%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC382+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 : n007.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 01:03:44 PM UTC 2026
% Result : Theorem 1.92s 1.14s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of formulae : 157 ( 22 unt; 11 def)
% Number of atoms : 570 ( 99 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 702 ( 289 ~; 307 |; 63 &)
% ( 17 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 12 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn 106 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
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(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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| ( singletonP(X0)
& segmentP(X1,X0) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& X2 != X4
& ? [X5] :
( ssItem(X5)
& cons(X5,nil) = X4
& hd(X3) = X5
& neq(nil,X3) ) )
| ( singletonP(X0)
& segmentP(X1,X0) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
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) ) )
& ( ~ singletonP(X0)
| ~ 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) ) )
& ( ~ singletonP(X0)
| ~ segmentP(X1,X0) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f237,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK10(X0))
& cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
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) ) )
& ( ~ singletonP(sK53)
| ~ 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(f308,plain,
! [X0,X1] :
( singletonP(X0)
| ~ ssItem(X1)
| cons(X1,nil) != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
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,
( ~ singletonP(sK53)
| ~ 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(f510,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f308]) ).
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(f556,definition,
( spl57_3
<=> singletonP(sK53) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f559,plain,
( ~ spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f500,f556,f552,f548]) ).
fof(f561,definition,
( spl57_4
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f563,plain,
( neq(sK54,nil)
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f566,definition,
( spl57_5
<=> neq(nil,sK56) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f568,plain,
( ~ neq(nil,sK56)
| spl57_5 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f570,definition,
( spl57_6
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f571,plain,
( ssItem(hd(sK56))
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f572,plain,
( ~ ssItem(hd(sK56))
| spl57_6 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f574,definition,
( spl57_7
<=> sK55 = cons(hd(sK56),nil) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f576,plain,
( sK55 = cons(hd(sK56),nil)
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f578,definition,
( spl57_8
<=> ssList(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f580,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl57_8 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f581,plain,
( ~ spl57_1
| ~ spl57_5
| ~ spl57_6
| spl57_7
| ~ spl57_8 ),
inference(avatar_split_clause,[],[f538,f578,f574,f570,f566,f548]) ).
fof(f584,plain,
spl57_4,
inference(avatar_split_clause,[],[f539,f561]) ).
fof(f586,definition,
( spl57_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_9])],[avatar_definition]) ).
fof(f587,plain,
( ssList(nil)
| ~ spl57_9 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f619,plain,
spl57_9,
inference(avatar_split_clause,[],[f389,f586]) ).
fof(f622,plain,
( neq(sK56,nil)
| ~ spl57_4 ),
inference(forward_demodulation,[],[f563,f507]) ).
fof(f625,plain,
( ~ segmentP(sK56,sK53)
| spl57_2 ),
inference(forward_demodulation,[],[f554,f507]) ).
fof(f626,plain,
( spl57_1
| ~ spl57_4 ),
inference(avatar_split_clause,[],[f622,f561,f548]) ).
fof(f627,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| spl57_8 ),
inference(resolution,[],[f388,f580]) ).
fof(f628,plain,
( ~ ssItem(hd(sK56))
| spl57_8
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f627,f587]) ).
fof(f629,plain,
( ~ spl57_6
| spl57_8
| ~ spl57_9 ),
inference(avatar_split_clause,[],[f628,f586,f578,f570]) ).
fof(f630,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_6 ),
inference(resolution,[],[f397,f572]) ).
fof(f631,plain,
( nil = sK56
| spl57_6 ),
inference(forward_subsumption_resolution,[],[f630,f499]) ).
fof(f635,plain,
( neq(nil,nil)
| ~ spl57_1
| spl57_6 ),
inference(superposition,[],[f549,f631]) ).
fof(f650,plain,
( ~ ssList(nil)
| ~ spl57_1
| spl57_6 ),
inference(resolution,[],[f635,f544]) ).
fof(f651,plain,
( $false
| ~ spl57_1
| spl57_6
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f650,f587]) ).
fof(f652,plain,
( ~ spl57_1
| spl57_6
| ~ spl57_9 ),
inference(avatar_contradiction_clause,[],[f651]) ).
fof(f677,definition,
( spl57_18
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_18])],[avatar_definition]) ).
fof(f678,plain,
( nil != sK56
| spl57_18 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f679,plain,
( nil = sK56
| ~ spl57_18 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f683,plain,
( nil = sK56
| ~ ssList(sK56)
| ~ ssList(nil)
| spl57_5 ),
inference(resolution,[],[f387,f568]) ).
fof(f686,plain,
( nil = sK56
| ~ ssList(nil)
| spl57_5 ),
inference(forward_subsumption_resolution,[],[f683,f499]) ).
fof(f687,plain,
( nil = sK56
| spl57_5
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f686,f587]) ).
fof(f688,plain,
( spl57_18
| spl57_5
| ~ spl57_9 ),
inference(avatar_split_clause,[],[f687,f586,f566,f677]) ).
fof(f691,plain,
( neq(nil,nil)
| ~ spl57_1
| ~ spl57_18 ),
inference(superposition,[],[f549,f679]) ).
fof(f698,plain,
( ~ ssList(nil)
| ~ spl57_1
| ~ spl57_18 ),
inference(resolution,[],[f691,f544]) ).
fof(f699,plain,
( $false
| ~ spl57_1
| ~ spl57_9
| ~ spl57_18 ),
inference(forward_subsumption_resolution,[],[f698,f587]) ).
fof(f700,plain,
( ~ spl57_1
| ~ spl57_9
| ~ spl57_18 ),
inference(avatar_contradiction_clause,[],[f699]) ).
fof(f701,plain,
( sK53 = cons(hd(sK56),nil)
| ~ spl57_7 ),
inference(forward_demodulation,[],[f576,f506]) ).
fof(f746,plain,
( singletonP(sK53)
| ~ ssItem(hd(sK56))
| ~ ssList(sK53)
| ~ spl57_7 ),
inference(superposition,[],[f510,f701]) ).
fof(f748,plain,
( singletonP(sK53)
| ~ ssList(sK53)
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f746,f571]) ).
fof(f749,plain,
( singletonP(sK53)
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f748,f496]) ).
fof(f750,plain,
( spl57_3
| ~ spl57_6
| ~ spl57_7 ),
inference(avatar_split_clause,[],[f749,f574,f570,f556]) ).
fof(f888,plain,
( ! [X0] :
( cons(hd(sK56),X0) = app(sK53,X0)
| ~ ssItem(hd(sK56))
| ~ ssList(X0) )
| ~ spl57_7 ),
inference(superposition,[],[f477,f701]) ).
fof(f897,plain,
( ! [X0] :
( cons(hd(sK56),X0) = app(sK53,X0)
| ~ ssList(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f888,f571]) ).
fof(f918,plain,
( sK56 = app(sK53,tl(sK56))
| nil = sK56
| ~ ssList(sK56)
| ~ ssList(tl(sK56))
| ~ spl57_6
| ~ spl57_7 ),
inference(superposition,[],[f474,f897]) ).
fof(f925,plain,
( sK56 = app(sK53,tl(sK56))
| nil = sK56
| ~ ssList(sK56)
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f918,f399]) ).
fof(f945,plain,
( sK56 = app(sK53,tl(sK56))
| ~ ssList(sK56)
| ~ spl57_6
| ~ spl57_7
| spl57_18 ),
inference(forward_subsumption_resolution,[],[f925,f678]) ).
fof(f956,plain,
( sK56 = app(sK53,tl(sK56))
| ~ spl57_6
| ~ spl57_7
| spl57_18 ),
inference(forward_subsumption_resolution,[],[f945,f499]) ).
fof(f1112,definition,
( spl57_24
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_24])],[avatar_definition]) ).
fof(f1113,plain,
( ssList(tl(sK56))
| ~ spl57_24 ),
inference(avatar_component_clause,[],[f1112]) ).
fof(f1114,plain,
( ~ ssList(tl(sK56))
| spl57_24 ),
inference(avatar_component_clause,[],[f1112]) ).
fof(f1143,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_24 ),
inference(resolution,[],[f1114,f399]) ).
fof(f1144,plain,
( ~ ssList(sK56)
| spl57_18
| spl57_24 ),
inference(forward_subsumption_resolution,[],[f1143,f678]) ).
fof(f1145,plain,
( $false
| spl57_18
| spl57_24 ),
inference(forward_subsumption_resolution,[],[f1144,f499]) ).
fof(f1146,plain,
( spl57_18
| spl57_24 ),
inference(avatar_contradiction_clause,[],[f1145]) ).
fof(f1888,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(f1897,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1888]) ).
fof(f1907,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1897,f401]) ).
fof(f1914,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl57_9 ),
inference(forward_subsumption_resolution,[],[f1907,f587]) ).
fof(f2993,plain,
( segmentP(sK56,sK53)
| ~ ssList(sK53)
| ~ ssList(tl(sK56))
| ~ spl57_6
| ~ spl57_7
| ~ spl57_9
| spl57_18 ),
inference(superposition,[],[f1914,f956]) ).
fof(f3007,plain,
( ~ ssList(sK53)
| ~ ssList(tl(sK56))
| spl57_2
| ~ spl57_6
| ~ spl57_7
| ~ spl57_9
| spl57_18 ),
inference(forward_subsumption_resolution,[],[f2993,f625]) ).
fof(f3017,plain,
( ~ ssList(tl(sK56))
| spl57_2
| ~ spl57_6
| ~ spl57_7
| ~ spl57_9
| spl57_18 ),
inference(forward_subsumption_resolution,[],[f3007,f496]) ).
fof(f3027,plain,
( $false
| spl57_2
| ~ spl57_6
| ~ spl57_7
| ~ spl57_9
| spl57_18
| ~ spl57_24 ),
inference(forward_subsumption_resolution,[],[f3017,f1113]) ).
fof(f3028,plain,
( spl57_2
| ~ spl57_6
| ~ spl57_7
| ~ spl57_9
| spl57_18
| ~ spl57_24 ),
inference(avatar_contradiction_clause,[],[f3027]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(sat_conversion,[],[f559]) ).
cnf(s3,plain,
( ~ spl57_1
| ~ spl57_5
| ~ spl57_6
| spl57_7
| ~ spl57_8 ),
inference(sat_conversion,[],[f581]) ).
cnf(s6,plain,
spl57_4,
inference(sat_conversion,[],[f584]) ).
cnf(s15,plain,
spl57_9,
inference(sat_conversion,[],[f619]) ).
cnf(s17,plain,
( spl57_1
| ~ spl57_4 ),
inference(sat_conversion,[],[f626]) ).
cnf(s18,plain,
( ~ spl57_6
| spl57_8
| ~ spl57_9 ),
inference(sat_conversion,[],[f629]) ).
cnf(s19,plain,
( ~ spl57_1
| spl57_6
| ~ spl57_9 ),
inference(sat_conversion,[],[f652]) ).
cnf(s21,plain,
( spl57_5
| ~ spl57_9
| spl57_18 ),
inference(sat_conversion,[],[f688]) ).
cnf(s22,plain,
( ~ spl57_1
| ~ spl57_9
| ~ spl57_18 ),
inference(sat_conversion,[],[f700]) ).
cnf(s23,plain,
( spl57_3
| ~ spl57_6
| ~ spl57_7 ),
inference(sat_conversion,[],[f750]) ).
cnf(s33,plain,
( spl57_18
| spl57_24 ),
inference(sat_conversion,[],[f1146]) ).
cnf(s103,plain,
( spl57_2
| ~ spl57_6
| ~ spl57_7
| ~ spl57_9
| spl57_18
| ~ spl57_24 ),
inference(sat_conversion,[],[f3028]) ).
cnf(s115,plain,
spl57_1,
inference(rat,[],[s17,s6]) ).
cnf(s116,plain,
~ spl57_18,
inference(rat,[],[s22,s15,s115]) ).
cnf(s117,plain,
spl57_6,
inference(rat,[],[s19,s15,s115]) ).
cnf(s118,plain,
spl57_24,
inference(rat,[],[s33,s116]) ).
cnf(s119,plain,
spl57_5,
inference(rat,[],[s21,s15,s116]) ).
cnf(s121,plain,
spl57_8,
inference(rat,[],[s18,s15,s117]) ).
cnf(s122,plain,
spl57_7,
inference(rat,[],[s3,s121,s117,s119,s115]) ).
cnf(s132,plain,
spl57_2,
inference(rat,[],[s103,s118,s116,s15,s117,s122]) ).
cnf(s133,plain,
spl57_3,
inference(rat,[],[s23,s117,s122]) ).
cnf(s158,plain,
$false,
inference(rat,[],[s1,s133,s132,s115]) ).
fof(f3029,plain,
$false,
inference(avatar_sat_refutation,[],[s158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC382+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 09:20:55 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running first-order theorem proving
% 0.09/0.20 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
% 1.92/1.14 % (2263140)Detected formulas, will run a generic FOF schedule.
% 1.92/1.14 % (2263148)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1976429367:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.92/1.14 % (2263148)Instruction limit reached!
% 1.92/1.14 % (2263148)------------------------------
% 1.92/1.14 % (2263148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.14 % (2263148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.14 % (2263148)CaDiCaL version: 2.1.3
% 1.92/1.14 % (2263148)Termination reason: Instruction limit
% 1.92/1.14 % (2263148)Termination phase: Saturation
% 1.92/1.14 % (2263148)Time elapsed: 0.036 s
% 1.92/1.14 % (2263148)Peak memory usage: 89 MB
% 1.92/1.14 % (2263148)Instructions burned: 111 (million)
% 1.92/1.14 % (2263147)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=1194513720:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.92/1.14 % (2263149)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=202535787:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.92/1.14 % (2263150)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4173427326:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.92/1.14 % (2263151)dis-21_1_sil=8000:lcm=predicate:random_seed=1253588843: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)
% 1.92/1.14 % (2263145)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=4137331406:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.92/1.14 % (2263146)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=1610938747:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.92/1.14 % (2263150)First to succeed.
% 1.92/1.14 % (2263150)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2263140"
% 1.92/1.14 % (2263149)Instruction limit reached!
% 1.92/1.14 % (2263149)------------------------------
% 1.92/1.14 % (2263149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.14 % (2263149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.14 % (2263149)CaDiCaL version: 2.1.3
% 1.92/1.14 % (2263149)Termination reason: Instruction limit
% 1.92/1.14 % (2263149)Termination phase: Saturation
% 1.92/1.14 % (2263149)Time elapsed: 0.069 s
% 1.92/1.14 % (2263149)Peak memory usage: 88 MB
% 1.92/1.14 % (2263149)Instructions burned: 120 (million)
% 1.92/1.14 % (2263151)Instruction limit reached!
% 1.92/1.14 % (2263151)------------------------------
% 1.92/1.14 % (2263151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.14 % (2263151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.14 % (2263151)CaDiCaL version: 2.1.3
% 1.92/1.14 % (2263151)Termination reason: Instruction limit
% 1.92/1.14 % (2263151)Termination phase: Saturation
% 1.92/1.14 % (2263151)Time elapsed: 0.070 s
% 1.92/1.14 % (2263151)Peak memory usage: 90 MB
% 1.92/1.14 % (2263151)Instructions burned: 129 (million)
% 1.92/1.14 % (2263153)lrs+10_1_sil=8000:sp=occurrence:random_seed=2629098142:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 1.92/1.14 % (2263153)Instruction limit reached!
% 1.92/1.14 % (2263153)------------------------------
% 1.92/1.14 % (2263153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.14 % (2263153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.14 % (2263153)CaDiCaL version: 2.1.3
% 1.92/1.14 % (2263153)Termination reason: Instruction limit
% 1.92/1.14 % (2263153)Termination phase: Saturation
% 1.92/1.14 % (2263153)Time elapsed: 0.092 s
% 1.92/1.14 % (2263153)Peak memory usage: 93 MB
% 1.92/1.14 % (2263153)Instructions burned: 287 (million)
% 1.92/1.14 % (2263161)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2932062652:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 1.92/1.14 % (2263160)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1410051742:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.92/1.14 % (2263150)Refutation found. Thanks to Tanya!
% 1.92/1.14 % SZS status Theorem for theBenchmark
% 1.92/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 4.09/1.34 % (2263150)------------------------------
% 4.09/1.34 % (2263150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.09/1.34 % (2263150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.34 % (2263150)CaDiCaL version: 2.1.3
% 4.09/1.34 % (2263150)Termination reason: Refutation
% 4.09/1.34 % (2263150)Time elapsed: 0.066 s
% 4.09/1.34 % (2263150)Peak memory usage: 91 MB
% 4.09/1.34 % (2263150)Instructions burned: 97 (million)
% 4.09/1.34 % (2263150)------------------------------
% 4.09/1.34 % (2263150)------------------------------
% 4.09/1.34 % (2263140)Success in time 0.49 s
% 4.09/1.34 % Vampire exiting
%------------------------------------------------------------------------------