60 % (3479022)Instruction limit reached!
% 4.67/1.60 % (3479022)------------------------------
% 4.67/1.60 % (3479022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479022)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479022)Termination reason: Instruction limit
% 4.67/1.60 % (3479022)Termination phase: Saturation
% 4.67/1.60 % (3479022)Time elapsed: 0.036 s
% 4.67/1.60 % (3479022)Peak memory usage: 89 MB
% 4.67/1.60 % (3479022)Instructions burned: 115 (million)
% 4.67/1.60 % (3479020)Instruction limit reached!
% 4.67/1.60 % (3479020)------------------------------
% 4.67/1.60 % (3479020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479020)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479020)Termination reason: Instruction limit
% 4.67/1.60 % (3479020)Termination phase: Saturation
% 4.67/1.60 % (3479020)Time elapsed: 0.076 s
% 4.67/1.60 % (3479020)Peak memory usage: 90 MB
% 4.67/1.60 % (3479020)Instructions burned: 114 (million)
% 4.67/1.60 % (3479021)Instruction limit reached!
% 4.67/1.60 % (3479021)------------------------------
% 4.67/1.60 % (3479021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479021)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479021)Termination reason: Instruction limit
% 4.67/1.60 % (3479021)Termination phase: Saturation
% 4.67/1.60 % (3479021)Time elapsed: 0.064 s
% 4.67/1.60 % (3479021)Peak memory usage: 89 MB
% 4.67/1.60 % (3479021)Instructions burned: 127 (million)
% 4.67/1.60 % (3479027)lrs+10_1_sil=8000:sp=occurrence:random_seed=538786038:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 4.67/1.60 % (3478995)First to succeed.
% 4.67/1.60 % (3479028)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4128113552:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 4.67/1.60 % (3479029)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1753736636:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 4.67/1.60 % (3478995)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3478990"
% 4.67/1.60 % (3478997)Also succeeded, but the first one will report.
% 4.67/1.60 % (3479027)Instruction limit reached!
% 4.67/1.60 % (3479027)------------------------------
% 4.67/1.60 % (3479027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.67/1.60 % (3479027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.67/1.60 % (3479027)CaDiCaL version: 2.1.3
% 4.67/1.60 % (3479027)Termination reason: Instruction limit
% 4.67/1.60 % (3479027)Termination phase: Saturation
% 4.67/1.60 % (3479027)Time elapsed: 0.268 s
% 4.67/1.60 % (3479027)Peak memory usage: 100 MB
% 4.67/1.60 % (3479027)Instructions burned: 907 (million)
% 4.67/1.60 % (3479028)Also succeeded, but the first one will report.
% 4.67/1.60 % (3478995)Refutation found. Thanks to Tanya!
% 4.67/1.60 % SZS status Theorem for theBenchmark
% 4.67/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 8.86/1.80 % (3478995)------------------------------
% 8.86/1.80 % (3478995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.86/1.80 % (3478995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.86/1.80 % (3478995)CaDiCaL version: 2.1.3
% 8.86/1.80 % (3478995)Termination reason: Refutation
% 8.86/1.80 % (3478995)Time elapsed: 0.777 s
% 8.86/1.80 % (3478995)Peak memory usage: 131 MB
% 8.86/1.80 % (3478995)Instructions burned: 1171 (million)
% 8.86/1.80 % (3478995)------------------------------
% 8.86/1.80 % (3478995)------------------------------
% 8.86/1.80 % (3478990)Success in time 1.2 s
% 8.86/1.80 % Vampire exiting
%------------------------------------------------------------------------------