TSTP Solution File: SWC165+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC165+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:41:25 EDT 2023
% Result : Theorem 273.86s 36.84s
% Output : CNFRefutation 274.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 52
% Syntax : Number of formulae : 373 ( 66 unt; 0 def)
% Number of atoms : 1588 ( 495 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 1932 ( 717 ~; 739 |; 356 &)
% ( 16 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-2 aty)
% Number of variables : 667 ( 0 sgn; 314 !; 168 ?)
% 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] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,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)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
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(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
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 = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X12] :
( lt(X12,X8)
& memberP(X10,X12)
& ssItem(X12) )
| ? [X11] :
( lt(X8,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,X2),X10) != X3
| cons(X8,nil) != X2 ) ) ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( neq(X4,X5)
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ? [X12] :
( lt(X12,X8)
& memberP(X10,X12)
& ssItem(X12) )
| ? [X11] :
( lt(X8,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,X2),X10) != X3
| cons(X8,nil) != X2 ) ) ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( neq(X4,X5)
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0 ) ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X7] :
( lt(X7,X4)
& memberP(X6,X7)
& ssItem(X7) )
| ? [X8] :
( lt(X4,X8)
& memberP(X5,X8)
& ssItem(X8) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2 ) ) ) ) )
| ! [X9] :
( ssItem(X9)
=> ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssList(X11)
=> ! [X12] :
( ssList(X12)
=> ( neq(X9,X10)
| app(app(app(X11,cons(X9,nil)),cons(X10,nil)),X12) != X0 ) ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f122]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f131,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f130]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f149,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f152]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f171]) ).
fof(f187,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f188,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f190,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f194,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f200,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(f201,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ~ neq(X9,X10)
& app(app(app(X11,cons(X9,nil)),cons(X10,nil)),X12) = X0
& ssList(X12) )
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ~ neq(X9,X10)
& app(app(app(X11,cons(X9,nil)),cons(X10,nil)),X12) = X0
& ssList(X12) )
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f233,plain,
! [X3,X2] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP6(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f234,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X9] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ~ neq(X9,X10)
& app(app(app(X11,cons(X9,nil)),cons(X10,nil)),X12) = X0
& ssList(X12) )
& ssList(X11) )
& ssItem(X10) )
& ssItem(X9) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f223,f233]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f240,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f239]) ).
fof(f241,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK9(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f242,plain,
! [X0,X1] :
( ? [X5] :
( app(sK9(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
& ssList(sK10(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f243,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f240,f242,f241]) ).
fof(f244,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f245,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f244]) ).
fof(f246,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f247,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f245,f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f249,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f248]) ).
fof(f250,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK12(X0,X1)) = X0
& ssList(sK12(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK12(X0,X1)) = X0
& ssList(sK12(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f249,f250]) ).
fof(f256,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f256]) ).
fof(f258,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK14(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK14(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
& ssList(sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
& ssList(sK15(X0,X1))
& ssList(sK14(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f257,f259,f258]) ).
fof(f325,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f147]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f325]) ).
fof(f327,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f328,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f327]) ).
fof(f338,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK52(X0)
& ssItem(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ( hd(X0) = sK52(X0)
& ssItem(sK52(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f188,f338]) ).
fof(f340,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK53(X0)
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ( tl(X0) = sK53(X0)
& ssList(sK53(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f190,f340]) ).
fof(f342,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f343,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f342]) ).
fof(f346,plain,
! [X3,X2] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP6(X3,X2) ),
inference(nnf_transformation,[],[f233]) ).
fof(f347,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,X2)
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(X2,X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(X2,nil) = X1
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f346]) ).
fof(f348,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,X2)
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(X2,X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(X2,nil) = X1
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
& ssList(X3) )
& ssItem(sK54(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0,X1] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
& ssList(sK55(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0,X1] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
=> ( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(sK56(X0,X1),X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(sK56(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0,X1] :
( ( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(sK56(X0,X1),X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(sK56(X0,X1))
& ssList(sK55(X0,X1))
& ssItem(sK54(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56])],[f347,f350,f349,f348]) ).
fof(f352,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f234]) ).
fof(f353,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
( ? [X3] :
( ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
=> ( ( ( nil = sK59
& nil = sK60 )
| sP6(sK60,sK59) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60) ) ),
introduced(choice_axiom,[]) ).
fof(f357,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(X4,X5)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = sK57
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(sK61,X5)
& sK57 = app(app(app(X6,cons(sK61,nil)),cons(X5,nil)),X7)
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(sK61) ) ),
introduced(choice_axiom,[]) ).
fof(f358,plain,
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ~ neq(sK61,X5)
& sK57 = app(app(app(X6,cons(sK61,nil)),cons(X5,nil)),X7)
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
=> ( ? [X6] :
( ? [X7] :
( ~ neq(sK61,sK62)
& sK57 = app(app(app(X6,cons(sK61,nil)),cons(sK62,nil)),X7)
& ssList(X7) )
& ssList(X6) )
& ssItem(sK62) ) ),
introduced(choice_axiom,[]) ).
fof(f359,plain,
( ? [X6] :
( ? [X7] :
( ~ neq(sK61,sK62)
& sK57 = app(app(app(X6,cons(sK61,nil)),cons(sK62,nil)),X7)
& ssList(X7) )
& ssList(X6) )
=> ( ? [X7] :
( ~ neq(sK61,sK62)
& sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),X7)
& ssList(X7) )
& ssList(sK63) ) ),
introduced(choice_axiom,[]) ).
fof(f360,plain,
( ? [X7] :
( ~ neq(sK61,sK62)
& sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),X7)
& ssList(X7) )
=> ( ~ neq(sK61,sK62)
& sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64)
& ssList(sK64) ) ),
introduced(choice_axiom,[]) ).
fof(f361,plain,
( ( ( nil = sK59
& nil = sK60 )
| sP6(sK60,sK59) )
& ~ neq(sK61,sK62)
& sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64)
& ssList(sK64)
& ssList(sK63)
& ssItem(sK62)
& ssItem(sK61)
& sK57 = sK59
& sK58 = sK60
& ssList(sK60)
& ssList(sK59)
& ssList(sK58)
& ssList(sK57) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60,sK61,sK62,sK63,sK64])],[f352,f360,f359,f358,f357,f356,f355,f354,f353]) ).
fof(f363,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f372,plain,
! [X0] :
( cons(sK11(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f373,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f376,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f453,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f454,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f455,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f457,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f461,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f464,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f466,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f468,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f479,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f481,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f484,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f487,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f504,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f534,plain,
! [X0] :
( ssItem(sK52(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f535,plain,
! [X0] :
( hd(X0) = sK52(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f536,plain,
! [X0] :
( ssList(sK53(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f537,plain,
! [X0] :
( tl(X0) = sK53(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f539,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f542,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f543,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f200]) ).
fof(f544,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f545,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f547,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f561,plain,
! [X0,X1] :
( ssItem(sK54(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f351]) ).
fof(f564,plain,
! [X0,X1] :
( cons(sK54(X0,X1),nil) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f351]) ).
fof(f568,plain,
ssList(sK57),
inference(cnf_transformation,[],[f361]) ).
fof(f573,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f361]) ).
fof(f574,plain,
ssItem(sK61),
inference(cnf_transformation,[],[f361]) ).
fof(f575,plain,
ssItem(sK62),
inference(cnf_transformation,[],[f361]) ).
fof(f576,plain,
ssList(sK63),
inference(cnf_transformation,[],[f361]) ).
fof(f577,plain,
ssList(sK64),
inference(cnf_transformation,[],[f361]) ).
fof(f578,plain,
sK57 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64),
inference(cnf_transformation,[],[f361]) ).
fof(f579,plain,
~ neq(sK61,sK62),
inference(cnf_transformation,[],[f361]) ).
fof(f580,plain,
( nil = sK60
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f361]) ).
fof(f581,plain,
( nil = sK59
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f361]) ).
fof(f582,plain,
sK59 = app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64),
inference(definition_unfolding,[],[f578,f573]) ).
fof(f584,plain,
ssList(sK59),
inference(definition_unfolding,[],[f568,f573]) ).
fof(f586,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f370]) ).
fof(f587,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f373]) ).
fof(f588,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f376]) ).
fof(f590,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f383]) ).
cnf(c_49,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f363]) ).
cnf(c_54,plain,
( ~ ssList(app(X0,cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ),
inference(cnf_transformation,[],[f586]) ).
cnf(c_58,plain,
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f587]) ).
cnf(c_59,plain,
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sK11(X0),nil) = X0 ),
inference(cnf_transformation,[],[f372]) ).
cnf(c_61,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(cnf_transformation,[],[f588]) ).
cnf(c_67,plain,
( ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f590]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f453]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f454]) ).
cnf(c_142,plain,
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f455]) ).
cnf(c_143,plain,
( cons(X0,X1) != cons(X2,X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f457]) ).
cnf(c_148,plain,
( cons(X0,X1) != nil
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f461]) ).
cnf(c_151,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f464]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f466]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f468]) ).
cnf(c_166,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f479]) ).
cnf(c_170,plain,
( ~ memberP(cons(X0,X1),X2)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2) ),
inference(cnf_transformation,[],[f481]) ).
cnf(c_171,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f484]) ).
cnf(c_174,plain,
( ~ frontsegP(X0,X1)
| ~ frontsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f487]) ).
cnf(c_191,plain,
( ~ segmentP(X0,X1)
| ~ segmentP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f504]) ).
cnf(c_219,plain,
( ~ ssList(X0)
| hd(X0) = sK52(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f535]) ).
cnf(c_220,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(sK52(X0)) ),
inference(cnf_transformation,[],[f534]) ).
cnf(c_221,plain,
( ~ ssList(X0)
| tl(X0) = sK53(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f537]) ).
cnf(c_222,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(sK53(X0)) ),
inference(cnf_transformation,[],[f536]) ).
cnf(c_224,plain,
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f539]) ).
cnf(c_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f542]) ).
cnf(c_228,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2)) ),
inference(cnf_transformation,[],[f543]) ).
cnf(c_230,plain,
( app(X0,X1) != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = nil ),
inference(cnf_transformation,[],[f545]) ).
cnf(c_231,plain,
( app(X0,X1) != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X1 = nil ),
inference(cnf_transformation,[],[f544]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f547]) ).
cnf(c_249,plain,
( ~ sP6(X0,X1)
| cons(sK54(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f564]) ).
cnf(c_252,plain,
( ~ sP6(X0,X1)
| ssItem(sK54(X0,X1)) ),
inference(cnf_transformation,[],[f561]) ).
cnf(c_253,negated_conjecture,
( nil = sK59
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f581]) ).
cnf(c_254,negated_conjecture,
( nil = sK60
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f580]) ).
cnf(c_255,negated_conjecture,
~ neq(sK61,sK62),
inference(cnf_transformation,[],[f579]) ).
cnf(c_256,negated_conjecture,
app(app(app(sK63,cons(sK61,nil)),cons(sK62,nil)),sK64) = sK59,
inference(cnf_transformation,[],[f582]) ).
cnf(c_257,negated_conjecture,
ssList(sK64),
inference(cnf_transformation,[],[f577]) ).
cnf(c_258,negated_conjecture,
ssList(sK63),
inference(cnf_transformation,[],[f576]) ).
cnf(c_259,negated_conjecture,
ssItem(sK62),
inference(cnf_transformation,[],[f575]) ).
cnf(c_260,negated_conjecture,
ssItem(sK61),
inference(cnf_transformation,[],[f574]) ).
cnf(c_264,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f584]) ).
cnf(c_393,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(app(X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
cnf(c_3323,plain,
( X0 != sK61
| X1 != sK62
| ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_49,c_255]) ).
cnf(c_3324,plain,
( ~ ssItem(sK61)
| ~ ssItem(sK62)
| sK61 = sK62 ),
inference(unflattening,[status(thm)],[c_3323]) ).
cnf(c_3325,plain,
sK61 = sK62,
inference(global_subsumption_just,[status(thm)],[c_3324,c_260,c_259,c_3324]) ).
cnf(c_3331,plain,
( X0 != sK60
| X1 != sK59
| nil = sK60
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_254]) ).
cnf(c_3332,plain,
( nil = sK60
| ssItem(sK54(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3331]) ).
cnf(c_3339,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_253]) ).
cnf(c_3340,plain,
( nil = sK59
| ssItem(sK54(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3339]) ).
cnf(c_3379,plain,
( X0 != sK60
| X1 != sK59
| cons(sK54(X0,X1),nil) = X1
| nil = sK60 ),
inference(resolution_lifted,[status(thm)],[c_249,c_254]) ).
cnf(c_3380,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK60 ),
inference(unflattening,[status(thm)],[c_3379]) ).
cnf(c_3387,plain,
( X0 != sK60
| X1 != sK59
| cons(sK54(X0,X1),nil) = X1
| nil = sK59 ),
inference(resolution_lifted,[status(thm)],[c_249,c_253]) ).
cnf(c_3388,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK59 ),
inference(unflattening,[status(thm)],[c_3387]) ).
cnf(c_6897,plain,
app(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK64) = sK59,
inference(light_normalisation,[status(thm)],[c_256,c_3325]) ).
cnf(c_13422,plain,
app(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK64) = sK59,
inference(subtyping,[status(esa)],[c_6897]) ).
cnf(c_13429,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK59 ),
inference(subtyping,[status(esa)],[c_3388]) ).
cnf(c_13430,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK60 ),
inference(subtyping,[status(esa)],[c_3380]) ).
cnf(c_13435,plain,
( nil = sK59
| ssItem(sK54(sK60,sK59)) ),
inference(subtyping,[status(esa)],[c_3340]) ).
cnf(c_13436,plain,
( nil = sK60
| ssItem(sK54(sK60,sK59)) ),
inference(subtyping,[status(esa)],[c_3332]) ).
cnf(c_13444,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| frontsegP(app(X0_13,X1_13),X0_13) ),
inference(subtyping,[status(esa)],[c_393]) ).
cnf(c_13450,negated_conjecture,
ssList(sK59),
inference(subtyping,[status(esa)],[c_264]) ).
cnf(c_13452,negated_conjecture,
ssItem(sK61),
inference(subtyping,[status(esa)],[c_260]) ).
cnf(c_13453,negated_conjecture,
ssList(sK63),
inference(subtyping,[status(esa)],[c_258]) ).
cnf(c_13454,negated_conjecture,
ssList(sK64),
inference(subtyping,[status(esa)],[c_257]) ).
cnf(c_13466,plain,
( ~ ssList(X0_13)
| app(X0_13,nil) = X0_13 ),
inference(subtyping,[status(esa)],[c_232]) ).
cnf(c_13467,plain,
( app(X0_13,X1_13) != nil
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| X1_13 = nil ),
inference(subtyping,[status(esa)],[c_231]) ).
cnf(c_13468,plain,
( app(X0_13,X1_13) != nil
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_230]) ).
cnf(c_13469,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| app(app(X0_13,X1_13),X2_13) = app(X0_13,app(X1_13,X2_13)) ),
inference(subtyping,[status(esa)],[c_228]) ).
cnf(c_13470,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| app(cons(X0_14,nil),X0_13) = cons(X0_14,X0_13) ),
inference(subtyping,[status(esa)],[c_227]) ).
cnf(c_13473,plain,
( ~ ssList(X0_13)
| cons(hd(X0_13),tl(X0_13)) = X0_13
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_224]) ).
cnf(c_13475,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssList(sK53(X0_13)) ),
inference(subtyping,[status(esa)],[c_222]) ).
cnf(c_13476,plain,
( ~ ssList(X0_13)
| tl(X0_13) = sK53(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_221]) ).
cnf(c_13477,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssItem(sK52(X0_13)) ),
inference(subtyping,[status(esa)],[c_220]) ).
cnf(c_13478,plain,
( ~ ssList(X0_13)
| hd(X0_13) = sK52(X0_13)
| X0_13 = nil ),
inference(subtyping,[status(esa)],[c_219]) ).
cnf(c_13497,plain,
( ~ segmentP(X0_13,X1_13)
| ~ segmentP(X1_13,X0_13)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_191]) ).
cnf(c_13512,plain,
( ~ frontsegP(X0_13,X1_13)
| ~ frontsegP(X1_13,X0_13)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_174]) ).
cnf(c_13515,plain,
( ~ memberP(nil,X0_14)
| ~ ssItem(X0_14) ),
inference(subtyping,[status(esa)],[c_171]) ).
cnf(c_13516,plain,
( ~ memberP(cons(X0_14,X0_13),X1_14)
| ~ ssItem(X0_14)
| ~ ssItem(X1_14)
| ~ ssList(X0_13)
| X0_14 = X1_14
| memberP(X0_13,X1_14) ),
inference(subtyping,[status(esa)],[c_170]) ).
cnf(c_13520,plain,
( ~ memberP(X0_13,X0_14)
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| memberP(app(X0_13,X1_13),X0_14) ),
inference(subtyping,[status(esa)],[c_166]) ).
cnf(c_13531,plain,
( ~ ssList(X0_13)
| app(nil,X0_13) = X0_13 ),
inference(subtyping,[status(esa)],[c_155]) ).
cnf(c_13533,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ssList(app(X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_153]) ).
cnf(c_13535,plain,
( ~ ssList(X0_13)
| X0_13 = nil
| ssList(tl(X0_13)) ),
inference(subtyping,[status(esa)],[c_151]) ).
cnf(c_13538,plain,
( cons(X0_14,X0_13) != nil
| ~ ssItem(X0_14)
| ~ ssList(X0_13) ),
inference(subtyping,[status(esa)],[c_148]) ).
cnf(c_13543,plain,
( cons(X0_14,X0_13) != cons(X1_14,X1_13)
| ~ ssItem(X0_14)
| ~ ssItem(X1_14)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_143]) ).
cnf(c_13544,plain,
( cons(X0_14,X0_13) != X0_13
| ~ ssItem(X0_14)
| ~ ssList(X0_13) ),
inference(subtyping,[status(esa)],[c_142]) ).
cnf(c_13545,plain,
ssList(nil),
inference(subtyping,[status(esa)],[c_141]) ).
cnf(c_13546,plain,
( ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ssList(cons(X0_14,X0_13)) ),
inference(subtyping,[status(esa)],[c_140]) ).
cnf(c_13608,plain,
( ~ ssList(app(app(X0_13,X1_13),X2_13))
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_13614,plain,
( ~ ssList(X0_13)
| ~ singletonP(X0_13)
| cons(sK11(X0_13),nil) = X0_13 ),
inference(subtyping,[status(esa)],[c_59]) ).
cnf(c_13615,plain,
( ~ ssList(cons(X0_14,nil))
| ~ ssItem(X0_14)
| singletonP(cons(X0_14,nil)) ),
inference(subtyping,[status(esa)],[c_58]) ).
cnf(c_13619,plain,
( ~ ssList(app(X0_13,cons(X0_14,X1_13)))
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| memberP(app(X0_13,cons(X0_14,X1_13)),X0_14) ),
inference(subtyping,[status(esa)],[c_54]) ).
cnf(c_13624,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_13625,plain,
X0_14 = X0_14,
theory(equality) ).
cnf(c_13626,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_13627,plain,
( X0_14 != X1_14
| X2_14 != X1_14
| X2_14 = X0_14 ),
theory(equality) ).
cnf(c_13629,plain,
( X0_13 != X1_13
| X0_14 != X1_14
| cons(X0_14,X0_13) = cons(X1_14,X1_13) ),
theory(equality) ).
cnf(c_13632,plain,
( X0_13 != X1_13
| ~ ssList(X1_13)
| ssList(X0_13) ),
theory(equality) ).
cnf(c_13659,plain,
nil = nil,
inference(instantiation,[status(thm)],[c_13624]) ).
cnf(c_13660,plain,
sK61 = sK61,
inference(instantiation,[status(thm)],[c_13625]) ).
cnf(c_13679,plain,
( ~ memberP(nil,sK61)
| ~ ssItem(sK61) ),
inference(instantiation,[status(thm)],[c_13515]) ).
cnf(c_13689,plain,
( cons(sK61,nil) != nil
| ~ ssItem(sK61)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_13538]) ).
cnf(c_13690,plain,
( ~ ssItem(sK61)
| ~ ssList(nil)
| ssList(cons(sK61,nil)) ),
inference(instantiation,[status(thm)],[c_13546]) ).
cnf(c_16694,plain,
( app(X0_13,cons(X0_14,X1_13)) != nil
| ~ ssList(cons(X0_14,X1_13))
| ~ ssList(X0_13)
| cons(X0_14,X1_13) = nil ),
inference(instantiation,[status(thm)],[c_13467]) ).
cnf(c_16781,plain,
( ~ ssList(cons(X0_14,X0_13))
| ~ ssList(X1_13)
| ssList(app(X1_13,cons(X0_14,X0_13))) ),
inference(instantiation,[status(thm)],[c_13533]) ).
cnf(c_17154,plain,
( ~ ssList(app(X0_13,cons(X0_14,X1_13)))
| ~ ssList(cons(X0_14,X2_13))
| ssList(app(app(X0_13,cons(X0_14,X1_13)),cons(X0_14,X2_13))) ),
inference(instantiation,[status(thm)],[c_16781]) ).
cnf(c_17922,plain,
( ~ ssItem(X0_14)
| ~ ssList(nil)
| singletonP(cons(X0_14,nil)) ),
inference(superposition,[status(thm)],[c_13546,c_13615]) ).
cnf(c_17925,plain,
( ~ ssItem(X0_14)
| singletonP(cons(X0_14,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17922,c_13545]) ).
cnf(c_17935,plain,
( ~ ssItem(sK54(sK60,sK59))
| nil = sK60
| singletonP(sK59) ),
inference(superposition,[status(thm)],[c_13430,c_17925]) ).
cnf(c_19294,plain,
( ~ ssList(sK59)
| ssList(app(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK64)) ),
inference(resolution,[status(thm)],[c_13632,c_13422]) ).
cnf(c_20603,plain,
( X0_13 != X1_13
| X1_13 = X0_13 ),
inference(resolution,[status(thm)],[c_13626,c_13624]) ).
cnf(c_21807,plain,
( X0_13 != X1_13
| X0_14 != X1_14
| X2_13 != cons(X1_14,X1_13)
| cons(X0_14,X0_13) = X2_13 ),
inference(resolution,[status(thm)],[c_13629,c_13626]) ).
cnf(c_24215,plain,
( ~ ssList(X0_13)
| app(cons(sK61,nil),X0_13) = cons(sK61,X0_13) ),
inference(superposition,[status(thm)],[c_13452,c_13470]) ).
cnf(c_24968,plain,
( nil != sK59
| ~ ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)))
| ~ ssList(sK64)
| app(app(sK63,cons(sK61,nil)),cons(sK61,nil)) = nil ),
inference(superposition,[status(thm)],[c_13422,c_13468]) ).
cnf(c_24988,plain,
( nil != sK59
| ~ ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)))
| app(app(sK63,cons(sK61,nil)),cons(sK61,nil)) = nil ),
inference(forward_subsumption_resolution,[status(thm)],[c_24968,c_13454]) ).
cnf(c_25915,plain,
app(cons(sK61,nil),sK59) = cons(sK61,sK59),
inference(superposition,[status(thm)],[c_13450,c_24215]) ).
cnf(c_26782,plain,
( ~ memberP(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),X0_14)
| ~ ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)))
| ~ ssItem(X0_14)
| ~ ssList(sK64)
| memberP(sK59,X0_14) ),
inference(superposition,[status(thm)],[c_13422,c_13520]) ).
cnf(c_26806,plain,
( ~ memberP(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),X0_14)
| ~ ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)))
| ~ ssItem(X0_14)
| memberP(sK59,X0_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26782,c_13454]) ).
cnf(c_26808,plain,
( ~ memberP(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK61)
| ~ ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)))
| ~ ssItem(sK61)
| memberP(sK59,sK61) ),
inference(instantiation,[status(thm)],[c_26806]) ).
cnf(c_27620,plain,
( ~ ssList(cons(sK61,nil))
| ~ ssList(sK59)
| ssList(cons(sK61,sK59)) ),
inference(superposition,[status(thm)],[c_25915,c_13533]) ).
cnf(c_27624,plain,
( ~ ssList(cons(sK61,nil))
| ssList(cons(sK61,sK59)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27620,c_13450]) ).
cnf(c_38749,plain,
( nil = sK59
| sK59 = cons(sK54(sK60,sK59),nil) ),
inference(resolution,[status(thm)],[c_20603,c_13429]) ).
cnf(c_44323,plain,
( ~ ssList(app(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK64))
| ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssList(cons(sK61,nil))
| ~ ssList(sK64)
| segmentP(sK59,cons(sK61,nil)) ),
inference(superposition,[status(thm)],[c_13422,c_13608]) ).
cnf(c_44404,plain,
( ~ ssList(app(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK64))
| ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssList(cons(sK61,nil))
| segmentP(sK59,cons(sK61,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44323,c_13454]) ).
cnf(c_44710,plain,
( ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssList(cons(sK61,nil))
| ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil))) ),
inference(instantiation,[status(thm)],[c_17154]) ).
cnf(c_53977,plain,
( ~ ssList(cons(sK61,nil))
| ~ ssList(sK63)
| ssList(app(sK63,cons(sK61,nil))) ),
inference(instantiation,[status(thm)],[c_16781]) ).
cnf(c_56713,plain,
( ~ ssItem(X0_14)
| singletonP(cons(X0_14,nil)) ),
inference(global_subsumption_just,[status(thm)],[c_13615,c_17925]) ).
cnf(c_56717,plain,
( ~ ssItem(sK54(sK60,sK59))
| nil = sK60
| singletonP(sK59) ),
inference(superposition,[status(thm)],[c_13430,c_56713]) ).
cnf(c_56726,plain,
( tl(sK59) = sK53(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_13476]) ).
cnf(c_56763,plain,
( hd(sK59) = sK52(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_13478]) ).
cnf(c_56799,plain,
( nil = sK60
| singletonP(sK59) ),
inference(global_subsumption_just,[status(thm)],[c_56717,c_13436,c_17935]) ).
cnf(c_56862,plain,
( ~ ssList(sK59)
| nil = sK59
| ssList(tl(sK59)) ),
inference(superposition,[status(thm)],[c_56726,c_13475]) ).
cnf(c_56864,plain,
( nil = sK59
| ssList(tl(sK59)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56862,c_13450]) ).
cnf(c_57121,plain,
( ~ ssList(sK59)
| cons(sK11(sK59),nil) = sK59
| nil = sK60 ),
inference(superposition,[status(thm)],[c_56799,c_13614]) ).
cnf(c_57122,plain,
( cons(sK11(sK59),nil) = sK59
| nil = sK60 ),
inference(forward_subsumption_resolution,[status(thm)],[c_57121,c_13450]) ).
cnf(c_57326,plain,
( ~ ssList(sK59)
| nil = sK59
| ssItem(hd(sK59)) ),
inference(superposition,[status(thm)],[c_56763,c_13477]) ).
cnf(c_57327,plain,
( nil = sK59
| ssItem(hd(sK59)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_57326,c_13450]) ).
cnf(c_57339,plain,
( cons(hd(sK59),tl(sK59)) = sK59
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_13473]) ).
cnf(c_57683,plain,
( nil != sK59
| ~ ssItem(sK11(sK59))
| ~ ssList(nil)
| nil = sK60 ),
inference(superposition,[status(thm)],[c_57122,c_13544]) ).
cnf(c_57688,plain,
( nil != sK59
| ~ ssItem(sK11(sK59))
| nil = sK60 ),
inference(forward_subsumption_resolution,[status(thm)],[c_57683,c_13545]) ).
cnf(c_60127,plain,
( ~ ssItem(sK54(sK60,sK59))
| ~ memberP(sK59,X0_14)
| ~ ssItem(X0_14)
| ~ ssList(nil)
| sK54(sK60,sK59) = X0_14
| nil = sK59
| memberP(nil,X0_14) ),
inference(superposition,[status(thm)],[c_13429,c_13516]) ).
cnf(c_60140,plain,
( ~ ssItem(sK54(sK60,sK59))
| ~ memberP(sK59,X0_14)
| ~ ssItem(X0_14)
| sK54(sK60,sK59) = X0_14
| nil = sK59
| memberP(nil,X0_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60127,c_13545]) ).
cnf(c_61215,plain,
( cons(X0_14,X0_13) != sK59
| ~ ssItem(hd(sK59))
| ~ ssList(tl(sK59))
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| tl(sK59) = X0_13
| nil = sK59 ),
inference(superposition,[status(thm)],[c_57339,c_13543]) ).
cnf(c_69743,plain,
( app(app(sK63,cons(sK61,nil)),cons(sK61,nil)) != nil
| ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssList(cons(sK61,nil))
| cons(sK61,nil) = nil ),
inference(instantiation,[status(thm)],[c_16694]) ).
cnf(c_79045,plain,
nil != sK59,
inference(global_subsumption_just,[status(thm)],[c_57688,c_260,c_258,c_141,c_13689,c_13690,c_24988,c_44710,c_53977,c_69743]) ).
cnf(c_79216,plain,
( cons(X0_14,X0_13) != sK59
| ~ ssItem(hd(sK59))
| ~ ssList(tl(sK59))
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| tl(sK59) = X0_13 ),
inference(backward_subsumption_resolution,[status(thm)],[c_61215,c_79045]) ).
cnf(c_79259,plain,
( ~ ssItem(sK54(sK60,sK59))
| ~ memberP(sK59,X0_14)
| ~ ssItem(X0_14)
| sK54(sK60,sK59) = X0_14
| memberP(nil,X0_14) ),
inference(backward_subsumption_resolution,[status(thm)],[c_60140,c_79045]) ).
cnf(c_79357,plain,
ssItem(hd(sK59)),
inference(backward_subsumption_resolution,[status(thm)],[c_57327,c_79045]) ).
cnf(c_79365,plain,
ssList(tl(sK59)),
inference(backward_subsumption_resolution,[status(thm)],[c_56864,c_79045]) ).
cnf(c_79385,plain,
ssItem(sK54(sK60,sK59)),
inference(backward_subsumption_resolution,[status(thm)],[c_13435,c_79045]) ).
cnf(c_79455,plain,
( ~ memberP(sK59,X0_14)
| ~ ssItem(X0_14)
| sK54(sK60,sK59) = X0_14
| memberP(nil,X0_14) ),
inference(forward_subsumption_resolution,[status(thm)],[c_79259,c_79385]) ).
cnf(c_79485,plain,
( cons(X0_14,X0_13) != sK59
| ~ ssItem(X0_14)
| ~ ssList(X0_13)
| tl(sK59) = X0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[c_79216,c_79365,c_79357]) ).
cnf(c_79645,plain,
( ~ memberP(sK59,sK61)
| ~ ssItem(sK61)
| sK54(sK60,sK59) = sK61
| memberP(nil,sK61) ),
inference(instantiation,[status(thm)],[c_79455]) ).
cnf(c_79658,plain,
( cons(sK61,nil) != sK59
| ~ ssItem(sK61)
| ~ ssList(nil)
| tl(sK59) = nil ),
inference(instantiation,[status(thm)],[c_79485]) ).
cnf(c_88863,plain,
( X0_13 != nil
| X0_14 != sK54(sK60,sK59)
| cons(X0_14,X0_13) = sK59
| nil = sK59 ),
inference(resolution,[status(thm)],[c_21807,c_38749]) ).
cnf(c_88866,plain,
( nil != nil
| sK61 != sK54(sK60,sK59)
| cons(sK61,nil) = sK59
| nil = sK59 ),
inference(instantiation,[status(thm)],[c_88863]) ).
cnf(c_110546,plain,
( ~ ssList(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)))
| ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssItem(sK61)
| ~ ssList(nil)
| memberP(app(app(sK63,cons(sK61,nil)),cons(sK61,nil)),sK61) ),
inference(instantiation,[status(thm)],[c_13619]) ).
cnf(c_115977,plain,
( ~ ssList(app(X0_13,X1_13))
| ~ ssList(X2_13)
| ssList(app(app(X0_13,X1_13),X2_13)) ),
inference(instantiation,[status(thm)],[c_13533]) ).
cnf(c_117244,plain,
( sK54(sK60,sK59) != X0_14
| X1_14 != X0_14
| X1_14 = sK54(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_13627]) ).
cnf(c_117245,plain,
( sK54(sK60,sK59) != sK61
| sK61 != sK61
| sK61 = sK54(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_117244]) ).
cnf(c_150720,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_13608,c_13533,c_13608,c_115977]) ).
cnf(c_241280,plain,
( ~ ssList(X0_13)
| app(nil,tl(X0_13)) = tl(X0_13)
| X0_13 = nil ),
inference(superposition,[status(thm)],[c_13535,c_13531]) ).
cnf(c_241336,plain,
( app(nil,tl(sK59)) = tl(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_241280]) ).
cnf(c_241363,plain,
app(nil,tl(sK59)) = tl(sK59),
inference(forward_subsumption_resolution,[status(thm)],[c_241336,c_79045]) ).
cnf(c_241595,plain,
( tl(sK59) = sK53(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_13476]) ).
cnf(c_241623,plain,
tl(sK59) = sK53(sK59),
inference(forward_subsumption_resolution,[status(thm)],[c_241595,c_79045]) ).
cnf(c_241631,plain,
( hd(sK59) = sK52(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_13478]) ).
cnf(c_241659,plain,
hd(sK59) = sK52(sK59),
inference(forward_subsumption_resolution,[status(thm)],[c_241631,c_79045]) ).
cnf(c_242063,plain,
( cons(hd(sK59),tl(sK59)) = sK59
| nil = sK59 ),
inference(superposition,[status(thm)],[c_13450,c_13473]) ).
cnf(c_242100,plain,
cons(hd(sK59),tl(sK59)) = sK59,
inference(forward_subsumption_resolution,[status(thm)],[c_242063,c_79045]) ).
cnf(c_242131,plain,
( ~ ssList(sK59)
| nil = sK59
| ssList(tl(sK59)) ),
inference(superposition,[status(thm)],[c_241623,c_13475]) ).
cnf(c_242132,plain,
ssList(tl(sK59)),
inference(forward_subsumption_resolution,[status(thm)],[c_242131,c_79045,c_13450]) ).
cnf(c_242204,plain,
( ~ ssList(X0_13)
| app(cons(sK61,nil),X0_13) = cons(sK61,X0_13) ),
inference(superposition,[status(thm)],[c_13452,c_13470]) ).
cnf(c_242283,plain,
app(cons(sK61,nil),sK59) = cons(sK61,sK59),
inference(superposition,[status(thm)],[c_13450,c_242204]) ).
cnf(c_242320,plain,
app(cons(sK61,nil),tl(sK59)) = cons(sK61,tl(sK59)),
inference(superposition,[status(thm)],[c_242132,c_242204]) ).
cnf(c_242487,plain,
( ~ ssList(cons(sK61,nil))
| ~ ssList(sK59)
| ssList(cons(sK61,sK59)) ),
inference(superposition,[status(thm)],[c_242283,c_13533]) ).
cnf(c_242488,plain,
( ~ ssList(cons(sK61,nil))
| ssList(cons(sK61,sK59)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_242487,c_13450]) ).
cnf(c_242492,plain,
ssList(cons(sK61,sK59)),
inference(global_subsumption_just,[status(thm)],[c_242488,c_260,c_141,c_13690,c_27624]) ).
cnf(c_243700,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| app(app(sK63,X0_13),X1_13) = app(sK63,app(X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_13453,c_13469]) ).
cnf(c_244729,plain,
( ~ ssList(cons(sK61,nil))
| ~ ssList(tl(sK59))
| ssList(cons(sK61,tl(sK59))) ),
inference(superposition,[status(thm)],[c_242320,c_13533]) ).
cnf(c_244735,plain,
( ~ ssList(cons(sK61,nil))
| ssList(cons(sK61,tl(sK59))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_244729,c_242132]) ).
cnf(c_245001,plain,
( ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_13608,c_150720]) ).
cnf(c_245008,plain,
( ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssList(cons(sK61,nil))
| ~ ssList(sK64)
| segmentP(sK59,cons(sK61,nil)) ),
inference(superposition,[status(thm)],[c_13422,c_245001]) ).
cnf(c_245100,plain,
( ~ ssList(app(sK63,cons(sK61,nil)))
| ~ ssList(cons(sK61,nil))
| segmentP(sK59,cons(sK61,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_245008,c_13454]) ).
cnf(c_245982,plain,
( ~ ssList(sK59)
| nil = sK59
| ssItem(hd(sK59)) ),
inference(superposition,[status(thm)],[c_241659,c_13477]) ).
cnf(c_245983,plain,
ssItem(hd(sK59)),
inference(forward_subsumption_resolution,[status(thm)],[c_245982,c_79045,c_13450]) ).
cnf(c_246015,plain,
( ~ ssList(X0_13)
| app(cons(hd(sK59),nil),X0_13) = cons(hd(sK59),X0_13) ),
inference(superposition,[status(thm)],[c_245983,c_13470]) ).
cnf(c_246220,plain,
( ~ ssList(tl(sK59))
| ~ ssList(nil)
| frontsegP(tl(sK59),nil) ),
inference(superposition,[status(thm)],[c_241363,c_13444]) ).
cnf(c_246233,plain,
frontsegP(tl(sK59),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_246220,c_13545,c_242132]) ).
cnf(c_246246,plain,
( ~ frontsegP(nil,tl(sK59))
| ~ ssList(tl(sK59))
| ~ ssList(nil)
| tl(sK59) = nil ),
inference(superposition,[status(thm)],[c_246233,c_13512]) ).
cnf(c_246247,plain,
( ~ frontsegP(nil,tl(sK59))
| tl(sK59) = nil ),
inference(forward_subsumption_resolution,[status(thm)],[c_246246,c_13545,c_242132]) ).
cnf(c_246265,plain,
tl(sK59) = nil,
inference(global_subsumption_just,[status(thm)],[c_246247,c_260,c_258,c_141,c_13659,c_13660,c_13679,c_13689,c_13690,c_24988,c_26808,c_44710,c_53977,c_69743,c_79645,c_79658,c_88866,c_110546,c_117245]) ).
cnf(c_246278,plain,
cons(hd(sK59),nil) = sK59,
inference(demodulation,[status(thm)],[c_242100,c_246265]) ).
cnf(c_252330,plain,
ssList(cons(sK61,tl(sK59))),
inference(global_subsumption_just,[status(thm)],[c_244735,c_260,c_141,c_13690,c_244735]) ).
cnf(c_252332,plain,
ssList(cons(sK61,nil)),
inference(light_normalisation,[status(thm)],[c_252330,c_246265]) ).
cnf(c_252360,plain,
( ~ ssList(app(sK63,cons(sK61,nil)))
| segmentP(sK59,cons(sK61,nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_245100,c_252332]) ).
cnf(c_260086,plain,
( ~ ssList(X0_13)
| app(app(sK63,sK59),X0_13) = app(sK63,app(sK59,X0_13)) ),
inference(superposition,[status(thm)],[c_13450,c_243700]) ).
cnf(c_270564,plain,
( ~ ssList(X0_13)
| cons(hd(sK59),X0_13) = app(sK59,X0_13) ),
inference(light_normalisation,[status(thm)],[c_246015,c_246278]) ).
cnf(c_270571,plain,
cons(hd(sK59),sK59) = app(sK59,sK59),
inference(superposition,[status(thm)],[c_13450,c_270564]) ).
cnf(c_279726,plain,
( app(sK59,sK59) != sK59
| ~ ssItem(hd(sK59))
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_270571,c_13544]) ).
cnf(c_279729,plain,
( ~ ssItem(hd(sK59))
| ~ ssList(sK59)
| ssList(app(sK59,sK59)) ),
inference(superposition,[status(thm)],[c_270571,c_13546]) ).
cnf(c_279744,plain,
ssList(app(sK59,sK59)),
inference(forward_subsumption_resolution,[status(thm)],[c_279729,c_13450,c_245983]) ).
cnf(c_279747,plain,
app(sK59,sK59) != sK59,
inference(forward_subsumption_resolution,[status(thm)],[c_279726,c_13450,c_245983]) ).
cnf(c_280054,plain,
app(app(sK59,sK59),nil) = app(sK59,sK59),
inference(superposition,[status(thm)],[c_279744,c_13466]) ).
cnf(c_288587,plain,
app(app(sK63,sK59),sK59) = app(sK63,app(sK59,sK59)),
inference(superposition,[status(thm)],[c_13450,c_260086]) ).
cnf(c_298890,plain,
( ~ ssList(nil)
| ~ ssList(sK59)
| segmentP(app(sK59,sK59),sK59) ),
inference(superposition,[status(thm)],[c_280054,c_245001]) ).
cnf(c_298898,plain,
segmentP(app(sK59,sK59),sK59),
inference(forward_subsumption_resolution,[status(thm)],[c_298890,c_13450,c_13545]) ).
cnf(c_298913,plain,
( ~ segmentP(sK59,app(sK59,sK59))
| ~ ssList(app(sK59,sK59))
| ~ ssList(sK59)
| app(sK59,sK59) = sK59 ),
inference(superposition,[status(thm)],[c_298898,c_13497]) ).
cnf(c_298914,plain,
~ segmentP(sK59,app(sK59,sK59)),
inference(forward_subsumption_resolution,[status(thm)],[c_298913,c_279747,c_13450,c_279744]) ).
cnf(c_425056,plain,
segmentP(sK59,cons(sK61,nil)),
inference(global_subsumption_just,[status(thm)],[c_252360,c_264,c_260,c_258,c_141,c_13690,c_19294,c_44404,c_53977]) ).
cnf(c_425060,plain,
( ~ segmentP(cons(sK61,nil),sK59)
| ~ ssList(cons(sK61,nil))
| ~ ssList(sK59)
| cons(sK61,nil) = sK59 ),
inference(superposition,[status(thm)],[c_425056,c_13497]) ).
cnf(c_425063,plain,
( ~ segmentP(cons(sK61,nil),sK59)
| cons(sK61,nil) = sK59 ),
inference(forward_subsumption_resolution,[status(thm)],[c_425060,c_13450,c_252332]) ).
cnf(c_425986,plain,
cons(sK61,nil) = sK59,
inference(global_subsumption_just,[status(thm)],[c_425063,c_260,c_258,c_141,c_13659,c_13660,c_13679,c_13689,c_13690,c_24988,c_26808,c_44710,c_53977,c_69743,c_79645,c_88866,c_110546,c_117245]) ).
cnf(c_426031,plain,
cons(sK61,sK59) = app(sK59,sK59),
inference(demodulation,[status(thm)],[c_242283,c_425986]) ).
cnf(c_426037,plain,
app(app(app(sK63,sK59),sK59),sK64) = sK59,
inference(demodulation,[status(thm)],[c_13422,c_425986]) ).
cnf(c_429404,plain,
~ segmentP(sK59,cons(sK61,sK59)),
inference(demodulation,[status(thm)],[c_298914,c_426031]) ).
cnf(c_429415,plain,
app(app(sK63,sK59),sK59) = app(sK63,cons(sK61,sK59)),
inference(demodulation,[status(thm)],[c_288587,c_426031]) ).
cnf(c_431390,plain,
app(app(sK63,cons(sK61,sK59)),sK64) = sK59,
inference(light_normalisation,[status(thm)],[c_426037,c_429415]) ).
cnf(c_431401,plain,
( ~ ssList(cons(sK61,sK59))
| ~ ssList(sK63)
| ~ ssList(sK64)
| segmentP(sK59,cons(sK61,sK59)) ),
inference(superposition,[status(thm)],[c_431390,c_245001]) ).
cnf(c_431410,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_431401,c_429404,c_13454,c_13453,c_242492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC165+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 17:18:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 273.86/36.84 % SZS status Started for theBenchmark.p
% 273.86/36.84 % SZS status Theorem for theBenchmark.p
% 273.86/36.84
% 273.86/36.84 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 273.86/36.84
% 273.86/36.84 ------ iProver source info
% 273.86/36.84
% 273.86/36.84 git: date: 2023-05-31 18:12:56 +0000
% 273.86/36.84 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 273.86/36.84 git: non_committed_changes: false
% 273.86/36.84 git: last_make_outside_of_git: false
% 273.86/36.84
% 273.86/36.84 ------ Parsing...
% 273.86/36.84 ------ Clausification by vclausify_rel & Parsing by iProver...
% 273.86/36.84
% 273.86/36.84 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 3 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e
% 273.86/36.84
% 273.86/36.84 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 273.86/36.84
% 273.86/36.84 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 273.86/36.84 ------ Proving...
% 273.86/36.84 ------ Problem Properties
% 273.86/36.84
% 273.86/36.84
% 273.86/36.84 clauses 201
% 273.86/36.84 conjectures 5
% 273.86/36.84 EPR 55
% 273.86/36.84 Horn 123
% 273.86/36.84 unary 23
% 273.86/36.84 binary 50
% 273.86/36.84 lits 661
% 273.86/36.84 lits eq 98
% 273.86/36.84 fd_pure 0
% 273.86/36.84 fd_pseudo 0
% 273.86/36.84 fd_cond 21
% 273.86/36.84 fd_pseudo_cond 14
% 273.86/36.84 AC symbols 0
% 273.86/36.84
% 273.86/36.84 ------ Input Options Time Limit: Unbounded
% 273.86/36.84
% 273.86/36.84
% 273.86/36.84 ------
% 273.86/36.84 Current options:
% 273.86/36.84 ------
% 273.86/36.84
% 273.86/36.84
% 273.86/36.84
% 273.86/36.84
% 273.86/36.84 ------ Proving...
% 273.86/36.84
% 273.86/36.84
% 273.86/36.84 % SZS status Theorem for theBenchmark.p
% 273.86/36.84
% 273.86/36.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 274.21/36.84
% 274.21/36.86
%------------------------------------------------------------------------------