%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC005+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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:02:00 PM UTC 2026
% Result : Theorem 2.54s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 132 ( 20 unt; 9 def)
% Number of atoms : 501 ( 124 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 657 ( 288 ~; 289 |; 46 &)
% ( 11 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn 100 !; 16 ?)
% 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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0
& neq(X5,nil) ) ) )
| ? [X7] :
( ssList(X7)
& X2 != X7
& tl(X3) = X7
& neq(nil,X3) ) )
& ( ~ neq(X1,nil)
| 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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0
& neq(X5,nil) ) ) )
| ? [X7] :
( ssList(X7)
& X2 != X7
& tl(X3) = X7
& neq(nil,X3) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(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(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
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(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ! [X7] :
( ~ ssList(X7)
| X2 = X7
| tl(X3) != X7
| ~ 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)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ! [X7] :
( ~ ssList(X7)
| X2 = X7
| tl(X3) != X7
| ~ neq(nil,X3) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != sK54
| app(X4,X6) != sK53
| ~ neq(X5,nil) ) ) )
& ! [X7] :
( ~ ssList(X7)
| sK55 = X7
| tl(sK56) != X7
| ~ neq(nil,sK56) ) )
| ( neq(sK54,nil)
& ~ neq(sK56,nil) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f386,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
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(f397,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f403,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f474,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X7] :
( ~ ssList(X7)
| sK55 = X7
| tl(sK56) != X7
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != sK54
| app(X4,X6) != sK53
| ~ neq(X5,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( neq(sK54,nil)
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f522,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f386]) ).
fof(f536,plain,
( ~ ssList(tl(sK56))
| sK55 = tl(sK56)
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f500]) ).
fof(f537,plain,
neq(sK54,nil),
inference(duplicate_literal_removal,[],[f505]) ).
fof(f542,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f522]) ).
fof(f546,definition,
( spl57_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f547,plain,
( neq(sK56,nil)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f550,definition,
( spl57_2
<=> neq(nil,sK56) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f552,plain,
( ~ neq(nil,sK56)
| spl57_2 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f554,definition,
( spl57_3
<=> sK55 = tl(sK56) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f556,plain,
( sK55 = tl(sK56)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f558,definition,
( spl57_4
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f560,plain,
( ~ ssList(tl(sK56))
| spl57_4 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f561,plain,
( ~ spl57_1
| ~ spl57_2
| spl57_3
| ~ spl57_4 ),
inference(avatar_split_clause,[],[f536,f558,f554,f550,f546]) ).
fof(f563,definition,
( spl57_5
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f565,plain,
( neq(sK54,nil)
| ~ spl57_5 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f568,definition,
( spl57_6
<=> ! [X6,X4,X5] :
( ~ ssList(X4)
| ~ neq(X5,nil)
| app(X4,X6) != sK53
| app(app(X4,X5),X6) != sK54
| ~ ssList(X6)
| ~ ssList(X5) ) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f569,plain,
( ! [X6,X4,X5] :
( ~ ssList(X4)
| ~ neq(X5,nil)
| app(X4,X6) != sK53
| app(app(X4,X5),X6) != sK54
| ~ ssList(X6)
| ~ ssList(X5) )
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f570,plain,
( ~ spl57_1
| spl57_6 ),
inference(avatar_split_clause,[],[f502,f568,f546]) ).
fof(f573,plain,
spl57_5,
inference(avatar_split_clause,[],[f537,f563]) ).
fof(f575,definition,
( spl57_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f576,plain,
( ssList(nil)
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f608,plain,
spl57_7,
inference(avatar_split_clause,[],[f389,f575]) ).
fof(f611,plain,
( neq(sK56,nil)
| ~ spl57_5 ),
inference(forward_demodulation,[],[f565,f507]) ).
fof(f614,plain,
( ! [X6,X4,X5] :
( app(X4,X6) != sK53
| ~ ssList(X4)
| ~ neq(X5,nil)
| app(app(X4,X5),X6) != sK56
| ~ ssList(X6)
| ~ ssList(X5) )
| ~ spl57_6 ),
inference(forward_demodulation,[],[f569,f507]) ).
fof(f615,plain,
( spl57_1
| ~ spl57_5 ),
inference(avatar_split_clause,[],[f611,f563,f546]) ).
fof(f627,plain,
( ! [X0,X1] :
( sK53 != X0
| ~ ssList(nil)
| ~ neq(X1,nil)
| sK56 != app(app(nil,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl57_6 ),
inference(superposition,[],[f614,f403]) ).
fof(f628,plain,
( ! [X0,X1] :
( sK53 != X0
| ~ ssList(nil)
| ~ neq(X1,nil)
| sK56 != app(app(nil,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl57_6 ),
inference(duplicate_literal_removal,[],[f627]) ).
fof(f629,plain,
( ! [X0,X1] :
( ~ neq(X1,nil)
| sK53 != X0
| sK56 != app(app(nil,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f628,f576]) ).
fof(f702,definition,
( spl57_22
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_22])],[avatar_definition]) ).
fof(f703,plain,
( nil != sK56
| spl57_22 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f704,plain,
( nil = sK56
| ~ spl57_22 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f706,plain,
( nil = sK56
| ~ ssList(sK56)
| ~ ssList(nil)
| spl57_2 ),
inference(resolution,[],[f387,f552]) ).
fof(f710,plain,
( ! [X0,X1] :
( nil = X0
| ~ ssList(nil)
| ~ ssList(X0)
| sK53 != X1
| sK56 != app(app(nil,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(resolution,[],[f387,f629]) ).
fof(f711,plain,
( ! [X0,X1] :
( nil = X0
| ~ ssList(nil)
| ~ ssList(X0)
| sK53 != X1
| sK56 != app(app(nil,X0),X1)
| ~ ssList(X1) )
| ~ spl57_6
| ~ spl57_7 ),
inference(duplicate_literal_removal,[],[f710]) ).
fof(f715,plain,
( ! [X0,X1] :
( sK53 != X1
| ~ ssList(X0)
| nil = X0
| sK56 != app(app(nil,X0),X1)
| ~ ssList(X1) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f711,f576]) ).
fof(f717,plain,
( nil = sK56
| ~ ssList(nil)
| spl57_2 ),
inference(forward_subsumption_resolution,[],[f706,f499]) ).
fof(f718,plain,
( nil = sK56
| spl57_2
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f717,f576]) ).
fof(f719,plain,
( spl57_22
| spl57_2
| ~ spl57_7 ),
inference(avatar_split_clause,[],[f718,f575,f550,f702]) ).
fof(f720,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_4 ),
inference(resolution,[],[f560,f399]) ).
fof(f721,plain,
( nil = sK56
| spl57_4 ),
inference(forward_subsumption_resolution,[],[f720,f499]) ).
fof(f722,plain,
( spl57_22
| spl57_4 ),
inference(avatar_split_clause,[],[f721,f558,f702]) ).
fof(f724,plain,
( neq(nil,nil)
| ~ spl57_1
| ~ spl57_22 ),
inference(superposition,[],[f547,f704]) ).
fof(f737,plain,
( ~ ssList(nil)
| ~ spl57_1
| ~ spl57_22 ),
inference(resolution,[],[f724,f542]) ).
fof(f738,plain,
( $false
| ~ spl57_1
| ~ spl57_7
| ~ spl57_22 ),
inference(forward_subsumption_resolution,[],[f737,f576]) ).
fof(f739,plain,
( ~ spl57_1
| ~ spl57_7
| ~ spl57_22 ),
inference(avatar_contradiction_clause,[],[f738]) ).
fof(f745,plain,
( sK53 = tl(sK56)
| ~ spl57_3 ),
inference(forward_demodulation,[],[f556,f506]) ).
fof(f748,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| sK56 != app(app(nil,X0),sK53)
| ~ ssList(sK53) )
| ~ spl57_6
| ~ spl57_7 ),
inference(equality_resolution,[],[f715]) ).
fof(f749,plain,
( ! [X0] :
( sK56 != app(app(nil,X0),sK53)
| nil = X0
| ~ ssList(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f748,f496]) ).
fof(f751,plain,
( ! [X0] :
( sK56 != app(X0,sK53)
| nil = X0
| ~ ssList(X0)
| ~ ssList(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(superposition,[],[f749,f403]) ).
fof(f752,plain,
( ! [X0] :
( sK56 != app(X0,sK53)
| nil = X0
| ~ ssList(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(duplicate_literal_removal,[],[f751]) ).
fof(f785,plain,
( sK56 = cons(hd(sK56),sK53)
| nil = sK56
| ~ ssList(sK56)
| ~ spl57_3 ),
inference(superposition,[],[f474,f745]) ).
fof(f794,plain,
( sK56 = cons(hd(sK56),sK53)
| ~ ssList(sK56)
| ~ spl57_3
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f785,f703]) ).
fof(f799,plain,
( sK56 = cons(hd(sK56),sK53)
| ~ spl57_3
| spl57_22 ),
inference(forward_subsumption_resolution,[],[f794,f499]) ).
fof(f809,definition,
( spl57_23
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_23])],[avatar_definition]) ).
fof(f810,plain,
( ssItem(hd(sK56))
| ~ spl57_23 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f811,plain,
( ~ ssItem(hd(sK56))
| spl57_23 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f824,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_23 ),
inference(resolution,[],[f811,f397]) ).
fof(f825,plain,
( ~ ssList(sK56)
| spl57_22
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f824,f703]) ).
fof(f826,plain,
( $false
| spl57_22
| spl57_23 ),
inference(forward_subsumption_resolution,[],[f825,f499]) ).
fof(f827,plain,
( spl57_22
| spl57_23 ),
inference(avatar_contradiction_clause,[],[f826]) ).
fof(f871,plain,
( ! [X0] :
( sK56 != cons(X0,sK53)
| nil = cons(X0,nil)
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(sK53) )
| ~ spl57_6
| ~ spl57_7 ),
inference(superposition,[],[f752,f477]) ).
fof(f876,plain,
( ! [X0] :
( ~ ssList(cons(X0,nil))
| nil = cons(X0,nil)
| sK56 != cons(X0,sK53)
| ~ ssItem(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f871,f496]) ).
fof(f877,plain,
( ! [X0] :
( nil = cons(X0,nil)
| sK56 != cons(X0,sK53)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssList(nil) )
| ~ spl57_6
| ~ spl57_7 ),
inference(resolution,[],[f876,f388]) ).
fof(f878,plain,
( ! [X0] :
( nil = cons(X0,nil)
| sK56 != cons(X0,sK53)
| ~ ssItem(X0)
| ~ ssList(nil) )
| ~ spl57_6
| ~ spl57_7 ),
inference(duplicate_literal_removal,[],[f877]) ).
fof(f879,plain,
( ! [X0] :
( sK56 != cons(X0,sK53)
| ~ ssItem(X0)
| ~ ssList(nil) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f878,f396]) ).
fof(f880,plain,
( ! [X0] :
( sK56 != cons(X0,sK53)
| ~ ssItem(X0) )
| ~ spl57_6
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f879,f576]) ).
fof(f887,plain,
( sK56 != sK56
| ~ ssItem(hd(sK56))
| ~ spl57_3
| ~ spl57_6
| ~ spl57_7
| spl57_22 ),
inference(superposition,[],[f880,f799]) ).
fof(f888,plain,
( ~ ssItem(hd(sK56))
| ~ spl57_3
| ~ spl57_6
| ~ spl57_7
| spl57_22 ),
inference(trivial_inequality_removal,[],[f887]) ).
fof(f889,plain,
( $false
| ~ spl57_3
| ~ spl57_6
| ~ spl57_7
| spl57_22
| ~ spl57_23 ),
inference(forward_subsumption_resolution,[],[f888,f810]) ).
fof(f890,plain,
( ~ spl57_3
| ~ spl57_6
| ~ spl57_7
| spl57_22
| ~ spl57_23 ),
inference(avatar_contradiction_clause,[],[f889]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2
| spl57_3
| ~ spl57_4 ),
inference(sat_conversion,[],[f561]) ).
cnf(s3,plain,
( ~ spl57_1
| spl57_6 ),
inference(sat_conversion,[],[f570]) ).
cnf(s6,plain,
spl57_5,
inference(sat_conversion,[],[f573]) ).
cnf(s15,plain,
spl57_7,
inference(sat_conversion,[],[f608]) ).
cnf(s17,plain,
( spl57_1
| ~ spl57_5 ),
inference(sat_conversion,[],[f615]) ).
cnf(s24,plain,
( spl57_2
| ~ spl57_7
| spl57_22 ),
inference(sat_conversion,[],[f719]) ).
cnf(s25,plain,
( spl57_4
| spl57_22 ),
inference(sat_conversion,[],[f722]) ).
cnf(s26,plain,
( ~ spl57_1
| ~ spl57_7
| ~ spl57_22 ),
inference(sat_conversion,[],[f739]) ).
cnf(s29,plain,
( spl57_22
| spl57_23 ),
inference(sat_conversion,[],[f827]) ).
cnf(s30,plain,
( ~ spl57_3
| ~ spl57_6
| ~ spl57_7
| spl57_22
| ~ spl57_23 ),
inference(sat_conversion,[],[f890]) ).
cnf(s36,plain,
spl57_1,
inference(rat,[],[s17,s6]) ).
cnf(s37,plain,
~ spl57_22,
inference(rat,[],[s26,s15,s36]) ).
cnf(s38,plain,
spl57_23,
inference(rat,[],[s29,s37]) ).
cnf(s39,plain,
spl57_4,
inference(rat,[],[s25,s37]) ).
cnf(s40,plain,
spl57_2,
inference(rat,[],[s24,s15,s37]) ).
cnf(s41,plain,
spl57_6,
inference(rat,[],[s3,s36]) ).
cnf(s42,plain,
~ spl57_3,
inference(rat,[],[s30,s38,s37,s15,s41]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s1,s39,s42,s40,s36]) ).
fof(f891,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC005+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 07:27:07 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.54/1.31 % (183781)Detected formulas, will run a generic FOF schedule.
% 2.54/1.31 % (183788)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=459869981:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.31 % (183786)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=634292052:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.31 % (183787)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=288084502:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.31 % (183789)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3746142357:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.31 % (183792)dis-21_1_sil=8000:lcm=predicate:random_seed=154229802: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)
% 2.54/1.31 % (183790)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2511200646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.31 % (183791)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1442881671:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.31 % (183791)First to succeed.
% 2.54/1.31 % (183791)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-183781"
% 2.54/1.31 % (183789)Instruction limit reached!
% 2.54/1.31 % (183789)------------------------------
% 2.54/1.31 % (183789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.31 % (183789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.31 % (183789)CaDiCaL version: 2.1.3
% 2.54/1.31 % (183789)Termination reason: Instruction limit
% 2.54/1.31 % (183789)Termination phase: Saturation
% 2.54/1.31 % (183789)Time elapsed: 0.064 s
% 2.54/1.31 % (183789)Peak memory usage: 89 MB
% 2.54/1.31 % (183789)Instructions burned: 111 (million)
% 2.54/1.31 % (183790)Instruction limit reached!
% 2.54/1.31 % (183790)------------------------------
% 2.54/1.31 % (183790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.31 % (183790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.31 % (183790)CaDiCaL version: 2.1.3
% 2.54/1.31 % (183790)Termination reason: Instruction limit
% 2.54/1.31 % (183790)Termination phase: Saturation
% 2.54/1.31 % (183790)Time elapsed: 0.066 s
% 2.54/1.31 % (183790)Peak memory usage: 88 MB
% 2.54/1.31 % (183790)Instructions burned: 120 (million)
% 2.54/1.31 % (183792)Instruction limit reached!
% 2.54/1.31 % (183792)------------------------------
% 2.54/1.31 % (183792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.31 % (183792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.31 % (183792)CaDiCaL version: 2.1.3
% 2.54/1.31 % (183792)Termination reason: Instruction limit
% 2.54/1.31 % (183792)Termination phase: Saturation
% 2.54/1.31 % (183792)Time elapsed: 0.074 s
% 2.54/1.31 % (183792)Peak memory usage: 90 MB
% 2.54/1.31 % (183792)Instructions burned: 129 (million)
% 2.54/1.31 % (183801)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2010293157:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.54/1.31 % (183800)lrs+10_1_sil=8000:sp=occurrence:random_seed=1474002820:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.54/1.31 % (183802)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3067344473:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.54/1.31 % (183791)Refutation found. Thanks to Tanya!
% 2.54/1.31 % SZS status Theorem for theBenchmark
% 2.54/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.41 % (183791)------------------------------
% 0.17/1.41 % (183791)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.41 % (183791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.41 % (183791)CaDiCaL version: 2.1.3
% 0.17/1.41 % (183791)Termination reason: Refutation
% 0.17/1.41 % (183791)Time elapsed: 0.019 s
% 0.17/1.41 % (183791)Peak memory usage: 90 MB
% 0.17/1.41 % (183791)Instructions burned: 26 (million)
% 0.17/1.41 % (183791)------------------------------
% 0.17/1.41 % (183791)------------------------------
% 0.17/1.41 % (183781)Success in time 0.449 s
% 0.17/1.41 % Vampire exiting
%------------------------------------------------------------------------------