%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC022+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 01:04:19 PM UTC 2026
% Result : Theorem 0.51s 0.57s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of formulae : 165 ( 28 unt; 13 def)
% Number of atoms : 551 ( 82 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 680 ( 294 ~; 302 |; 40 &)
% ( 19 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 92 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( X0 = X1
& frontsegP(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax44) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
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)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ? [X5] :
( ssList(X5)
& X2 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X3) = X6
& neq(nil,X3) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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)
& frontsegP(X1,X4)
& frontsegP(X0,X4) )
| ? [X5] :
( ssList(X5)
& X2 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X3) = X6
& neq(nil,X3) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f153,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( X0 = X1
& frontsegP(X2,X3) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f157,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f192,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ! [X5] :
( ~ ssList(X5)
| X2 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X3) != X6
| ~ neq(nil,X3) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X1,X4)
| ~ frontsegP(X0,X4) )
& ! [X5] :
( ~ ssList(X5)
| X2 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X3) != X6
| ~ neq(nil,X3) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f303,plain,
! [X0,X1] :
( neq(X0,X1)
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f305,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f314,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f316,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f337,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f340,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f344,plain,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3)) ),
inference(cnf_transformation,[],[f156]) ).
fof(f345,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[],[f157]) ).
fof(f389,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f412,plain,
! [X6,X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| hd(sK50) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK49 = X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ frontsegP(sK47,X4)
| ~ frontsegP(sK48,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
ssList(sK50),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
ssList(sK49),
inference(cnf_transformation,[],[f222]) ).
fof(f426,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f415,f419]) ).
fof(f428,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ frontsegP(sK49,X4)
| ~ frontsegP(sK50,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f413,f418,f419]) ).
fof(f432,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f234]) ).
fof(f444,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f446,plain,
! [X2,X3,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(equality_resolution,[],[f344]) ).
fof(f455,plain,
! [X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| cons(hd(sK50),nil) != X5
| ~ ssItem(hd(sK50))
| sK49 = X5
| ~ ssList(X5) ),
inference(equality_resolution,[],[f412]) ).
fof(f456,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| sK49 = cons(hd(sK50),nil)
| ~ ssList(cons(hd(sK50),nil)) ),
inference(equality_resolution,[],[f455]) ).
fof(f463,plain,
! [X1] :
( ~ singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(consistent_polarity_flipping,[],[f432]) ).
fof(f503,plain,
singletonP(nil),
inference(consistent_polarity_flipping,[],[f337]) ).
fof(f506,plain,
! [X0] :
( ~ frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f340]) ).
fof(f508,plain,
! [X2,X3,X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| frontsegP(X2,X3)
| ~ frontsegP(cons(X1,X2),cons(X1,X3)) ),
inference(consistent_polarity_flipping,[],[f446]) ).
fof(f511,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(consistent_polarity_flipping,[],[f345]) ).
fof(f534,plain,
! [X4] :
( ~ neq(sK50,nil)
| frontsegP(sK49,X4)
| frontsegP(sK50,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(consistent_polarity_flipping,[],[f428]) ).
fof(f537,plain,
! [X2,X3,X1] :
( ~ frontsegP(cons(X1,X2),cons(X1,X3))
| ~ ssList(X2)
| ~ ssList(X3)
| frontsegP(X2,X3)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f508]) ).
fof(f539,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f444]) ).
fof(f543,definition,
( spl51_1
<=> ssList(cons(hd(sK50),nil)) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f545,plain,
( ~ ssList(cons(hd(sK50),nil))
| spl51_1 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f547,definition,
( spl51_2
<=> sK49 = cons(hd(sK50),nil) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f549,plain,
( sK49 = cons(hd(sK50),nil)
| ~ spl51_2 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f551,definition,
( spl51_3
<=> ssItem(hd(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).
fof(f552,plain,
( ssItem(hd(sK50))
| ~ spl51_3 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f553,plain,
( ~ ssItem(hd(sK50))
| spl51_3 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f555,definition,
( spl51_4
<=> neq(nil,sK50) ),
introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).
fof(f557,plain,
( ~ neq(nil,sK50)
| spl51_4 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f559,definition,
( spl51_5
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).
fof(f561,plain,
( neq(sK50,nil)
| ~ spl51_5 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f563,plain,
( ~ spl51_1
| spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5 ),
inference(avatar_split_clause,[],[f456,f559,f555,f551,f547,f543]) ).
fof(f565,definition,
( spl51_6
<=> ! [X4] :
( frontsegP(sK49,X4)
| ~ ssList(X4)
| ~ neq(X4,nil)
| frontsegP(sK50,X4) ) ),
introduced(definition,[new_symbols(definition,[spl51_6])],[avatar_definition]) ).
fof(f566,plain,
( ! [X4] :
( ~ neq(X4,nil)
| ~ ssList(X4)
| frontsegP(sK49,X4)
| frontsegP(sK50,X4) )
| ~ spl51_6 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f567,plain,
( spl51_6
| ~ spl51_5 ),
inference(avatar_split_clause,[],[f534,f559,f565]) ).
fof(f569,plain,
spl51_5,
inference(avatar_split_clause,[],[f426,f559]) ).
fof(f575,definition,
( spl51_8
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl51_8])],[avatar_definition]) ).
fof(f576,plain,
( ssList(nil)
| ~ spl51_8 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f604,plain,
spl51_8,
inference(avatar_split_clause,[],[f306,f575]) ).
fof(f653,plain,
( ~ ssItem(hd(sK50))
| ~ ssList(nil)
| spl51_1 ),
inference(resolution,[],[f305,f545]) ).
fof(f656,plain,
( ~ ssItem(hd(sK50))
| spl51_1
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f653,f576]) ).
fof(f657,plain,
( ~ spl51_3
| spl51_1
| ~ spl51_8 ),
inference(avatar_split_clause,[],[f656,f575,f543,f551]) ).
fof(f660,plain,
( nil = sK50
| ~ ssList(sK50)
| spl51_3 ),
inference(resolution,[],[f314,f553]) ).
fof(f661,plain,
( nil = sK50
| spl51_3 ),
inference(forward_subsumption_resolution,[],[f660,f417]) ).
fof(f675,plain,
( neq(nil,nil)
| spl51_3
| ~ spl51_5 ),
inference(superposition,[],[f561,f661]) ).
fof(f688,plain,
( ~ ssList(nil)
| spl51_3
| ~ spl51_5 ),
inference(resolution,[],[f675,f539]) ).
fof(f689,plain,
( $false
| spl51_3
| ~ spl51_5
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f688,f576]) ).
fof(f690,plain,
( spl51_3
| ~ spl51_5
| ~ spl51_8 ),
inference(avatar_contradiction_clause,[],[f689]) ).
fof(f721,definition,
( spl51_17
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl51_17])],[avatar_definition]) ).
fof(f722,plain,
( nil != sK50
| spl51_17 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f723,plain,
( nil = sK50
| ~ spl51_17 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f733,plain,
( ! [X0] :
( ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ ssList(X0)
| frontsegP(sK49,X0)
| frontsegP(sK50,X0) )
| ~ spl51_6 ),
inference(resolution,[],[f303,f566]) ).
fof(f736,plain,
( ~ ssList(sK50)
| nil = sK50
| ~ ssList(nil)
| spl51_4 ),
inference(resolution,[],[f303,f557]) ).
fof(f739,plain,
( ! [X0] :
( ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| frontsegP(sK49,X0)
| frontsegP(sK50,X0) )
| ~ spl51_6 ),
inference(duplicate_literal_removal,[],[f733]) ).
fof(f740,plain,
( nil = sK50
| ~ ssList(nil)
| spl51_4 ),
inference(forward_subsumption_resolution,[],[f736,f417]) ).
fof(f741,plain,
( ! [X0] :
( frontsegP(sK49,X0)
| ~ ssList(X0)
| nil = X0
| frontsegP(sK50,X0) )
| ~ spl51_6
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f739,f576]) ).
fof(f742,plain,
( nil = sK50
| spl51_4
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f740,f576]) ).
fof(f743,plain,
( spl51_17
| spl51_4
| ~ spl51_8 ),
inference(avatar_split_clause,[],[f742,f575,f555,f721]) ).
fof(f823,definition,
( spl51_22
<=> nil = sK49 ),
introduced(definition,[new_symbols(definition,[spl51_22])],[avatar_definition]) ).
fof(f824,plain,
( nil != sK49
| spl51_22 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f825,plain,
( nil = sK49
| ~ spl51_22 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f832,definition,
( spl51_24
<=> nil = cons(hd(sK50),nil) ),
introduced(definition,[new_symbols(definition,[spl51_24])],[avatar_definition]) ).
fof(f834,plain,
( nil = cons(hd(sK50),nil)
| ~ spl51_24 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f880,plain,
( neq(nil,nil)
| ~ spl51_5
| ~ spl51_17 ),
inference(superposition,[],[f561,f723]) ).
fof(f919,plain,
( nil = cons(hd(sK50),nil)
| ~ spl51_2
| ~ spl51_22 ),
inference(forward_demodulation,[],[f549,f825]) ).
fof(f920,plain,
( spl51_24
| ~ spl51_2
| ~ spl51_22 ),
inference(avatar_split_clause,[],[f919,f823,f547,f832]) ).
fof(f958,plain,
( ~ singletonP(nil)
| ~ ssItem(hd(sK50))
| ~ ssList(nil)
| ~ spl51_24 ),
inference(superposition,[],[f463,f834]) ).
fof(f972,plain,
( ~ ssItem(hd(sK50))
| ~ ssList(nil)
| ~ spl51_24 ),
inference(forward_subsumption_resolution,[],[f958,f503]) ).
fof(f978,plain,
( ~ ssList(nil)
| ~ spl51_3
| ~ spl51_24 ),
inference(forward_subsumption_resolution,[],[f972,f552]) ).
fof(f981,plain,
( $false
| ~ spl51_3
| ~ spl51_8
| ~ spl51_24 ),
inference(forward_subsumption_resolution,[],[f978,f576]) ).
fof(f982,plain,
( ~ spl51_3
| ~ spl51_8
| ~ spl51_24 ),
inference(avatar_contradiction_clause,[],[f981]) ).
fof(f1076,plain,
( nil = sK50
| sK50 = cons(hd(sK50),tl(sK50)) ),
inference(resolution,[],[f389,f417]) ).
fof(f1077,plain,
( sK50 = cons(hd(sK50),tl(sK50))
| spl51_17 ),
inference(forward_subsumption_resolution,[],[f1076,f722]) ).
fof(f1453,definition,
( spl51_42
<=> sK50 = cons(hd(sK50),tl(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_42])],[avatar_definition]) ).
fof(f1455,plain,
( sK50 = cons(hd(sK50),tl(sK50))
| ~ spl51_42 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f1577,plain,
( ~ ssList(nil)
| ~ spl51_5
| ~ spl51_17 ),
inference(resolution,[],[f880,f539]) ).
fof(f1578,plain,
( $false
| ~ spl51_5
| ~ spl51_8
| ~ spl51_17 ),
inference(forward_subsumption_resolution,[],[f1577,f576]) ).
fof(f1579,plain,
( ~ spl51_5
| ~ spl51_8
| ~ spl51_17 ),
inference(avatar_contradiction_clause,[],[f1578]) ).
fof(f1584,plain,
( spl51_42
| spl51_17 ),
inference(avatar_split_clause,[],[f1077,f721,f1453]) ).
fof(f1675,plain,
( ! [X0] :
( ~ frontsegP(cons(hd(sK50),X0),sK49)
| ~ ssList(X0)
| ~ ssList(nil)
| frontsegP(X0,nil)
| ~ ssItem(hd(sK50)) )
| ~ spl51_2 ),
inference(superposition,[],[f537,f549]) ).
fof(f1678,plain,
( ! [X0] :
( ~ frontsegP(cons(hd(sK50),X0),sK49)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(hd(sK50)) )
| ~ spl51_2 ),
inference(forward_subsumption_resolution,[],[f1675,f511]) ).
fof(f1683,plain,
( ! [X0] :
( ~ frontsegP(cons(hd(sK50),X0),sK49)
| ~ ssList(X0)
| ~ ssItem(hd(sK50)) )
| ~ spl51_2
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f1678,f576]) ).
fof(f1688,plain,
( ! [X0] :
( ~ frontsegP(cons(hd(sK50),X0),sK49)
| ~ ssList(X0) )
| ~ spl51_2
| ~ spl51_3
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f1683,f552]) ).
fof(f2488,definition,
( spl51_97
<=> ssList(tl(sK50)) ),
introduced(definition,[new_symbols(definition,[spl51_97])],[avatar_definition]) ).
fof(f2490,plain,
( ~ ssList(tl(sK50))
| spl51_97 ),
inference(avatar_component_clause,[],[f2488]) ).
fof(f2589,plain,
( ~ frontsegP(sK50,sK49)
| ~ ssList(tl(sK50))
| ~ spl51_2
| ~ spl51_3
| ~ spl51_8
| ~ spl51_42 ),
inference(superposition,[],[f1688,f1455]) ).
fof(f2591,definition,
( spl51_120
<=> frontsegP(sK50,sK49) ),
introduced(definition,[new_symbols(definition,[spl51_120])],[avatar_definition]) ).
fof(f2594,plain,
( ~ spl51_97
| ~ spl51_120
| ~ spl51_2
| ~ spl51_3
| ~ spl51_8
| ~ spl51_42 ),
inference(avatar_split_clause,[],[f2589,f1453,f575,f551,f547,f2591,f2488]) ).
fof(f2773,plain,
( ~ ssList(sK49)
| nil = sK49
| frontsegP(sK50,sK49)
| ~ ssList(sK49)
| ~ spl51_6
| ~ spl51_8 ),
inference(resolution,[],[f741,f506]) ).
fof(f2779,plain,
( ~ ssList(sK49)
| nil = sK49
| frontsegP(sK50,sK49)
| ~ spl51_6
| ~ spl51_8 ),
inference(duplicate_literal_removal,[],[f2773]) ).
fof(f2782,plain,
( nil = sK49
| frontsegP(sK50,sK49)
| ~ spl51_6
| ~ spl51_8 ),
inference(forward_subsumption_resolution,[],[f2779,f420]) ).
fof(f2783,plain,
( frontsegP(sK50,sK49)
| ~ spl51_6
| ~ spl51_8
| spl51_22 ),
inference(forward_subsumption_resolution,[],[f2782,f824]) ).
fof(f2784,plain,
( spl51_120
| ~ spl51_6
| ~ spl51_8
| spl51_22 ),
inference(avatar_split_clause,[],[f2783,f823,f575,f565,f2591]) ).
fof(f3191,plain,
( nil = sK50
| ~ ssList(sK50)
| spl51_97 ),
inference(resolution,[],[f2490,f316]) ).
fof(f3192,plain,
( ~ ssList(sK50)
| spl51_17
| spl51_97 ),
inference(forward_subsumption_resolution,[],[f3191,f722]) ).
fof(f3193,plain,
( $false
| spl51_17
| spl51_97 ),
inference(forward_subsumption_resolution,[],[f3192,f417]) ).
fof(f3194,plain,
( spl51_17
| spl51_97 ),
inference(avatar_contradiction_clause,[],[f3193]) ).
cnf(s2,plain,
( ~ spl51_1
| spl51_2
| ~ spl51_3
| ~ spl51_4
| ~ spl51_5 ),
inference(sat_conversion,[],[f563]) ).
cnf(s3,plain,
( ~ spl51_5
| spl51_6 ),
inference(sat_conversion,[],[f567]) ).
cnf(s5,plain,
spl51_5,
inference(sat_conversion,[],[f569]) ).
cnf(s14,plain,
spl51_8,
inference(sat_conversion,[],[f604]) ).
cnf(s17,plain,
( spl51_1
| ~ spl51_3
| ~ spl51_8 ),
inference(sat_conversion,[],[f657]) ).
cnf(s18,plain,
( spl51_3
| ~ spl51_5
| ~ spl51_8 ),
inference(sat_conversion,[],[f690]) ).
cnf(s21,plain,
( spl51_4
| ~ spl51_8
| spl51_17 ),
inference(sat_conversion,[],[f743]) ).
cnf(s29,plain,
( ~ spl51_2
| ~ spl51_22
| spl51_24 ),
inference(sat_conversion,[],[f920]) ).
cnf(s33,plain,
( ~ spl51_3
| ~ spl51_8
| ~ spl51_24 ),
inference(sat_conversion,[],[f982]) ).
cnf(s46,plain,
( ~ spl51_5
| ~ spl51_8
| ~ spl51_17 ),
inference(sat_conversion,[],[f1579]) ).
cnf(s48,plain,
( spl51_17
| spl51_42 ),
inference(sat_conversion,[],[f1584]) ).
cnf(s137,plain,
( ~ spl51_2
| ~ spl51_3
| ~ spl51_8
| ~ spl51_42
| ~ spl51_97
| ~ spl51_120 ),
inference(sat_conversion,[],[f2594]) ).
cnf(s145,plain,
( ~ spl51_6
| ~ spl51_8
| spl51_22
| spl51_120 ),
inference(sat_conversion,[],[f2784]) ).
cnf(s175,plain,
( spl51_17
| spl51_97 ),
inference(sat_conversion,[],[f3194]) ).
cnf(s181,plain,
~ spl51_17,
inference(rat,[],[s46,s14,s5]) ).
cnf(s182,plain,
spl51_3,
inference(rat,[],[s18,s14,s5]) ).
cnf(s183,plain,
spl51_97,
inference(rat,[],[s175,s181]) ).
cnf(s185,plain,
spl51_42,
inference(rat,[],[s48,s181]) ).
cnf(s190,plain,
spl51_4,
inference(rat,[],[s21,s14,s181]) ).
cnf(s191,plain,
~ spl51_24,
inference(rat,[],[s33,s14,s182]) ).
cnf(s192,plain,
spl51_1,
inference(rat,[],[s17,s14,s182]) ).
cnf(s215,plain,
spl51_6,
inference(rat,[],[s3,s5]) ).
cnf(s217,plain,
spl51_2,
inference(rat,[],[s2,s5,s190,s182,s192]) ).
cnf(s220,plain,
~ spl51_120,
inference(rat,[],[s137,s182,s183,s185,s14,s217]) ).
cnf(s222,plain,
~ spl51_22,
inference(rat,[],[s29,s191,s217]) ).
cnf(s223,plain,
$false,
inference(rat,[],[s145,s215,s14,s220,s222]) ).
fof(f3195,plain,
$false,
inference(avatar_sat_refutation,[],[s223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC022+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.45 % Computer : n026.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8046.5625MB
% 0.12/0.45 % OS : Linux 6.8.0-71-generic
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Mon Sep 28 07:31:57 UTC 2026
% 0.12/0.45 % CPUTime :
% 0.12/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.48 Running first-order model finding
% 0.15/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.51/0.57 % (3676967)Will run a generic schedule for satisfiability detection.
% 0.51/0.57 % (3676973)% WARNING: option uhcvi not known.
% 0.51/0.57 % (3676973)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=933890891:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.51/0.57 % (3676972)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=272594146_2999 on theBenchmark for (2999ds/0Mi)
% 0.51/0.57 % (3676975)dis+10_1_sil=32000:sp=arity:random_seed=3367273943:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.51/0.57 % (3676974)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=151571137:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.51/0.57 % (3676976)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2350000318:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.51/0.57 % (3676977)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2442145142:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.51/0.57 % (3676978)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4158696555:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.51/0.57 % TRYING [1]
% 0.51/0.57 % TRYING [2]
% 0.51/0.57 % TRYING [3]
% 0.51/0.57 % TRYING [4]
% 0.51/0.57 % (3676973) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3676967-3676973"...
% 0.51/0.57 % (3676973)...printing done.
% 0.51/0.57 % (3676973)Refutation found. Thanks to Tanya!
% 0.51/0.57 % SZS status Theorem for theBenchmark
% 0.51/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.51/0.57 % (3676973)------------------------------
% 0.51/0.57 % (3676973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.57 % (3676973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.57 % (3676973)CaDiCaL version: 2.1.3
% 0.51/0.57 % (3676973)Termination reason: Refutation
% 0.51/0.57 % (3676973)Time elapsed: 0.047 s
% 0.51/0.57 % (3676973)Peak memory usage: 14 MB
% 0.51/0.57 % (3676973)Instructions burned: 108 (million)
% 0.51/0.57 % (3676967)Success in time 0.08 s
% 0.51/0.57 % Vampire exiting
%------------------------------------------------------------------------------