%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC053+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 01:02:13 PM UTC 2026
% Result : Theorem 2.57s 1.24s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 24
% Syntax : Number of formulae : 186 ( 20 unt; 14 def)
% Number of atoms : 689 ( 101 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 888 ( 385 ~; 384 |; 73 &)
% ( 22 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 100 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
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(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X0,X1)
& frontsegP(X1,X0) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ! [X4] :
( ssList(X4)
=> ( ~ neq(X4,nil)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X2,X4) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X1,X5)
& segmentP(X0,X5) ) ) ) ) ) ) ) ),
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
| ( ! [X4] :
( ssList(X4)
=> ( ~ neq(X4,nil)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X2,X4) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X1,X5)
& segmentP(X0,X5) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
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(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(f151,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X0,X1)
| ~ frontsegP(X1,X0)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X0,X1)
| ~ frontsegP(X1,X0)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f157,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f158,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( neq(X4,nil)
& frontsegP(X3,X4)
& frontsegP(X2,X4)
& ssList(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(X1,X5)
| ~ segmentP(X0,X5) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( neq(X4,nil)
& frontsegP(X3,X4)
& frontsegP(X2,X4)
& ssList(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(X1,X5)
| ~ segmentP(X0,X5) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f240,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK11(X0,X1))
& app(X1,sK11(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
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(f283,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f158]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( neq(sK57,nil)
& frontsegP(sK56,sK57)
& frontsegP(sK55,sK57)
& ssList(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5) ) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f309,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f310,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f242]) ).
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(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
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(f422,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| X0 = X1
| ~ frontsegP(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f428,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f157]) ).
fof(f429,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X5] :
( nil != sK53
| ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X5] :
( nil = sK54
| ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( ssList(sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( ssList(sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( frontsegP(sK55,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( frontsegP(sK55,sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
( frontsegP(sK56,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( neq(sK57,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
( neq(sK57,nil)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f519,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(f528,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f386]) ).
fof(f545,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f528]) ).
fof(f549,definition,
( spl58_1
<=> ! [X5] :
( ~ ssList(X5)
| ~ segmentP(sK53,X5)
| ~ segmentP(sK54,X5)
| ~ neq(X5,nil) ) ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f550,plain,
( ! [X5] :
( ~ ssList(X5)
| ~ segmentP(sK53,X5)
| ~ segmentP(sK54,X5)
| ~ neq(X5,nil) )
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,definition,
( spl58_2
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f554,plain,
( nil != sK53
| spl58_2 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f555,plain,
( spl58_1
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f500,f552,f549]) ).
fof(f557,definition,
( spl58_3
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f559,plain,
( neq(sK54,nil)
| ~ spl58_3 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f560,plain,
( spl58_3
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f501,f552,f557]) ).
fof(f562,definition,
( spl58_4
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f564,plain,
( nil = sK54
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f565,plain,
( spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f502,f562,f549]) ).
fof(f568,definition,
( spl58_5
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f570,plain,
( nil = sK55
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f572,definition,
( spl58_6
<=> ssList(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f574,plain,
( ssList(sK57)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f575,plain,
( spl58_5
| spl58_6 ),
inference(avatar_split_clause,[],[f504,f572,f568]) ).
fof(f577,definition,
( spl58_7
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_7])],[avatar_definition]) ).
fof(f579,plain,
( nil = sK56
| ~ spl58_7 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f580,plain,
( spl58_7
| spl58_6 ),
inference(avatar_split_clause,[],[f505,f572,f577]) ).
fof(f582,definition,
( spl58_8
<=> frontsegP(sK55,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_8])],[avatar_definition]) ).
fof(f584,plain,
( frontsegP(sK55,sK57)
| ~ spl58_8 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f585,plain,
( spl58_5
| spl58_8 ),
inference(avatar_split_clause,[],[f506,f582,f568]) ).
fof(f586,plain,
( spl58_7
| spl58_8 ),
inference(avatar_split_clause,[],[f507,f582,f577]) ).
fof(f588,definition,
( spl58_9
<=> frontsegP(sK56,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_9])],[avatar_definition]) ).
fof(f590,plain,
( frontsegP(sK56,sK57)
| ~ spl58_9 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f591,plain,
( spl58_5
| spl58_9 ),
inference(avatar_split_clause,[],[f508,f588,f568]) ).
fof(f594,definition,
( spl58_10
<=> neq(sK57,nil) ),
introduced(definition,[new_symbols(definition,[spl58_10])],[avatar_definition]) ).
fof(f596,plain,
( neq(sK57,nil)
| ~ spl58_10 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f597,plain,
( spl58_5
| spl58_10 ),
inference(avatar_split_clause,[],[f510,f594,f568]) ).
fof(f598,plain,
( spl58_7
| spl58_10 ),
inference(avatar_split_clause,[],[f511,f594,f577]) ).
fof(f600,definition,
( spl58_11
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_11])],[avatar_definition]) ).
fof(f601,plain,
( ssList(nil)
| ~ spl58_11 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f633,plain,
spl58_11,
inference(avatar_split_clause,[],[f389,f600]) ).
fof(f636,plain,
( nil != sK55
| spl58_2 ),
inference(forward_demodulation,[],[f554,f512]) ).
fof(f637,plain,
( ~ spl58_5
| spl58_2 ),
inference(avatar_split_clause,[],[f636,f552,f568]) ).
fof(f638,plain,
( frontsegP(sK54,sK57)
| ~ spl58_9 ),
inference(forward_demodulation,[],[f590,f513]) ).
fof(f642,plain,
( nil = sK54
| ~ spl58_7 ),
inference(superposition,[],[f513,f579]) ).
fof(f645,plain,
( frontsegP(nil,sK57)
| ~ spl58_4
| ~ spl58_9 ),
inference(forward_demodulation,[],[f638,f564]) ).
fof(f652,plain,
( nil = sK57
| ~ ssList(sK57)
| ~ spl58_4
| ~ spl58_9 ),
inference(resolution,[],[f429,f645]) ).
fof(f658,plain,
( nil = sK57
| ~ spl58_4
| ~ spl58_6
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f652,f574]) ).
fof(f672,plain,
( ! [X5] :
( ~ segmentP(sK55,X5)
| ~ ssList(X5)
| ~ segmentP(sK54,X5)
| ~ neq(X5,nil) )
| ~ spl58_1 ),
inference(forward_demodulation,[],[f550,f512]) ).
fof(f673,plain,
( spl58_4
| ~ spl58_7 ),
inference(avatar_split_clause,[],[f642,f577,f562]) ).
fof(f926,definition,
( spl58_26
<=> ssList(sK11(sK54,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_26])],[avatar_definition]) ).
fof(f927,plain,
( ssList(sK11(sK54,sK57))
| ~ spl58_26 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f928,plain,
( ~ ssList(sK11(sK54,sK57))
| spl58_26 ),
inference(avatar_component_clause,[],[f926]) ).
fof(f945,plain,
( ~ frontsegP(sK54,sK57)
| ~ ssList(sK57)
| ~ ssList(sK54)
| spl58_26 ),
inference(resolution,[],[f928,f310]) ).
fof(f946,plain,
( ~ ssList(sK57)
| ~ ssList(sK54)
| ~ spl58_9
| spl58_26 ),
inference(forward_subsumption_resolution,[],[f945,f638]) ).
fof(f947,plain,
( ~ ssList(sK54)
| ~ spl58_6
| ~ spl58_9
| spl58_26 ),
inference(forward_subsumption_resolution,[],[f946,f574]) ).
fof(f948,plain,
( $false
| ~ spl58_6
| ~ spl58_9
| spl58_26 ),
inference(forward_subsumption_resolution,[],[f947,f497]) ).
fof(f949,plain,
( ~ spl58_6
| ~ spl58_9
| spl58_26 ),
inference(avatar_contradiction_clause,[],[f948]) ).
fof(f1015,definition,
( spl58_30
<=> ssList(sK11(sK55,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_30])],[avatar_definition]) ).
fof(f1016,plain,
( ssList(sK11(sK55,sK57))
| ~ spl58_30 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1017,plain,
( ~ ssList(sK11(sK55,sK57))
| spl58_30 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1036,plain,
( ~ frontsegP(sK55,sK57)
| ~ ssList(sK57)
| ~ ssList(sK55)
| spl58_30 ),
inference(resolution,[],[f1017,f310]) ).
fof(f1037,plain,
( ~ ssList(sK57)
| ~ ssList(sK55)
| ~ spl58_8
| spl58_30 ),
inference(forward_subsumption_resolution,[],[f1036,f584]) ).
fof(f1038,plain,
( ~ ssList(sK55)
| ~ spl58_6
| ~ spl58_8
| spl58_30 ),
inference(forward_subsumption_resolution,[],[f1037,f574]) ).
fof(f1039,plain,
( $false
| ~ spl58_6
| ~ spl58_8
| spl58_30 ),
inference(forward_subsumption_resolution,[],[f1038,f498]) ).
fof(f1040,plain,
( ~ spl58_6
| ~ spl58_8
| spl58_30 ),
inference(avatar_contradiction_clause,[],[f1039]) ).
fof(f1058,definition,
( spl58_32
<=> nil = sK57 ),
introduced(definition,[new_symbols(definition,[spl58_32])],[avatar_definition]) ).
fof(f1060,plain,
( nil = sK57
| ~ spl58_32 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1270,plain,
( neq(nil,nil)
| ~ spl58_10
| ~ spl58_32 ),
inference(superposition,[],[f596,f1060]) ).
fof(f1353,plain,
( ~ ssList(nil)
| ~ spl58_10
| ~ spl58_32 ),
inference(resolution,[],[f1270,f545]) ).
fof(f1354,plain,
( $false
| ~ spl58_10
| ~ spl58_11
| ~ spl58_32 ),
inference(forward_subsumption_resolution,[],[f1353,f601]) ).
fof(f1355,plain,
( ~ spl58_10
| ~ spl58_11
| ~ spl58_32 ),
inference(avatar_contradiction_clause,[],[f1354]) ).
fof(f1381,plain,
( neq(nil,nil)
| ~ spl58_3
| ~ spl58_4 ),
inference(superposition,[],[f559,f564]) ).
fof(f1453,plain,
( spl58_32
| ~ spl58_4
| ~ spl58_6
| ~ spl58_9 ),
inference(avatar_split_clause,[],[f658,f588,f572,f562,f1058]) ).
fof(f1457,plain,
( frontsegP(nil,sK57)
| ~ spl58_5
| ~ spl58_8 ),
inference(forward_demodulation,[],[f584,f570]) ).
fof(f1489,plain,
( nil = sK57
| ~ frontsegP(sK57,nil)
| ~ ssList(sK57)
| ~ ssList(nil)
| ~ spl58_5
| ~ spl58_8 ),
inference(resolution,[],[f1457,f422]) ).
fof(f1490,plain,
( nil = sK57
| ~ ssList(sK57)
| ~ ssList(nil)
| ~ spl58_5
| ~ spl58_8 ),
inference(forward_subsumption_resolution,[],[f1489,f428]) ).
fof(f1494,plain,
( nil = sK57
| ~ ssList(nil)
| ~ spl58_5
| ~ spl58_6
| ~ spl58_8 ),
inference(forward_subsumption_resolution,[],[f1490,f574]) ).
fof(f1498,plain,
( nil = sK57
| ~ spl58_5
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f1494,f601]) ).
fof(f1499,plain,
( spl58_32
| ~ spl58_5
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11 ),
inference(avatar_split_clause,[],[f1498,f600,f582,f572,f568,f1058]) ).
fof(f1505,plain,
( ~ ssList(nil)
| ~ spl58_3
| ~ spl58_4 ),
inference(resolution,[],[f1381,f545]) ).
fof(f1506,plain,
( $false
| ~ spl58_3
| ~ spl58_4
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f1505,f601]) ).
fof(f1507,plain,
( ~ spl58_3
| ~ spl58_4
| ~ spl58_11 ),
inference(avatar_contradiction_clause,[],[f1506]) ).
fof(f1512,plain,
( sK55 = app(sK57,sK11(sK55,sK57))
| ~ ssList(sK57)
| ~ ssList(sK55)
| ~ spl58_8 ),
inference(resolution,[],[f584,f309]) ).
fof(f1515,plain,
( sK55 = app(sK57,sK11(sK55,sK57))
| ~ ssList(sK55)
| ~ spl58_6
| ~ spl58_8 ),
inference(forward_subsumption_resolution,[],[f1512,f574]) ).
fof(f1518,plain,
( sK55 = app(sK57,sK11(sK55,sK57))
| ~ spl58_6
| ~ spl58_8 ),
inference(forward_subsumption_resolution,[],[f1515,f498]) ).
fof(f1522,plain,
( sK54 = app(sK57,sK11(sK54,sK57))
| ~ ssList(sK57)
| ~ ssList(sK54)
| ~ spl58_9 ),
inference(resolution,[],[f638,f309]) ).
fof(f1525,plain,
( sK54 = app(sK57,sK11(sK54,sK57))
| ~ ssList(sK54)
| ~ spl58_6
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f1522,f574]) ).
fof(f1528,plain,
( sK54 = app(sK57,sK11(sK54,sK57))
| ~ spl58_6
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f1525,f497]) ).
fof(f1944,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f519,f403]) ).
fof(f1950,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1944]) ).
fof(f1959,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1950,f401]) ).
fof(f1965,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f1959,f601]) ).
fof(f2716,plain,
( segmentP(sK55,sK57)
| ~ ssList(sK57)
| ~ ssList(sK11(sK55,sK57))
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11 ),
inference(superposition,[],[f1965,f1518]) ).
fof(f2717,plain,
( segmentP(sK54,sK57)
| ~ ssList(sK57)
| ~ ssList(sK11(sK54,sK57))
| ~ spl58_6
| ~ spl58_9
| ~ spl58_11 ),
inference(superposition,[],[f1965,f1528]) ).
fof(f2730,plain,
( segmentP(sK54,sK57)
| ~ ssList(sK11(sK54,sK57))
| ~ spl58_6
| ~ spl58_9
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f2717,f574]) ).
fof(f2731,plain,
( segmentP(sK55,sK57)
| ~ ssList(sK11(sK55,sK57))
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f2716,f574]) ).
fof(f2740,plain,
( segmentP(sK54,sK57)
| ~ spl58_6
| ~ spl58_9
| ~ spl58_11
| ~ spl58_26 ),
inference(forward_subsumption_resolution,[],[f2730,f927]) ).
fof(f2741,plain,
( segmentP(sK55,sK57)
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11
| ~ spl58_30 ),
inference(forward_subsumption_resolution,[],[f2731,f1016]) ).
fof(f2765,plain,
( ~ ssList(sK57)
| ~ segmentP(sK54,sK57)
| ~ neq(sK57,nil)
| ~ spl58_1
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11
| ~ spl58_30 ),
inference(resolution,[],[f2741,f672]) ).
fof(f2774,plain,
( ~ segmentP(sK54,sK57)
| ~ neq(sK57,nil)
| ~ spl58_1
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11
| ~ spl58_30 ),
inference(forward_subsumption_resolution,[],[f2765,f574]) ).
fof(f2779,plain,
( ~ neq(sK57,nil)
| ~ spl58_1
| ~ spl58_6
| ~ spl58_8
| ~ spl58_9
| ~ spl58_11
| ~ spl58_26
| ~ spl58_30 ),
inference(forward_subsumption_resolution,[],[f2774,f2740]) ).
fof(f2781,plain,
( $false
| ~ spl58_1
| ~ spl58_6
| ~ spl58_8
| ~ spl58_9
| ~ spl58_10
| ~ spl58_11
| ~ spl58_26
| ~ spl58_30 ),
inference(forward_subsumption_resolution,[],[f2779,f596]) ).
fof(f2782,plain,
( ~ spl58_1
| ~ spl58_6
| ~ spl58_8
| ~ spl58_9
| ~ spl58_10
| ~ spl58_11
| ~ spl58_26
| ~ spl58_30 ),
inference(avatar_contradiction_clause,[],[f2781]) ).
cnf(s1,plain,
( spl58_1
| ~ spl58_2 ),
inference(sat_conversion,[],[f555]) ).
cnf(s2,plain,
( ~ spl58_2
| spl58_3 ),
inference(sat_conversion,[],[f560]) ).
cnf(s3,plain,
( spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f565]) ).
cnf(s5,plain,
( spl58_5
| spl58_6 ),
inference(sat_conversion,[],[f575]) ).
cnf(s6,plain,
( spl58_6
| spl58_7 ),
inference(sat_conversion,[],[f580]) ).
cnf(s7,plain,
( spl58_5
| spl58_8 ),
inference(sat_conversion,[],[f585]) ).
cnf(s8,plain,
( spl58_7
| spl58_8 ),
inference(sat_conversion,[],[f586]) ).
cnf(s9,plain,
( spl58_5
| spl58_9 ),
inference(sat_conversion,[],[f591]) ).
cnf(s11,plain,
( spl58_5
| spl58_10 ),
inference(sat_conversion,[],[f597]) ).
cnf(s12,plain,
( spl58_7
| spl58_10 ),
inference(sat_conversion,[],[f598]) ).
cnf(s21,plain,
spl58_11,
inference(sat_conversion,[],[f633]) ).
cnf(s22,plain,
( spl58_2
| ~ spl58_5 ),
inference(sat_conversion,[],[f637]) ).
cnf(s26,plain,
( spl58_4
| ~ spl58_7 ),
inference(sat_conversion,[],[f673]) ).
cnf(s35,plain,
( ~ spl58_6
| ~ spl58_9
| spl58_26 ),
inference(sat_conversion,[],[f949]) ).
cnf(s38,plain,
( ~ spl58_6
| ~ spl58_8
| spl58_30 ),
inference(sat_conversion,[],[f1040]) ).
cnf(s52,plain,
( ~ spl58_10
| ~ spl58_11
| ~ spl58_32 ),
inference(sat_conversion,[],[f1355]) ).
cnf(s66,plain,
( ~ spl58_4
| ~ spl58_6
| ~ spl58_9
| spl58_32 ),
inference(sat_conversion,[],[f1453]) ).
cnf(s75,plain,
( ~ spl58_5
| ~ spl58_6
| ~ spl58_8
| ~ spl58_11
| spl58_32 ),
inference(sat_conversion,[],[f1499]) ).
cnf(s76,plain,
( ~ spl58_3
| ~ spl58_4
| ~ spl58_11 ),
inference(sat_conversion,[],[f1507]) ).
cnf(s139,plain,
( ~ spl58_1
| ~ spl58_6
| ~ spl58_8
| ~ spl58_9
| ~ spl58_10
| ~ spl58_11
| ~ spl58_26
| ~ spl58_30 ),
inference(sat_conversion,[],[f2782]) ).
cnf(s144,plain,
spl58_1,
inference(rat,[],[s66,s52,s5,s9,s11,s22,s1,s3,s21]) ).
cnf(s145,plain,
spl58_5,
inference(rat,[],[s139,s35,s38,s5,s7,s9,s11,s144,s21]) ).
cnf(s146,plain,
spl58_2,
inference(rat,[],[s22,s145]) ).
cnf(s147,plain,
spl58_3,
inference(rat,[],[s2,s146]) ).
cnf(s148,plain,
~ spl58_4,
inference(rat,[],[s76,s21,s147]) ).
cnf(s150,plain,
~ spl58_7,
inference(rat,[],[s26,s148]) ).
cnf(s151,plain,
spl58_10,
inference(rat,[],[s12,s150]) ).
cnf(s153,plain,
spl58_8,
inference(rat,[],[s8,s150]) ).
cnf(s154,plain,
spl58_6,
inference(rat,[],[s6,s150]) ).
cnf(s155,plain,
~ spl58_32,
inference(rat,[],[s52,s21,s151]) ).
cnf(s156,plain,
$false,
inference(rat,[],[s75,s155,s21,s145,s153,s154]) ).
fof(f2783,plain,
$false,
inference(avatar_sat_refutation,[],[s156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC053+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:40:37 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 2.57/1.24 % (187881)Detected formulas, will run a generic FOF schedule.
% 2.57/1.24 % (187992)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1631348669:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.24 % (187988)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=516422434:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.24 % (187991)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4094892241:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.24 % (187989)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=1809067957:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.24 % (187987)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=4244822579:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.24 % (187992)First to succeed.
% 2.57/1.24 % (187992)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-187881"
% 2.57/1.24 % (187993)dis-21_1_sil=8000:lcm=predicate:random_seed=1696591610: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)
% 2.57/1.24 % (187990)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1468423275:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.24 % (187991)Instruction limit reached!
% 2.57/1.24 % (187991)------------------------------
% 2.57/1.24 % (187991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.24 % (187991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.24 % (187991)CaDiCaL version: 2.1.3
% 2.57/1.24 % (187991)Termination reason: Instruction limit
% 2.57/1.24 % (187991)Termination phase: Saturation
% 2.57/1.24 % (187991)Time elapsed: 0.071 s
% 2.57/1.24 % (187991)Peak memory usage: 88 MB
% 2.57/1.24 % (187991)Instructions burned: 120 (million)
% 2.57/1.24 % (187993)Instruction limit reached!
% 2.57/1.24 % (187993)------------------------------
% 2.57/1.24 % (187993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.24 % (187993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.24 % (187993)CaDiCaL version: 2.1.3
% 2.57/1.24 % (187993)Termination reason: Instruction limit
% 2.57/1.24 % (187993)Termination phase: Saturation
% 2.57/1.24 % (187993)Time elapsed: 0.081 s
% 2.57/1.24 % (187993)Peak memory usage: 90 MB
% 2.57/1.24 % (187993)Instructions burned: 129 (million)
% 2.57/1.24 % (187990)Instruction limit reached!
% 2.57/1.24 % (187990)------------------------------
% 2.57/1.24 % (187990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.24 % (187990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.24 % (187990)CaDiCaL version: 2.1.3
% 2.57/1.24 % (187990)Termination reason: Instruction limit
% 2.57/1.24 % (187990)Termination phase: Saturation
% 2.57/1.24 % (187990)Time elapsed: 0.070 s
% 2.57/1.24 % (187990)Peak memory usage: 89 MB
% 2.57/1.24 % (187990)Instructions burned: 109 (million)
% 2.57/1.24 % (187992)Refutation found. Thanks to Tanya!
% 2.57/1.24 % SZS status Theorem for theBenchmark
% 2.57/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.51 % (187992)------------------------------
% 0.18/1.51 % (187992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.51 % (187992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.51 % (187992)CaDiCaL version: 2.1.3
% 0.18/1.51 % (187992)Termination reason: Refutation
% 0.18/1.51 % (187992)Time elapsed: 0.033 s
% 0.18/1.51 % (187992)Peak memory usage: 91 MB
% 0.18/1.51 % (187992)Instructions burned: 86 (million)
% 0.18/1.51 % (187992)------------------------------
% 0.18/1.51 % (187992)------------------------------
% 0.18/1.51 % (187881)Success in time 0.368 s
% 0.18/1.51 % Vampire exiting
%------------------------------------------------------------------------------