%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC307+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 : 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 01:03:23 PM UTC 2026
% Result : Theorem 5.71s 1.35s
% Output : Refutation 6.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 36
% Syntax : Number of formulae : 252 ( 49 unt; 21 def)
% Number of atoms : 814 ( 182 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 987 ( 425 ~; 436 |; 60 &)
% ( 23 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 16 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 16 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 113 !; 22 ?)
% 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(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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
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(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ segmentP(X3,X2)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| ~ lt(X5,X4) ) ) ) ) ) )
| ( ~ singletonP(X2)
& 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
| ~ segmentP(X3,X2)
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ( app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != X0
| ~ lt(X5,X4) ) ) ) ) ) )
| ( ~ singletonP(X2)
& 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(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(f125,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
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(f131,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f204]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& segmentP(X3,X2)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X0
& lt(X5,X4)
& ssList(X8) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ( singletonP(X2)
| ~ 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
& segmentP(X3,X2)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X0
& lt(X5,X4)
& ssList(X8) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ( singletonP(X2)
| ~ 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(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f285,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f292]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& segmentP(sK56,sK55)
& sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61)
& lt(sK58,sK57)
& ssList(sK61)
& ssList(sK60)
& ssList(sK59)
& ssItem(sK58)
& ssItem(sK57)
& ( singletonP(sK55)
| ~ neq(sK56,nil) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61)],[f222]) ).
fof(f306,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK10(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f307,plain,
! [X0] :
( ssItem(sK10(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
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(f396,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f399,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f443,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f478,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f479,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f480,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f484,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( singletonP(sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
ssList(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
ssList(sK61),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK53 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK55 = app(app(app(app(sK59,cons(sK57,nil)),sK60),cons(sK58,nil)),sK61),
inference(definition_unfolding,[],[f507,f509]) ).
fof(f512,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f510]) ).
fof(f513,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f509]) ).
fof(f541,definition,
sF62 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[sF62])],[function_definition]) ).
fof(f542,plain,
cons(sK57,nil) = sF62,
inference(reorient_equations,[],[f541]) ).
fof(f543,definition,
sF63 = app(sK59,sF62),
introduced(definition,[new_symbols(definition,[sF63])],[function_definition]) ).
fof(f544,plain,
app(sK59,sF62) = sF63,
inference(reorient_equations,[],[f543]) ).
fof(f545,definition,
sF64 = app(sF63,sK60),
introduced(definition,[new_symbols(definition,[sF64])],[function_definition]) ).
fof(f546,plain,
app(sF63,sK60) = sF64,
inference(reorient_equations,[],[f545]) ).
fof(f547,definition,
sF65 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f548,plain,
cons(sK58,nil) = sF65,
inference(reorient_equations,[],[f547]) ).
fof(f549,definition,
sF66 = app(sF64,sF65),
introduced(definition,[new_symbols(definition,[sF66])],[function_definition]) ).
fof(f550,plain,
app(sF64,sF65) = sF66,
inference(reorient_equations,[],[f549]) ).
fof(f551,definition,
sF67 = app(sF66,sK61),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f552,plain,
app(sF66,sK61) = sF67,
inference(reorient_equations,[],[f551]) ).
fof(f553,plain,
sK55 = sF67,
inference(definition_folding,[],[f511,f552,f550,f548,f546,f544,f542]) ).
fof(f562,definition,
( spl68_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl68_1])],[avatar_definition]) ).
fof(f564,plain,
( ~ neq(sK56,nil)
| spl68_1 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f566,definition,
( spl68_2
<=> singletonP(sK55) ),
introduced(definition,[new_symbols(definition,[spl68_2])],[avatar_definition]) ).
fof(f568,plain,
( singletonP(sK55)
| ~ spl68_2 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f569,plain,
( ~ spl68_1
| spl68_2 ),
inference(avatar_split_clause,[],[f500,f566,f562]) ).
fof(f571,definition,
( spl68_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl68_3])],[avatar_definition]) ).
fof(f572,plain,
( ssList(nil)
| ~ spl68_3 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f599,plain,
spl68_3,
inference(avatar_split_clause,[],[f389,f571]) ).
fof(f602,plain,
sK55 = app(sF66,sK61),
inference(forward_demodulation,[],[f552,f553]) ).
fof(f603,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl68_1 ),
inference(resolution,[],[f387,f564]) ).
fof(f604,plain,
( nil = sK56
| ~ ssList(sK56)
| spl68_1
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f603,f572]) ).
fof(f605,plain,
( nil = sK56
| spl68_1
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f604,f512]) ).
fof(f607,plain,
( segmentP(nil,sK55)
| spl68_1
| ~ spl68_3 ),
inference(superposition,[],[f508,f605]) ).
fof(f608,plain,
( ssList(sF63)
| ~ ssList(sF62)
| ~ ssList(sK59) ),
inference(superposition,[],[f401,f544]) ).
fof(f609,plain,
( ssList(sF64)
| ~ ssList(sK60)
| ~ ssList(sF63) ),
inference(superposition,[],[f401,f546]) ).
fof(f610,plain,
( ssList(sF66)
| ~ ssList(sF65)
| ~ ssList(sF64) ),
inference(superposition,[],[f401,f550]) ).
fof(f613,definition,
( spl68_9
<=> ssList(sF64) ),
introduced(definition,[new_symbols(definition,[spl68_9])],[avatar_definition]) ).
fof(f614,plain,
( ssList(sF64)
| ~ spl68_9 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f617,definition,
( spl68_10
<=> ssList(sF65) ),
introduced(definition,[new_symbols(definition,[spl68_10])],[avatar_definition]) ).
fof(f618,plain,
( ssList(sF65)
| ~ spl68_10 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f621,definition,
( spl68_11
<=> ssList(sF66) ),
introduced(definition,[new_symbols(definition,[spl68_11])],[avatar_definition]) ).
fof(f623,plain,
( ssList(sF66)
| ~ spl68_11 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f624,plain,
( ~ spl68_9
| ~ spl68_10
| spl68_11 ),
inference(avatar_split_clause,[],[f610,f621,f617,f613]) ).
fof(f625,plain,
( ssList(sF64)
| ~ ssList(sF63) ),
inference(forward_subsumption_resolution,[],[f609,f504]) ).
fof(f626,plain,
( ssList(sF63)
| ~ ssList(sF62) ),
inference(forward_subsumption_resolution,[],[f608,f503]) ).
fof(f628,definition,
( spl68_12
<=> ssList(sF63) ),
introduced(definition,[new_symbols(definition,[spl68_12])],[avatar_definition]) ).
fof(f631,plain,
( ~ spl68_12
| spl68_9 ),
inference(avatar_split_clause,[],[f625,f613,f628]) ).
fof(f633,definition,
( spl68_13
<=> ssList(sF62) ),
introduced(definition,[new_symbols(definition,[spl68_13])],[avatar_definition]) ).
fof(f634,plain,
( ssList(sF62)
| ~ spl68_13 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f635,plain,
( ~ ssList(sF62)
| spl68_13 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f636,plain,
( ~ spl68_13
| spl68_12 ),
inference(avatar_split_clause,[],[f626,f628,f633]) ).
fof(f638,plain,
( ssList(sF62)
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f388,f542]) ).
fof(f639,plain,
( ssList(sF65)
| ~ ssItem(sK58)
| ~ ssList(nil) ),
inference(superposition,[],[f388,f548]) ).
fof(f640,plain,
( ssList(sF65)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f639,f502]) ).
fof(f641,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| spl68_13 ),
inference(forward_subsumption_resolution,[],[f638,f635]) ).
fof(f642,plain,
( ssList(sF65)
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f640,f572]) ).
fof(f643,plain,
( ~ ssList(nil)
| spl68_13 ),
inference(forward_subsumption_resolution,[],[f641,f501]) ).
fof(f644,plain,
( spl68_10
| ~ spl68_3 ),
inference(avatar_split_clause,[],[f642,f571,f617]) ).
fof(f645,plain,
( $false
| ~ spl68_3
| spl68_13 ),
inference(forward_subsumption_resolution,[],[f643,f572]) ).
fof(f646,plain,
( ~ spl68_3
| spl68_13 ),
inference(avatar_contradiction_clause,[],[f645]) ).
fof(f647,plain,
( nil = sK55
| ~ ssList(sK55)
| spl68_1
| ~ spl68_3 ),
inference(resolution,[],[f607,f443]) ).
fof(f648,plain,
( nil = sK55
| spl68_1
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f647,f513]) ).
fof(f676,plain,
( sF66 = app(sF66,nil)
| ~ spl68_11 ),
inference(resolution,[],[f482,f623]) ).
fof(f687,plain,
! [X0,X1] :
( ~ ssList(X1)
| app(app(X0,X1),sK60) = app(X0,app(X1,sK60))
| ~ ssList(X0) ),
inference(resolution,[],[f478,f504]) ).
fof(f702,plain,
( ! [X0] :
( ~ ssList(X0)
| app(app(X0,sF62),sK60) = app(X0,app(sF62,sK60)) )
| ~ spl68_13 ),
inference(resolution,[],[f687,f634]) ).
fof(f765,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK60) = app(cons(X0,nil),sK60) ),
inference(resolution,[],[f477,f504]) ).
fof(f784,plain,
( nil != sF62
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f396,f542]) ).
fof(f785,plain,
( nil != sF65
| ~ ssItem(sK58)
| ~ ssList(nil) ),
inference(superposition,[],[f396,f548]) ).
fof(f786,plain,
( nil != sF65
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f785,f502]) ).
fof(f787,plain,
( nil != sF62
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f784,f501]) ).
fof(f788,plain,
( nil != sF65
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f786,f572]) ).
fof(f789,plain,
( nil != sF62
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f787,f572]) ).
fof(f836,plain,
cons(sK57,sK60) = app(cons(sK57,nil),sK60),
inference(resolution,[],[f765,f501]) ).
fof(f837,plain,
app(sF62,sK60) = cons(sK57,sK60),
inference(forward_demodulation,[],[f836,f542]) ).
fof(f839,plain,
( ssList(cons(sK57,sK60))
| ~ ssList(sK60)
| ~ ssList(sF62) ),
inference(superposition,[],[f401,f837]) ).
fof(f840,plain,
( ssList(cons(sK57,sK60))
| ~ ssList(sF62) ),
inference(forward_subsumption_resolution,[],[f839,f504]) ).
fof(f841,plain,
( ssList(cons(sK57,sK60))
| ~ spl68_13 ),
inference(forward_subsumption_resolution,[],[f840,f634]) ).
fof(f917,plain,
( app(app(sK59,sF62),sK60) = app(sK59,app(sF62,sK60))
| ~ spl68_13 ),
inference(resolution,[],[f702,f503]) ).
fof(f932,plain,
( app(app(sK59,sF62),sK60) = app(sK59,cons(sK57,sK60))
| ~ spl68_13 ),
inference(forward_demodulation,[],[f917,f837]) ).
fof(f939,plain,
( app(sF63,sK60) = app(sK59,cons(sK57,sK60))
| ~ spl68_13 ),
inference(forward_demodulation,[],[f932,f544]) ).
fof(f943,plain,
( sF64 = app(sK59,cons(sK57,sK60))
| ~ spl68_13 ),
inference(forward_demodulation,[],[f939,f546]) ).
fof(f1019,plain,
( nil != sF64
| nil = cons(sK57,sK60)
| ~ ssList(cons(sK57,sK60))
| ~ ssList(sK59)
| ~ spl68_13 ),
inference(superposition,[],[f480,f943]) ).
fof(f1025,plain,
( nil != sF66
| nil = sF65
| ~ ssList(sF65)
| ~ ssList(sF64) ),
inference(superposition,[],[f480,f550]) ).
fof(f1029,plain,
( nil != sK55
| nil = sK61
| ~ ssList(sK61)
| ~ ssList(sF66) ),
inference(superposition,[],[f480,f602]) ).
fof(f1030,plain,
( nil = sK61
| ~ ssList(sK61)
| ~ ssList(sF66)
| spl68_1
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f1029,f648]) ).
fof(f1034,plain,
( nil != sF66
| ~ ssList(sF65)
| ~ ssList(sF64)
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f1025,f788]) ).
fof(f1040,plain,
( nil != sF64
| nil = cons(sK57,sK60)
| ~ ssList(sK59)
| ~ spl68_13 ),
inference(forward_subsumption_resolution,[],[f1019,f841]) ).
fof(f1043,plain,
( nil = sK61
| ~ ssList(sF66)
| spl68_1
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f1030,f505]) ).
fof(f1047,plain,
( nil != sF66
| ~ ssList(sF64)
| ~ spl68_3
| ~ spl68_10 ),
inference(forward_subsumption_resolution,[],[f1034,f618]) ).
fof(f1053,plain,
( nil != sF64
| nil = cons(sK57,sK60)
| ~ spl68_13 ),
inference(forward_subsumption_resolution,[],[f1040,f503]) ).
fof(f1056,plain,
( nil = sK61
| spl68_1
| ~ spl68_3
| ~ spl68_11 ),
inference(forward_subsumption_resolution,[],[f1043,f623]) ).
fof(f1076,definition,
( spl68_18
<=> nil = sK61 ),
introduced(definition,[new_symbols(definition,[spl68_18])],[avatar_definition]) ).
fof(f1078,plain,
( nil = sK61
| ~ spl68_18 ),
inference(avatar_component_clause,[],[f1076]) ).
fof(f1084,plain,
( nil != sF66
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10 ),
inference(forward_subsumption_resolution,[],[f1047,f614]) ).
fof(f1086,definition,
( spl68_20
<=> nil = sF64 ),
introduced(definition,[new_symbols(definition,[spl68_20])],[avatar_definition]) ).
fof(f1088,plain,
( nil != sF64
| spl68_20 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1096,definition,
( spl68_22
<=> nil = cons(sK57,sK60) ),
introduced(definition,[new_symbols(definition,[spl68_22])],[avatar_definition]) ).
fof(f1110,plain,
( spl68_22
| ~ spl68_20
| ~ spl68_13 ),
inference(avatar_split_clause,[],[f1053,f633,f1086,f1096]) ).
fof(f1117,plain,
( spl68_18
| spl68_1
| ~ spl68_3
| ~ spl68_11 ),
inference(avatar_split_clause,[],[f1056,f621,f571,f562,f1076]) ).
fof(f1124,plain,
( sK55 = app(sF66,nil)
| ~ spl68_18 ),
inference(superposition,[],[f602,f1078]) ).
fof(f1125,plain,
( sK55 = sF66
| ~ spl68_11
| ~ spl68_18 ),
inference(forward_demodulation,[],[f1124,f676]) ).
fof(f1129,plain,
( nil = sF66
| spl68_1
| ~ spl68_3
| ~ spl68_11
| ~ spl68_18 ),
inference(forward_demodulation,[],[f1125,f648]) ).
fof(f1131,plain,
( $false
| spl68_1
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_18 ),
inference(forward_subsumption_resolution,[],[f1129,f1084]) ).
fof(f1132,plain,
( spl68_1
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_18 ),
inference(avatar_contradiction_clause,[],[f1131]) ).
fof(f1145,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ ssList(sK55)
| ~ spl68_2 ),
inference(resolution,[],[f568,f306]) ).
fof(f1146,plain,
( sK55 = cons(sK10(sK55),nil)
| ~ spl68_2 ),
inference(forward_subsumption_resolution,[],[f1145,f513]) ).
fof(f1557,plain,
( nil != cons(sK57,sK60)
| nil = sF62
| ~ ssList(sK60)
| ~ ssList(sF62) ),
inference(superposition,[],[f479,f837]) ).
fof(f1651,plain,
! [X0] :
( ~ ssList(X0)
| tl(app(X0,sK61)) = app(tl(X0),sK61)
| nil = X0 ),
inference(resolution,[],[f484,f505]) ).
fof(f1655,plain,
( ! [X0] :
( ~ ssList(X0)
| tl(app(X0,sF65)) = app(tl(X0),sF65)
| nil = X0 )
| ~ spl68_10 ),
inference(resolution,[],[f484,f618]) ).
fof(f1787,plain,
( tl(app(sF64,sF65)) = app(tl(sF64),sF65)
| nil = sF64
| ~ spl68_9
| ~ spl68_10 ),
inference(resolution,[],[f1655,f614]) ).
fof(f1846,definition,
( spl68_38
<=> ssList(tl(sF66)) ),
introduced(definition,[new_symbols(definition,[spl68_38])],[avatar_definition]) ).
fof(f1847,plain,
( ~ ssList(tl(sF66))
| spl68_38 ),
inference(avatar_component_clause,[],[f1846]) ).
fof(f1856,definition,
( spl68_40
<=> nil = tl(sF66) ),
introduced(definition,[new_symbols(definition,[spl68_40])],[avatar_definition]) ).
fof(f1857,plain,
( nil = tl(sF66)
| ~ spl68_40 ),
inference(avatar_component_clause,[],[f1856]) ).
fof(f1858,plain,
( nil != tl(sF66)
| spl68_40 ),
inference(avatar_component_clause,[],[f1856]) ).
fof(f2001,plain,
( ! [X0] :
( ~ ssItem(X0)
| nil = tl(cons(X0,nil)) )
| ~ spl68_3 ),
inference(resolution,[],[f400,f572]) ).
fof(f2112,plain,
( nil != cons(sK57,sK60)
| ~ ssList(sK60)
| ~ ssList(sF62)
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f1557,f789]) ).
fof(f2144,plain,
( nil != cons(sK57,sK60)
| ~ ssList(sF62)
| ~ spl68_3 ),
inference(forward_subsumption_resolution,[],[f2112,f504]) ).
fof(f2160,plain,
( nil != cons(sK57,sK60)
| ~ spl68_3
| ~ spl68_13 ),
inference(forward_subsumption_resolution,[],[f2144,f634]) ).
fof(f4187,definition,
( spl68_84
<=> ssItem(sK10(sK55)) ),
introduced(definition,[new_symbols(definition,[spl68_84])],[avatar_definition]) ).
fof(f4188,plain,
( ssItem(sK10(sK55))
| ~ spl68_84 ),
inference(avatar_component_clause,[],[f4187]) ).
fof(f4189,plain,
( ~ ssItem(sK10(sK55))
| spl68_84 ),
inference(avatar_component_clause,[],[f4187]) ).
fof(f4207,plain,
( ~ singletonP(sK55)
| ~ ssList(sK55)
| spl68_84 ),
inference(resolution,[],[f4189,f307]) ).
fof(f4208,plain,
( ~ ssList(sK55)
| ~ spl68_2
| spl68_84 ),
inference(forward_subsumption_resolution,[],[f4207,f568]) ).
fof(f4209,plain,
( $false
| ~ spl68_2
| spl68_84 ),
inference(forward_subsumption_resolution,[],[f4208,f513]) ).
fof(f4210,plain,
( ~ spl68_2
| spl68_84 ),
inference(avatar_contradiction_clause,[],[f4209]) ).
fof(f4221,plain,
( nil = tl(cons(sK10(sK55),nil))
| ~ spl68_3
| ~ spl68_84 ),
inference(resolution,[],[f4188,f2001]) ).
fof(f4224,plain,
( nil = tl(sK55)
| ~ spl68_2
| ~ spl68_3
| ~ spl68_84 ),
inference(forward_demodulation,[],[f4221,f1146]) ).
fof(f4276,plain,
( tl(app(sF66,sK61)) = app(tl(sF66),sK61)
| nil = sF66
| ~ spl68_11 ),
inference(resolution,[],[f1651,f623]) ).
fof(f4277,plain,
( tl(app(sF66,sK61)) = app(tl(sF66),sK61)
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11 ),
inference(forward_subsumption_resolution,[],[f4276,f1084]) ).
fof(f4288,plain,
( tl(sK55) = app(tl(sF66),sK61)
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11 ),
inference(forward_demodulation,[],[f4277,f602]) ).
fof(f4296,plain,
( nil = app(tl(sF66),sK61)
| ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_84 ),
inference(forward_demodulation,[],[f4288,f4224]) ).
fof(f4310,plain,
( nil != nil
| nil = tl(sF66)
| ~ ssList(sK61)
| ~ ssList(tl(sF66))
| ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_84 ),
inference(superposition,[],[f479,f4296]) ).
fof(f4314,plain,
( nil = tl(sF66)
| ~ ssList(sK61)
| ~ ssList(tl(sF66))
| ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_84 ),
inference(trivial_inequality_removal,[],[f4310]) ).
fof(f4316,plain,
( ~ ssList(sK61)
| ~ ssList(tl(sF66))
| ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| spl68_40
| ~ spl68_84 ),
inference(forward_subsumption_resolution,[],[f4314,f1858]) ).
fof(f4319,plain,
( ~ ssList(tl(sF66))
| ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| spl68_40
| ~ spl68_84 ),
inference(forward_subsumption_resolution,[],[f4316,f505]) ).
fof(f4325,plain,
( ~ spl68_38
| ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| spl68_40
| ~ spl68_84 ),
inference(avatar_split_clause,[],[f4319,f4187,f1856,f621,f617,f613,f571,f566,f1846]) ).
fof(f4326,plain,
( nil = sF66
| ~ ssList(sF66)
| spl68_38 ),
inference(resolution,[],[f1847,f399]) ).
fof(f4327,plain,
( ~ ssList(sF66)
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| spl68_38 ),
inference(forward_subsumption_resolution,[],[f4326,f1084]) ).
fof(f4328,plain,
( $false
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| spl68_38 ),
inference(forward_subsumption_resolution,[],[f4327,f623]) ).
fof(f4329,plain,
( ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| spl68_38 ),
inference(avatar_contradiction_clause,[],[f4328]) ).
fof(f4337,plain,
( tl(sF66) = app(tl(sF64),sF65)
| nil = sF64
| ~ spl68_9
| ~ spl68_10 ),
inference(forward_demodulation,[],[f1787,f550]) ).
fof(f4374,plain,
( ~ spl68_22
| ~ spl68_3
| ~ spl68_13 ),
inference(avatar_split_clause,[],[f2160,f633,f571,f1096]) ).
fof(f4547,plain,
( tl(sF66) = app(tl(sF64),sF65)
| ~ spl68_9
| ~ spl68_10
| spl68_20 ),
inference(forward_subsumption_resolution,[],[f4337,f1088]) ).
fof(f4614,plain,
( nil = app(tl(sF64),sF65)
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40 ),
inference(forward_demodulation,[],[f4547,f1857]) ).
fof(f4683,plain,
( nil != nil
| nil = sF65
| ~ ssList(sF65)
| ~ ssList(tl(sF64))
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40 ),
inference(superposition,[],[f480,f4614]) ).
fof(f4685,plain,
( nil = sF65
| ~ ssList(sF65)
| ~ ssList(tl(sF64))
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40 ),
inference(trivial_inequality_removal,[],[f4683]) ).
fof(f4687,plain,
( ~ ssList(sF65)
| ~ ssList(tl(sF64))
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40 ),
inference(forward_subsumption_resolution,[],[f4685,f788]) ).
fof(f4690,plain,
( ~ ssList(tl(sF64))
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40 ),
inference(forward_subsumption_resolution,[],[f4687,f618]) ).
fof(f4692,definition,
( spl68_113
<=> ssList(tl(sF64)) ),
introduced(definition,[new_symbols(definition,[spl68_113])],[avatar_definition]) ).
fof(f4694,plain,
( ~ ssList(tl(sF64))
| spl68_113 ),
inference(avatar_component_clause,[],[f4692]) ).
fof(f4704,plain,
( ~ spl68_113
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40 ),
inference(avatar_split_clause,[],[f4690,f1856,f1086,f617,f613,f571,f4692]) ).
fof(f4766,plain,
( nil = sF64
| ~ ssList(sF64)
| spl68_113 ),
inference(resolution,[],[f4694,f399]) ).
fof(f4767,plain,
( ~ ssList(sF64)
| spl68_20
| spl68_113 ),
inference(forward_subsumption_resolution,[],[f4766,f1088]) ).
fof(f4768,plain,
( $false
| ~ spl68_9
| spl68_20
| spl68_113 ),
inference(forward_subsumption_resolution,[],[f4767,f614]) ).
fof(f4769,plain,
( ~ spl68_9
| spl68_20
| spl68_113 ),
inference(avatar_contradiction_clause,[],[f4768]) ).
cnf(s1,plain,
( ~ spl68_1
| spl68_2 ),
inference(sat_conversion,[],[f569]) ).
cnf(s9,plain,
spl68_3,
inference(sat_conversion,[],[f599]) ).
cnf(s10,plain,
( ~ spl68_9
| ~ spl68_10
| spl68_11 ),
inference(sat_conversion,[],[f624]) ).
cnf(s11,plain,
( spl68_9
| ~ spl68_12 ),
inference(sat_conversion,[],[f631]) ).
cnf(s12,plain,
( spl68_12
| ~ spl68_13 ),
inference(sat_conversion,[],[f636]) ).
cnf(s13,plain,
( ~ spl68_3
| spl68_10 ),
inference(sat_conversion,[],[f644]) ).
cnf(s14,plain,
( ~ spl68_3
| spl68_13 ),
inference(sat_conversion,[],[f646]) ).
cnf(s23,plain,
( ~ spl68_13
| ~ spl68_20
| spl68_22 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s25,plain,
( spl68_1
| ~ spl68_3
| ~ spl68_11
| spl68_18 ),
inference(sat_conversion,[],[f1117]) ).
cnf(s26,plain,
( spl68_1
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_18 ),
inference(sat_conversion,[],[f1132]) ).
cnf(s98,plain,
( ~ spl68_2
| spl68_84 ),
inference(sat_conversion,[],[f4210]) ).
cnf(s101,plain,
( ~ spl68_2
| ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| ~ spl68_38
| spl68_40
| ~ spl68_84 ),
inference(sat_conversion,[],[f4325]) ).
cnf(s102,plain,
( ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| ~ spl68_11
| spl68_38 ),
inference(sat_conversion,[],[f4329]) ).
cnf(s109,plain,
( ~ spl68_3
| ~ spl68_13
| ~ spl68_22 ),
inference(sat_conversion,[],[f4374]) ).
cnf(s129,plain,
( ~ spl68_3
| ~ spl68_9
| ~ spl68_10
| spl68_20
| ~ spl68_40
| ~ spl68_113 ),
inference(sat_conversion,[],[f4704]) ).
cnf(s130,plain,
( ~ spl68_9
| spl68_20
| spl68_113 ),
inference(sat_conversion,[],[f4769]) ).
cnf(s132,plain,
spl68_13,
inference(rat,[],[s14,s9]) ).
cnf(s133,plain,
spl68_10,
inference(rat,[],[s13,s9]) ).
cnf(s135,plain,
~ spl68_22,
inference(rat,[],[s109,s9,s132]) ).
cnf(s136,plain,
~ spl68_20,
inference(rat,[],[s23,s135,s132]) ).
cnf(s137,plain,
spl68_12,
inference(rat,[],[s12,s132]) ).
cnf(s140,plain,
spl68_9,
inference(rat,[],[s11,s137]) ).
cnf(s143,plain,
spl68_113,
inference(rat,[],[s130,s136,s140]) ).
cnf(s144,plain,
~ spl68_40,
inference(rat,[],[s129,s143,s133,s136,s9,s140]) ).
cnf(s150,plain,
spl68_11,
inference(rat,[],[s10,s133,s140]) ).
cnf(s153,plain,
spl68_38,
inference(rat,[],[s102,s140,s133,s9,s150]) ).
cnf(s157,plain,
spl68_1,
inference(rat,[],[s25,s26,s9,s150,s133,s140]) ).
cnf(s158,plain,
spl68_2,
inference(rat,[],[s1,s157]) ).
cnf(s159,plain,
~ spl68_84,
inference(rat,[],[s101,s153,s144,s140,s150,s133,s9,s158]) ).
cnf(s160,plain,
$false,
inference(rat,[],[s98,s159,s158]) ).
fof(f4770,plain,
$false,
inference(avatar_sat_refutation,[],[s160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC307+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:00:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 5.71/1.35 % (2899752)Detected formulas, will run a generic FOF schedule.
% 5.71/1.35 % (2899757)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=4281421562:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.71/1.35 % (2899761)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3213387667:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.71/1.35 % (2899760)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1688904177:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.71/1.35 % (2899763)dis-21_1_sil=8000:lcm=predicate:random_seed=2667402365: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)
% 5.71/1.35 % (2899762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2276336777:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.71/1.35 % (2899758)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=1760991709:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.71/1.35 % (2899759)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=2588338959:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.71/1.35 % (2899760)Instruction limit reached!
% 5.71/1.35 % (2899760)------------------------------
% 5.71/1.35 % (2899760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899760)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899760)Termination reason: Instruction limit
% 5.71/1.35 % (2899760)Termination phase: Saturation
% 5.71/1.35 % (2899760)Time elapsed: 0.071 s
% 5.71/1.35 % (2899760)Peak memory usage: 89 MB
% 5.71/1.35 % (2899760)Instructions burned: 109 (million)
% 5.71/1.35 % (2899761)Instruction limit reached!
% 5.71/1.35 % (2899761)------------------------------
% 5.71/1.35 % (2899761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899761)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899761)Termination reason: Instruction limit
% 5.71/1.35 % (2899761)Termination phase: Saturation
% 5.71/1.35 % (2899761)Time elapsed: 0.071 s
% 5.71/1.35 % (2899761)Peak memory usage: 88 MB
% 5.71/1.35 % (2899761)Instructions burned: 120 (million)
% 5.71/1.35 % (2899763)Instruction limit reached!
% 5.71/1.35 % (2899763)------------------------------
% 5.71/1.35 % (2899763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899763)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899763)Termination reason: Instruction limit
% 5.71/1.35 % (2899763)Termination phase: Saturation
% 5.71/1.35 % (2899763)Time elapsed: 0.072 s
% 5.71/1.35 % (2899763)Peak memory usage: 90 MB
% 5.71/1.35 % (2899763)Instructions burned: 131 (million)
% 5.71/1.35 % (2899762)Instruction limit reached!
% 5.71/1.35 % (2899762)------------------------------
% 5.71/1.35 % (2899762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899762)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899762)Termination reason: Instruction limit
% 5.71/1.35 % (2899762)Termination phase: Saturation
% 5.71/1.35 % (2899762)Time elapsed: 0.093 s
% 5.71/1.35 % (2899762)Peak memory usage: 90 MB
% 5.71/1.35 % (2899762)Instructions burned: 139 (million)
% 5.71/1.35 % (2899772)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2801630326:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.71/1.35 % (2899771)lrs+10_1_sil=8000:sp=occurrence:random_seed=2888014154:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.71/1.35 % (2899773)lrs+1011_1_sil=32000:sp=occurrence:random_seed=128139346:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.71/1.35 % (2899774)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3265241013:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.71/1.35 % (2899772)Instruction limit reached!
% 5.71/1.35 % (2899772)------------------------------
% 5.71/1.35 % (2899772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899772)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899772)Termination reason: Instruction limit
% 5.71/1.35 % (2899772)Termination phase: Saturation
% 5.71/1.35 % (2899772)Time elapsed: 0.072 s
% 5.71/1.35 % (2899772)Peak memory usage: 91 MB
% 5.71/1.35 % (2899772)Instructions burned: 157 (million)
% 5.71/1.35 % (2899774)Instruction limit reached!
% 5.71/1.35 % (2899774)------------------------------
% 5.71/1.35 % (2899774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899774)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899774)Termination reason: Instruction limit
% 5.71/1.35 % (2899774)Termination phase: Saturation
% 5.71/1.35 % (2899774)Time elapsed: 0.115 s
% 5.71/1.35 % (2899774)Peak memory usage: 94 MB
% 5.71/1.35 % (2899774)Instructions burned: 249 (million)
% 5.71/1.35 % (2899771)Instruction limit reached!
% 5.71/1.35 % (2899771)------------------------------
% 5.71/1.35 % (2899771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899771)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899771)Termination reason: Instruction limit
% 5.71/1.35 % (2899771)Termination phase: Saturation
% 5.71/1.35 % (2899771)Time elapsed: 0.169 s
% 5.71/1.35 % (2899771)Peak memory usage: 92 MB
% 5.71/1.35 % (2899771)Instructions burned: 286 (million)
% 5.71/1.35 % (2899773)Instruction limit reached!
% 5.71/1.35 % (2899773)------------------------------
% 5.71/1.35 % (2899773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899773)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899773)Termination reason: Instruction limit
% 5.71/1.35 % (2899773)Termination phase: Saturation
% 5.71/1.35 % (2899773)Time elapsed: 0.199 s
% 5.71/1.35 % (2899773)Peak memory usage: 92 MB
% 5.71/1.35 % (2899773)Instructions burned: 326 (million)
% 5.71/1.35 % (2899779)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1620398816:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.71/1.35 % (2899780)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1580351115:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.71/1.35 % (2899782)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=367671109:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.71/1.35 % (2899757)First to succeed.
% 5.71/1.35 % (2899757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2899752"
% 5.71/1.35 % (2899783)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2576462883:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.71/1.35 % (2899782)Instruction limit reached!
% 5.71/1.35 % (2899782)------------------------------
% 5.71/1.35 % (2899782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899782)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899782)Termination reason: Instruction limit
% 5.71/1.35 % (2899782)Termination phase: Saturation
% 5.71/1.35 % (2899782)Time elapsed: 0.076 s
% 5.71/1.35 % (2899782)Peak memory usage: 90 MB
% 5.71/1.35 % (2899782)Instructions burned: 114 (million)
% 5.71/1.35 % (2899779)Instruction limit reached!
% 5.71/1.35 % (2899779)------------------------------
% 5.71/1.35 % (2899779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899779)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899779)Termination reason: Instruction limit
% 5.71/1.35 % (2899779)Termination phase: Saturation
% 5.71/1.35 % (2899779)Time elapsed: 0.173 s
% 5.71/1.35 % (2899779)Peak memory usage: 90 MB
% 5.71/1.35 % (2899779)Instructions burned: 294 (million)
% 5.71/1.35 % (2899783)Instruction limit reached!
% 5.71/1.35 % (2899783)------------------------------
% 5.71/1.35 % (2899783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.35 % (2899783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.35 % (2899783)CaDiCaL version: 2.1.3
% 5.71/1.35 % (2899783)Termination reason: Instruction limit
% 5.71/1.35 % (2899783)Termination phase: Saturation
% 5.71/1.35 % (2899783)Time elapsed: 0.065 s
% 5.71/1.35 % (2899783)Peak memory usage: 90 MB
% 5.71/1.35 % (2899783)Instructions burned: 129 (million)
% 5.71/1.35 % (2899757)Refutation found. Thanks to Tanya!
% 5.71/1.35 % SZS status Theorem for theBenchmark
% 5.71/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 6.32/1.48 % (2899757)------------------------------
% 6.32/1.48 % (2899757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.48 % (2899757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.48 % (2899757)CaDiCaL version: 2.1.3
% 6.32/1.48 % (2899757)Termination reason: Refutation
% 6.32/1.48 % (2899757)Time elapsed: 0.584 s
% 6.32/1.48 % (2899757)Peak memory usage: 137 MB
% 6.32/1.48 % (2899757)Instructions burned: 1664 (million)
% 6.32/1.48 % (2899757)------------------------------
% 6.32/1.48 % (2899757)------------------------------
% 6.32/1.48 % (2899752)Success in time 0.847 s
% 6.32/1.48 % Vampire exiting
%------------------------------------------------------------------------------