%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC107+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 01:02:28 PM UTC 2026
% Result : Theorem 5.66s 1.92s
% Output : Refutation 8.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 28
% Syntax : Number of formulae : 216 ( 23 unt; 15 def)
% Number of atoms : 842 ( 125 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1114 ( 488 ~; 494 |; 79 &)
% ( 22 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 15 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 134 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ) ) ),
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
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X4,X5) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ( neq(X0,nil)
& segmentP(X1,X0) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
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(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f173,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f173]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f201,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X4,X5) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ( ~ neq(X0,nil)
| ~ segmentP(X1,X0) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,cons(X1,X5)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK8(X0,X1))
& ssList(sK9(X0,X1))
& app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f285,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( sK55 = cons(sK57,nil)
& memberP(sK56,sK57)
& ! [X5] :
( ~ ssItem(X5)
| sK57 = X5
| ~ memberP(sK56,X5)
| ~ leq(sK57,X5) )
& ssItem(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ( ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f302,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f303,plain,
! [X0,X1] :
( ssList(sK9(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f304,plain,
! [X0,X1] :
( ssList(sK8(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
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(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f441,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f444,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK53
| ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil = sK54
| ~ neq(sK53,nil)
| ~ segmentP(sK54,sK53) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( ssItem(sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( ssItem(sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
( memberP(sK56,sK57)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( sK55 = cons(sK57,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
( sK55 = cons(sK57,nil)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f515,plain,
( nil = sK56
| ~ neq(sK55,nil)
| ~ segmentP(sK56,sK55) ),
inference(definition_unfolding,[],[f502,f513,f512,f513,f512]) ).
fof(f516,plain,
( nil != sK55
| neq(sK56,nil) ),
inference(definition_unfolding,[],[f501,f512,f513]) ).
fof(f517,plain,
( nil != sK55
| ~ neq(sK55,nil)
| ~ segmentP(sK56,sK55) ),
inference(definition_unfolding,[],[f500,f512,f512,f513,f512]) ).
fof(f518,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f513]) ).
fof(f519,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f512]) ).
fof(f525,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f318]) ).
fof(f539,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f444]) ).
fof(f547,definition,
sF58 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[sF58])],[function_definition]) ).
fof(f548,plain,
cons(sK57,nil) = sF58,
inference(reorient_equations,[],[f547]) ).
fof(f549,plain,
( sK55 = sF58
| nil = sK56 ),
inference(definition_folding,[],[f511,f548]) ).
fof(f550,plain,
( sK55 = sF58
| nil = sK55 ),
inference(definition_folding,[],[f510,f548]) ).
fof(f559,definition,
( spl59_1
<=> segmentP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f561,plain,
( ~ segmentP(sK56,sK55)
| spl59_1 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f563,definition,
( spl59_2
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f565,plain,
( ~ neq(sK55,nil)
| spl59_2 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f567,definition,
( spl59_3
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f568,plain,
( nil = sK55
| ~ spl59_3 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f569,plain,
( nil != sK55
| spl59_3 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f570,plain,
( ~ spl59_1
| ~ spl59_2
| ~ spl59_3 ),
inference(avatar_split_clause,[],[f517,f567,f563,f559]) ).
fof(f572,definition,
( spl59_4
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
fof(f574,plain,
( neq(sK56,nil)
| ~ spl59_4 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f575,plain,
( spl59_4
| ~ spl59_3 ),
inference(avatar_split_clause,[],[f516,f567,f572]) ).
fof(f577,definition,
( spl59_5
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
fof(f579,plain,
( nil = sK56
| ~ spl59_5 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f580,plain,
( ~ spl59_1
| ~ spl59_2
| spl59_5 ),
inference(avatar_split_clause,[],[f515,f577,f563,f559]) ).
fof(f583,definition,
( spl59_6
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f585,plain,
( ssItem(sK57)
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f586,plain,
( spl59_3
| spl59_6 ),
inference(avatar_split_clause,[],[f504,f583,f567]) ).
fof(f587,plain,
( spl59_5
| spl59_6 ),
inference(avatar_split_clause,[],[f505,f583,f577]) ).
fof(f594,definition,
( spl59_8
<=> memberP(sK56,sK57) ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
fof(f596,plain,
( memberP(sK56,sK57)
| ~ spl59_8 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f597,plain,
( spl59_3
| spl59_8 ),
inference(avatar_split_clause,[],[f508,f594,f567]) ).
fof(f600,definition,
( spl59_9
<=> sK55 = sF58 ),
introduced(definition,[new_symbols(definition,[spl59_9])],[avatar_definition]) ).
fof(f602,plain,
( sK55 = sF58
| ~ spl59_9 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f603,plain,
( spl59_3
| spl59_9 ),
inference(avatar_split_clause,[],[f550,f600,f567]) ).
fof(f604,plain,
( spl59_5
| spl59_9 ),
inference(avatar_split_clause,[],[f549,f600,f577]) ).
fof(f606,definition,
( spl59_10
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl59_10])],[avatar_definition]) ).
fof(f607,plain,
( ssList(nil)
| ~ spl59_10 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f620,definition,
( spl59_13
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl59_13])],[avatar_definition]) ).
fof(f622,plain,
( segmentP(nil,nil)
| ~ spl59_13 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f623,plain,
( ~ spl59_10
| spl59_13 ),
inference(avatar_split_clause,[],[f539,f620,f606]) ).
fof(f634,plain,
spl59_10,
inference(avatar_split_clause,[],[f389,f606]) ).
fof(f637,plain,
( ~ segmentP(nil,sK55)
| spl59_1
| ~ spl59_5 ),
inference(superposition,[],[f561,f579]) ).
fof(f640,plain,
( ~ segmentP(nil,nil)
| spl59_1
| ~ spl59_3
| ~ spl59_5 ),
inference(forward_demodulation,[],[f637,f568]) ).
fof(f643,plain,
( $false
| spl59_1
| ~ spl59_3
| ~ spl59_5
| ~ spl59_13 ),
inference(forward_subsumption_resolution,[],[f640,f622]) ).
fof(f644,plain,
( spl59_1
| ~ spl59_3
| ~ spl59_5
| ~ spl59_13 ),
inference(avatar_contradiction_clause,[],[f643]) ).
fof(f646,plain,
( memberP(nil,sK57)
| ~ spl59_5
| ~ spl59_8 ),
inference(forward_demodulation,[],[f596,f579]) ).
fof(f647,plain,
( ~ ssItem(sK57)
| ~ spl59_5
| ~ spl59_8 ),
inference(resolution,[],[f419,f646]) ).
fof(f650,plain,
( nil != sF58
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f396,f548]) ).
fof(f651,plain,
( nil != sF58
| ~ ssList(nil)
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f650,f585]) ).
fof(f652,plain,
( nil != sF58
| ~ spl59_6
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f651,f607]) ).
fof(f653,plain,
( nil != sK55
| ~ spl59_6
| ~ spl59_9
| ~ spl59_10 ),
inference(forward_demodulation,[],[f652,f602]) ).
fof(f654,plain,
sK55 = app(nil,sK55),
inference(resolution,[],[f403,f519]) ).
fof(f657,plain,
! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(app(sK55,X0)) ),
inference(superposition,[],[f525,f654]) ).
fof(f658,plain,
( ! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(app(sK55,X0)) )
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f657,f607]) ).
fof(f659,plain,
( ! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0)
| ~ ssList(app(sK55,X0)) )
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f658,f519]) ).
fof(f668,plain,
sK56 = app(sK56,nil),
inference(resolution,[],[f482,f518]) ).
fof(f678,plain,
( sK56 = app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57)))
| ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_8 ),
inference(resolution,[],[f302,f596]) ).
fof(f679,plain,
( sK56 = app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57)))
| ~ ssList(sK56)
| ~ spl59_6
| ~ spl59_8 ),
inference(forward_subsumption_resolution,[],[f678,f585]) ).
fof(f680,plain,
( sK56 = app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57)))
| ~ spl59_6
| ~ spl59_8 ),
inference(forward_subsumption_resolution,[],[f679,f518]) ).
fof(f683,definition,
( spl59_16
<=> ssList(cons(sK57,sK9(sK56,sK57))) ),
introduced(definition,[new_symbols(definition,[spl59_16])],[avatar_definition]) ).
fof(f684,plain,
( ssList(cons(sK57,sK9(sK56,sK57)))
| ~ spl59_16 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f685,plain,
( ~ ssList(cons(sK57,sK9(sK56,sK57)))
| spl59_16 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f687,definition,
( spl59_17
<=> ssList(sK8(sK56,sK57)) ),
introduced(definition,[new_symbols(definition,[spl59_17])],[avatar_definition]) ).
fof(f688,plain,
( ssList(sK8(sK56,sK57))
| ~ spl59_17 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f689,plain,
( ~ ssList(sK8(sK56,sK57))
| spl59_17 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f694,plain,
( ~ ssItem(sK57)
| ~ ssList(sK9(sK56,sK57))
| spl59_16 ),
inference(resolution,[],[f685,f388]) ).
fof(f695,plain,
( ~ ssList(sK9(sK56,sK57))
| ~ spl59_6
| spl59_16 ),
inference(forward_subsumption_resolution,[],[f694,f585]) ).
fof(f700,plain,
( ~ memberP(sK56,sK57)
| ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_6
| spl59_16 ),
inference(resolution,[],[f303,f695]) ).
fof(f701,plain,
! [X2,X0,X1] :
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| cons(X2,sK9(X0,X1)) = app(cons(X2,nil),sK9(X0,X1)) ),
inference(resolution,[],[f303,f477]) ).
fof(f704,plain,
( ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_6
| ~ spl59_8
| spl59_16 ),
inference(forward_subsumption_resolution,[],[f700,f596]) ).
fof(f705,plain,
( ~ ssList(sK56)
| ~ spl59_6
| ~ spl59_8
| spl59_16 ),
inference(forward_subsumption_resolution,[],[f704,f585]) ).
fof(f706,plain,
( $false
| ~ spl59_6
| ~ spl59_8
| spl59_16 ),
inference(forward_subsumption_resolution,[],[f705,f518]) ).
fof(f707,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_16 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f708,plain,
( ! [X0] :
( ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ ssItem(X0)
| cons(X0,sK9(sK56,sK57)) = app(cons(X0,nil),sK9(sK56,sK57)) )
| ~ spl59_8 ),
inference(resolution,[],[f701,f596]) ).
fof(f709,plain,
( ! [X0] :
( ~ ssList(sK56)
| ~ ssItem(X0)
| cons(X0,sK9(sK56,sK57)) = app(cons(X0,nil),sK9(sK56,sK57)) )
| ~ spl59_6
| ~ spl59_8 ),
inference(forward_subsumption_resolution,[],[f708,f585]) ).
fof(f710,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK9(sK56,sK57)) = app(cons(X0,nil),sK9(sK56,sK57)) )
| ~ spl59_6
| ~ spl59_8 ),
inference(forward_subsumption_resolution,[],[f709,f518]) ).
fof(f711,plain,
( cons(sK57,sK9(sK56,sK57)) = app(cons(sK57,nil),sK9(sK56,sK57))
| ~ spl59_6
| ~ spl59_8 ),
inference(resolution,[],[f710,f585]) ).
fof(f712,plain,
( cons(sK57,sK9(sK56,sK57)) = app(sF58,sK9(sK56,sK57))
| ~ spl59_6
| ~ spl59_8 ),
inference(forward_demodulation,[],[f711,f548]) ).
fof(f713,plain,
( cons(sK57,sK9(sK56,sK57)) = app(sK55,sK9(sK56,sK57))
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9 ),
inference(forward_demodulation,[],[f712,f602]) ).
fof(f715,plain,
( ssList(app(sK55,sK9(sK56,sK57)))
| ~ ssItem(sK57)
| ~ ssList(sK9(sK56,sK57))
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9 ),
inference(superposition,[],[f388,f713]) ).
fof(f718,plain,
( ssList(app(sK55,sK9(sK56,sK57)))
| ~ ssList(sK9(sK56,sK57))
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9 ),
inference(forward_subsumption_resolution,[],[f715,f585]) ).
fof(f720,definition,
( spl59_19
<=> ssList(sK9(sK56,sK57)) ),
introduced(definition,[new_symbols(definition,[spl59_19])],[avatar_definition]) ).
fof(f721,plain,
( ssList(sK9(sK56,sK57))
| ~ spl59_19 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f722,plain,
( ~ ssList(sK9(sK56,sK57))
| spl59_19 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f729,definition,
( spl59_21
<=> ssList(app(sK55,sK9(sK56,sK57))) ),
introduced(definition,[new_symbols(definition,[spl59_21])],[avatar_definition]) ).
fof(f731,plain,
( ssList(app(sK55,sK9(sK56,sK57)))
| ~ spl59_21 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f732,plain,
( ~ spl59_19
| spl59_21
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9 ),
inference(avatar_split_clause,[],[f718,f600,f594,f583,f729,f720]) ).
fof(f733,plain,
( ~ memberP(sK56,sK57)
| ~ ssItem(sK57)
| ~ ssList(sK56)
| spl59_19 ),
inference(resolution,[],[f722,f303]) ).
fof(f734,plain,
( ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_8
| spl59_19 ),
inference(forward_subsumption_resolution,[],[f733,f596]) ).
fof(f735,plain,
( ~ ssList(sK56)
| ~ spl59_6
| ~ spl59_8
| spl59_19 ),
inference(forward_subsumption_resolution,[],[f734,f585]) ).
fof(f736,plain,
( $false
| ~ spl59_6
| ~ spl59_8
| spl59_19 ),
inference(forward_subsumption_resolution,[],[f735,f518]) ).
fof(f737,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_19 ),
inference(avatar_contradiction_clause,[],[f736]) ).
fof(f756,plain,
( ~ memberP(sK56,sK57)
| ~ ssItem(sK57)
| ~ ssList(sK56)
| spl59_17 ),
inference(resolution,[],[f304,f689]) ).
fof(f760,plain,
( ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_8
| spl59_17 ),
inference(forward_subsumption_resolution,[],[f756,f596]) ).
fof(f761,plain,
( ~ ssList(sK56)
| ~ spl59_6
| ~ spl59_8
| spl59_17 ),
inference(forward_subsumption_resolution,[],[f760,f585]) ).
fof(f762,plain,
( $false
| ~ spl59_6
| ~ spl59_8
| spl59_17 ),
inference(forward_subsumption_resolution,[],[f761,f518]) ).
fof(f763,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_17 ),
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f773,plain,
( ! [X0,X1] :
( segmentP(app(sK56,X0),X1)
| ~ segmentP(cons(sK57,sK9(sK56,sK57)),X1)
| ~ ssList(X0)
| ~ ssList(sK8(sK56,sK57))
| ~ ssList(X1)
| ~ ssList(cons(sK57,sK9(sK56,sK57))) )
| ~ spl59_6
| ~ spl59_8 ),
inference(superposition,[],[f441,f680]) ).
fof(f778,plain,
( ! [X0,X1] :
( segmentP(app(sK56,X0),X1)
| ~ segmentP(cons(sK57,sK9(sK56,sK57)),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(cons(sK57,sK9(sK56,sK57))) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_17 ),
inference(forward_subsumption_resolution,[],[f773,f688]) ).
fof(f783,plain,
( ! [X0,X1] :
( segmentP(app(sK56,X0),X1)
| ~ segmentP(cons(sK57,sK9(sK56,sK57)),X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_16
| ~ spl59_17 ),
inference(forward_subsumption_resolution,[],[f778,f684]) ).
fof(f786,plain,
( ! [X0,X1] :
( ~ segmentP(app(sK55,sK9(sK56,sK57)),X1)
| segmentP(app(sK56,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_16
| ~ spl59_17 ),
inference(forward_demodulation,[],[f783,f713]) ).
fof(f787,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(sK9(sK56,sK57))
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17 ),
inference(resolution,[],[f786,f659]) ).
fof(f791,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK9(sK56,sK57))
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17 ),
inference(forward_subsumption_resolution,[],[f787,f519]) ).
fof(f792,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19 ),
inference(forward_subsumption_resolution,[],[f791,f721]) ).
fof(f793,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0) )
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19
| ~ spl59_21 ),
inference(forward_subsumption_resolution,[],[f792,f731]) ).
fof(f794,plain,
( segmentP(sK56,sK55)
| ~ ssList(nil)
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19
| ~ spl59_21 ),
inference(superposition,[],[f793,f668]) ).
fof(f795,plain,
( ~ ssList(nil)
| spl59_1
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19
| ~ spl59_21 ),
inference(forward_subsumption_resolution,[],[f794,f561]) ).
fof(f796,plain,
( $false
| spl59_1
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19
| ~ spl59_21 ),
inference(forward_subsumption_resolution,[],[f795,f607]) ).
fof(f797,plain,
( spl59_1
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19
| ~ spl59_21 ),
inference(avatar_contradiction_clause,[],[f796]) ).
fof(f798,plain,
( nil = sK55
| ~ ssList(nil)
| ~ ssList(sK55)
| spl59_2 ),
inference(resolution,[],[f565,f387]) ).
fof(f799,plain,
( ~ ssList(nil)
| ~ ssList(sK55)
| spl59_2
| spl59_3 ),
inference(forward_subsumption_resolution,[],[f798,f569]) ).
fof(f800,plain,
( ~ ssList(sK55)
| spl59_2
| spl59_3
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f799,f607]) ).
fof(f801,plain,
( $false
| spl59_2
| spl59_3
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f800,f519]) ).
fof(f802,plain,
( spl59_2
| spl59_3
| ~ spl59_10 ),
inference(avatar_contradiction_clause,[],[f801]) ).
fof(f803,plain,
( $false
| ~ spl59_3
| ~ spl59_6
| ~ spl59_9
| ~ spl59_10 ),
inference(forward_subsumption_resolution,[],[f653,f568]) ).
fof(f804,plain,
( ~ spl59_3
| ~ spl59_6
| ~ spl59_9
| ~ spl59_10 ),
inference(avatar_contradiction_clause,[],[f803]) ).
fof(f805,plain,
( ~ spl59_6
| ~ spl59_5
| ~ spl59_8 ),
inference(avatar_split_clause,[],[f647,f594,f577,f583]) ).
fof(f813,plain,
( neq(nil,nil)
| ~ spl59_4
| ~ spl59_5 ),
inference(superposition,[],[f574,f579]) ).
fof(f822,plain,
( ~ neq(nil,nil)
| spl59_2
| ~ spl59_3 ),
inference(superposition,[],[f565,f568]) ).
fof(f826,plain,
( $false
| spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f822,f813]) ).
fof(f827,plain,
( spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5 ),
inference(avatar_contradiction_clause,[],[f826]) ).
cnf(s1,plain,
( ~ spl59_1
| ~ spl59_2
| ~ spl59_3 ),
inference(sat_conversion,[],[f570]) ).
cnf(s2,plain,
( ~ spl59_3
| spl59_4 ),
inference(sat_conversion,[],[f575]) ).
cnf(s3,plain,
( ~ spl59_1
| ~ spl59_2
| spl59_5 ),
inference(sat_conversion,[],[f580]) ).
cnf(s5,plain,
( spl59_3
| spl59_6 ),
inference(sat_conversion,[],[f586]) ).
cnf(s6,plain,
( spl59_5
| spl59_6 ),
inference(sat_conversion,[],[f587]) ).
cnf(s9,plain,
( spl59_3
| spl59_8 ),
inference(sat_conversion,[],[f597]) ).
cnf(s11,plain,
( spl59_3
| spl59_9 ),
inference(sat_conversion,[],[f603]) ).
cnf(s12,plain,
( spl59_5
| spl59_9 ),
inference(sat_conversion,[],[f604]) ).
cnf(s17,plain,
( ~ spl59_10
| spl59_13 ),
inference(sat_conversion,[],[f623]) ).
cnf(s20,plain,
spl59_10,
inference(sat_conversion,[],[f634]) ).
cnf(s22,plain,
( spl59_1
| ~ spl59_3
| ~ spl59_5
| ~ spl59_13 ),
inference(sat_conversion,[],[f644]) ).
cnf(s25,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_16 ),
inference(sat_conversion,[],[f707]) ).
cnf(s27,plain,
( ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_19
| spl59_21 ),
inference(sat_conversion,[],[f732]) ).
cnf(s28,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_19 ),
inference(sat_conversion,[],[f737]) ).
cnf(s29,plain,
( ~ spl59_6
| ~ spl59_8
| spl59_17 ),
inference(sat_conversion,[],[f763]) ).
cnf(s30,plain,
( spl59_1
| ~ spl59_6
| ~ spl59_8
| ~ spl59_9
| ~ spl59_10
| ~ spl59_16
| ~ spl59_17
| ~ spl59_19
| ~ spl59_21 ),
inference(sat_conversion,[],[f797]) ).
cnf(s31,plain,
( spl59_2
| spl59_3
| ~ spl59_10 ),
inference(sat_conversion,[],[f802]) ).
cnf(s32,plain,
( ~ spl59_3
| ~ spl59_6
| ~ spl59_9
| ~ spl59_10 ),
inference(sat_conversion,[],[f804]) ).
cnf(s33,plain,
( ~ spl59_5
| ~ spl59_6
| ~ spl59_8 ),
inference(sat_conversion,[],[f805]) ).
cnf(s34,plain,
( spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_5 ),
inference(sat_conversion,[],[f827]) ).
cnf(s37,plain,
spl59_13,
inference(rat,[],[s17,s20]) ).
cnf(s38,plain,
( ~ spl59_3
| spl59_1 ),
inference(rat,[],[s32,s6,s12,s22,s37,s20]) ).
cnf(s39,plain,
spl59_1,
inference(rat,[],[s30,s25,s27,s28,s29,s5,s9,s11,s38,s20]) ).
cnf(s40,plain,
( ~ spl59_4
| ~ spl59_3
| spl59_2 ),
inference(rat,[],[s32,s6,s12,s34,s20]) ).
cnf(s41,plain,
~ spl59_3,
inference(rat,[],[s40,s1,s2,s39]) ).
cnf(s42,plain,
spl59_2,
inference(rat,[],[s31,s20,s41]) ).
cnf(s44,plain,
spl59_8,
inference(rat,[],[s9,s41]) ).
cnf(s46,plain,
spl59_6,
inference(rat,[],[s5,s41]) ).
cnf(s47,plain,
spl59_5,
inference(rat,[],[s3,s39,s42]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s33,s44,s47,s46]) ).
fof(f828,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC107+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 07:54:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.66/1.92 % (1753275)Detected formulas, will run a generic FOF schedule.
% 5.66/1.92 % (1753282)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=3369695519:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.66/1.92 % (1753284)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4058142251:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.66/1.92 % (1753280)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=3863919351:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.66/1.92 % (1753286)dis-21_1_sil=8000:lcm=predicate:random_seed=1371710125:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.66/1.92 % (1753283)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=682435606:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.66/1.92 % (1753281)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=1756662225:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.66/1.92 % (1753285)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=549191826:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.66/1.92 % (1753283)Refutation not found, incomplete strategy
% 5.66/1.92 % (1753283)------------------------------
% 5.66/1.92 % (1753283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753283)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753283)Termination reason: Refutation not found, incomplete strategy
% 5.66/1.92 % (1753283)Time elapsed: 0.005 s
% 5.66/1.92 % (1753283)Peak memory usage: 89 MB
% 5.66/1.92 % (1753283)Instructions burned: 5 (million)
% 5.66/1.92 % (1753284)Instruction limit reached!
% 5.66/1.92 % (1753284)------------------------------
% 5.66/1.92 % (1753284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753284)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753284)Termination reason: Instruction limit
% 5.66/1.92 % (1753284)Termination phase: Saturation
% 5.66/1.92 % (1753284)Time elapsed: 0.069 s
% 5.66/1.92 % (1753284)Peak memory usage: 88 MB
% 5.66/1.92 % (1753284)Instructions burned: 119 (million)
% 5.66/1.92 % (1753286)Instruction limit reached!
% 5.66/1.92 % (1753286)------------------------------
% 5.66/1.92 % (1753286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753286)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753286)Termination reason: Instruction limit
% 5.66/1.92 % (1753286)Termination phase: Saturation
% 5.66/1.92 % (1753286)Time elapsed: 0.072 s
% 5.66/1.92 % (1753286)Peak memory usage: 90 MB
% 5.66/1.92 % (1753286)Instructions burned: 130 (million)
% 5.66/1.92 % (1753285)Instruction limit reached!
% 5.66/1.92 % (1753285)------------------------------
% 5.66/1.92 % (1753285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753285)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753285)Termination reason: Instruction limit
% 5.66/1.92 % (1753285)Termination phase: Saturation
% 5.66/1.92 % (1753285)Time elapsed: 0.114 s
% 5.66/1.92 % (1753285)Peak memory usage: 90 MB
% 5.66/1.92 % (1753285)Instructions burned: 140 (million)
% 5.66/1.92 % (1753294)lrs+10_1_sil=8000:sp=occurrence:random_seed=3047331856:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.66/1.92 % (1753295)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2190189891:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.66/1.92 % (1753283)------------------------------
% 5.66/1.92 % (1753283)------------------------------
% 5.66/1.92 % (1753296)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3640995108:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.66/1.92 % (1753295)Instruction limit reached!
% 5.66/1.92 % (1753295)------------------------------
% 5.66/1.92 % (1753295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753295)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753295)Termination reason: Instruction limit
% 5.66/1.92 % (1753295)Termination phase: Saturation
% 5.66/1.92 % (1753295)Time elapsed: 0.076 s
% 5.66/1.92 % (1753295)Peak memory usage: 91 MB
% 5.66/1.92 % (1753295)Instructions burned: 158 (million)
% 5.66/1.92 % (1753300)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=2477498151:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 5.66/1.92 % (1753294)Instruction limit reached!
% 5.66/1.92 % (1753294)------------------------------
% 5.66/1.92 % (1753294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753294)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753294)Termination reason: Instruction limit
% 5.66/1.92 % (1753294)Termination phase: Saturation
% 5.66/1.92 % (1753294)Time elapsed: 0.171 s
% 5.66/1.92 % (1753294)Peak memory usage: 93 MB
% 5.66/1.92 % (1753294)Instructions burned: 285 (million)
% 5.66/1.92 % (1753301)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4068925641:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.66/1.92 % (1753296)Instruction limit reached!
% 5.66/1.92 % (1753296)------------------------------
% 5.66/1.92 % (1753296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753296)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753296)Termination reason: Instruction limit
% 5.66/1.92 % (1753296)Termination phase: Saturation
% 5.66/1.92 % (1753296)Time elapsed: 0.208 s
% 5.66/1.92 % (1753296)Peak memory usage: 92 MB
% 5.66/1.92 % (1753296)Instructions burned: 326 (million)
% 5.66/1.92 % (1753300)Instruction limit reached!
% 5.66/1.92 % (1753300)------------------------------
% 5.66/1.92 % (1753300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753300)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753300)Termination reason: Instruction limit
% 5.66/1.92 % (1753300)Termination phase: Saturation
% 5.66/1.92 % (1753300)Time elapsed: 0.119 s
% 5.66/1.92 % (1753300)Peak memory usage: 93 MB
% 5.66/1.92 % (1753300)Instructions burned: 248 (million)
% 5.66/1.92 % (1753303)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=13965726:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.66/1.92 % (1753301)Instruction limit reached!
% 5.66/1.92 % (1753301)------------------------------
% 5.66/1.92 % (1753301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753301)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753301)Termination reason: Instruction limit
% 5.66/1.92 % (1753301)Termination phase: Saturation
% 5.66/1.92 % (1753301)Time elapsed: 0.174 s
% 5.66/1.92 % (1753301)Peak memory usage: 90 MB
% 5.66/1.92 % (1753301)Instructions burned: 295 (million)
% 5.66/1.92 % (1753305)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=447616222:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.66/1.92 % (1753306)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1926652117:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.66/1.92 % (1753305)Instruction limit reached!
% 5.66/1.92 % (1753305)------------------------------
% 5.66/1.92 % (1753305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753305)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753305)Termination reason: Instruction limit
% 5.66/1.92 % (1753305)Termination phase: Saturation
% 5.66/1.92 % (1753305)Time elapsed: 0.076 s
% 5.66/1.92 % (1753305)Peak memory usage: 90 MB
% 5.66/1.92 % (1753305)Instructions burned: 114 (million)
% 5.66/1.92 % (1753280)First to succeed.
% 5.66/1.92 % (1753280)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1753275"
% 5.66/1.92 % (1753306)Instruction limit reached!
% 5.66/1.92 % (1753306)------------------------------
% 5.66/1.92 % (1753306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753306)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753306)Termination reason: Instruction limit
% 5.66/1.92 % (1753306)Termination phase: Saturation
% 5.66/1.92 % (1753306)Time elapsed: 0.063 s
% 5.66/1.92 % (1753306)Peak memory usage: 90 MB
% 5.66/1.92 % (1753306)Instructions burned: 128 (million)
% 5.66/1.92 % (1753308)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3076179467:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 5.66/1.92 % (1753281)Also succeeded, but the first one will report.
% 5.66/1.92 % (1753308)Instruction limit reached!
% 5.66/1.92 % (1753308)------------------------------
% 5.66/1.92 % (1753308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.66/1.92 % (1753308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.66/1.92 % (1753308)CaDiCaL version: 2.1.3
% 5.66/1.92 % (1753308)Termination reason: Instruction limit
% 5.66/1.92 % (1753308)Termination phase: Saturation
% 5.66/1.92 % (1753308)Time elapsed: 0.069 s
% 5.66/1.92 % (1753308)Peak memory usage: 89 MB
% 5.66/1.92 % (1753308)Instructions burned: 114 (million)
% 5.66/1.92 % (1753311)lrs+10_1_sil=8000:sp=occurrence:random_seed=4011314934:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 5.66/1.92 % (1753312)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=10836255:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 5.66/1.92 % (1753314)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=900942807:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 5.66/1.92 % (1753280)Refutation found. Thanks to Tanya!
% 5.66/1.92 % SZS status Theorem for theBenchmark
% 5.66/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 8.12/2.12 % (1753280)------------------------------
% 8.12/2.12 % (1753280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.12/2.12 % (1753280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.12/2.12 % (1753280)CaDiCaL version: 2.1.3
% 8.12/2.12 % (1753280)Termination reason: Refutation
% 8.12/2.12 % (1753280)Time elapsed: 0.664 s
% 8.12/2.12 % (1753280)Peak memory usage: 130 MB
% 8.12/2.12 % (1753280)Instructions burned: 1017 (million)
% 8.12/2.12 % (1753280)------------------------------
% 8.12/2.12 % (1753280)------------------------------
% 8.12/2.12 % (1753275)Success in time 1.075 s
% 8.12/2.12 % Vampire exiting
%------------------------------------------------------------------------------