%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC117+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:02:31 PM UTC 2026
% Result : Theorem 4.29s 1.56s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 25
% Syntax : Number of formulae : 165 ( 25 unt; 12 def)
% Number of atoms : 566 ( 86 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 691 ( 290 ~; 302 |; 56 &)
% ( 16 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 86 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| ~ equalelemsP(X2)
| ? [X4] :
( ssList(X4)
& neq(X2,X4)
& segmentP(X3,X4)
& segmentP(X4,X2)
& equalelemsP(X4) )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| ~ equalelemsP(X2)
| ? [X4] :
( ssList(X4)
& neq(X2,X4)
& segmentP(X3,X4)
& segmentP(X4,X2)
& equalelemsP(X4) )
| ( nil = X1
& nil = X0 )
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
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(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f185,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
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] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& equalelemsP(X2)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X2,X4)
| ~ segmentP(X3,X4)
| ~ segmentP(X4,X2)
| ~ equalelemsP(X4) )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& equalelemsP(X2)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X2,X4)
| ~ segmentP(X3,X4)
| ~ segmentP(X4,X2)
| ~ equalelemsP(X4) )
& ( nil != X1
| nil != X0 )
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& segmentP(sK56,sK55)
& equalelemsP(sK55)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ segmentP(X4,sK55)
| ~ equalelemsP(X4) )
& ( nil != sK54
| nil != sK53 )
& ( ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f390,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f397,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f442,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f467,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil != sK54
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4] :
( ~ segmentP(sK56,X4)
| ~ neq(sK55,X4)
| ~ ssList(X4)
| ~ segmentP(X4,sK55)
| ~ equalelemsP(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( nil != sK56
| nil != sK55 ),
inference(definition_unfolding,[],[f501,f506,f505]) ).
fof(f508,plain,
( ~ neq(sK55,nil)
| ~ segmentP(sK56,sK55) ),
inference(definition_unfolding,[],[f500,f505,f506,f505]) ).
fof(f509,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f506]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
fof(f516,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f318]) ).
fof(f546,definition,
( spl57_1
<=> segmentP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f550,definition,
( spl57_2
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f552,plain,
( ~ neq(sK55,nil)
| spl57_2 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f553,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f508,f550,f546]) ).
fof(f555,definition,
( spl57_3
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f556,plain,
( nil = sK55
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f557,plain,
( nil != sK55
| spl57_3 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f559,definition,
( spl57_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f561,plain,
( nil != sK56
| spl57_4 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f562,plain,
( ~ spl57_3
| ~ spl57_4 ),
inference(avatar_split_clause,[],[f507,f559,f555]) ).
fof(f563,plain,
spl57_1,
inference(avatar_split_clause,[],[f504,f546]) ).
fof(f565,definition,
( spl57_5
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f566,plain,
( ssList(nil)
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f593,plain,
spl57_5,
inference(avatar_split_clause,[],[f389,f565]) ).
fof(f596,plain,
( nil = sK55
| ~ ssList(nil)
| ~ ssList(sK55)
| spl57_2 ),
inference(resolution,[],[f552,f387]) ).
fof(f597,plain,
( ~ ssList(nil)
| ~ ssList(sK55)
| spl57_2
| spl57_3 ),
inference(forward_subsumption_resolution,[],[f596,f557]) ).
fof(f598,plain,
( ~ ssList(sK55)
| spl57_2
| spl57_3
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f597,f566]) ).
fof(f599,plain,
( $false
| spl57_2
| spl57_3
| ~ spl57_5 ),
inference(forward_subsumption_resolution,[],[f598,f510]) ).
fof(f600,plain,
( spl57_2
| spl57_3
| ~ spl57_5 ),
inference(avatar_contradiction_clause,[],[f599]) ).
fof(f633,plain,
( nil = sK56
| sK56 = cons(hd(sK56),tl(sK56)) ),
inference(resolution,[],[f474,f509]) ).
fof(f634,plain,
( sK56 = cons(hd(sK56),tl(sK56))
| spl57_4 ),
inference(forward_subsumption_resolution,[],[f633,f561]) ).
fof(f656,definition,
( spl57_13
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_13])],[avatar_definition]) ).
fof(f657,plain,
( ssList(tl(sK56))
| ~ spl57_13 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f658,plain,
( ~ ssList(tl(sK56))
| spl57_13 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f660,definition,
( spl57_14
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_14])],[avatar_definition]) ).
fof(f661,plain,
( ssItem(hd(sK56))
| ~ spl57_14 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f662,plain,
( ~ ssItem(hd(sK56))
| spl57_14 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f668,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_13 ),
inference(resolution,[],[f658,f399]) ).
fof(f669,plain,
( ~ ssList(sK56)
| spl57_4
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f668,f561]) ).
fof(f670,plain,
( $false
| spl57_4
| spl57_13 ),
inference(forward_subsumption_resolution,[],[f669,f509]) ).
fof(f671,plain,
( spl57_4
| spl57_13 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f684,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_14 ),
inference(resolution,[],[f662,f397]) ).
fof(f685,plain,
( ~ ssList(sK56)
| spl57_4
| spl57_14 ),
inference(forward_subsumption_resolution,[],[f684,f561]) ).
fof(f686,plain,
( $false
| spl57_4
| spl57_14 ),
inference(forward_subsumption_resolution,[],[f685,f509]) ).
fof(f687,plain,
( spl57_4
| spl57_14 ),
inference(avatar_contradiction_clause,[],[f686]) ).
fof(f692,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,tl(sK56)) = app(cons(X0,nil),tl(sK56)) )
| ~ spl57_13 ),
inference(resolution,[],[f477,f657]) ).
fof(f697,plain,
( cons(hd(sK56),tl(sK56)) = app(cons(hd(sK56),nil),tl(sK56))
| ~ spl57_13
| ~ spl57_14 ),
inference(resolution,[],[f692,f661]) ).
fof(f698,plain,
( sK56 = app(cons(hd(sK56),nil),tl(sK56))
| spl57_4
| ~ spl57_13
| ~ spl57_14 ),
inference(forward_demodulation,[],[f697,f634]) ).
fof(f706,definition,
( spl57_18
<=> ssList(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_18])],[avatar_definition]) ).
fof(f707,plain,
( ssList(cons(hd(sK56),nil))
| ~ spl57_18 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f708,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl57_18 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f714,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| spl57_18 ),
inference(resolution,[],[f708,f388]) ).
fof(f715,plain,
( ~ ssList(nil)
| ~ spl57_14
| spl57_18 ),
inference(forward_subsumption_resolution,[],[f714,f661]) ).
fof(f716,plain,
( $false
| ~ spl57_5
| ~ spl57_14
| spl57_18 ),
inference(forward_subsumption_resolution,[],[f715,f566]) ).
fof(f717,plain,
( ~ spl57_5
| ~ spl57_14
| spl57_18 ),
inference(avatar_contradiction_clause,[],[f716]) ).
fof(f721,plain,
( cons(hd(sK56),nil) = app(nil,cons(hd(sK56),nil))
| ~ spl57_18 ),
inference(resolution,[],[f707,f403]) ).
fof(f727,definition,
( spl57_21
<=> nil = cons(hd(sK56),nil) ),
introduced(definition,[new_symbols(definition,[spl57_21])],[avatar_definition]) ).
fof(f729,plain,
( nil = cons(hd(sK56),nil)
| ~ spl57_21 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f731,plain,
( ! [X0] :
( segmentP(app(cons(hd(sK56),nil),X0),cons(hd(sK56),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(cons(hd(sK56),nil),X0)) )
| ~ spl57_18 ),
inference(superposition,[],[f516,f721]) ).
fof(f733,plain,
( ! [X0] :
( segmentP(app(cons(hd(sK56),nil),X0),cons(hd(sK56),nil))
| ~ ssList(X0)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(cons(hd(sK56),nil),X0)) )
| ~ spl57_5
| ~ spl57_18 ),
inference(forward_subsumption_resolution,[],[f731,f566]) ).
fof(f734,plain,
( ! [X0] :
( segmentP(app(cons(hd(sK56),nil),X0),cons(hd(sK56),nil))
| ~ ssList(X0)
| ~ ssList(app(cons(hd(sK56),nil),X0)) )
| ~ spl57_5
| ~ spl57_18 ),
inference(forward_subsumption_resolution,[],[f733,f707]) ).
fof(f735,plain,
( segmentP(sK56,cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssList(sK56)
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(superposition,[],[f734,f698]) ).
fof(f736,plain,
( segmentP(sK56,cons(hd(sK56),nil))
| ~ ssList(sK56)
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(forward_subsumption_resolution,[],[f735,f657]) ).
fof(f737,plain,
( segmentP(sK56,cons(hd(sK56),nil))
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(forward_subsumption_resolution,[],[f736,f509]) ).
fof(f738,plain,
( ~ neq(sK55,cons(hd(sK56),nil))
| ~ ssList(cons(hd(sK56),nil))
| ~ segmentP(cons(hd(sK56),nil),sK55)
| ~ equalelemsP(cons(hd(sK56),nil))
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(resolution,[],[f737,f502]) ).
fof(f739,plain,
( ~ neq(sK55,cons(hd(sK56),nil))
| ~ segmentP(cons(hd(sK56),nil),sK55)
| ~ equalelemsP(cons(hd(sK56),nil))
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(forward_subsumption_resolution,[],[f738,f707]) ).
fof(f740,plain,
( ~ neq(nil,cons(hd(sK56),nil))
| ~ segmentP(cons(hd(sK56),nil),sK55)
| ~ equalelemsP(cons(hd(sK56),nil))
| ~ spl57_3
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(forward_demodulation,[],[f739,f556]) ).
fof(f741,plain,
( ~ segmentP(cons(hd(sK56),nil),nil)
| ~ neq(nil,cons(hd(sK56),nil))
| ~ equalelemsP(cons(hd(sK56),nil))
| ~ spl57_3
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(forward_demodulation,[],[f740,f556]) ).
fof(f743,definition,
( spl57_22
<=> equalelemsP(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_22])],[avatar_definition]) ).
fof(f745,plain,
( ~ equalelemsP(cons(hd(sK56),nil))
| spl57_22 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f747,definition,
( spl57_23
<=> neq(nil,cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_23])],[avatar_definition]) ).
fof(f749,plain,
( ~ neq(nil,cons(hd(sK56),nil))
| spl57_23 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f751,definition,
( spl57_24
<=> segmentP(cons(hd(sK56),nil),nil) ),
introduced(definition,[new_symbols(definition,[spl57_24])],[avatar_definition]) ).
fof(f753,plain,
( ~ segmentP(cons(hd(sK56),nil),nil)
| spl57_24 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f754,plain,
( ~ spl57_22
| ~ spl57_23
| ~ spl57_24
| ~ spl57_3
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18 ),
inference(avatar_split_clause,[],[f741,f706,f660,f656,f565,f559,f555,f751,f747,f743]) ).
fof(f755,plain,
( ~ ssItem(hd(sK56))
| spl57_22 ),
inference(resolution,[],[f745,f467]) ).
fof(f756,plain,
( $false
| ~ spl57_14
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f755,f661]) ).
fof(f757,plain,
( ~ spl57_14
| spl57_22 ),
inference(avatar_contradiction_clause,[],[f756]) ).
fof(f758,plain,
( nil = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(nil)
| spl57_23 ),
inference(resolution,[],[f749,f387]) ).
fof(f759,plain,
( nil = cons(hd(sK56),nil)
| ~ ssList(nil)
| ~ spl57_18
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f758,f707]) ).
fof(f760,plain,
( nil = cons(hd(sK56),nil)
| ~ spl57_5
| ~ spl57_18
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f759,f566]) ).
fof(f761,plain,
( spl57_21
| ~ spl57_5
| ~ spl57_18
| spl57_23 ),
inference(avatar_split_clause,[],[f760,f747,f706,f565,f727]) ).
fof(f770,plain,
( nil != nil
| ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ~ spl57_21 ),
inference(superposition,[],[f390,f729]) ).
fof(f772,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ~ spl57_21 ),
inference(trivial_inequality_removal,[],[f770]) ).
fof(f773,plain,
( ~ ssList(nil)
| ~ spl57_14
| ~ spl57_21 ),
inference(forward_subsumption_resolution,[],[f772,f661]) ).
fof(f775,plain,
( $false
| ~ spl57_5
| ~ spl57_14
| ~ spl57_21 ),
inference(forward_subsumption_resolution,[],[f773,f566]) ).
fof(f776,plain,
( ~ spl57_5
| ~ spl57_14
| ~ spl57_21 ),
inference(avatar_contradiction_clause,[],[f775]) ).
fof(f779,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl57_24 ),
inference(resolution,[],[f753,f442]) ).
fof(f780,plain,
( $false
| ~ spl57_18
| spl57_24 ),
inference(forward_subsumption_resolution,[],[f779,f707]) ).
fof(f781,plain,
( ~ spl57_18
| spl57_24 ),
inference(avatar_contradiction_clause,[],[f780]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(sat_conversion,[],[f553]) ).
cnf(s2,plain,
( ~ spl57_3
| ~ spl57_4 ),
inference(sat_conversion,[],[f562]) ).
cnf(s3,plain,
spl57_1,
inference(sat_conversion,[],[f563]) ).
cnf(s11,plain,
spl57_5,
inference(sat_conversion,[],[f593]) ).
cnf(s12,plain,
( spl57_2
| spl57_3
| ~ spl57_5 ),
inference(sat_conversion,[],[f600]) ).
cnf(s15,plain,
( spl57_4
| spl57_13 ),
inference(sat_conversion,[],[f671]) ).
cnf(s17,plain,
( spl57_4
| spl57_14 ),
inference(sat_conversion,[],[f687]) ).
cnf(s19,plain,
( ~ spl57_5
| ~ spl57_14
| spl57_18 ),
inference(sat_conversion,[],[f717]) ).
cnf(s21,plain,
( ~ spl57_3
| spl57_4
| ~ spl57_5
| ~ spl57_13
| ~ spl57_14
| ~ spl57_18
| ~ spl57_22
| ~ spl57_23
| ~ spl57_24 ),
inference(sat_conversion,[],[f754]) ).
cnf(s22,plain,
( ~ spl57_14
| spl57_22 ),
inference(sat_conversion,[],[f757]) ).
cnf(s23,plain,
( ~ spl57_5
| ~ spl57_18
| spl57_21
| spl57_23 ),
inference(sat_conversion,[],[f761]) ).
cnf(s24,plain,
( ~ spl57_5
| ~ spl57_14
| ~ spl57_21 ),
inference(sat_conversion,[],[f776]) ).
cnf(s26,plain,
( ~ spl57_18
| spl57_24 ),
inference(sat_conversion,[],[f781]) ).
cnf(s30,plain,
~ spl57_2,
inference(rat,[],[s1,s3]) ).
cnf(s31,plain,
spl57_3,
inference(rat,[],[s12,s11,s30]) ).
cnf(s32,plain,
~ spl57_4,
inference(rat,[],[s2,s31]) ).
cnf(s33,plain,
spl57_14,
inference(rat,[],[s17,s32]) ).
cnf(s34,plain,
spl57_13,
inference(rat,[],[s15,s32]) ).
cnf(s35,plain,
~ spl57_21,
inference(rat,[],[s24,s11,s33]) ).
cnf(s36,plain,
spl57_22,
inference(rat,[],[s22,s33]) ).
cnf(s37,plain,
spl57_18,
inference(rat,[],[s19,s11,s33]) ).
cnf(s40,plain,
spl57_24,
inference(rat,[],[s26,s37]) ).
cnf(s41,plain,
spl57_23,
inference(rat,[],[s23,s35,s11,s37]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s21,s34,s33,s36,s37,s32,s31,s11,s40,s41]) ).
fof(f782,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC117+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 08:02:07 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.29/1.56 % (199882)Detected formulas, will run a generic FOF schedule.
% 4.29/1.56 % (199887)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=3666336329:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.29/1.56 % (199891)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2866167635:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.29/1.56 % (199890)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3429195018:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.29/1.56 % (199892)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=783155480:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.29/1.56 % (199889)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=3570229617:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.29/1.56 % (199888)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=986210335:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.29/1.56 % (199893)dis-21_1_sil=8000:lcm=predicate:random_seed=943662148: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)
% 4.29/1.56 % (199890)Refutation not found, incomplete strategy
% 4.29/1.56 % (199890)------------------------------
% 4.29/1.56 % (199890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199890)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199890)Termination reason: Refutation not found, incomplete strategy
% 4.29/1.56 % (199890)Time elapsed: 0.004 s
% 4.29/1.56 % (199890)Peak memory usage: 88 MB
% 4.29/1.56 % (199890)Instructions burned: 4 (million)
% 4.29/1.56 % (199891)Instruction limit reached!
% 4.29/1.56 % (199891)------------------------------
% 4.29/1.56 % (199891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199891)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199891)Termination reason: Instruction limit
% 4.29/1.56 % (199891)Termination phase: Saturation
% 4.29/1.56 % (199891)Time elapsed: 0.071 s
% 4.29/1.56 % (199891)Peak memory usage: 88 MB
% 4.29/1.56 % (199891)Instructions burned: 120 (million)
% 4.29/1.56 % (199893)Instruction limit reached!
% 4.29/1.56 % (199893)------------------------------
% 4.29/1.56 % (199893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199893)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199893)Termination reason: Instruction limit
% 4.29/1.56 % (199893)Termination phase: Saturation
% 4.29/1.56 % (199893)Time elapsed: 0.077 s
% 4.29/1.56 % (199893)Peak memory usage: 90 MB
% 4.29/1.56 % (199893)Instructions burned: 129 (million)
% 4.29/1.56 % (199892)Instruction limit reached!
% 4.29/1.56 % (199892)------------------------------
% 4.29/1.56 % (199892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199892)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199892)Termination reason: Instruction limit
% 4.29/1.56 % (199892)Termination phase: Saturation
% 4.29/1.56 % (199892)Time elapsed: 0.093 s
% 4.29/1.56 % (199892)Peak memory usage: 90 MB
% 4.29/1.56 % (199892)Instructions burned: 139 (million)
% 4.29/1.56 % (199902)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2363117564:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.29/1.56 % (199901)lrs+10_1_sil=8000:sp=occurrence:random_seed=101491490:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.29/1.56 % (199903)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2784348770:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.29/1.56 % (199890)------------------------------
% 4.29/1.56 % (199890)------------------------------
% 4.29/1.56 % (199902)Instruction limit reached!
% 4.29/1.56 % (199902)------------------------------
% 4.29/1.56 % (199902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199902)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199902)Termination reason: Instruction limit
% 4.29/1.56 % (199902)Termination phase: Saturation
% 4.29/1.56 % (199902)Time elapsed: 0.076 s
% 4.29/1.56 % (199902)Peak memory usage: 91 MB
% 4.29/1.56 % (199902)Instructions burned: 158 (million)
% 4.29/1.56 % (199903)Instruction limit reached!
% 4.29/1.56 % (199903)------------------------------
% 4.29/1.56 % (199903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199903)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199903)Termination reason: Instruction limit
% 4.29/1.56 % (199903)Termination phase: Saturation
% 4.29/1.56 % (199903)Time elapsed: 0.129 s
% 4.29/1.56 % (199903)Peak memory usage: 89 MB
% 4.29/1.56 % (199903)Instructions burned: 327 (million)
% 4.29/1.56 % (199887)First to succeed.
% 4.29/1.56 % (199901)Instruction limit reached!
% 4.29/1.56 % (199901)------------------------------
% 4.29/1.56 % (199901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199901)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199901)Termination reason: Instruction limit
% 4.29/1.56 % (199901)Termination phase: Saturation
% 4.29/1.56 % (199901)Time elapsed: 0.172 s
% 4.29/1.56 % (199901)Peak memory usage: 93 MB
% 4.29/1.56 % (199901)Instructions burned: 285 (million)
% 4.29/1.56 % (199887)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-199882"
% 4.29/1.56 % (199907)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=238108184:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.29/1.56 % (199908)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4278505121:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.29/1.56 % (199909)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3457010539:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.29/1.56 % (199910)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=461470062:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.29/1.56 % (199907)Instruction limit reached!
% 4.29/1.56 % (199907)------------------------------
% 4.29/1.56 % (199907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.29/1.56 % (199907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.56 % (199907)CaDiCaL version: 2.1.3
% 4.29/1.56 % (199907)Termination reason: Instruction limit
% 4.29/1.56 % (199907)Termination phase: Saturation
% 4.29/1.56 % (199907)Time elapsed: 0.126 s
% 4.29/1.56 % (199907)Peak memory usage: 93 MB
% 4.29/1.56 % (199907)Instructions burned: 249 (million)
% 4.29/1.56 % (199887)Refutation found. Thanks to Tanya!
% 4.29/1.56 % SZS status Theorem for theBenchmark
% 4.29/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.70 % (199887)------------------------------
% 0.18/1.70 % (199887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.70 % (199887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.70 % (199887)CaDiCaL version: 2.1.3
% 0.18/1.70 % (199887)Termination reason: Refutation
% 0.18/1.70 % (199887)Time elapsed: 0.432 s
% 0.18/1.70 % (199887)Peak memory usage: 131 MB
% 0.18/1.70 % (199887)Instructions burned: 1005 (million)
% 0.18/1.70 % (199887)------------------------------
% 0.18/1.70 % (199887)------------------------------
% 0.18/1.70 % (199882)Success in time 0.7 s
% 0.18/1.70 % Vampire exiting
%------------------------------------------------------------------------------