%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC081+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 : n009.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 01:02:21 PM UTC 2026
% Result : Theorem 2.58s 1.29s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 26
% Syntax : Number of formulae : 184 ( 22 unt; 15 def)
% Number of atoms : 645 ( 77 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 814 ( 353 ~; 349 |; 67 &)
% ( 21 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 94 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
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(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X0,X1)
& frontsegP(X1,X0) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
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)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ( ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ( ! [X5] :
( ssList(X5)
=> ( ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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(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(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( ? [X5] :
( neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5)
& ssList(X5) )
| ( nil = X3
& nil = X2 ) )
& 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)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( ? [X5] :
( neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5)
& ssList(X5) )
| ( nil = X3
& nil = X2 ) )
& 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(f285,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) )
& ( ( neq(sK57,nil)
& frontsegP(sK56,sK57)
& frontsegP(sK55,sK57)
& ssList(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& 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(X5,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(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(f440,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f442,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f444,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ssList(sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ssList(sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( frontsegP(sK55,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( frontsegP(sK55,sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( frontsegP(sK56,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( neq(sK57,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( neq(sK57,nil)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f517,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(f531,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f444]) ).
fof(f547,definition,
( spl58_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f549,plain,
( nil = sK55
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f551,definition,
( spl58_2
<=> ssList(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f553,plain,
( ssList(sK57)
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f554,plain,
( spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f500,f551,f547]) ).
fof(f556,definition,
( spl58_3
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f558,plain,
( nil = sK56
| ~ spl58_3 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( spl58_3
| spl58_2 ),
inference(avatar_split_clause,[],[f501,f551,f556]) ).
fof(f561,definition,
( spl58_4
<=> frontsegP(sK55,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f563,plain,
( frontsegP(sK55,sK57)
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f564,plain,
( spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f502,f561,f547]) ).
fof(f565,plain,
( spl58_3
| spl58_4 ),
inference(avatar_split_clause,[],[f503,f561,f556]) ).
fof(f567,definition,
( spl58_5
<=> frontsegP(sK56,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f569,plain,
( frontsegP(sK56,sK57)
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f570,plain,
( spl58_1
| spl58_5 ),
inference(avatar_split_clause,[],[f504,f567,f547]) ).
fof(f573,definition,
( spl58_6
<=> neq(sK57,nil) ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f575,plain,
( neq(sK57,nil)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f576,plain,
( spl58_1
| spl58_6 ),
inference(avatar_split_clause,[],[f506,f573,f547]) ).
fof(f577,plain,
( spl58_3
| spl58_6 ),
inference(avatar_split_clause,[],[f507,f573,f556]) ).
fof(f579,definition,
( spl58_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_7])],[avatar_definition]) ).
fof(f580,plain,
( ssList(nil)
| ~ spl58_7 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f598,definition,
( spl58_11
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl58_11])],[avatar_definition]) ).
fof(f600,plain,
( segmentP(nil,nil)
| ~ spl58_11 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f601,plain,
( ~ spl58_7
| spl58_11 ),
inference(avatar_split_clause,[],[f531,f598,f579]) ).
fof(f612,plain,
spl58_7,
inference(avatar_split_clause,[],[f389,f579]) ).
fof(f614,plain,
neq(sK56,nil),
inference(superposition,[],[f509,f511]) ).
fof(f616,plain,
! [X4] :
( ~ segmentP(sK56,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK53,X4) ),
inference(forward_demodulation,[],[f508,f511]) ).
fof(f617,plain,
! [X4] :
( ~ segmentP(sK56,X4)
| ~ segmentP(sK55,X4)
| ~ ssList(X4)
| ~ neq(X4,nil) ),
inference(forward_demodulation,[],[f616,f510]) ).
fof(f618,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56)
| ~ ssList(sK56)
| ~ neq(sK56,nil) ),
inference(resolution,[],[f440,f617]) ).
fof(f619,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56)
| ~ neq(sK56,nil) ),
inference(duplicate_literal_removal,[],[f618]) ).
fof(f620,plain,
( ~ segmentP(sK55,sK56)
| ~ neq(sK56,nil) ),
inference(forward_subsumption_resolution,[],[f619,f499]) ).
fof(f621,plain,
~ segmentP(sK55,sK56),
inference(forward_subsumption_resolution,[],[f620,f614]) ).
fof(f622,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,nil)
| ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(resolution,[],[f442,f617]) ).
fof(f623,plain,
( ~ segmentP(sK55,nil)
| ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(forward_subsumption_resolution,[],[f622,f499]) ).
fof(f624,plain,
( ~ segmentP(sK55,nil)
| ~ neq(nil,nil)
| ~ spl58_7 ),
inference(forward_subsumption_resolution,[],[f623,f580]) ).
fof(f626,definition,
( spl58_14
<=> neq(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl58_14])],[avatar_definition]) ).
fof(f630,definition,
( spl58_15
<=> segmentP(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl58_15])],[avatar_definition]) ).
fof(f632,plain,
( ~ segmentP(sK55,nil)
| spl58_15 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f633,plain,
( ~ spl58_14
| ~ spl58_15
| ~ spl58_7 ),
inference(avatar_split_clause,[],[f624,f579,f630,f626]) ).
fof(f855,plain,
( sK55 = app(sK57,sK11(sK55,sK57))
| ~ ssList(sK57)
| ~ ssList(sK55)
| ~ spl58_4 ),
inference(resolution,[],[f309,f563]) ).
fof(f856,plain,
( sK56 = app(sK57,sK11(sK56,sK57))
| ~ ssList(sK57)
| ~ ssList(sK56)
| ~ spl58_5 ),
inference(resolution,[],[f309,f569]) ).
fof(f881,definition,
( spl58_20
<=> ssList(sK11(sK56,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_20])],[avatar_definition]) ).
fof(f882,plain,
( ssList(sK11(sK56,sK57))
| ~ spl58_20 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f883,plain,
( ~ ssList(sK11(sK56,sK57))
| spl58_20 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f885,definition,
( spl58_21
<=> nil = sK57 ),
introduced(definition,[new_symbols(definition,[spl58_21])],[avatar_definition]) ).
fof(f887,plain,
( nil = sK57
| ~ spl58_21 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f910,plain,
( ~ frontsegP(sK56,sK57)
| ~ ssList(sK57)
| ~ ssList(sK56)
| spl58_20 ),
inference(resolution,[],[f883,f310]) ).
fof(f911,plain,
( ~ ssList(sK57)
| ~ ssList(sK56)
| ~ spl58_5
| spl58_20 ),
inference(forward_subsumption_resolution,[],[f910,f569]) ).
fof(f915,plain,
( sK56 = app(sK57,sK11(sK56,sK57))
| ~ ssList(sK57)
| ~ spl58_5 ),
inference(forward_subsumption_resolution,[],[f856,f499]) ).
fof(f916,plain,
( sK55 = app(sK57,sK11(sK55,sK57))
| ~ ssList(sK57)
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f855,f498]) ).
fof(f917,plain,
( ~ ssList(sK57)
| ~ spl58_5
| spl58_20 ),
inference(forward_subsumption_resolution,[],[f911,f499]) ).
fof(f919,definition,
( spl58_24
<=> sK56 = app(sK57,sK11(sK56,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_24])],[avatar_definition]) ).
fof(f921,plain,
( sK56 = app(sK57,sK11(sK56,sK57))
| ~ spl58_24 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f922,plain,
( ~ spl58_2
| spl58_24
| ~ spl58_5 ),
inference(avatar_split_clause,[],[f915,f567,f919,f551]) ).
fof(f924,definition,
( spl58_25
<=> sK55 = app(sK57,sK11(sK55,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_25])],[avatar_definition]) ).
fof(f926,plain,
( sK55 = app(sK57,sK11(sK55,sK57))
| ~ spl58_25 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f927,plain,
( ~ spl58_2
| spl58_25
| ~ spl58_4 ),
inference(avatar_split_clause,[],[f916,f561,f924,f551]) ).
fof(f928,plain,
( ~ spl58_2
| ~ spl58_5
| spl58_20 ),
inference(avatar_split_clause,[],[f917,f881,f567,f551]) ).
fof(f931,plain,
( frontsegP(nil,sK57)
| ~ spl58_1
| ~ spl58_4 ),
inference(superposition,[],[f563,f549]) ).
fof(f937,plain,
( ~ segmentP(sK55,nil)
| ~ spl58_3 ),
inference(superposition,[],[f621,f558]) ).
fof(f940,plain,
( ~ segmentP(nil,nil)
| ~ spl58_1
| ~ spl58_3 ),
inference(forward_demodulation,[],[f937,f549]) ).
fof(f945,plain,
( $false
| ~ spl58_1
| ~ spl58_3
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f940,f600]) ).
fof(f946,plain,
( ~ spl58_1
| ~ spl58_3
| ~ spl58_11 ),
inference(avatar_contradiction_clause,[],[f945]) ).
fof(f950,plain,
( nil = sK57
| ~ frontsegP(sK57,nil)
| ~ ssList(sK57)
| ~ ssList(nil)
| ~ spl58_1
| ~ spl58_4 ),
inference(resolution,[],[f931,f422]) ).
fof(f951,plain,
( nil = sK57
| ~ ssList(sK57)
| ~ ssList(nil)
| ~ spl58_1
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f950,f428]) ).
fof(f954,plain,
( nil = sK57
| ~ ssList(nil)
| ~ spl58_1
| ~ spl58_2
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f951,f553]) ).
fof(f957,plain,
( nil = sK57
| ~ spl58_1
| ~ spl58_2
| ~ spl58_4
| ~ spl58_7 ),
inference(forward_subsumption_resolution,[],[f954,f580]) ).
fof(f958,plain,
( spl58_21
| ~ spl58_1
| ~ spl58_2
| ~ spl58_4
| ~ spl58_7 ),
inference(avatar_split_clause,[],[f957,f579,f561,f551,f547,f885]) ).
fof(f971,plain,
( neq(nil,nil)
| ~ spl58_6
| ~ spl58_21 ),
inference(superposition,[],[f575,f887]) ).
fof(f981,plain,
( ~ segmentP(nil,nil)
| ~ spl58_1
| spl58_15 ),
inference(forward_demodulation,[],[f632,f549]) ).
fof(f985,plain,
( spl58_14
| ~ spl58_6
| ~ spl58_21 ),
inference(avatar_split_clause,[],[f971,f885,f573,f626]) ).
fof(f986,plain,
( $false
| ~ spl58_1
| ~ spl58_11
| spl58_15 ),
inference(forward_subsumption_resolution,[],[f981,f600]) ).
fof(f987,plain,
( ~ spl58_1
| ~ spl58_11
| spl58_15 ),
inference(avatar_contradiction_clause,[],[f986]) ).
fof(f1660,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f517,f403]) ).
fof(f1665,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1660]) ).
fof(f1672,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1665,f401]) ).
fof(f1676,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl58_7 ),
inference(forward_subsumption_resolution,[],[f1672,f580]) ).
fof(f1864,definition,
( spl58_40
<=> ssList(sK11(sK55,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_40])],[avatar_definition]) ).
fof(f1865,plain,
( ssList(sK11(sK55,sK57))
| ~ spl58_40 ),
inference(avatar_component_clause,[],[f1864]) ).
fof(f1866,plain,
( ~ ssList(sK11(sK55,sK57))
| spl58_40 ),
inference(avatar_component_clause,[],[f1864]) ).
fof(f1920,plain,
( ~ frontsegP(sK55,sK57)
| ~ ssList(sK57)
| ~ ssList(sK55)
| spl58_40 ),
inference(resolution,[],[f1866,f310]) ).
fof(f1921,plain,
( ~ ssList(sK57)
| ~ ssList(sK55)
| ~ spl58_4
| spl58_40 ),
inference(forward_subsumption_resolution,[],[f1920,f563]) ).
fof(f1922,plain,
( ~ ssList(sK55)
| ~ spl58_2
| ~ spl58_4
| spl58_40 ),
inference(forward_subsumption_resolution,[],[f1921,f553]) ).
fof(f1923,plain,
( $false
| ~ spl58_2
| ~ spl58_4
| spl58_40 ),
inference(forward_subsumption_resolution,[],[f1922,f498]) ).
fof(f1924,plain,
( ~ spl58_2
| ~ spl58_4
| spl58_40 ),
inference(avatar_contradiction_clause,[],[f1923]) ).
fof(f2339,plain,
( segmentP(sK56,sK57)
| ~ ssList(sK57)
| ~ ssList(sK11(sK56,sK57))
| ~ spl58_7
| ~ spl58_24 ),
inference(superposition,[],[f1676,f921]) ).
fof(f2340,plain,
( segmentP(sK55,sK57)
| ~ ssList(sK57)
| ~ ssList(sK11(sK55,sK57))
| ~ spl58_7
| ~ spl58_25 ),
inference(superposition,[],[f1676,f926]) ).
fof(f2352,plain,
( segmentP(sK55,sK57)
| ~ ssList(sK11(sK55,sK57))
| ~ spl58_2
| ~ spl58_7
| ~ spl58_25 ),
inference(forward_subsumption_resolution,[],[f2340,f553]) ).
fof(f2353,plain,
( segmentP(sK56,sK57)
| ~ ssList(sK11(sK56,sK57))
| ~ spl58_2
| ~ spl58_7
| ~ spl58_24 ),
inference(forward_subsumption_resolution,[],[f2339,f553]) ).
fof(f2361,plain,
( segmentP(sK55,sK57)
| ~ spl58_2
| ~ spl58_7
| ~ spl58_25
| ~ spl58_40 ),
inference(forward_subsumption_resolution,[],[f2352,f1865]) ).
fof(f2362,plain,
( segmentP(sK56,sK57)
| ~ spl58_2
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24 ),
inference(forward_subsumption_resolution,[],[f2353,f882]) ).
fof(f2392,plain,
( ~ segmentP(sK55,sK57)
| ~ ssList(sK57)
| ~ neq(sK57,nil)
| ~ spl58_2
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24 ),
inference(resolution,[],[f2362,f617]) ).
fof(f2401,plain,
( ~ ssList(sK57)
| ~ neq(sK57,nil)
| ~ spl58_2
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24
| ~ spl58_25
| ~ spl58_40 ),
inference(forward_subsumption_resolution,[],[f2392,f2361]) ).
fof(f2406,plain,
( ~ neq(sK57,nil)
| ~ spl58_2
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24
| ~ spl58_25
| ~ spl58_40 ),
inference(forward_subsumption_resolution,[],[f2401,f553]) ).
fof(f2412,plain,
( $false
| ~ spl58_2
| ~ spl58_6
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24
| ~ spl58_25
| ~ spl58_40 ),
inference(forward_subsumption_resolution,[],[f2406,f575]) ).
fof(f2413,plain,
( ~ spl58_2
| ~ spl58_6
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24
| ~ spl58_25
| ~ spl58_40 ),
inference(avatar_contradiction_clause,[],[f2412]) ).
cnf(s1,plain,
( spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f554]) ).
cnf(s2,plain,
( spl58_2
| spl58_3 ),
inference(sat_conversion,[],[f559]) ).
cnf(s3,plain,
( spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f564]) ).
cnf(s4,plain,
( spl58_3
| spl58_4 ),
inference(sat_conversion,[],[f565]) ).
cnf(s5,plain,
( spl58_1
| spl58_5 ),
inference(sat_conversion,[],[f570]) ).
cnf(s7,plain,
( spl58_1
| spl58_6 ),
inference(sat_conversion,[],[f576]) ).
cnf(s8,plain,
( spl58_3
| spl58_6 ),
inference(sat_conversion,[],[f577]) ).
cnf(s14,plain,
( ~ spl58_7
| spl58_11 ),
inference(sat_conversion,[],[f601]) ).
cnf(s17,plain,
spl58_7,
inference(sat_conversion,[],[f612]) ).
cnf(s18,plain,
( ~ spl58_7
| ~ spl58_14
| ~ spl58_15 ),
inference(sat_conversion,[],[f633]) ).
cnf(s25,plain,
( ~ spl58_2
| ~ spl58_5
| spl58_24 ),
inference(sat_conversion,[],[f922]) ).
cnf(s26,plain,
( ~ spl58_2
| ~ spl58_4
| spl58_25 ),
inference(sat_conversion,[],[f927]) ).
cnf(s27,plain,
( ~ spl58_2
| ~ spl58_5
| spl58_20 ),
inference(sat_conversion,[],[f928]) ).
cnf(s29,plain,
( ~ spl58_1
| ~ spl58_3
| ~ spl58_11 ),
inference(sat_conversion,[],[f946]) ).
cnf(s31,plain,
( ~ spl58_1
| ~ spl58_2
| ~ spl58_4
| ~ spl58_7
| spl58_21 ),
inference(sat_conversion,[],[f958]) ).
cnf(s34,plain,
( ~ spl58_6
| spl58_14
| ~ spl58_21 ),
inference(sat_conversion,[],[f985]) ).
cnf(s35,plain,
( ~ spl58_1
| ~ spl58_11
| spl58_15 ),
inference(sat_conversion,[],[f987]) ).
cnf(s61,plain,
( ~ spl58_2
| ~ spl58_4
| spl58_40 ),
inference(sat_conversion,[],[f1924]) ).
cnf(s88,plain,
( ~ spl58_2
| ~ spl58_6
| ~ spl58_7
| ~ spl58_20
| ~ spl58_24
| ~ spl58_25
| ~ spl58_40 ),
inference(sat_conversion,[],[f2413]) ).
cnf(s98,plain,
spl58_11,
inference(rat,[],[s14,s17]) ).
cnf(s100,plain,
spl58_1,
inference(rat,[],[s88,s25,s26,s27,s61,s1,s3,s5,s7,s17]) ).
cnf(s101,plain,
spl58_15,
inference(rat,[],[s35,s98,s100]) ).
cnf(s102,plain,
~ spl58_3,
inference(rat,[],[s29,s98,s100]) ).
cnf(s103,plain,
~ spl58_14,
inference(rat,[],[s18,s17,s101]) ).
cnf(s104,plain,
spl58_6,
inference(rat,[],[s8,s102]) ).
cnf(s106,plain,
spl58_4,
inference(rat,[],[s4,s102]) ).
cnf(s107,plain,
spl58_2,
inference(rat,[],[s2,s102]) ).
cnf(s108,plain,
~ spl58_21,
inference(rat,[],[s34,s104,s103]) ).
cnf(s109,plain,
$false,
inference(rat,[],[s31,s108,s17,s100,s106,s107]) ).
fof(f2414,plain,
$false,
inference(avatar_sat_refutation,[],[s109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC081+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 28 07:45:00 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 2.58/1.29 % (2868849)Detected formulas, will run a generic FOF schedule.
% 2.58/1.29 % (2868854)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=91194170:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.29 % (2868859)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2340747693:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.29 % (2868858)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2375067736:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.29 % (2868860)dis-21_1_sil=8000:lcm=predicate:random_seed=222293687: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)
% 2.58/1.29 % (2868857)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=417742349:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.29 % (2868855)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=2325048811:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.29 % (2868856)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=3709187024:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.29 % (2868859)First to succeed.
% 2.58/1.29 % (2868859)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2868849"
% 2.58/1.29 % (2868857)Instruction limit reached!
% 2.58/1.29 % (2868857)------------------------------
% 2.58/1.29 % (2868857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2868857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2868857)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2868857)Termination reason: Instruction limit
% 2.58/1.29 % (2868857)Termination phase: Saturation
% 2.58/1.29 % (2868857)Time elapsed: 0.067 s
% 2.58/1.29 % (2868857)Peak memory usage: 89 MB
% 2.58/1.29 % (2868857)Instructions burned: 109 (million)
% 2.58/1.29 % (2868858)Instruction limit reached!
% 2.58/1.29 % (2868858)------------------------------
% 2.58/1.29 % (2868858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2868858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2868858)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2868858)Termination reason: Instruction limit
% 2.58/1.29 % (2868858)Termination phase: Saturation
% 2.58/1.29 % (2868858)Time elapsed: 0.067 s
% 2.58/1.29 % (2868858)Peak memory usage: 88 MB
% 2.58/1.29 % (2868858)Instructions burned: 119 (million)
% 2.58/1.29 % (2868860)Instruction limit reached!
% 2.58/1.29 % (2868860)------------------------------
% 2.58/1.29 % (2868860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2868860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2868860)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2868860)Termination reason: Instruction limit
% 2.58/1.29 % (2868860)Termination phase: Saturation
% 2.58/1.29 % (2868860)Time elapsed: 0.073 s
% 2.58/1.29 % (2868860)Peak memory usage: 90 MB
% 2.58/1.29 % (2868860)Instructions burned: 129 (million)
% 2.58/1.29 % (2868868)lrs+10_1_sil=8000:sp=occurrence:random_seed=969045859:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.58/1.29 % (2868869)lrs+10_1_sil=32000:urr=on:br=off:random_seed=658207389:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.58/1.29 % (2868870)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4013732082:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.58/1.29 % (2868869)Instruction limit reached!
% 2.58/1.29 % (2868869)------------------------------
% 2.58/1.29 % (2868869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.29 % (2868869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.29 % (2868869)CaDiCaL version: 2.1.3
% 2.58/1.29 % (2868869)Termination reason: Instruction limit
% 2.58/1.29 % (2868869)Termination phase: Saturation
% 2.58/1.29 % (2868869)Time elapsed: 0.074 s
% 2.58/1.29 % (2868869)Peak memory usage: 91 MB
% 2.58/1.29 % (2868869)Instructions burned: 159 (million)
% 2.58/1.29 % (2868859)Refutation found. Thanks to Tanya!
% 2.58/1.29 % SZS status Theorem for theBenchmark
% 2.58/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.38 % (2868859)------------------------------
% 3.72/1.38 % (2868859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.38 % (2868859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.38 % (2868859)CaDiCaL version: 2.1.3
% 3.72/1.38 % (2868859)Termination reason: Refutation
% 3.72/1.38 % (2868859)Time elapsed: 0.054 s
% 3.72/1.38 % (2868859)Peak memory usage: 90 MB
% 3.72/1.38 % (2868859)Instructions burned: 75 (million)
% 3.72/1.38 % (2868859)------------------------------
% 3.72/1.38 % (2868859)------------------------------
% 3.72/1.38 % (2868849)Success in time 0.468 s
% 3.72/1.38 % Vampire exiting
%------------------------------------------------------------------------------