%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC416+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 : n001.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 01:05:57 PM UTC 2026
% Result : Theorem 0.97s 0.42s
% Output : Refutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 155 ( 31 unt; 12 def)
% Number of atoms : 532 ( 96 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 586 ( 209 ~; 301 |; 38 &)
% ( 16 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 77 !; 18 ?)
% 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(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax39) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(app(X0,X1)) = hd(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax85) ).
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)
& X1 = X4
& ? [X5] :
( ssList(X5)
& app(X5,X0) = X4
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X1) = X6
& neq(nil,X1) ) ) )
| ! [X7] :
( ssItem(X7)
=> app(cons(X7,nil),X2) != 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)
& X1 = X4
& ? [X5] :
( ssList(X5)
& app(X5,X0) = X4
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X1) = X6
& neq(nil,X1) ) ) )
| ! [X7] :
( ssItem(X7)
=> app(cons(X7,nil),X2) != 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(f128,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( hd(app(X0,X1)) = hd(X0)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( hd(app(X0,X1)) = hd(X0)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f202]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X1 != X4
| ! [X5] :
( ~ ssList(X5)
| app(X5,X0) != X4
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X1) != X6
| ~ neq(nil,X1) ) ) )
& ? [X7] :
( app(cons(X7,nil),X2) = X3
& ssItem(X7) ) )
| ( 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)
| X1 != X4
| ! [X5] :
( ~ ssList(X5)
| app(X5,X0) != X4
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X1) != X6
| ~ neq(nil,X1) ) ) )
& ? [X7] :
( app(cons(X7,nil),X2) = X3
& ssItem(X7) ) )
| ( 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] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
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(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f314,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f315,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f337,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f398,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f411,plain,
! [X6,X4,X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK48)
| hd(sK48) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| app(X5,sK47) != X4
| ~ ssList(X5)
| sK48 != X4
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| sK50 = app(cons(sK51,nil),sK49) ),
inference(cnf_transformation,[],[f222]) ).
fof(f417,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
ssList(sK48),
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
ssList(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
ssList(sK49),
inference(definition_unfolding,[],[f424,f420]) ).
fof(f426,plain,
ssList(sK50),
inference(definition_unfolding,[],[f423,f421]) ).
fof(f428,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f417,f421]) ).
fof(f432,plain,
! [X6,X4,X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| hd(sK50) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| app(X5,sK49) != X4
| ~ ssList(X5)
| sK50 != X4
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f411,f421,f421,f420,f421]) ).
fof(f435,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f234]) ).
fof(f447,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f461,plain,
! [X4,X5] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| cons(hd(sK50),nil) != X5
| ~ ssItem(hd(sK50))
| app(X5,sK49) != X4
| ~ ssList(X5)
| sK50 != X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f432]) ).
fof(f462,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| app(cons(hd(sK50),nil),sK49) != X4
| ~ ssList(cons(hd(sK50),nil))
| sK50 != X4
| ~ ssList(X4) ),
inference(equality_resolution,[],[f461]) ).
fof(f463,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ~ ssItem(hd(sK50))
| ~ ssList(cons(hd(sK50),nil))
| sK50 != app(cons(hd(sK50),nil),sK49)
| ~ ssList(app(cons(hd(sK50),nil),sK49)) ),
inference(equality_resolution,[],[f462]) ).
fof(f472,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(consistent_polarity_flipping,[],[f435]) ).
fof(f543,plain,
! [X1] :
( ssList(X1)
| ssList(X1)
| ~ neq(X1,X1) ),
inference(consistent_polarity_flipping,[],[f447]) ).
fof(f544,plain,
! [X0,X1] :
( neq(X0,X1)
| ssList(X1)
| X0 = X1
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f303]) ).
fof(f545,plain,
! [X0,X1] :
( ~ ssList(cons(X1,X0))
| ssItem(X1)
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f305]) ).
fof(f546,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f306]) ).
fof(f554,plain,
! [X0] :
( ~ ssItem(hd(X0))
| nil = X0
| ssList(X0) ),
inference(consistent_polarity_flipping,[],[f314]) ).
fof(f555,plain,
! [X0,X1] :
( ssList(X0)
| ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(consistent_polarity_flipping,[],[f315]) ).
fof(f633,plain,
! [X0,X1] :
( ssList(X0)
| ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f398]) ).
fof(f646,plain,
~ ssList(sK49),
inference(consistent_polarity_flipping,[],[f425]) ).
fof(f647,plain,
~ ssList(sK50),
inference(consistent_polarity_flipping,[],[f426]) ).
fof(f651,plain,
( ~ neq(sK50,nil)
| ~ ssItem(sK51) ),
inference(consistent_polarity_flipping,[],[f413]) ).
fof(f653,plain,
( ~ neq(sK50,nil)
| ~ neq(nil,sK50)
| ssItem(hd(sK50))
| ssList(cons(hd(sK50),nil))
| sK50 != app(cons(hd(sK50),nil),sK49)
| ssList(app(cons(hd(sK50),nil),sK49)) ),
inference(consistent_polarity_flipping,[],[f463]) ).
fof(f658,plain,
! [X1] :
( ~ neq(X1,X1)
| ssList(X1) ),
inference(duplicate_literal_removal,[],[f543]) ).
fof(f662,definition,
( spl52_1
<=> ssList(app(cons(hd(sK50),nil),sK49)) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f664,plain,
( ssList(app(cons(hd(sK50),nil),sK49))
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f666,definition,
( spl52_2
<=> sK50 = app(cons(hd(sK50),nil),sK49) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f668,plain,
( sK50 != app(cons(hd(sK50),nil),sK49)
| spl52_2 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f670,definition,
( spl52_3
<=> ssList(cons(hd(sK50),nil)) ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
fof(f672,plain,
( ssList(cons(hd(sK50),nil))
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f674,definition,
( spl52_4
<=> ssItem(hd(sK50)) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f676,plain,
( ssItem(hd(sK50))
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f678,definition,
( spl52_5
<=> neq(nil,sK50) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
fof(f680,plain,
( ~ neq(nil,sK50)
| spl52_5 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f682,definition,
( spl52_6
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl52_6])],[avatar_definition]) ).
fof(f683,plain,
( neq(sK50,nil)
| ~ spl52_6 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f685,plain,
( spl52_1
| ~ spl52_2
| spl52_3
| spl52_4
| ~ spl52_5
| ~ spl52_6 ),
inference(avatar_split_clause,[],[f653,f682,f678,f674,f670,f666,f662]) ).
fof(f688,definition,
( spl52_7
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl52_7])],[avatar_definition]) ).
fof(f690,plain,
( ~ ssItem(sK51)
| spl52_7 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f691,plain,
( ~ spl52_7
| ~ spl52_6 ),
inference(avatar_split_clause,[],[f651,f682,f688]) ).
fof(f693,definition,
( spl52_8
<=> sK50 = app(cons(sK51,nil),sK49) ),
introduced(definition,[new_symbols(definition,[spl52_8])],[avatar_definition]) ).
fof(f695,plain,
( sK50 = app(cons(sK51,nil),sK49)
| ~ spl52_8 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f696,plain,
( spl52_8
| ~ spl52_6 ),
inference(avatar_split_clause,[],[f414,f682,f693]) ).
fof(f699,plain,
spl52_6,
inference(avatar_split_clause,[],[f428,f682]) ).
fof(f705,definition,
( spl52_10
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl52_10])],[avatar_definition]) ).
fof(f706,plain,
( ~ ssList(nil)
| spl52_10 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f734,plain,
~ spl52_10,
inference(avatar_split_clause,[],[f546,f705]) ).
fof(f868,plain,
( ! [X0] :
( ssList(X0)
| sK51 = hd(cons(sK51,X0)) )
| spl52_7 ),
inference(resolution,[],[f555,f690]) ).
fof(f871,plain,
( sK51 = hd(cons(sK51,nil))
| spl52_7
| spl52_10 ),
inference(resolution,[],[f868,f706]) ).
fof(f986,definition,
( spl52_17
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl52_17])],[avatar_definition]) ).
fof(f987,plain,
( nil != sK50
| spl52_17 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f988,plain,
( nil = sK50
| ~ spl52_17 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f1067,plain,
( neq(nil,nil)
| ~ spl52_6
| ~ spl52_17 ),
inference(superposition,[],[f683,f988]) ).
fof(f1171,plain,
( ssList(nil)
| ~ spl52_6
| ~ spl52_17 ),
inference(resolution,[],[f1067,f658]) ).
fof(f1172,plain,
( $false
| ~ spl52_6
| spl52_10
| ~ spl52_17 ),
inference(forward_subsumption_resolution,[],[f1171,f706]) ).
fof(f1173,plain,
( ~ spl52_6
| spl52_10
| ~ spl52_17 ),
inference(avatar_contradiction_clause,[],[f1172]) ).
fof(f1189,definition,
( spl52_24
<=> ssList(cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl52_24])],[avatar_definition]) ).
fof(f1190,plain,
( ~ ssList(cons(sK51,nil))
| spl52_24 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1191,plain,
( ssList(cons(sK51,nil))
| ~ spl52_24 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1193,definition,
( spl52_25
<=> nil = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl52_25])],[avatar_definition]) ).
fof(f1194,plain,
( nil != cons(sK51,nil)
| spl52_25 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f1195,plain,
( nil = cons(sK51,nil)
| ~ spl52_25 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f1214,plain,
( ssItem(sK51)
| ssList(nil)
| ~ spl52_24 ),
inference(resolution,[],[f1191,f545]) ).
fof(f1215,plain,
( ssList(nil)
| spl52_7
| ~ spl52_24 ),
inference(forward_subsumption_resolution,[],[f1214,f690]) ).
fof(f1216,plain,
( $false
| spl52_7
| spl52_10
| ~ spl52_24 ),
inference(forward_subsumption_resolution,[],[f1215,f706]) ).
fof(f1217,plain,
( spl52_7
| spl52_10
| ~ spl52_24 ),
inference(avatar_contradiction_clause,[],[f1216]) ).
fof(f1307,plain,
( singletonP(nil)
| ssItem(sK51)
| ssList(nil)
| ~ spl52_25 ),
inference(superposition,[],[f472,f1195]) ).
fof(f1324,plain,
( ssItem(sK51)
| ssList(nil)
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1307,f337]) ).
fof(f1331,plain,
( ssList(nil)
| spl52_7
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1324,f690]) ).
fof(f1335,plain,
( $false
| spl52_7
| spl52_10
| ~ spl52_25 ),
inference(forward_subsumption_resolution,[],[f1331,f706]) ).
fof(f1336,plain,
( spl52_7
| spl52_10
| ~ spl52_25 ),
inference(avatar_contradiction_clause,[],[f1335]) ).
fof(f1649,plain,
! [X0] :
( ssList(X0)
| nil = X0
| hd(X0) = hd(app(X0,sK49)) ),
inference(resolution,[],[f633,f646]) ).
fof(f2705,plain,
( nil = sK50
| ssList(sK50)
| ~ spl52_4 ),
inference(resolution,[],[f676,f554]) ).
fof(f2706,plain,
( ssList(sK50)
| ~ spl52_4
| spl52_17 ),
inference(forward_subsumption_resolution,[],[f2705,f987]) ).
fof(f2707,plain,
( $false
| ~ spl52_4
| spl52_17 ),
inference(forward_subsumption_resolution,[],[f2706,f647]) ).
fof(f2708,plain,
( ~ spl52_4
| spl52_17 ),
inference(avatar_contradiction_clause,[],[f2707]) ).
fof(f5153,plain,
( ssList(sK50)
| nil = sK50
| ssList(nil)
| spl52_5 ),
inference(resolution,[],[f680,f544]) ).
fof(f5156,plain,
( nil = sK50
| ssList(nil)
| spl52_5 ),
inference(forward_subsumption_resolution,[],[f5153,f647]) ).
fof(f5166,plain,
( ssList(nil)
| spl52_5
| spl52_17 ),
inference(forward_subsumption_resolution,[],[f5156,f987]) ).
fof(f5167,plain,
( $false
| spl52_5
| spl52_10
| spl52_17 ),
inference(forward_subsumption_resolution,[],[f5166,f706]) ).
fof(f5168,plain,
( spl52_5
| spl52_10
| spl52_17 ),
inference(avatar_contradiction_clause,[],[f5167]) ).
fof(f5707,plain,
( nil = cons(sK51,nil)
| hd(cons(sK51,nil)) = hd(app(cons(sK51,nil),sK49))
| spl52_24 ),
inference(resolution,[],[f1649,f1190]) ).
fof(f5773,plain,
( hd(cons(sK51,nil)) = hd(app(cons(sK51,nil),sK49))
| spl52_24
| spl52_25 ),
inference(forward_subsumption_resolution,[],[f5707,f1194]) ).
fof(f5775,plain,
( hd(sK50) = hd(cons(sK51,nil))
| ~ spl52_8
| spl52_24
| spl52_25 ),
inference(forward_demodulation,[],[f5773,f695]) ).
fof(f5776,plain,
( sK51 = hd(sK50)
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_demodulation,[],[f5775,f871]) ).
fof(f7182,plain,
( sK50 != app(cons(sK51,nil),sK49)
| spl52_2
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(superposition,[],[f668,f5776]) ).
fof(f7188,plain,
( $false
| spl52_2
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_subsumption_resolution,[],[f7182,f695]) ).
fof(f7189,plain,
( spl52_2
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(avatar_contradiction_clause,[],[f7188]) ).
fof(f7193,plain,
( ssList(cons(sK51,nil))
| ~ spl52_3
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_demodulation,[],[f672,f5776]) ).
fof(f7211,plain,
( $false
| ~ spl52_3
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_subsumption_resolution,[],[f7193,f1190]) ).
fof(f7212,plain,
( ~ spl52_3
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(avatar_contradiction_clause,[],[f7211]) ).
fof(f7215,plain,
( ssList(app(cons(sK51,nil),sK49))
| ~ spl52_1
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_demodulation,[],[f664,f5776]) ).
fof(f7217,plain,
( ssList(sK50)
| ~ spl52_1
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_demodulation,[],[f7215,f695]) ).
fof(f7218,plain,
( $false
| ~ spl52_1
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(forward_subsumption_resolution,[],[f7217,f647]) ).
fof(f7219,plain,
( ~ spl52_1
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(avatar_contradiction_clause,[],[f7218]) ).
cnf(s1,plain,
( spl52_1
| ~ spl52_2
| spl52_3
| spl52_4
| ~ spl52_5
| ~ spl52_6 ),
inference(sat_conversion,[],[f685]) ).
cnf(s3,plain,
( ~ spl52_6
| ~ spl52_7 ),
inference(sat_conversion,[],[f691]) ).
cnf(s4,plain,
( ~ spl52_6
| spl52_8 ),
inference(sat_conversion,[],[f696]) ).
cnf(s7,plain,
spl52_6,
inference(sat_conversion,[],[f699]) ).
cnf(s16,plain,
~ spl52_10,
inference(sat_conversion,[],[f734]) ).
cnf(s21,plain,
( ~ spl52_6
| spl52_10
| ~ spl52_17 ),
inference(sat_conversion,[],[f1173]) ).
cnf(s26,plain,
( spl52_7
| spl52_10
| ~ spl52_24 ),
inference(sat_conversion,[],[f1217]) ).
cnf(s35,plain,
( spl52_7
| spl52_10
| ~ spl52_25 ),
inference(sat_conversion,[],[f1336]) ).
cnf(s127,plain,
( ~ spl52_4
| spl52_17 ),
inference(sat_conversion,[],[f2708]) ).
cnf(s335,plain,
( spl52_5
| spl52_10
| spl52_17 ),
inference(sat_conversion,[],[f5168]) ).
cnf(s438,plain,
( spl52_2
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(sat_conversion,[],[f7189]) ).
cnf(s442,plain,
( ~ spl52_3
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(sat_conversion,[],[f7212]) ).
cnf(s443,plain,
( ~ spl52_1
| spl52_7
| ~ spl52_8
| spl52_10
| spl52_24
| spl52_25 ),
inference(sat_conversion,[],[f7219]) ).
cnf(s449,plain,
~ spl52_17,
inference(rat,[],[s21,s16,s7]) ).
cnf(s451,plain,
~ spl52_4,
inference(rat,[],[s127,s449]) ).
cnf(s458,plain,
spl52_5,
inference(rat,[],[s335,s16,s449]) ).
cnf(s485,plain,
spl52_8,
inference(rat,[],[s4,s7]) ).
cnf(s486,plain,
~ spl52_7,
inference(rat,[],[s3,s7]) ).
cnf(s487,plain,
~ spl52_25,
inference(rat,[],[s35,s16,s486]) ).
cnf(s488,plain,
~ spl52_24,
inference(rat,[],[s26,s16,s486]) ).
cnf(s495,plain,
~ spl52_1,
inference(rat,[],[s443,s487,s486,s16,s485,s488]) ).
cnf(s496,plain,
~ spl52_3,
inference(rat,[],[s442,s487,s486,s16,s485,s488]) ).
cnf(s497,plain,
spl52_2,
inference(rat,[],[s438,s487,s486,s16,s485,s488]) ).
cnf(s499,plain,
$false,
inference(rat,[],[s1,s7,s458,s451,s496,s497,s495]) ).
fof(f7220,plain,
$false,
inference(avatar_sat_refutation,[],[s499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC416+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 09:39:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.97/0.42 % (245451)Will run a generic schedule for satisfiability detection.
% 0.97/0.42 % (245461)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2156256290:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.97/0.42 % (245457)% WARNING: option uhcvi not known.
% 0.97/0.42 % (245456)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3172008299_2999 on theBenchmark for (2999ds/0Mi)
% 0.97/0.42 % (245458)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3222469843:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.97/0.42 % (245457)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4198123090:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.97/0.42 % (245459)dis+10_1_sil=32000:sp=arity:random_seed=3044794445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.97/0.42 % (245460)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2462042734:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.97/0.42 % (245462)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1717025801:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.97/0.42 % TRYING [1]
% 0.97/0.42 % TRYING [2]
% 0.97/0.42 % TRYING [3]
% 0.97/0.42 % (245461)Instruction limit reached!
% 0.97/0.42 % (245461)------------------------------
% 0.97/0.42 % (245461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.42 % (245461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.42 % (245461)CaDiCaL version: 2.1.3
% 0.97/0.42 % (245461)Termination reason: Instruction limit
% 0.97/0.42 % (245461)Termination phase: Saturation
% 0.97/0.42 % (245461)Time elapsed: 0.042 s
% 0.97/0.42 % (245461)Peak memory usage: 15 MB
% 0.97/0.42 % (245461)Instructions burned: 134 (million)
% 0.97/0.42 % TRYING [4]
% 0.97/0.42 % (245470)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3252341397:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.97/0.42 % TRYING [1]
% 0.97/0.42 % TRYING [2]
% 0.97/0.42 % TRYING [3]
% 0.97/0.42 % (245459)Instruction limit reached!
% 0.97/0.42 % (245459)------------------------------
% 0.97/0.42 % (245459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.42 % (245459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.42 % (245459)CaDiCaL version: 2.1.3
% 0.97/0.42 % (245459)Termination reason: Instruction limit
% 0.97/0.42 % (245459)Termination phase: Saturation
% 0.97/0.42 % (245459)Time elapsed: 0.062 s
% 0.97/0.42 % (245459)Peak memory usage: 13 MB
% 0.97/0.42 % (245459)Instructions burned: 105 (million)
% 0.97/0.42 % TRYING [4]
% 0.97/0.42 % (245460)Instruction limit reached!
% 0.97/0.42 % (245460)------------------------------
% 0.97/0.42 % (245460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.42 % (245460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.42 % (245460)CaDiCaL version: 2.1.3
% 0.97/0.42 % (245460)Termination reason: Instruction limit
% 0.97/0.42 % (245460)Termination phase: Saturation
% 0.97/0.42 % (245460)Time elapsed: 0.069 s
% 0.97/0.42 % (245460)Peak memory usage: 13 MB
% 0.97/0.42 % (245460)Instructions burned: 117 (million)
% 0.97/0.42 % (245472)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3659135144:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.97/0.42 % TRYING [5]
% 0.97/0.42 % (245473)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4133634164:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.97/0.42 % TRYING [5]
% 0.97/0.42 % (245462)Instruction limit reached!
% 0.97/0.42 % (245462)------------------------------
% 0.97/0.42 % (245462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.42 % (245462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.42 % (245462)CaDiCaL version: 2.1.3
% 0.97/0.42 % (245462)Termination reason: Instruction limit
% 0.97/0.42 % (245462)Termination phase: Saturation
% 0.97/0.42 % (245462)Time elapsed: 0.096 s
% 0.97/0.42 % (245462)Peak memory usage: 14 MB
% 0.97/0.42 % (245462)Instructions burned: 160 (million)
% 0.97/0.42 % (245476)ott-21_1_sil=16000:fs=off:random_seed=1673962895:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.97/0.42 % (245472)Instruction limit reached!
% 0.97/0.42 % (245472)------------------------------
% 0.97/0.42 % (245472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.42 % (245472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.42 % (245472)CaDiCaL version: 2.1.3
% 0.97/0.42 % (245472)Termination reason: Instruction limit
% 0.97/0.42 % (245472)Termination phase: Saturation
% 0.97/0.42 % (245472)Time elapsed: 0.072 s
% 0.97/0.42 % (245472)Peak memory usage: 13 MB
% 0.97/0.42 % (245472)Instructions burned: 132 (million)
% 0.97/0.42 % (245457) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-245451-245457"...
% 0.97/0.42 % (245457)...printing done.
% 0.97/0.42 % (245457)Refutation found. Thanks to Tanya!
% 0.97/0.42 % SZS status Theorem for theBenchmark
% 0.97/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.97/0.43 % (245457)------------------------------
% 0.97/0.43 % (245457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.43 % (245457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.43 % (245457)CaDiCaL version: 2.1.3
% 0.97/0.43 % (245457)Termination reason: Refutation
% 0.97/0.43 % (245457)Time elapsed: 0.158 s
% 0.97/0.43 % (245457)Peak memory usage: 16 MB
% 0.97/0.43 % (245457)Instructions burned: 288 (million)
% 0.97/0.43 % (245451)Success in time 0.199 s
% 0.97/0.43 % Vampire exiting
%------------------------------------------------------------------------------