%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC315+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 : n012.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 01:03:25 PM UTC 2026
% Result : Theorem 2.66s 0.73s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 173 ( 18 unt; 13 def)
% Number of atoms : 603 ( 159 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 766 ( 336 ~; 348 |; 43 &)
% ( 17 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 14 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
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(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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X1
| app(X5,cons(X4,nil)) = X0 ) )
& ( nil != X1
| nil = X0 ) )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != 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
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X1
| app(X5,cons(X4,nil)) = X0 ) )
& ( nil != X1
| nil = X0 ) )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X3
| app(X7,cons(X6,nil)) != X2 ) )
& neq(X3,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X1
& app(X5,cons(X4,nil)) != X0 )
& ssItem(X4) )
| ( nil = X1
& nil != X0 ) )
& ( ? [X6] :
( ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X3
& app(X7,cons(X6,nil)) = X2 )
& ssItem(X6) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f144,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f162,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f173,plain,
( ssList(sK9)
& sK7 = sK9
& sK6 = sK8
& ( nil = sK8
| nil != sK9 )
& ( ( ssList(sK11)
& sK7 = app(cons(sK10,nil),sK11)
& sK6 != app(sK11,cons(sK10,nil))
& ssItem(sK10) )
| ( nil = sK7
& nil != sK6 ) )
& ( ( ssList(sK13)
& sK9 = app(cons(sK12,nil),sK13)
& sK8 = app(sK13,cons(sK12,nil))
& ssItem(sK12) )
| ~ neq(sK9,nil) )
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10),skolemize(X5,sK11),skolemize(X6,sK12),skolemize(X7,sK13)],[f98]) ).
fof(f214,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,[],[f144]) ).
fof(f215,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,[],[f214]) ).
fof(f227,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f162]) ).
fof(f230,plain,
ssList(sK7),
inference(cnf_transformation,[],[f173]) ).
fof(f232,plain,
( ssItem(sK12)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f173]) ).
fof(f233,plain,
( sK8 = app(sK13,cons(sK12,nil))
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f173]) ).
fof(f234,plain,
( sK9 = app(cons(sK12,nil),sK13)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f173]) ).
fof(f235,plain,
( ssList(sK13)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f173]) ).
fof(f236,plain,
( ssItem(sK10)
| nil != sK6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f237,plain,
( ssItem(sK10)
| nil = sK7 ),
inference(cnf_transformation,[],[f173]) ).
fof(f238,plain,
( sK6 != app(sK11,cons(sK10,nil))
| nil != sK6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f239,plain,
( sK6 != app(sK11,cons(sK10,nil))
| nil = sK7 ),
inference(cnf_transformation,[],[f173]) ).
fof(f240,plain,
( sK7 = app(cons(sK10,nil),sK11)
| nil != sK6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f241,plain,
( sK7 = app(cons(sK10,nil),sK11)
| nil = sK7 ),
inference(cnf_transformation,[],[f173]) ).
fof(f242,plain,
( ssList(sK11)
| nil != sK6 ),
inference(cnf_transformation,[],[f173]) ).
fof(f243,plain,
( ssList(sK11)
| nil = sK7 ),
inference(cnf_transformation,[],[f173]) ).
fof(f244,plain,
( nil = sK8
| nil != sK9 ),
inference(cnf_transformation,[],[f173]) ).
fof(f245,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f173]) ).
fof(f246,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f173]) ).
fof(f251,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f277,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f278,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f364,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f365,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f389,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f392,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f393,plain,
( ssList(sK11)
| nil = sK9 ),
inference(definition_unfolding,[],[f243,f246]) ).
fof(f394,plain,
( ssList(sK11)
| nil != sK8 ),
inference(definition_unfolding,[],[f242,f245]) ).
fof(f395,plain,
( sK9 = app(cons(sK10,nil),sK11)
| nil = sK9 ),
inference(definition_unfolding,[],[f241,f246,f246]) ).
fof(f396,plain,
( sK9 = app(cons(sK10,nil),sK11)
| nil != sK8 ),
inference(definition_unfolding,[],[f240,f246,f245]) ).
fof(f397,plain,
( sK8 != app(sK11,cons(sK10,nil))
| nil = sK9 ),
inference(definition_unfolding,[],[f239,f245,f246]) ).
fof(f398,plain,
( sK8 != app(sK11,cons(sK10,nil))
| nil != sK8 ),
inference(definition_unfolding,[],[f238,f245,f245]) ).
fof(f399,plain,
( ssItem(sK10)
| nil = sK9 ),
inference(definition_unfolding,[],[f237,f246]) ).
fof(f400,plain,
( ssItem(sK10)
| nil != sK8 ),
inference(definition_unfolding,[],[f236,f245]) ).
fof(f401,plain,
ssList(sK9),
inference(definition_unfolding,[],[f230,f246]) ).
fof(f433,definition,
( spl59_1
<=> neq(sK9,nil) ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f435,plain,
( ~ neq(sK9,nil)
| spl59_1 ),
inference(avatar_component_clause,[],[f433]) ).
fof(f437,definition,
( spl59_2
<=> ssItem(sK12) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f439,plain,
( ssItem(sK12)
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f440,plain,
( ~ spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f232,f437,f433]) ).
fof(f442,definition,
( spl59_3
<=> sK8 = app(sK13,cons(sK12,nil)) ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f444,plain,
( sK8 = app(sK13,cons(sK12,nil))
| ~ spl59_3 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f445,plain,
( ~ spl59_1
| spl59_3 ),
inference(avatar_split_clause,[],[f233,f442,f433]) ).
fof(f447,definition,
( spl59_4
<=> sK9 = app(cons(sK12,nil),sK13) ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
fof(f449,plain,
( sK9 = app(cons(sK12,nil),sK13)
| ~ spl59_4 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f450,plain,
( ~ spl59_1
| spl59_4 ),
inference(avatar_split_clause,[],[f234,f447,f433]) ).
fof(f452,definition,
( spl59_5
<=> ssList(sK13) ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
fof(f454,plain,
( ssList(sK13)
| ~ spl59_5 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f455,plain,
( ~ spl59_1
| spl59_5 ),
inference(avatar_split_clause,[],[f235,f452,f433]) ).
fof(f457,definition,
( spl59_6
<=> nil = sK8 ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f458,plain,
( nil = sK8
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f461,definition,
( spl59_7
<=> ssItem(sK10) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f463,plain,
( ssItem(sK10)
| ~ spl59_7 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f464,plain,
( ~ spl59_6
| spl59_7 ),
inference(avatar_split_clause,[],[f400,f461,f457]) ).
fof(f466,definition,
( spl59_8
<=> nil = sK9 ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
fof(f467,plain,
( nil != sK9
| spl59_8 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f468,plain,
( nil = sK9
| ~ spl59_8 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f469,plain,
( spl59_8
| spl59_7 ),
inference(avatar_split_clause,[],[f399,f461,f466]) ).
fof(f471,definition,
( spl59_9
<=> sK8 = app(sK11,cons(sK10,nil)) ),
introduced(definition,[new_symbols(definition,[spl59_9])],[avatar_definition]) ).
fof(f473,plain,
( sK8 != app(sK11,cons(sK10,nil))
| spl59_9 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f474,plain,
( ~ spl59_6
| ~ spl59_9 ),
inference(avatar_split_clause,[],[f398,f471,f457]) ).
fof(f475,plain,
( spl59_8
| ~ spl59_9 ),
inference(avatar_split_clause,[],[f397,f471,f466]) ).
fof(f477,definition,
( spl59_10
<=> sK9 = app(cons(sK10,nil),sK11) ),
introduced(definition,[new_symbols(definition,[spl59_10])],[avatar_definition]) ).
fof(f479,plain,
( sK9 = app(cons(sK10,nil),sK11)
| ~ spl59_10 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f480,plain,
( ~ spl59_6
| spl59_10 ),
inference(avatar_split_clause,[],[f396,f477,f457]) ).
fof(f481,plain,
( spl59_8
| spl59_10 ),
inference(avatar_split_clause,[],[f395,f477,f466]) ).
fof(f483,definition,
( spl59_11
<=> ssList(sK11) ),
introduced(definition,[new_symbols(definition,[spl59_11])],[avatar_definition]) ).
fof(f485,plain,
( ssList(sK11)
| ~ spl59_11 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f486,plain,
( ~ spl59_6
| spl59_11 ),
inference(avatar_split_clause,[],[f394,f483,f457]) ).
fof(f487,plain,
( spl59_8
| spl59_11 ),
inference(avatar_split_clause,[],[f393,f483,f466]) ).
fof(f488,plain,
( ~ spl59_8
| spl59_6 ),
inference(avatar_split_clause,[],[f244,f457,f466]) ).
fof(f489,plain,
( nil != app(sK11,cons(sK10,nil))
| ~ spl59_6
| spl59_9 ),
inference(forward_demodulation,[],[f473,f458]) ).
fof(f490,plain,
( nil = app(cons(sK10,nil),sK11)
| ~ spl59_8
| ~ spl59_10 ),
inference(forward_demodulation,[],[f479,f468]) ).
fof(f499,plain,
( nil = sK9
| ~ ssList(nil)
| ~ ssList(sK9)
| spl59_1 ),
inference(resolution,[],[f389,f435]) ).
fof(f539,plain,
( nil != nil
| nil = cons(sK10,nil)
| ~ ssList(sK11)
| ~ ssList(cons(sK10,nil))
| ~ spl59_8
| ~ spl59_10 ),
inference(superposition,[],[f364,f490]) ).
fof(f542,plain,
( nil = cons(sK10,nil)
| ~ ssList(sK11)
| ~ ssList(cons(sK10,nil))
| ~ spl59_8
| ~ spl59_10 ),
inference(trivial_inequality_removal,[],[f539]) ).
fof(f543,plain,
( nil = cons(sK10,nil)
| ~ ssList(cons(sK10,nil))
| ~ spl59_8
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f542,f485]) ).
fof(f545,definition,
( spl59_12
<=> ssList(cons(sK10,nil)) ),
introduced(definition,[new_symbols(definition,[spl59_12])],[avatar_definition]) ).
fof(f546,plain,
( ssList(cons(sK10,nil))
| ~ spl59_12 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f547,plain,
( ~ ssList(cons(sK10,nil))
| spl59_12 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f549,definition,
( spl59_13
<=> nil = cons(sK10,nil) ),
introduced(definition,[new_symbols(definition,[spl59_13])],[avatar_definition]) ).
fof(f551,plain,
( nil = cons(sK10,nil)
| ~ spl59_13 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,plain,
( ~ spl59_12
| spl59_13
| ~ spl59_8
| ~ spl59_10
| ~ spl59_11 ),
inference(avatar_split_clause,[],[f543,f483,f477,f466,f549,f545]) ).
fof(f553,plain,
( ~ ssItem(sK10)
| ~ ssList(nil)
| spl59_12 ),
inference(resolution,[],[f547,f286]) ).
fof(f554,plain,
( ~ ssList(nil)
| ~ spl59_7
| spl59_12 ),
inference(forward_subsumption_resolution,[],[f553,f463]) ).
fof(f555,plain,
( $false
| ~ spl59_7
| spl59_12 ),
inference(forward_subsumption_resolution,[],[f554,f392]) ).
fof(f556,plain,
( ~ spl59_7
| spl59_12 ),
inference(avatar_contradiction_clause,[],[f555]) ).
fof(f557,plain,
( nil != nil
| nil = sK11
| ~ ssList(sK11)
| ~ ssList(cons(sK10,nil))
| ~ spl59_8
| ~ spl59_10 ),
inference(superposition,[],[f365,f490]) ).
fof(f560,plain,
( nil = sK11
| ~ ssList(sK11)
| ~ ssList(cons(sK10,nil))
| ~ spl59_8
| ~ spl59_10 ),
inference(trivial_inequality_removal,[],[f557]) ).
fof(f561,plain,
( nil = sK11
| ~ ssList(cons(sK10,nil))
| ~ spl59_8
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f560,f485]) ).
fof(f562,plain,
( nil = sK11
| ~ spl59_8
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12 ),
inference(forward_subsumption_resolution,[],[f561,f546]) ).
fof(f563,plain,
( nil = app(cons(sK10,nil),nil)
| ~ spl59_8
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12 ),
inference(superposition,[],[f490,f562]) ).
fof(f564,plain,
( nil != app(nil,cons(sK10,nil))
| ~ spl59_6
| ~ spl59_8
| spl59_9
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12 ),
inference(superposition,[],[f489,f562]) ).
fof(f566,plain,
( nil != app(nil,nil)
| ~ spl59_6
| ~ spl59_8
| spl59_9
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12
| ~ spl59_13 ),
inference(forward_demodulation,[],[f564,f551]) ).
fof(f567,plain,
( nil = app(nil,nil)
| ~ spl59_8
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12
| ~ spl59_13 ),
inference(forward_demodulation,[],[f563,f551]) ).
fof(f568,plain,
( $false
| ~ spl59_6
| ~ spl59_8
| spl59_9
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12
| ~ spl59_13 ),
inference(forward_subsumption_resolution,[],[f567,f566]) ).
fof(f569,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_9
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12
| ~ spl59_13 ),
inference(avatar_contradiction_clause,[],[f568]) ).
fof(f570,plain,
( ~ ssList(nil)
| ~ ssList(sK9)
| spl59_1
| spl59_8 ),
inference(forward_subsumption_resolution,[],[f499,f467]) ).
fof(f572,plain,
( ~ ssList(sK9)
| spl59_1
| spl59_8 ),
inference(forward_subsumption_resolution,[],[f570,f392]) ).
fof(f582,plain,
( $false
| spl59_1
| spl59_8 ),
inference(forward_subsumption_resolution,[],[f572,f401]) ).
fof(f583,plain,
( spl59_1
| spl59_8 ),
inference(avatar_contradiction_clause,[],[f582]) ).
fof(f614,plain,
( sK9 = cons(sK12,sK13)
| ~ ssItem(sK12)
| ~ ssList(sK13)
| ~ spl59_4 ),
inference(superposition,[],[f449,f251]) ).
fof(f615,plain,
( sK9 = cons(sK10,sK11)
| ~ ssItem(sK10)
| ~ ssList(sK11)
| ~ spl59_10 ),
inference(superposition,[],[f479,f251]) ).
fof(f622,plain,
( sK9 = cons(sK10,sK11)
| ~ ssList(sK11)
| ~ spl59_7
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f615,f463]) ).
fof(f623,plain,
( sK9 = cons(sK12,sK13)
| ~ ssList(sK13)
| ~ spl59_2
| ~ spl59_4 ),
inference(forward_subsumption_resolution,[],[f614,f439]) ).
fof(f626,plain,
( sK9 = cons(sK10,sK11)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f622,f485]) ).
fof(f627,plain,
( sK9 = cons(sK12,sK13)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f623,f454]) ).
fof(f772,plain,
( sK10 = hd(sK9)
| ~ ssItem(sK10)
| ~ ssList(sK11)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(superposition,[],[f278,f626]) ).
fof(f773,plain,
( sK11 = tl(sK9)
| ~ ssItem(sK10)
| ~ ssList(sK11)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(superposition,[],[f277,f626]) ).
fof(f780,plain,
( sK11 = tl(sK9)
| ~ ssList(sK11)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f773,f463]) ).
fof(f781,plain,
( sK10 = hd(sK9)
| ~ ssList(sK11)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f772,f463]) ).
fof(f784,plain,
( sK11 = tl(sK9)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f780,f485]) ).
fof(f785,plain,
( sK10 = hd(sK9)
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f781,f485]) ).
fof(f849,plain,
( sK12 = hd(sK9)
| ~ ssItem(sK12)
| ~ ssList(sK13)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(superposition,[],[f278,f627]) ).
fof(f850,plain,
( sK13 = tl(sK9)
| ~ ssItem(sK12)
| ~ ssList(sK13)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(superposition,[],[f277,f627]) ).
fof(f857,plain,
( sK13 = tl(sK9)
| ~ ssList(sK13)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f850,f439]) ).
fof(f858,plain,
( sK12 = hd(sK9)
| ~ ssList(sK13)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f849,f439]) ).
fof(f862,plain,
( sK13 = tl(sK9)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f857,f454]) ).
fof(f863,plain,
( sK12 = hd(sK9)
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f858,f454]) ).
fof(f866,plain,
( sK11 = sK13
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_demodulation,[],[f862,f784]) ).
fof(f867,plain,
( sK10 = sK12
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_demodulation,[],[f863,f785]) ).
fof(f1052,plain,
( sK8 = app(sK13,cons(sK10,nil))
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_demodulation,[],[f444,f867]) ).
fof(f1062,plain,
( sK8 = app(sK11,cons(sK10,nil))
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_demodulation,[],[f1052,f866]) ).
fof(f1069,plain,
( $false
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| spl59_9
| ~ spl59_10
| ~ spl59_11 ),
inference(forward_subsumption_resolution,[],[f1062,f473]) ).
fof(f1070,plain,
( ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| spl59_9
| ~ spl59_10
| ~ spl59_11 ),
inference(avatar_contradiction_clause,[],[f1069]) ).
cnf(s1,plain,
( ~ spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f440]) ).
cnf(s2,plain,
( ~ spl59_1
| spl59_3 ),
inference(sat_conversion,[],[f445]) ).
cnf(s3,plain,
( ~ spl59_1
| spl59_4 ),
inference(sat_conversion,[],[f450]) ).
cnf(s4,plain,
( ~ spl59_1
| spl59_5 ),
inference(sat_conversion,[],[f455]) ).
cnf(s5,plain,
( ~ spl59_6
| spl59_7 ),
inference(sat_conversion,[],[f464]) ).
cnf(s6,plain,
( spl59_7
| spl59_8 ),
inference(sat_conversion,[],[f469]) ).
cnf(s7,plain,
( ~ spl59_6
| ~ spl59_9 ),
inference(sat_conversion,[],[f474]) ).
cnf(s8,plain,
( spl59_8
| ~ spl59_9 ),
inference(sat_conversion,[],[f475]) ).
cnf(s9,plain,
( ~ spl59_6
| spl59_10 ),
inference(sat_conversion,[],[f480]) ).
cnf(s10,plain,
( spl59_8
| spl59_10 ),
inference(sat_conversion,[],[f481]) ).
cnf(s11,plain,
( ~ spl59_6
| spl59_11 ),
inference(sat_conversion,[],[f486]) ).
cnf(s12,plain,
( spl59_8
| spl59_11 ),
inference(sat_conversion,[],[f487]) ).
cnf(s13,plain,
( spl59_6
| ~ spl59_8 ),
inference(sat_conversion,[],[f488]) ).
cnf(s14,plain,
( ~ spl59_8
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12
| spl59_13 ),
inference(sat_conversion,[],[f552]) ).
cnf(s15,plain,
( ~ spl59_7
| spl59_12 ),
inference(sat_conversion,[],[f556]) ).
cnf(s16,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_9
| ~ spl59_10
| ~ spl59_11
| ~ spl59_12
| ~ spl59_13 ),
inference(sat_conversion,[],[f569]) ).
cnf(s18,plain,
( spl59_1
| spl59_8 ),
inference(sat_conversion,[],[f583]) ).
cnf(s28,plain,
( ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5
| ~ spl59_7
| spl59_9
| ~ spl59_10
| ~ spl59_11 ),
inference(sat_conversion,[],[f1070]) ).
cnf(s29,plain,
~ spl59_8,
inference(rat,[],[s16,s14,s15,s5,s7,s9,s11,s13]) ).
cnf(s30,plain,
spl59_1,
inference(rat,[],[s18,s29]) ).
cnf(s31,plain,
spl59_11,
inference(rat,[],[s12,s29]) ).
cnf(s32,plain,
spl59_10,
inference(rat,[],[s10,s29]) ).
cnf(s33,plain,
~ spl59_9,
inference(rat,[],[s8,s29]) ).
cnf(s34,plain,
spl59_7,
inference(rat,[],[s6,s29]) ).
cnf(s35,plain,
spl59_5,
inference(rat,[],[s4,s30]) ).
cnf(s36,plain,
spl59_4,
inference(rat,[],[s3,s30]) ).
cnf(s37,plain,
spl59_3,
inference(rat,[],[s2,s30]) ).
cnf(s38,plain,
spl59_2,
inference(rat,[],[s1,s30]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s28,s31,s32,s33,s37,s35,s34,s36,s38]) ).
fof(f1072,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC315+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 09:00:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 2.66/0.73 % (3247539)Detected formulas, will run a generic FOF schedule.
% 2.66/0.73 % (3247550)dis-21_1_sil=8000:lcm=predicate:random_seed=104240678: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)
% 2.66/0.73 % (3247544)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=3453757888:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.66/0.73 % (3247548)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=695918376:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.66/0.73 % (3247545)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=817372118:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.66/0.73 % (3247546)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=3703315869:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.66/0.73 % (3247547)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3329114239:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.66/0.73 % (3247549)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2535953241:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.66/0.73 % (3247548)Instruction limit reached!
% 2.66/0.73 % (3247548)------------------------------
% 2.66/0.73 % (3247548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/0.73 % (3247548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.73 % (3247548)CaDiCaL version: 2.1.3
% 2.66/0.73 % (3247548)Termination reason: Instruction limit
% 2.66/0.73 % (3247548)Termination phase: Saturation
% 2.66/0.73 % (3247548)Time elapsed: 0.035 s
% 2.66/0.73 % (3247548)Peak memory usage: 88 MB
% 2.66/0.73 % (3247548)Instructions burned: 121 (million)
% 2.66/0.73 % (3247547)Instruction limit reached!
% 2.66/0.73 % (3247547)------------------------------
% 2.66/0.73 % (3247547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/0.73 % (3247547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.73 % (3247547)CaDiCaL version: 2.1.3
% 2.66/0.73 % (3247547)Termination reason: Instruction limit
% 2.66/0.73 % (3247547)Termination phase: Saturation
% 2.66/0.73 % (3247547)Time elapsed: 0.036 s
% 2.66/0.73 % (3247547)Peak memory usage: 89 MB
% 2.66/0.73 % (3247547)Instructions burned: 111 (million)
% 2.66/0.73 % (3247550)Instruction limit reached!
% 2.66/0.73 % (3247550)------------------------------
% 2.66/0.73 % (3247550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/0.73 % (3247550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.73 % (3247550)CaDiCaL version: 2.1.3
% 2.66/0.73 % (3247550)Termination reason: Instruction limit
% 2.66/0.73 % (3247550)Termination phase: Saturation
% 2.66/0.73 % (3247550)Time elapsed: 0.040 s
% 2.66/0.73 % (3247550)Peak memory usage: 90 MB
% 2.66/0.73 % (3247550)Instructions burned: 131 (million)
% 2.66/0.73 % (3247549)Instruction limit reached!
% 2.66/0.73 % (3247549)------------------------------
% 2.66/0.73 % (3247549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/0.73 % (3247549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.73 % (3247549)CaDiCaL version: 2.1.3
% 2.66/0.73 % (3247549)Termination reason: Instruction limit
% 2.66/0.73 % (3247549)Termination phase: Saturation
% 2.66/0.73 % (3247549)Time elapsed: 0.049 s
% 2.66/0.73 % (3247549)Peak memory usage: 90 MB
% 2.66/0.73 % (3247549)Instructions burned: 141 (million)
% 2.66/0.73 % (3247559)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4005843263:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 2.66/0.73 % (3247558)lrs+10_1_sil=8000:sp=occurrence:random_seed=1316120782:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.66/0.73 % (3247560)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3061584616:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 2.66/0.73 % (3247560)First to succeed.
% 2.66/0.73 % (3247561)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=4287315158:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 2.66/0.73 % (3247560)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3247539"
% 2.66/0.73 % (3247559)Instruction limit reached!
% 2.66/0.73 % (3247559)------------------------------
% 2.66/0.73 % (3247559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/0.73 % (3247559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.73 % (3247559)CaDiCaL version: 2.1.3
% 2.66/0.73 % (3247559)Termination reason: Instruction limit
% 2.66/0.73 % (3247559)Termination phase: Saturation
% 2.66/0.73 % (3247559)Time elapsed: 0.042 s
% 2.66/0.73 % (3247559)Peak memory usage: 92 MB
% 2.66/0.73 % (3247559)Instructions burned: 158 (million)
% 2.66/0.73 % (3247558)Also succeeded, but the first one will report.
% 2.66/0.73 % (3247561)Instruction limit reached!
% 2.66/0.73 % (3247561)------------------------------
% 2.66/0.73 % (3247561)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/0.73 % (3247561)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.73 % (3247561)CaDiCaL version: 2.1.3
% 2.66/0.73 % (3247561)Termination reason: Instruction limit
% 2.66/0.73 % (3247561)Termination phase: Saturation
% 2.66/0.73 % (3247561)Time elapsed: 0.066 s
% 2.66/0.73 % (3247561)Peak memory usage: 94 MB
% 2.66/0.73 % (3247561)Instructions burned: 251 (million)
% 2.66/0.73 % (3247566)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=135965460:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2997 on theBenchmark for (2997ds/294Mi)
% 2.66/0.73 % (3247560)Refutation found. Thanks to Tanya!
% 2.66/0.73 % SZS status Theorem for theBenchmark
% 2.66/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 3.15/0.82 % (3247560)------------------------------
% 3.15/0.82 % (3247560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/0.82 % (3247560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/0.82 % (3247560)CaDiCaL version: 2.1.3
% 3.15/0.82 % (3247560)Termination reason: Refutation
% 3.15/0.82 % (3247560)Time elapsed: 0.012 s
% 3.15/0.82 % (3247560)Peak memory usage: 90 MB
% 3.15/0.82 % (3247560)Instructions burned: 33 (million)
% 3.15/0.82 % (3247560)------------------------------
% 3.15/0.82 % (3247560)------------------------------
% 3.15/0.82 % (3247539)Success in time 0.416 s
% 3.15/0.82 % Vampire exiting
%------------------------------------------------------------------------------