%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC354+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 : n005.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 01:03:36 PM UTC 2026
% Result : Theorem 3.67s 1.16s
% Output : Refutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 140 ( 21 unt; 10 def)
% Number of atoms : 494 ( 90 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 598 ( 244 ~; 262 |; 53 &)
% ( 14 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 95 !; 20 ?)
% 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/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| segmentP(X1,X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| segmentP(X1,X0) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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(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(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
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
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(X3) != X5
| ~ neq(nil,X3) ) )
& ~ segmentP(X1,X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X2 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(X3) != X5
| ~ neq(nil,X3) ) )
& ~ segmentP(X1,X0) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& 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
& ( ( neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| sK55 = X4
| ! [X5] :
( ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(sK56) != X5
| ~ neq(nil,sK56) ) )
& ~ segmentP(sK54,sK53) )
| ( neq(sK54,nil)
& ~ neq(sK56,nil) ) )
& 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(f386,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
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(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(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f474,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ segmentP(sK54,sK53)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4,X5] :
( ~ ssList(X4)
| sK55 = X4
| ~ ssItem(X5)
| cons(X5,nil) != X4
| hd(sK56) != X5
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( neq(sK54,nil)
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f318]) ).
fof(f522,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f386]) ).
fof(f537,plain,
! [X5] :
( ~ ssList(cons(X5,nil))
| cons(X5,nil) = sK55
| ~ ssItem(X5)
| hd(sK56) != X5
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f502]) ).
fof(f538,plain,
( ~ ssList(cons(hd(sK56),nil))
| sK55 = cons(hd(sK56),nil)
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f537]) ).
fof(f539,plain,
neq(sK54,nil),
inference(duplicate_literal_removal,[],[f505]) ).
fof(f544,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f522]) ).
fof(f548,definition,
( spl57_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f549,plain,
( neq(sK56,nil)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f552,definition,
( spl57_2
<=> segmentP(sK54,sK53) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f554,plain,
( ~ segmentP(sK54,sK53)
| spl57_2 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f555,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(avatar_split_clause,[],[f500,f552,f548]) ).
fof(f557,definition,
( spl57_3
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f559,plain,
( neq(sK54,nil)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f562,definition,
( spl57_4
<=> neq(nil,sK56) ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f564,plain,
( ~ neq(nil,sK56)
| spl57_4 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f566,definition,
( spl57_5
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f567,plain,
( ssItem(hd(sK56))
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f568,plain,
( ~ ssItem(hd(sK56))
| spl57_5 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f570,definition,
( spl57_6
<=> sK55 = cons(hd(sK56),nil) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f572,plain,
( sK55 = cons(hd(sK56),nil)
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f574,definition,
( spl57_7
<=> ssList(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f576,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl57_7 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f577,plain,
( ~ spl57_1
| ~ spl57_4
| ~ spl57_5
| spl57_6
| ~ spl57_7 ),
inference(avatar_split_clause,[],[f538,f574,f570,f566,f562,f548]) ).
fof(f580,plain,
spl57_3,
inference(avatar_split_clause,[],[f539,f557]) ).
fof(f582,definition,
( spl57_8
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f583,plain,
( ssList(nil)
| ~ spl57_8 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f615,plain,
spl57_8,
inference(avatar_split_clause,[],[f389,f582]) ).
fof(f618,plain,
( neq(sK56,nil)
| ~ spl57_3 ),
inference(forward_demodulation,[],[f559,f507]) ).
fof(f621,plain,
( ~ segmentP(sK56,sK53)
| spl57_2 ),
inference(forward_demodulation,[],[f554,f507]) ).
fof(f622,plain,
( spl57_1
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f618,f557,f548]) ).
fof(f658,definition,
( spl57_17
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_17])],[avatar_definition]) ).
fof(f659,plain,
( nil != sK56
| spl57_17 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f660,plain,
( nil = sK56
| ~ spl57_17 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f662,plain,
( nil = sK56
| ~ ssList(sK56)
| ~ ssList(nil)
| spl57_4 ),
inference(resolution,[],[f387,f564]) ).
fof(f667,plain,
( nil = sK56
| ~ ssList(nil)
| spl57_4 ),
inference(forward_subsumption_resolution,[],[f662,f499]) ).
fof(f668,plain,
( nil = sK56
| spl57_4
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f667,f583]) ).
fof(f669,plain,
( spl57_17
| spl57_4
| ~ spl57_8 ),
inference(avatar_split_clause,[],[f668,f582,f562,f658]) ).
fof(f670,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| spl57_7 ),
inference(resolution,[],[f576,f388]) ).
fof(f671,plain,
( ~ ssItem(hd(sK56))
| spl57_7
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f670,f583]) ).
fof(f672,plain,
( ~ spl57_5
| spl57_7
| ~ spl57_8 ),
inference(avatar_split_clause,[],[f671,f582,f574,f566]) ).
fof(f673,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_5 ),
inference(resolution,[],[f568,f397]) ).
fof(f674,plain,
( nil = sK56
| spl57_5 ),
inference(forward_subsumption_resolution,[],[f673,f499]) ).
fof(f675,plain,
( spl57_17
| spl57_5 ),
inference(avatar_split_clause,[],[f674,f566,f658]) ).
fof(f677,plain,
( neq(nil,nil)
| ~ spl57_1
| ~ spl57_17 ),
inference(superposition,[],[f549,f660]) ).
fof(f684,plain,
( ~ ssList(nil)
| ~ spl57_1
| ~ spl57_17 ),
inference(resolution,[],[f677,f544]) ).
fof(f685,plain,
( $false
| ~ spl57_1
| ~ spl57_8
| ~ spl57_17 ),
inference(forward_subsumption_resolution,[],[f684,f583]) ).
fof(f686,plain,
( ~ spl57_1
| ~ spl57_8
| ~ spl57_17 ),
inference(avatar_contradiction_clause,[],[f685]) ).
fof(f687,plain,
( sK53 = cons(hd(sK56),nil)
| ~ spl57_6 ),
inference(forward_demodulation,[],[f572,f506]) ).
fof(f874,plain,
( ! [X0] :
( cons(hd(sK56),X0) = app(sK53,X0)
| ~ ssItem(hd(sK56))
| ~ ssList(X0) )
| ~ spl57_6 ),
inference(superposition,[],[f477,f687]) ).
fof(f883,plain,
( ! [X0] :
( cons(hd(sK56),X0) = app(sK53,X0)
| ~ ssList(X0) )
| ~ spl57_5
| ~ spl57_6 ),
inference(forward_subsumption_resolution,[],[f874,f567]) ).
fof(f889,plain,
( sK56 = app(sK53,tl(sK56))
| nil = sK56
| ~ ssList(sK56)
| ~ ssList(tl(sK56))
| ~ spl57_5
| ~ spl57_6 ),
inference(superposition,[],[f474,f883]) ).
fof(f926,plain,
( sK56 = app(sK53,tl(sK56))
| nil = sK56
| ~ ssList(sK56)
| ~ spl57_5
| ~ spl57_6 ),
inference(forward_subsumption_resolution,[],[f889,f399]) ).
fof(f940,plain,
( sK56 = app(sK53,tl(sK56))
| ~ ssList(sK56)
| ~ spl57_5
| ~ spl57_6
| spl57_17 ),
inference(forward_subsumption_resolution,[],[f926,f659]) ).
fof(f951,plain,
( sK56 = app(sK53,tl(sK56))
| ~ spl57_5
| ~ spl57_6
| spl57_17 ),
inference(forward_subsumption_resolution,[],[f940,f499]) ).
fof(f1098,definition,
( spl57_23
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_23])],[avatar_definition]) ).
fof(f1099,plain,
( ssList(tl(sK56))
| ~ spl57_23 ),
inference(avatar_component_clause,[],[f1098]) ).
fof(f1100,plain,
( ~ ssList(tl(sK56))
| spl57_23 ),
inference(avatar_component_clause,[],[f1098]) ).
fof(f1129,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_23 ),
inference(resolution,[],[f1100,f399]) ).
fof(f1130,plain,
( ~ ssList(sK56)
| spl57_17
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f1129,f659]) ).
fof(f1131,plain,
( $false
| spl57_17
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f1130,f499]) ).
fof(f1132,plain,
( spl57_17
| spl57_23 ),
inference(avatar_contradiction_clause,[],[f1131]) ).
fof(f1874,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f513,f403]) ).
fof(f1883,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1874]) ).
fof(f1893,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1883,f401]) ).
fof(f1900,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f1893,f583]) ).
fof(f2979,plain,
( segmentP(sK56,sK53)
| ~ ssList(sK53)
| ~ ssList(tl(sK56))
| ~ spl57_5
| ~ spl57_6
| ~ spl57_8
| spl57_17 ),
inference(superposition,[],[f1900,f951]) ).
fof(f2993,plain,
( ~ ssList(sK53)
| ~ ssList(tl(sK56))
| spl57_2
| ~ spl57_5
| ~ spl57_6
| ~ spl57_8
| spl57_17 ),
inference(forward_subsumption_resolution,[],[f2979,f621]) ).
fof(f3003,plain,
( ~ ssList(tl(sK56))
| spl57_2
| ~ spl57_5
| ~ spl57_6
| ~ spl57_8
| spl57_17 ),
inference(forward_subsumption_resolution,[],[f2993,f496]) ).
fof(f3013,plain,
( $false
| spl57_2
| ~ spl57_5
| ~ spl57_6
| ~ spl57_8
| spl57_17
| ~ spl57_23 ),
inference(forward_subsumption_resolution,[],[f3003,f1099]) ).
fof(f3014,plain,
( spl57_2
| ~ spl57_5
| ~ spl57_6
| ~ spl57_8
| spl57_17
| ~ spl57_23 ),
inference(avatar_contradiction_clause,[],[f3013]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2 ),
inference(sat_conversion,[],[f555]) ).
cnf(s3,plain,
( ~ spl57_1
| ~ spl57_4
| ~ spl57_5
| spl57_6
| ~ spl57_7 ),
inference(sat_conversion,[],[f577]) ).
cnf(s6,plain,
spl57_3,
inference(sat_conversion,[],[f580]) ).
cnf(s15,plain,
spl57_8,
inference(sat_conversion,[],[f615]) ).
cnf(s17,plain,
( spl57_1
| ~ spl57_3 ),
inference(sat_conversion,[],[f622]) ).
cnf(s19,plain,
( spl57_4
| ~ spl57_8
| spl57_17 ),
inference(sat_conversion,[],[f669]) ).
cnf(s20,plain,
( ~ spl57_5
| spl57_7
| ~ spl57_8 ),
inference(sat_conversion,[],[f672]) ).
cnf(s21,plain,
( spl57_5
| spl57_17 ),
inference(sat_conversion,[],[f675]) ).
cnf(s22,plain,
( ~ spl57_1
| ~ spl57_8
| ~ spl57_17 ),
inference(sat_conversion,[],[f686]) ).
cnf(s32,plain,
( spl57_17
| spl57_23 ),
inference(sat_conversion,[],[f1132]) ).
cnf(s102,plain,
( spl57_2
| ~ spl57_5
| ~ spl57_6
| ~ spl57_8
| spl57_17
| ~ spl57_23 ),
inference(sat_conversion,[],[f3014]) ).
cnf(s114,plain,
spl57_1,
inference(rat,[],[s17,s6]) ).
cnf(s115,plain,
~ spl57_17,
inference(rat,[],[s22,s15,s114]) ).
cnf(s116,plain,
spl57_23,
inference(rat,[],[s32,s115]) ).
cnf(s117,plain,
spl57_5,
inference(rat,[],[s21,s115]) ).
cnf(s118,plain,
spl57_4,
inference(rat,[],[s19,s15,s115]) ).
cnf(s120,plain,
spl57_7,
inference(rat,[],[s20,s15,s117]) ).
cnf(s121,plain,
spl57_6,
inference(rat,[],[s3,s120,s117,s118,s114]) ).
cnf(s132,plain,
spl57_2,
inference(rat,[],[s102,s116,s115,s15,s117,s121]) ).
cnf(s156,plain,
$false,
inference(rat,[],[s1,s132,s114]) ).
fof(f3015,plain,
$false,
inference(avatar_sat_refutation,[],[s156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC354+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:14:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.67/1.16 % (661047)Detected formulas, will run a generic FOF schedule.
% 3.67/1.16 % (661056)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=129701473:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.16 % (661056)Instruction limit reached!
% 3.67/1.16 % (661056)------------------------------
% 3.67/1.16 % (661056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.16 % (661056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.16 % (661056)CaDiCaL version: 2.1.3
% 3.67/1.16 % (661056)Termination reason: Instruction limit
% 3.67/1.16 % (661056)Termination phase: Saturation
% 3.67/1.16 % (661056)Time elapsed: 0.038 s
% 3.67/1.16 % (661056)Peak memory usage: 88 MB
% 3.67/1.16 % (661056)Instructions burned: 121 (million)
% 3.67/1.16 % (661052)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=13622277:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.16 % (661053)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=945896619:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.16 % (661055)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1954747642:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.16 % (661054)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=1094339318:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.16 % (661058)dis-21_1_sil=8000:lcm=predicate:random_seed=3213330220: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)
% 3.67/1.16 % (661057)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=621045717:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.16 % (661055)Instruction limit reached!
% 3.67/1.16 % (661055)------------------------------
% 3.67/1.16 % (661055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.16 % (661055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.16 % (661055)CaDiCaL version: 2.1.3
% 3.67/1.16 % (661055)Termination reason: Instruction limit
% 3.67/1.16 % (661055)Termination phase: Saturation
% 3.67/1.16 % (661055)Time elapsed: 0.062 s
% 3.67/1.16 % (661055)Peak memory usage: 89 MB
% 3.67/1.16 % (661055)Instructions burned: 111 (million)
% 3.67/1.16 % (661057)First to succeed.
% 3.67/1.16 % (661057)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-661047"
% 3.67/1.16 % (661058)Instruction limit reached!
% 3.67/1.16 % (661058)------------------------------
% 3.67/1.16 % (661058)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.16 % (661058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.16 % (661058)CaDiCaL version: 2.1.3
% 3.67/1.16 % (661058)Termination reason: Instruction limit
% 3.67/1.16 % (661058)Termination phase: Saturation
% 3.67/1.16 % (661058)Time elapsed: 0.073 s
% 3.67/1.16 % (661058)Peak memory usage: 90 MB
% 3.67/1.16 % (661058)Instructions burned: 129 (million)
% 3.67/1.16 % (661060)lrs+10_1_sil=8000:sp=occurrence:random_seed=1290623166:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.67/1.16 % (661060)Instruction limit reached!
% 3.67/1.16 % (661060)------------------------------
% 3.67/1.16 % (661060)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.16 % (661060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.16 % (661060)CaDiCaL version: 2.1.3
% 3.67/1.16 % (661060)Termination reason: Instruction limit
% 3.67/1.16 % (661060)Termination phase: Saturation
% 3.67/1.16 % (661060)Time elapsed: 0.094 s
% 3.67/1.16 % (661060)Peak memory usage: 93 MB
% 3.67/1.16 % (661060)Instructions burned: 289 (million)
% 3.67/1.16 % (661067)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3781863218:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.67/1.16 % (661068)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1779252441:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.67/1.16 % (661067)Instruction limit reached!
% 3.67/1.16 % (661067)------------------------------
% 3.67/1.16 % (661067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.16 % (661067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.16 % (661067)CaDiCaL version: 2.1.3
% 3.67/1.16 % (661067)Termination reason: Instruction limit
% 3.67/1.16 % (661067)Termination phase: Saturation
% 3.67/1.16 % (661067)Time elapsed: 0.077 s
% 3.67/1.16 % (661067)Peak memory usage: 91 MB
% 3.67/1.16 % (661067)Instructions burned: 159 (million)
% 3.67/1.16 % (661057)Refutation found. Thanks to Tanya!
% 3.67/1.16 % SZS status Theorem for theBenchmark
% 3.67/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 4.17/1.36 % (661057)------------------------------
% 4.17/1.36 % (661057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.36 % (661057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.36 % (661057)CaDiCaL version: 2.1.3
% 4.17/1.36 % (661057)Termination reason: Refutation
% 4.17/1.36 % (661057)Time elapsed: 0.066 s
% 4.17/1.36 % (661057)Peak memory usage: 91 MB
% 4.17/1.36 % (661057)Instructions burned: 96 (million)
% 4.17/1.36 % (661057)------------------------------
% 4.17/1.36 % (661057)------------------------------
% 4.17/1.36 % (661047)Success in time 0.502 s
% 4.17/1.36 % Vampire exiting
%------------------------------------------------------------------------------