%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC177+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 : n005.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 01:02:48 PM UTC 2026
% Result : Theorem 6.52s 1.99s
% Output : Refutation 8.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 29
% Syntax : Number of formulae : 211 ( 40 unt; 14 def)
% Number of atoms : 911 ( 166 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 1278 ( 578 ~; 554 |; 81 &)
% ( 21 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 16 con; 0-2 aty)
% Number of variables : 244 ( 0 sgn 217 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
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(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
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(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) )
| neq(X4,X5) ) )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X2
| ~ memberP(X3,X8) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
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)
=> ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) )
| neq(X4,X5) ) )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X2
| ~ memberP(X3,X8) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
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(f114,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f115,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f114]) ).
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(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f184,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ? [X7] :
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ~ neq(X4,X5) )
& ssItem(X4) )
& ( ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X2
& memberP(X3,X8) )
| ( nil = X3
& nil = X2 ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f98]) ).
fof(f233,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(f234,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,[],[f233]) ).
fof(f235,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))],[f234]) ).
fof(f266,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ duplicatefreeP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f115]) ).
fof(f267,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ duplicatefreeP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f266]) ).
fof(f268,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ( sK40(X0) = sK41(X0)
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
& ssList(sK44(X0))
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssItem(sK41(X0))
& ssItem(sK40(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ duplicatefreeP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43,sK44]),skolemize(X1,sK40(X0)),skolemize(X2,sK41(X0)),skolemize(X3,sK42(X0)),skolemize(X4,sK43(X0)),skolemize(X5,sK44(X0))],[f267]) ).
fof(f276,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f146]) ).
fof(f277,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f276]) ).
fof(f278,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f147]) ).
fof(f279,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f278]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f291]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& ssItem(sK58)
& sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60)
& ssList(sK60)
& ssList(sK59)
& ~ neq(sK57,sK58)
& ssItem(sK57)
& ( ( ssItem(sK61)
& sK55 = cons(sK61,nil)
& memberP(sK56,sK61) )
| ( nil = sK56
& nil = sK55 ) )
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61)],[f221]) ).
fof(f297,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f304,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f370,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f387,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f395,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f400,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f414,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f418,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f464,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f476,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f477,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f478,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f479,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f500,plain,
( sK55 = cons(sK61,nil)
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( ssItem(sK61)
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
~ neq(sK57,sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
ssList(sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
ssList(sK60),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f513,plain,
sK55 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(definition_unfolding,[],[f508,f510]) ).
fof(f517,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f304]) ).
fof(f527,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f370]) ).
fof(f528,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ duplicatefreeP(app(app(X8,cons(X7,X9)),cons(X7,X10)))
| ~ ssList(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f527]) ).
fof(f543,definition,
sF62 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[sF62])],[function_definition]) ).
fof(f544,plain,
cons(sK57,nil) = sF62,
inference(reorient_equations,[],[f543]) ).
fof(f545,definition,
sF63 = app(sK59,sF62),
introduced(definition,[new_symbols(definition,[sF63])],[function_definition]) ).
fof(f546,plain,
app(sK59,sF62) = sF63,
inference(reorient_equations,[],[f545]) ).
fof(f547,definition,
sF64 = cons(sK58,nil),
introduced(definition,[new_symbols(definition,[sF64])],[function_definition]) ).
fof(f548,plain,
cons(sK58,nil) = sF64,
inference(reorient_equations,[],[f547]) ).
fof(f549,definition,
sF65 = app(sF63,sF64),
introduced(definition,[new_symbols(definition,[sF65])],[function_definition]) ).
fof(f550,plain,
app(sF63,sF64) = sF65,
inference(reorient_equations,[],[f549]) ).
fof(f551,definition,
sF66 = app(sF65,sK60),
introduced(definition,[new_symbols(definition,[sF66])],[function_definition]) ).
fof(f552,plain,
app(sF65,sK60) = sF66,
inference(reorient_equations,[],[f551]) ).
fof(f553,plain,
sK55 = sF66,
inference(definition_folding,[],[f513,f552,f550,f548,f546,f544]) ).
fof(f554,definition,
sF67 = cons(sK61,nil),
introduced(definition,[new_symbols(definition,[sF67])],[function_definition]) ).
fof(f555,plain,
cons(sK61,nil) = sF67,
inference(reorient_equations,[],[f554]) ).
fof(f557,plain,
( sK55 = sF67
| nil = sK55 ),
inference(definition_folding,[],[f500,f555]) ).
fof(f563,plain,
! [X10,X8,X9,X7] :
( ~ duplicatefreeP(app(app(X8,cons(X7,X9)),cons(X7,X10)))
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssList(X10)
| ~ ssList(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f528]) ).
fof(f566,definition,
( spl68_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl68_1])],[avatar_definition]) ).
fof(f568,plain,
( nil = sK55
| ~ spl68_1 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f580,definition,
( spl68_4
<=> sK55 = sF67 ),
introduced(definition,[new_symbols(definition,[spl68_4])],[avatar_definition]) ).
fof(f582,plain,
( sK55 = sF67
| ~ spl68_4 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f583,plain,
( spl68_1
| spl68_4 ),
inference(avatar_split_clause,[],[f557,f580,f566]) ).
fof(f586,definition,
( spl68_5
<=> ssItem(sK61) ),
introduced(definition,[new_symbols(definition,[spl68_5])],[avatar_definition]) ).
fof(f588,plain,
( ssItem(sK61)
| ~ spl68_5 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f589,plain,
( spl68_1
| spl68_5 ),
inference(avatar_split_clause,[],[f502,f586,f566]) ).
fof(f592,definition,
( spl68_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl68_6])],[avatar_definition]) ).
fof(f593,plain,
( ssList(nil)
| ~ spl68_6 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f620,plain,
spl68_6,
inference(avatar_split_clause,[],[f388,f592]) ).
fof(f623,plain,
sK55 = app(sF65,sK60),
inference(forward_demodulation,[],[f552,f553]) ).
fof(f626,plain,
! [X0] :
( ~ memberP(sF67,X0)
| memberP(nil,X0)
| sK61 = X0
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0) ),
inference(superposition,[],[f415,f555]) ).
fof(f627,plain,
( ! [X0] :
( ~ memberP(sF67,X0)
| memberP(nil,X0)
| sK61 = X0
| ~ ssItem(sK61)
| ~ ssItem(X0) )
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f626,f593]) ).
fof(f630,plain,
( ! [X0] :
( ~ memberP(sF67,X0)
| memberP(nil,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_5
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f627,f588]) ).
fof(f633,plain,
( ! [X0] :
( ~ memberP(sF67,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_5
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f630,f418]) ).
fof(f636,plain,
( ! [X0] :
( ~ memberP(sK55,X0)
| sK61 = X0
| ~ ssItem(X0) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6 ),
inference(forward_demodulation,[],[f633,f582]) ).
fof(f637,plain,
( sK57 = sK58
| ~ ssItem(sK58)
| ~ ssItem(sK57) ),
inference(resolution,[],[f505,f297]) ).
fof(f648,definition,
( spl68_14
<=> sK57 = sK58 ),
introduced(definition,[new_symbols(definition,[spl68_14])],[avatar_definition]) ).
fof(f650,plain,
( sK57 = sK58
| ~ spl68_14 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f652,plain,
( sK57 = sK58
| ~ ssItem(sK57) ),
inference(forward_subsumption_resolution,[],[f637,f509]) ).
fof(f653,plain,
sK57 = sK58,
inference(forward_subsumption_resolution,[],[f652,f504]) ).
fof(f654,plain,
spl68_14,
inference(avatar_split_clause,[],[f653,f648]) ).
fof(f657,plain,
( cons(sK57,nil) = sF64
| ~ spl68_14 ),
inference(superposition,[],[f548,f650]) ).
fof(f658,plain,
( sF62 = sF64
| ~ spl68_14 ),
inference(forward_demodulation,[],[f657,f544]) ).
fof(f660,plain,
( sF65 = app(sF63,sF62)
| ~ spl68_14 ),
inference(superposition,[],[f550,f658]) ).
fof(f662,plain,
! [X0] :
( memberP(app(X0,sF62),sK57)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(app(X0,sF62)) ),
inference(superposition,[],[f517,f544]) ).
fof(f667,plain,
( ! [X0] :
( memberP(app(X0,sF62),sK57)
| ~ ssList(X0)
| ~ ssItem(sK57)
| ~ ssList(app(X0,sF62)) )
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f662,f593]) ).
fof(f670,plain,
( ! [X0] :
( memberP(app(X0,sF62),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,sF62)) )
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f667,f504]) ).
fof(f676,plain,
( nil != sF62
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[],[f395,f544]) ).
fof(f681,plain,
( nil != sF62
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f676,f504]) ).
fof(f684,plain,
( nil != sF62
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f681,f593]) ).
fof(f690,plain,
( nil != sF65
| nil = sF64
| ~ ssList(sF64)
| ~ ssList(sF63) ),
inference(superposition,[],[f479,f550]) ).
fof(f691,plain,
( nil = sF62
| nil != sF65
| ~ ssList(sF64)
| ~ ssList(sF63)
| ~ spl68_14 ),
inference(forward_demodulation,[],[f690,f658]) ).
fof(f693,plain,
( nil != sF65
| ~ ssList(sF64)
| ~ ssList(sF63)
| ~ spl68_6
| ~ spl68_14 ),
inference(forward_subsumption_resolution,[],[f691,f684]) ).
fof(f695,plain,
( ~ ssList(sF62)
| nil != sF65
| ~ ssList(sF63)
| ~ spl68_6
| ~ spl68_14 ),
inference(forward_demodulation,[],[f693,f658]) ).
fof(f697,definition,
( spl68_15
<=> ssList(sF62) ),
introduced(definition,[new_symbols(definition,[spl68_15])],[avatar_definition]) ).
fof(f698,plain,
( ssList(sF62)
| ~ spl68_15 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f699,plain,
( ~ ssList(sF62)
| spl68_15 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f706,definition,
( spl68_17
<=> ssList(sF63) ),
introduced(definition,[new_symbols(definition,[spl68_17])],[avatar_definition]) ).
fof(f707,plain,
( ssList(sF63)
| ~ spl68_17 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f708,plain,
( ~ ssList(sF63)
| spl68_17 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f710,definition,
( spl68_18
<=> nil = sF65 ),
introduced(definition,[new_symbols(definition,[spl68_18])],[avatar_definition]) ).
fof(f712,plain,
( nil != sF65
| spl68_18 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f713,plain,
( ~ spl68_17
| ~ spl68_18
| ~ spl68_15
| ~ spl68_6
| ~ spl68_14 ),
inference(avatar_split_clause,[],[f695,f648,f592,f697,f710,f706]) ).
fof(f715,plain,
( ssList(sF64)
| ~ ssItem(sK58)
| ~ ssList(nil) ),
inference(superposition,[],[f387,f548]) ).
fof(f718,plain,
( ssList(sF64)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f715,f509]) ).
fof(f721,plain,
( ssList(sF64)
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f718,f593]) ).
fof(f724,plain,
( ssList(sF62)
| ~ spl68_6
| ~ spl68_14 ),
inference(forward_demodulation,[],[f721,f658]) ).
fof(f727,plain,
( $false
| ~ spl68_6
| ~ spl68_14
| spl68_15 ),
inference(forward_subsumption_resolution,[],[f724,f699]) ).
fof(f728,plain,
( ~ spl68_6
| ~ spl68_14
| spl68_15 ),
inference(avatar_contradiction_clause,[],[f727]) ).
fof(f735,plain,
( ssList(sF63)
| ~ ssList(sF62)
| ~ ssList(sK59) ),
inference(superposition,[],[f400,f546]) ).
fof(f737,plain,
( ssList(sF65)
| ~ ssList(sF64)
| ~ ssList(sF63) ),
inference(superposition,[],[f400,f550]) ).
fof(f738,plain,
( ~ ssList(sF62)
| ~ ssList(sK59)
| spl68_17 ),
inference(forward_subsumption_resolution,[],[f735,f708]) ).
fof(f739,plain,
( ~ ssList(sK59)
| ~ spl68_15
| spl68_17 ),
inference(forward_subsumption_resolution,[],[f738,f698]) ).
fof(f740,plain,
( $false
| ~ spl68_15
| spl68_17 ),
inference(forward_subsumption_resolution,[],[f739,f506]) ).
fof(f741,plain,
( ~ spl68_15
| spl68_17 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f742,plain,
( ssList(sF65)
| ~ ssList(sF64)
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f737,f707]) ).
fof(f743,plain,
( ~ ssList(sF62)
| ssList(sF65)
| ~ spl68_14
| ~ spl68_17 ),
inference(forward_demodulation,[],[f742,f658]) ).
fof(f744,plain,
( ssList(sF65)
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f743,f698]) ).
fof(f748,plain,
( nil != sK55
| nil = sF65
| ~ ssList(sK60)
| ~ ssList(sF65) ),
inference(superposition,[],[f478,f623]) ).
fof(f765,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK60) = app(cons(X0,nil),sK60) ),
inference(resolution,[],[f476,f507]) ).
fof(f769,plain,
( memberP(sF65,sK57)
| ~ ssList(sF63)
| ~ ssList(sF65)
| ~ spl68_6
| ~ spl68_14 ),
inference(superposition,[],[f670,f660]) ).
fof(f773,plain,
( memberP(sF65,sK57)
| ~ ssList(sF65)
| ~ spl68_6
| ~ spl68_14
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f769,f707]) ).
fof(f774,plain,
( memberP(sF65,sK57)
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f773,f744]) ).
fof(f787,plain,
( duplicatefreeP(sF62)
| ~ ssItem(sK57) ),
inference(superposition,[],[f464,f544]) ).
fof(f792,plain,
duplicatefreeP(sF62),
inference(forward_subsumption_resolution,[],[f787,f504]) ).
fof(f796,plain,
! [X0] :
( memberP(sK55,X0)
| ~ memberP(sF65,X0)
| ~ ssList(sK60)
| ~ ssList(sF65)
| ~ ssItem(X0) ),
inference(superposition,[],[f414,f623]) ).
fof(f801,plain,
! [X0] :
( memberP(sK55,X0)
| ~ memberP(sF65,X0)
| ~ ssList(sF65)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f796,f507]) ).
fof(f805,plain,
( ! [X0] :
( ~ memberP(sF65,X0)
| memberP(sK55,X0)
| ~ ssItem(X0) )
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f801,f744]) ).
fof(f807,plain,
( memberP(sK55,sK57)
| ~ ssItem(sK57)
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(resolution,[],[f805,f774]) ).
fof(f808,plain,
( memberP(sK55,sK57)
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f807,f504]) ).
fof(f809,plain,
( sK57 = sK61
| ~ ssItem(sK57)
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(resolution,[],[f808,f636]) ).
fof(f810,plain,
( sK57 = sK61
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f809,f504]) ).
fof(f813,plain,
( cons(sK61,nil) = sF62
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(superposition,[],[f544,f810]) ).
fof(f818,plain,
( sF62 = sF67
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f813,f555]) ).
fof(f820,plain,
( sK55 = sF62
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f818,f582]) ).
fof(f827,plain,
! [X0,X1] :
( ~ duplicatefreeP(app(app(X0,sF67),cons(sK61,X1)))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK61)
| ~ ssList(X1)
| ~ ssList(app(app(X0,sF67),cons(sK61,X1))) ),
inference(superposition,[],[f563,f555]) ).
fof(f834,plain,
( ! [X0,X1] :
( ~ duplicatefreeP(app(app(X0,sF67),cons(sK61,X1)))
| ~ ssList(X0)
| ~ ssItem(sK61)
| ~ ssList(X1)
| ~ ssList(app(app(X0,sF67),cons(sK61,X1))) )
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f827,f593]) ).
fof(f880,plain,
cons(sK57,sK60) = app(cons(sK57,nil),sK60),
inference(resolution,[],[f765,f504]) ).
fof(f883,plain,
cons(sK57,sK60) = app(sF62,sK60),
inference(forward_demodulation,[],[f880,f544]) ).
fof(f952,plain,
! [X0,X1] :
( ~ ssList(X1)
| app(app(X0,X1),sK60) = app(X0,app(X1,sK60))
| ~ ssList(X0) ),
inference(resolution,[],[f477,f507]) ).
fof(f965,plain,
( ! [X0] :
( app(app(X0,sF62),sK60) = app(X0,app(sF62,sK60))
| ~ ssList(X0) )
| ~ spl68_15 ),
inference(resolution,[],[f952,f698]) ).
fof(f1105,plain,
( ! [X0] :
( ~ ssList(X0)
| app(app(X0,sF62),sK60) = app(X0,cons(sK57,sK60)) )
| ~ spl68_15 ),
inference(forward_demodulation,[],[f965,f883]) ).
fof(f1109,plain,
( nil = sF65
| ~ ssList(sK60)
| ~ ssList(sF65)
| ~ spl68_1 ),
inference(forward_subsumption_resolution,[],[f748,f568]) ).
fof(f1114,plain,
( ~ ssList(sK60)
| ~ ssList(sF65)
| ~ spl68_1
| spl68_18 ),
inference(forward_subsumption_resolution,[],[f1109,f712]) ).
fof(f1117,plain,
( ~ ssList(sF65)
| ~ spl68_1
| spl68_18 ),
inference(forward_subsumption_resolution,[],[f1114,f507]) ).
fof(f1118,plain,
( $false
| ~ spl68_1
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17
| spl68_18 ),
inference(forward_subsumption_resolution,[],[f1117,f744]) ).
fof(f1119,plain,
( ~ spl68_1
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17
| spl68_18 ),
inference(avatar_contradiction_clause,[],[f1118]) ).
fof(f1128,plain,
( ! [X0,X1] :
( ~ duplicatefreeP(app(app(X0,sF67),cons(sK61,X1)))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,sF67),cons(sK61,X1))) )
| ~ spl68_5
| ~ spl68_6 ),
inference(forward_subsumption_resolution,[],[f834,f588]) ).
fof(f1143,plain,
( ! [X0,X1] :
( ~ duplicatefreeP(app(app(X0,sK55),cons(sK61,X1)))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,sF67),cons(sK61,X1))) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6 ),
inference(forward_demodulation,[],[f1128,f582]) ).
fof(f1151,plain,
( ! [X0,X1] :
( ~ duplicatefreeP(app(app(X0,sF62),cons(sK61,X1)))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,sF67),cons(sK61,X1))) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1143,f820]) ).
fof(f1155,plain,
( ! [X0,X1] :
( ~ ssList(app(app(X0,sK55),cons(sK61,X1)))
| ~ duplicatefreeP(app(app(X0,sF62),cons(sK61,X1)))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1151,f582]) ).
fof(f1158,plain,
( ! [X0,X1] :
( ~ duplicatefreeP(app(app(X0,sF62),cons(sK61,X1)))
| ~ ssList(app(app(X0,sF62),cons(sK61,X1)))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1155,f820]) ).
fof(f1196,plain,
( app(app(sF63,sF62),sK60) = app(sF63,cons(sK57,sK60))
| ~ spl68_15
| ~ spl68_17 ),
inference(resolution,[],[f1105,f707]) ).
fof(f1199,plain,
( app(app(sF63,sF62),sK60) = app(sF63,cons(sK61,sK60))
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1196,f810]) ).
fof(f1209,plain,
( app(sF65,sK60) = app(sF63,cons(sK61,sK60))
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1199,f660]) ).
fof(f1214,plain,
( sK55 = app(sF63,cons(sK61,sK60))
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1209,f623]) ).
fof(f1217,plain,
( sF62 = app(sF63,cons(sK61,sK60))
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_demodulation,[],[f1214,f820]) ).
fof(f1428,plain,
( ! [X0] :
( ~ duplicatefreeP(app(sF63,cons(sK61,X0)))
| ~ ssList(app(sF63,cons(sK61,X0)))
| ~ ssList(sK59)
| ~ ssList(X0) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(superposition,[],[f1158,f546]) ).
fof(f1433,plain,
( ! [X0] :
( ~ duplicatefreeP(app(sF63,cons(sK61,X0)))
| ~ ssList(app(sF63,cons(sK61,X0)))
| ~ ssList(X0) )
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1428,f506]) ).
fof(f1439,plain,
( ~ duplicatefreeP(sF62)
| ~ ssList(sF62)
| ~ ssList(sK60)
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(superposition,[],[f1433,f1217]) ).
fof(f1440,plain,
( ~ ssList(sF62)
| ~ ssList(sK60)
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1439,f792]) ).
fof(f1442,plain,
( ~ ssList(sK60)
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1440,f698]) ).
fof(f1444,plain,
( $false
| ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(forward_subsumption_resolution,[],[f1442,f507]) ).
fof(f1445,plain,
( ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(avatar_contradiction_clause,[],[f1444]) ).
cnf(s3,plain,
( spl68_1
| spl68_4 ),
inference(sat_conversion,[],[f583]) ).
cnf(s5,plain,
( spl68_1
| spl68_5 ),
inference(sat_conversion,[],[f589]) ).
cnf(s14,plain,
spl68_6,
inference(sat_conversion,[],[f620]) ).
cnf(s16,plain,
spl68_14,
inference(sat_conversion,[],[f654]) ).
cnf(s19,plain,
( ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17
| ~ spl68_18 ),
inference(sat_conversion,[],[f713]) ).
cnf(s21,plain,
( ~ spl68_6
| ~ spl68_14
| spl68_15 ),
inference(sat_conversion,[],[f728]) ).
cnf(s22,plain,
( ~ spl68_15
| spl68_17 ),
inference(sat_conversion,[],[f741]) ).
cnf(s31,plain,
( ~ spl68_1
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17
| spl68_18 ),
inference(sat_conversion,[],[f1119]) ).
cnf(s42,plain,
( ~ spl68_4
| ~ spl68_5
| ~ spl68_6
| ~ spl68_14
| ~ spl68_15
| ~ spl68_17 ),
inference(sat_conversion,[],[f1445]) ).
cnf(s43,plain,
spl68_15,
inference(rat,[],[s21,s16,s14]) ).
cnf(s44,plain,
spl68_17,
inference(rat,[],[s22,s43]) ).
cnf(s46,plain,
~ spl68_18,
inference(rat,[],[s19,s43,s14,s16,s44]) ).
cnf(s47,plain,
~ spl68_1,
inference(rat,[],[s31,s43,s44,s16,s46]) ).
cnf(s51,plain,
spl68_5,
inference(rat,[],[s5,s47]) ).
cnf(s52,plain,
~ spl68_4,
inference(rat,[],[s42,s44,s43,s16,s14,s51]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s3,s52,s47]) ).
fof(f1452,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC177+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 08:16:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 6.52/1.99 % (635532)Detected formulas, will run a generic FOF schedule.
% 6.52/1.99 % (635541)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=124085891:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.52/1.99 % (635537)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=1730322753:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.52/1.99 % (635538)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=3922849518:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.52/1.99 % (635539)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=1846788254:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.52/1.99 % (635540)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2003579024:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.52/1.99 % (635541)Instruction limit reached!
% 6.52/1.99 % (635541)------------------------------
% 6.52/1.99 % (635541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635541)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635541)Termination reason: Instruction limit
% 6.52/1.99 % (635541)Termination phase: Saturation
% 6.52/1.99 % (635541)Time elapsed: 0.036 s
% 6.52/1.99 % (635541)Peak memory usage: 88 MB
% 6.52/1.99 % (635541)Instructions burned: 121 (million)
% 6.52/1.99 % (635543)dis-21_1_sil=8000:lcm=predicate:random_seed=3911543683: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)
% 6.52/1.99 % (635542)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3721858709:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.52/1.99 % (635540)Instruction limit reached!
% 6.52/1.99 % (635540)------------------------------
% 6.52/1.99 % (635540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635540)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635540)Termination reason: Instruction limit
% 6.52/1.99 % (635540)Termination phase: Saturation
% 6.52/1.99 % (635540)Time elapsed: 0.067 s
% 6.52/1.99 % (635540)Peak memory usage: 89 MB
% 6.52/1.99 % (635540)Instructions burned: 109 (million)
% 6.52/1.99 % (635543)Instruction limit reached!
% 6.52/1.99 % (635543)------------------------------
% 6.52/1.99 % (635543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635543)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635543)Termination reason: Instruction limit
% 6.52/1.99 % (635543)Termination phase: Saturation
% 6.52/1.99 % (635543)Time elapsed: 0.077 s
% 6.52/1.99 % (635543)Peak memory usage: 90 MB
% 6.52/1.99 % (635543)Instructions burned: 131 (million)
% 6.52/1.99 % (635542)Instruction limit reached!
% 6.52/1.99 % (635542)------------------------------
% 6.52/1.99 % (635542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635542)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635542)Termination reason: Instruction limit
% 6.52/1.99 % (635542)Termination phase: Saturation
% 6.52/1.99 % (635542)Time elapsed: 0.095 s
% 6.52/1.99 % (635542)Peak memory usage: 90 MB
% 6.52/1.99 % (635542)Instructions burned: 139 (million)
% 6.52/1.99 % (635549)lrs+10_1_sil=8000:sp=occurrence:random_seed=617662177:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.52/1.99 % (635549)Instruction limit reached!
% 6.52/1.99 % (635549)------------------------------
% 6.52/1.99 % (635549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635549)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635549)Termination reason: Instruction limit
% 6.52/1.99 % (635549)Termination phase: Saturation
% 6.52/1.99 % (635549)Time elapsed: 0.093 s
% 6.52/1.99 % (635549)Peak memory usage: 92 MB
% 6.52/1.99 % (635549)Instructions burned: 285 (million)
% 6.52/1.99 % (635552)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2553335803:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.52/1.99 % (635553)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1505121488:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.52/1.99 % (635555)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=3688303245:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.52/1.99 % (635552)Instruction limit reached!
% 6.52/1.99 % (635552)------------------------------
% 6.52/1.99 % (635552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635552)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635552)Termination reason: Instruction limit
% 6.52/1.99 % (635552)Termination phase: Saturation
% 6.52/1.99 % (635552)Time elapsed: 0.077 s
% 6.52/1.99 % (635552)Peak memory usage: 92 MB
% 6.52/1.99 % (635552)Instructions burned: 159 (million)
% 6.52/1.99 % (635556)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2500399121:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.52/1.99 % (635555)Instruction limit reached!
% 6.52/1.99 % (635555)------------------------------
% 6.52/1.99 % (635555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635555)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635555)Termination reason: Instruction limit
% 6.52/1.99 % (635555)Termination phase: Saturation
% 6.52/1.99 % (635555)Time elapsed: 0.120 s
% 6.52/1.99 % (635555)Peak memory usage: 94 MB
% 6.52/1.99 % (635555)Instructions burned: 250 (million)
% 6.52/1.99 % (635556)Instruction limit reached!
% 6.52/1.99 % (635556)------------------------------
% 6.52/1.99 % (635556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635556)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635556)Termination reason: Instruction limit
% 6.52/1.99 % (635556)Termination phase: Saturation
% 6.52/1.99 % (635556)Time elapsed: 0.098 s
% 6.52/1.99 % (635556)Peak memory usage: 90 MB
% 6.52/1.99 % (635556)Instructions burned: 297 (million)
% 6.52/1.99 % (635553)Instruction limit reached!
% 6.52/1.99 % (635553)------------------------------
% 6.52/1.99 % (635553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635553)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635553)Termination reason: Instruction limit
% 6.52/1.99 % (635553)Termination phase: Saturation
% 6.52/1.99 % (635553)Time elapsed: 0.203 s
% 6.52/1.99 % (635553)Peak memory usage: 92 MB
% 6.52/1.99 % (635553)Instructions burned: 326 (million)
% 6.52/1.99 % (635560)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=790282845:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.52/1.99 % (635562)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1912859384:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.52/1.99 % (635563)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=921648449:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.52/1.99 % (635563)Instruction limit reached!
% 6.52/1.99 % (635563)------------------------------
% 6.52/1.99 % (635563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635563)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635563)Termination reason: Instruction limit
% 6.52/1.99 % (635563)Termination phase: Saturation
% 6.52/1.99 % (635563)Time elapsed: 0.034 s
% 6.52/1.99 % (635563)Peak memory usage: 89 MB
% 6.52/1.99 % (635563)Instructions burned: 127 (million)
% 6.52/1.99 % (635564)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3640885150:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.52/1.99 % (635562)Instruction limit reached!
% 6.52/1.99 % (635562)------------------------------
% 6.52/1.99 % (635562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635562)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635562)Termination reason: Instruction limit
% 6.52/1.99 % (635562)Termination phase: Saturation
% 6.52/1.99 % (635562)Time elapsed: 0.077 s
% 6.52/1.99 % (635562)Peak memory usage: 90 MB
% 6.52/1.99 % (635562)Instructions burned: 114 (million)
% 6.52/1.99 % (635564)Instruction limit reached!
% 6.52/1.99 % (635564)------------------------------
% 6.52/1.99 % (635564)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635564)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635564)Termination reason: Instruction limit
% 6.52/1.99 % (635564)Termination phase: Saturation
% 6.52/1.99 % (635564)Time elapsed: 0.066 s
% 6.52/1.99 % (635564)Peak memory usage: 89 MB
% 6.52/1.99 % (635564)Instructions burned: 114 (million)
% 6.52/1.99 % (635568)lrs+10_1_sil=8000:sp=occurrence:random_seed=1722916714:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.52/1.99 % (635537)First to succeed.
% 6.52/1.99 % (635537)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-635532"
% 6.52/1.99 % (635570)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1269737224:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.52/1.99 % (635571)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2099847214:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.52/1.99 % (635568)Instruction limit reached!
% 6.52/1.99 % (635568)------------------------------
% 6.52/1.99 % (635568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.52/1.99 % (635568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.52/1.99 % (635568)CaDiCaL version: 2.1.3
% 6.52/1.99 % (635568)Termination reason: Instruction limit
% 6.52/1.99 % (635568)Termination phase: Saturation
% 6.52/1.99 % (635568)Time elapsed: 0.276 s
% 6.52/1.99 % (635568)Peak memory usage: 100 MB
% 6.52/1.99 % (635568)Instructions burned: 910 (million)
% 6.52/1.99 % (635537)Refutation found. Thanks to Tanya!
% 6.52/1.99 % SZS status Theorem for theBenchmark
% 6.52/1.99 % SZS output start Proof for theBenchmark
% See solution above
% 8.68/2.08 % (635537)------------------------------
% 8.68/2.08 % (635537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.68/2.08 % (635537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.68/2.08 % (635537)CaDiCaL version: 2.1.3
% 8.68/2.08 % (635537)Termination reason: Refutation
% 8.68/2.08 % (635537)Time elapsed: 0.740 s
% 8.68/2.08 % (635537)Peak memory usage: 130 MB
% 8.68/2.08 % (635537)Instructions burned: 1110 (million)
% 8.68/2.08 % (635537)------------------------------
% 8.68/2.08 % (635537)------------------------------
% 8.68/2.08 % (635532)Success in time 1.162 s
% 8.68/2.08 % Vampire exiting
%------------------------------------------------------------------------------