%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC056+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 : n014.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 01:02:14 PM UTC 2026
% Result : Theorem 5.00s 1.72s
% Output : Refutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 27
% Syntax : Number of formulae : 203 ( 23 unt; 13 def)
% Number of atoms : 858 ( 126 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1188 ( 533 ~; 520 |; 83 &)
% ( 20 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 174 ( 0 sgn 144 !; 30 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',ax7) ).
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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
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/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
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(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/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(X5,X4) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& neq(X6,nil)
& segmentP(X1,X6)
& segmentP(X0,X6) ) ) ) ) ) ) ) ),
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
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) )
& ( nil != X3
| nil != X2 ) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& neq(X6,nil)
& segmentP(X1,X6)
& segmentP(X0,X6) ) ) ) ) ) ) ) ),
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(f120,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
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(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
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(X5,X4) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(X1,X6)
| ~ segmentP(X0,X6) ) ) )
& 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(X5,X4) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(X1,X6)
| ~ segmentP(X0,X6) ) ) )
& 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(X5,sK57) )
& ssItem(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ! [X6] :
( ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK54,X6)
| ~ segmentP(sK53,X6) ) ) )
& 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(f390,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
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(f440,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
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,
! [X6] :
( nil != sK53
| ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK54,X6)
| ~ segmentP(sK53,X6) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X6] :
( nil = sK54
| ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK54,X6)
| ~ segmentP(sK53,X6) ),
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,
! [X6] :
( nil = sK56
| ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK56,X6)
| ~ segmentP(sK55,X6) ),
inference(definition_unfolding,[],[f502,f513,f513,f512]) ).
fof(f516,plain,
( nil != sK55
| neq(sK56,nil) ),
inference(definition_unfolding,[],[f501,f512,f513]) ).
fof(f517,plain,
! [X6] :
( nil != sK55
| ~ ssList(X6)
| ~ neq(X6,nil)
| ~ segmentP(sK56,X6)
| ~ segmentP(sK55,X6) ),
inference(definition_unfolding,[],[f500,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
<=> ! [X6] :
( ~ ssList(X6)
| ~ segmentP(sK55,X6)
| ~ segmentP(sK56,X6)
| ~ neq(X6,nil) ) ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f560,plain,
( ! [X6] :
( ~ segmentP(sK56,X6)
| ~ segmentP(sK55,X6)
| ~ ssList(X6)
| ~ neq(X6,nil) )
| ~ spl59_1 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f562,definition,
( spl59_2
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f563,plain,
( nil = sK55
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f564,plain,
( nil != sK55
| spl59_2 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f565,plain,
( spl59_1
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f517,f562,f559]) ).
fof(f567,definition,
( spl59_3
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f569,plain,
( neq(sK56,nil)
| ~ spl59_3 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f570,plain,
( spl59_3
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f516,f562,f567]) ).
fof(f572,definition,
( spl59_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
fof(f574,plain,
( nil = sK56
| ~ spl59_4 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f575,plain,
( spl59_1
| spl59_4 ),
inference(avatar_split_clause,[],[f515,f572,f559]) ).
fof(f578,definition,
( spl59_5
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
fof(f580,plain,
( ssItem(sK57)
| ~ spl59_5 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f581,plain,
( spl59_2
| spl59_5 ),
inference(avatar_split_clause,[],[f504,f578,f562]) ).
fof(f582,plain,
( spl59_4
| spl59_5 ),
inference(avatar_split_clause,[],[f505,f578,f572]) ).
fof(f589,definition,
( spl59_7
<=> memberP(sK56,sK57) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f591,plain,
( memberP(sK56,sK57)
| ~ spl59_7 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f592,plain,
( spl59_2
| spl59_7 ),
inference(avatar_split_clause,[],[f508,f589,f562]) ).
fof(f595,definition,
( spl59_8
<=> sK55 = sF58 ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
fof(f597,plain,
( sK55 = sF58
| ~ spl59_8 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f598,plain,
( spl59_2
| spl59_8 ),
inference(avatar_split_clause,[],[f550,f595,f562]) ).
fof(f599,plain,
( spl59_4
| spl59_8 ),
inference(avatar_split_clause,[],[f549,f595,f572]) ).
fof(f601,definition,
( spl59_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl59_9])],[avatar_definition]) ).
fof(f602,plain,
( ssList(nil)
| ~ spl59_9 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f615,definition,
( spl59_12
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[spl59_12])],[avatar_definition]) ).
fof(f617,plain,
( segmentP(nil,nil)
| ~ spl59_12 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f618,plain,
( ~ spl59_9
| spl59_12 ),
inference(avatar_split_clause,[],[f539,f615,f601]) ).
fof(f629,plain,
spl59_9,
inference(avatar_split_clause,[],[f389,f601]) ).
fof(f633,plain,
( memberP(nil,sK57)
| ~ spl59_4
| ~ spl59_7 ),
inference(forward_demodulation,[],[f591,f574]) ).
fof(f634,plain,
( ~ ssItem(sK57)
| ~ spl59_4
| ~ spl59_7 ),
inference(resolution,[],[f419,f633]) ).
fof(f647,plain,
sK55 = app(nil,sK55),
inference(resolution,[],[f403,f519]) ).
fof(f652,plain,
sK56 = app(sK56,nil),
inference(resolution,[],[f482,f518]) ).
fof(f653,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56)
| ~ ssList(sK56)
| ~ neq(sK56,nil)
| ~ spl59_1 ),
inference(resolution,[],[f440,f560]) ).
fof(f654,plain,
( ~ ssList(sK56)
| ~ segmentP(sK55,sK56)
| ~ neq(sK56,nil)
| ~ spl59_1 ),
inference(duplicate_literal_removal,[],[f653]) ).
fof(f655,plain,
( ~ segmentP(sK55,sK56)
| ~ neq(sK56,nil)
| ~ spl59_1 ),
inference(forward_subsumption_resolution,[],[f654,f518]) ).
fof(f656,plain,
( ~ segmentP(sK55,sK56)
| ~ spl59_1
| ~ spl59_3 ),
inference(forward_subsumption_resolution,[],[f655,f569]) ).
fof(f658,plain,
! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(app(sK55,X0)) ),
inference(superposition,[],[f525,f647]) ).
fof(f661,plain,
( ! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(app(sK55,X0)) )
| ~ spl59_9 ),
inference(forward_subsumption_resolution,[],[f658,f602]) ).
fof(f663,plain,
( ! [X0] :
( segmentP(app(sK55,X0),sK55)
| ~ ssList(X0)
| ~ ssList(app(sK55,X0)) )
| ~ spl59_9 ),
inference(forward_subsumption_resolution,[],[f661,f519]) ).
fof(f676,plain,
! [X2,X0,X1] :
( ~ memberP(X1,X2)
| cons(X0,sK9(X1,X2)) = app(cons(X0,nil),sK9(X1,X2))
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1) ),
inference(resolution,[],[f477,f303]) ).
fof(f679,plain,
( ! [X0] :
( cons(X0,sK9(sK56,sK57)) = app(cons(X0,nil),sK9(sK56,sK57))
| ~ ssItem(X0)
| ~ ssItem(sK57)
| ~ ssList(sK56) )
| ~ spl59_7 ),
inference(resolution,[],[f676,f591]) ).
fof(f680,plain,
( ! [X0] :
( cons(X0,sK9(sK56,sK57)) = app(cons(X0,nil),sK9(sK56,sK57))
| ~ ssItem(X0)
| ~ ssList(sK56) )
| ~ spl59_5
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f679,f580]) ).
fof(f681,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,sK9(sK56,sK57)) = app(cons(X0,nil),sK9(sK56,sK57)) )
| ~ spl59_5
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f680,f518]) ).
fof(f682,plain,
( cons(sK57,sK9(sK56,sK57)) = app(cons(sK57,nil),sK9(sK56,sK57))
| ~ spl59_5
| ~ spl59_7 ),
inference(resolution,[],[f681,f580]) ).
fof(f683,plain,
( cons(sK57,sK9(sK56,sK57)) = app(sF58,sK9(sK56,sK57))
| ~ spl59_5
| ~ spl59_7 ),
inference(forward_demodulation,[],[f682,f548]) ).
fof(f684,plain,
( cons(sK57,sK9(sK56,sK57)) = app(sK55,sK9(sK56,sK57))
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8 ),
inference(forward_demodulation,[],[f683,f597]) ).
fof(f686,plain,
( ssList(app(sK55,sK9(sK56,sK57)))
| ~ ssItem(sK57)
| ~ ssList(sK9(sK56,sK57))
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8 ),
inference(superposition,[],[f388,f684]) ).
fof(f687,plain,
( ssList(app(sK55,sK9(sK56,sK57)))
| ~ ssList(sK9(sK56,sK57))
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8 ),
inference(forward_subsumption_resolution,[],[f686,f580]) ).
fof(f690,definition,
( spl59_15
<=> ssList(sK9(sK56,sK57)) ),
introduced(definition,[new_symbols(definition,[spl59_15])],[avatar_definition]) ).
fof(f691,plain,
( ssList(sK9(sK56,sK57))
| ~ spl59_15 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f692,plain,
( ~ ssList(sK9(sK56,sK57))
| spl59_15 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f694,definition,
( spl59_16
<=> ssList(app(sK55,sK9(sK56,sK57))) ),
introduced(definition,[new_symbols(definition,[spl59_16])],[avatar_definition]) ).
fof(f696,plain,
( ssList(app(sK55,sK9(sK56,sK57)))
| ~ spl59_16 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f697,plain,
( ~ spl59_15
| spl59_16
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8 ),
inference(avatar_split_clause,[],[f687,f595,f589,f578,f694,f690]) ).
fof(f703,plain,
( ~ memberP(sK56,sK57)
| ~ ssItem(sK57)
| ~ ssList(sK56)
| spl59_15 ),
inference(resolution,[],[f692,f303]) ).
fof(f704,plain,
( ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_7
| spl59_15 ),
inference(forward_subsumption_resolution,[],[f703,f591]) ).
fof(f705,plain,
( ~ ssList(sK56)
| ~ spl59_5
| ~ spl59_7
| spl59_15 ),
inference(forward_subsumption_resolution,[],[f704,f580]) ).
fof(f706,plain,
( $false
| ~ spl59_5
| ~ spl59_7
| spl59_15 ),
inference(forward_subsumption_resolution,[],[f705,f518]) ).
fof(f707,plain,
( ~ spl59_5
| ~ spl59_7
| spl59_15 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f712,plain,
( sK56 = app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57)))
| ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_7 ),
inference(resolution,[],[f302,f591]) ).
fof(f713,plain,
( sK56 = app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57)))
| ~ ssList(sK56)
| ~ spl59_5
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f712,f580]) ).
fof(f714,plain,
( sK56 = app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57)))
| ~ spl59_5
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f713,f518]) ).
fof(f715,plain,
( sK56 = app(sK8(sK56,sK57),app(sK55,sK9(sK56,sK57)))
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8 ),
inference(forward_demodulation,[],[f714,f684]) ).
fof(f720,definition,
( spl59_18
<=> ssList(sK8(sK56,sK57)) ),
introduced(definition,[new_symbols(definition,[spl59_18])],[avatar_definition]) ).
fof(f721,plain,
( ssList(sK8(sK56,sK57))
| ~ spl59_18 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f722,plain,
( ~ ssList(sK8(sK56,sK57))
| spl59_18 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f727,plain,
( ~ memberP(sK56,sK57)
| ~ ssItem(sK57)
| ~ ssList(sK56)
| spl59_18 ),
inference(resolution,[],[f304,f722]) ).
fof(f731,plain,
( ~ ssItem(sK57)
| ~ ssList(sK56)
| ~ spl59_7
| spl59_18 ),
inference(forward_subsumption_resolution,[],[f727,f591]) ).
fof(f732,plain,
( ~ ssList(sK56)
| ~ spl59_5
| ~ spl59_7
| spl59_18 ),
inference(forward_subsumption_resolution,[],[f731,f580]) ).
fof(f733,plain,
( $false
| ~ spl59_5
| ~ spl59_7
| spl59_18 ),
inference(forward_subsumption_resolution,[],[f732,f518]) ).
fof(f734,plain,
( ~ spl59_5
| ~ spl59_7
| spl59_18 ),
inference(avatar_contradiction_clause,[],[f733]) ).
fof(f772,plain,
( nil != sF58
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f390,f548]) ).
fof(f777,plain,
( nil != sF58
| ~ ssList(nil)
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f772,f580]) ).
fof(f780,plain,
( nil != sF58
| ~ spl59_5
| ~ spl59_9 ),
inference(forward_subsumption_resolution,[],[f777,f602]) ).
fof(f781,plain,
( nil != sK55
| ~ spl59_5
| ~ spl59_8
| ~ spl59_9 ),
inference(forward_demodulation,[],[f780,f597]) ).
fof(f957,plain,
( ! [X0,X1] :
( segmentP(app(sK56,X0),X1)
| ~ segmentP(app(sK55,sK9(sK56,sK57)),X1)
| ~ ssList(X0)
| ~ ssList(sK8(sK56,sK57))
| ~ ssList(X1)
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8 ),
inference(superposition,[],[f441,f715]) ).
fof(f962,plain,
( ! [X0,X1] :
( segmentP(app(sK56,X0),X1)
| ~ segmentP(app(sK55,sK9(sK56,sK57)),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f957,f721]) ).
fof(f967,plain,
( ! [X0,X1] :
( ~ segmentP(app(sK55,sK9(sK56,sK57)),X1)
| segmentP(app(sK56,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f962,f696]) ).
fof(f985,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(sK9(sK56,sK57))
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_16
| ~ spl59_18 ),
inference(resolution,[],[f967,f663]) ).
fof(f989,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(sK9(sK56,sK57))
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f985,f519]) ).
fof(f990,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0)
| ~ ssList(app(sK55,sK9(sK56,sK57))) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f989,f691]) ).
fof(f991,plain,
( ! [X0] :
( segmentP(app(sK56,X0),sK55)
| ~ ssList(X0) )
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f990,f696]) ).
fof(f992,plain,
( segmentP(sK56,sK55)
| ~ ssList(nil)
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(superposition,[],[f991,f652]) ).
fof(f993,plain,
( segmentP(sK56,sK55)
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f992,f602]) ).
fof(f994,plain,
( ~ segmentP(sK55,sK55)
| ~ ssList(sK55)
| ~ neq(sK55,nil)
| ~ spl59_1
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(resolution,[],[f993,f560]) ).
fof(f995,plain,
( ~ ssList(sK55)
| ~ neq(sK55,nil)
| ~ spl59_1
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f994,f440]) ).
fof(f996,plain,
( ~ neq(sK55,nil)
| ~ spl59_1
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f995,f519]) ).
fof(f997,plain,
( nil = sK55
| ~ ssList(nil)
| ~ ssList(sK55)
| ~ spl59_1
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(resolution,[],[f996,f387]) ).
fof(f998,plain,
( ~ ssList(nil)
| ~ ssList(sK55)
| ~ spl59_1
| spl59_2
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f997,f564]) ).
fof(f999,plain,
( ~ ssList(sK55)
| ~ spl59_1
| spl59_2
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f998,f602]) ).
fof(f1000,plain,
( $false
| ~ spl59_1
| spl59_2
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(forward_subsumption_resolution,[],[f999,f519]) ).
fof(f1001,plain,
( ~ spl59_1
| spl59_2
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(avatar_contradiction_clause,[],[f1000]) ).
fof(f1004,plain,
( $false
| ~ spl59_2
| ~ spl59_5
| ~ spl59_8
| ~ spl59_9 ),
inference(forward_subsumption_resolution,[],[f781,f563]) ).
fof(f1005,plain,
( ~ spl59_2
| ~ spl59_5
| ~ spl59_8
| ~ spl59_9 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
fof(f1009,plain,
( ~ spl59_5
| ~ spl59_4
| ~ spl59_7 ),
inference(avatar_split_clause,[],[f634,f589,f572,f578]) ).
fof(f1018,plain,
( ~ segmentP(sK55,nil)
| ~ spl59_1
| ~ spl59_3
| ~ spl59_4 ),
inference(superposition,[],[f656,f574]) ).
fof(f1031,plain,
( ~ segmentP(nil,nil)
| ~ spl59_1
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4 ),
inference(forward_demodulation,[],[f1018,f563]) ).
fof(f1035,plain,
( $false
| ~ spl59_1
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_12 ),
inference(forward_subsumption_resolution,[],[f1031,f617]) ).
fof(f1036,plain,
( ~ spl59_1
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_12 ),
inference(avatar_contradiction_clause,[],[f1035]) ).
cnf(s1,plain,
( spl59_1
| ~ spl59_2 ),
inference(sat_conversion,[],[f565]) ).
cnf(s2,plain,
( ~ spl59_2
| spl59_3 ),
inference(sat_conversion,[],[f570]) ).
cnf(s3,plain,
( spl59_1
| spl59_4 ),
inference(sat_conversion,[],[f575]) ).
cnf(s5,plain,
( spl59_2
| spl59_5 ),
inference(sat_conversion,[],[f581]) ).
cnf(s6,plain,
( spl59_4
| spl59_5 ),
inference(sat_conversion,[],[f582]) ).
cnf(s9,plain,
( spl59_2
| spl59_7 ),
inference(sat_conversion,[],[f592]) ).
cnf(s11,plain,
( spl59_2
| spl59_8 ),
inference(sat_conversion,[],[f598]) ).
cnf(s12,plain,
( spl59_4
| spl59_8 ),
inference(sat_conversion,[],[f599]) ).
cnf(s17,plain,
( ~ spl59_9
| spl59_12 ),
inference(sat_conversion,[],[f618]) ).
cnf(s20,plain,
spl59_9,
inference(sat_conversion,[],[f629]) ).
cnf(s22,plain,
( ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_15
| spl59_16 ),
inference(sat_conversion,[],[f697]) ).
cnf(s24,plain,
( ~ spl59_5
| ~ spl59_7
| spl59_15 ),
inference(sat_conversion,[],[f707]) ).
cnf(s26,plain,
( ~ spl59_5
| ~ spl59_7
| spl59_18 ),
inference(sat_conversion,[],[f734]) ).
cnf(s42,plain,
( ~ spl59_1
| spl59_2
| ~ spl59_5
| ~ spl59_7
| ~ spl59_8
| ~ spl59_9
| ~ spl59_15
| ~ spl59_16
| ~ spl59_18 ),
inference(sat_conversion,[],[f1001]) ).
cnf(s44,plain,
( ~ spl59_2
| ~ spl59_5
| ~ spl59_8
| ~ spl59_9 ),
inference(sat_conversion,[],[f1005]) ).
cnf(s45,plain,
( ~ spl59_4
| ~ spl59_5
| ~ spl59_7 ),
inference(sat_conversion,[],[f1009]) ).
cnf(s46,plain,
( ~ spl59_1
| ~ spl59_2
| ~ spl59_3
| ~ spl59_4
| ~ spl59_12 ),
inference(sat_conversion,[],[f1036]) ).
cnf(s49,plain,
spl59_12,
inference(rat,[],[s17,s20]) ).
cnf(s50,plain,
spl59_1,
inference(rat,[],[s45,s5,s9,s1,s3]) ).
cnf(s51,plain,
spl59_2,
inference(rat,[],[s42,s22,s24,s26,s5,s9,s11,s50,s20]) ).
cnf(s52,plain,
spl59_3,
inference(rat,[],[s2,s51]) ).
cnf(s53,plain,
~ spl59_4,
inference(rat,[],[s46,s49,s51,s50,s52]) ).
cnf(s55,plain,
spl59_8,
inference(rat,[],[s12,s53]) ).
cnf(s58,plain,
spl59_5,
inference(rat,[],[s6,s53]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s44,s20,s51,s55,s58]) ).
fof(f1037,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC056+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n014.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 07:38:16 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 5.00/1.72 % (1612379)Detected formulas, will run a generic FOF schedule.
% 5.00/1.72 % (1612384)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=686949682:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.00/1.72 % (1612386)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=4274180087:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.00/1.72 % (1612385)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=1477023579:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.00/1.72 % (1612389)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3064595285:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.00/1.72 % (1612388)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=451527228:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.00/1.72 % (1612387)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1722823972:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.00/1.72 % (1612390)dis-21_1_sil=8000:lcm=predicate:random_seed=3643988257: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)
% 5.00/1.72 % (1612387)Refutation not found, incomplete strategy
% 5.00/1.72 % (1612387)------------------------------
% 5.00/1.72 % (1612387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612387)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612387)Termination reason: Refutation not found, incomplete strategy
% 5.00/1.72 % (1612387)Time elapsed: 0.005 s
% 5.00/1.72 % (1612387)Peak memory usage: 88 MB
% 5.00/1.72 % (1612387)Instructions burned: 5 (million)
% 5.00/1.72 % (1612388)Instruction limit reached!
% 5.00/1.72 % (1612388)------------------------------
% 5.00/1.72 % (1612388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612388)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612388)Termination reason: Instruction limit
% 5.00/1.72 % (1612388)Termination phase: Saturation
% 5.00/1.72 % (1612388)Time elapsed: 0.070 s
% 5.00/1.72 % (1612388)Peak memory usage: 88 MB
% 5.00/1.72 % (1612388)Instructions burned: 120 (million)
% 5.00/1.72 % (1612390)Instruction limit reached!
% 5.00/1.72 % (1612390)------------------------------
% 5.00/1.72 % (1612390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612390)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612390)Termination reason: Instruction limit
% 5.00/1.72 % (1612390)Termination phase: Saturation
% 5.00/1.72 % (1612390)Time elapsed: 0.073 s
% 5.00/1.72 % (1612390)Peak memory usage: 90 MB
% 5.00/1.72 % (1612390)Instructions burned: 131 (million)
% 5.00/1.72 % (1612389)Instruction limit reached!
% 5.00/1.72 % (1612389)------------------------------
% 5.00/1.72 % (1612389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612389)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612389)Termination reason: Instruction limit
% 5.00/1.72 % (1612389)Termination phase: Saturation
% 5.00/1.72 % (1612389)Time elapsed: 0.094 s
% 5.00/1.72 % (1612389)Peak memory usage: 90 MB
% 5.00/1.72 % (1612389)Instructions burned: 141 (million)
% 5.00/1.72 % (1612398)lrs+10_1_sil=8000:sp=occurrence:random_seed=1544414186:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.00/1.72 % (1612399)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1938536486:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.00/1.72 % (1612400)lrs+1011_1_sil=32000:sp=occurrence:random_seed=801431378:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.00/1.72 % (1612387)------------------------------
% 5.00/1.72 % (1612387)------------------------------
% 5.00/1.72 % (1612399)Instruction limit reached!
% 5.00/1.72 % (1612399)------------------------------
% 5.00/1.72 % (1612399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612399)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612399)Termination reason: Instruction limit
% 5.00/1.72 % (1612399)Termination phase: Saturation
% 5.00/1.72 % (1612399)Time elapsed: 0.077 s
% 5.00/1.72 % (1612399)Peak memory usage: 91 MB
% 5.00/1.72 % (1612399)Instructions burned: 157 (million)
% 5.00/1.72 % (1612404)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=4003500591:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.00/1.72 % (1612398)Instruction limit reached!
% 5.00/1.72 % (1612398)------------------------------
% 5.00/1.72 % (1612398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612398)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612398)Termination reason: Instruction limit
% 5.00/1.72 % (1612398)Termination phase: Saturation
% 5.00/1.72 % (1612398)Time elapsed: 0.173 s
% 5.00/1.72 % (1612398)Peak memory usage: 93 MB
% 5.00/1.72 % (1612398)Instructions burned: 285 (million)
% 5.00/1.72 % (1612384)First to succeed.
% 5.00/1.72 % (1612384)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1612379"
% 5.00/1.72 % (1612400)Instruction limit reached!
% 5.00/1.72 % (1612400)------------------------------
% 5.00/1.72 % (1612400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612400)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612400)Termination reason: Instruction limit
% 5.00/1.72 % (1612400)Termination phase: Saturation
% 5.00/1.72 % (1612400)Time elapsed: 0.208 s
% 5.00/1.72 % (1612400)Peak memory usage: 91 MB
% 5.00/1.72 % (1612400)Instructions burned: 325 (million)
% 5.00/1.72 % (1612404)Instruction limit reached!
% 5.00/1.72 % (1612404)------------------------------
% 5.00/1.72 % (1612404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612404)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612404)Termination reason: Instruction limit
% 5.00/1.72 % (1612404)Termination phase: Saturation
% 5.00/1.72 % (1612404)Time elapsed: 0.065 s
% 5.00/1.72 % (1612404)Peak memory usage: 94 MB
% 5.00/1.72 % (1612404)Instructions burned: 248 (million)
% 5.00/1.72 % (1612405)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1576229515:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.00/1.72 % (1612407)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3485055623:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.00/1.72 % (1612410)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2949326625:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.00/1.72 % (1612410)Instruction limit reached!
% 5.00/1.72 % (1612410)------------------------------
% 5.00/1.72 % (1612410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612410)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612410)Termination reason: Instruction limit
% 5.00/1.72 % (1612410)Termination phase: Saturation
% 5.00/1.72 % (1612410)Time elapsed: 0.034 s
% 5.00/1.72 % (1612410)Peak memory usage: 89 MB
% 5.00/1.72 % (1612410)Instructions burned: 129 (million)
% 5.00/1.72 % (1612409)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1856955017:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.00/1.72 % (1612405)Instruction limit reached!
% 5.00/1.72 % (1612405)------------------------------
% 5.00/1.72 % (1612405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.72 % (1612405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.72 % (1612405)CaDiCaL version: 2.1.3
% 5.00/1.72 % (1612405)Termination reason: Instruction limit
% 5.00/1.72 % (1612405)Termination phase: Saturation
% 5.00/1.72 % (1612405)Time elapsed: 0.178 s
% 5.00/1.72 % (1612405)Peak memory usage: 90 MB
% 5.00/1.72 % (1612405)Instructions burned: 295 (million)
% 5.00/1.72 % (1612385)Also succeeded, but the first one will report.
% 5.00/1.72 % (1612384)Refutation found. Thanks to Tanya!
% 5.00/1.72 % SZS status Theorem for theBenchmark
% 5.00/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 6.67/1.82 % (1612384)------------------------------
% 6.67/1.82 % (1612384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/1.82 % (1612384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/1.82 % (1612384)CaDiCaL version: 2.1.3
% 6.67/1.82 % (1612384)Termination reason: Refutation
% 6.67/1.82 % (1612384)Time elapsed: 0.468 s
% 6.67/1.82 % (1612384)Peak memory usage: 131 MB
% 6.67/1.82 % (1612384)Instructions burned: 1049 (million)
% 6.67/1.82 % (1612384)------------------------------
% 6.67/1.82 % (1612384)------------------------------
% 6.67/1.82 % (1612379)Success in time 0.871 s
% 6.67/1.82 % Vampire exiting
%------------------------------------------------------------------------------