%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC170+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:08:12 PM UTC 2026
% Result : Theorem 127.00s 45.75s
% Output : CNFRefutation 127.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 34
% Syntax : Number of formulae : 329 ( 83 unt; 4 def)
% Number of atoms : 1379 ( 315 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1375 ( 584 ~; 603 |; 104 &)
% ( 18 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 404 ( 0 sgn 362 !; 42 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',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/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
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/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X1 = X0
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax19) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',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/sandbox/benchmark/Axioms/SWC001+0.ax',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/sandbox/benchmark/Axioms/SWC001+0.ax',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax79) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X2 = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax80) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ~ singletonP(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 ) ) ) ) )
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ~ singletonP(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 ) ) ) ) )
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f121,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X2,X0) != cons(X3,X1)
| ( X1 = X0
& X2 = X3 ) ) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f122,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| ! [X3] :
( ~ ssItem(X3)
| cons(X2,X0) != cons(X3,X1)
| ( X1 = X0
& X2 = X3 ) ) ) ) ),
inference(flattening,[],[f121]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f146,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f147,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f170,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f171,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f170]) ).
fof(f175,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(ennf_transformation,[],[f57]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f186,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f187,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(f194,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f79]) ).
fof(f195,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X2 = X0 ) ) ),
inference(flattening,[],[f194]) ).
fof(f196,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X2 = X0 ) ) ),
inference(ennf_transformation,[],[f80]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X2 = X0 ) ) ),
inference(flattening,[],[f196]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| singletonP(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 ) ) ) )
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| singletonP(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 ) ) ) )
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f232,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(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) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
fof(f237,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK10(X0),nil) = X0
& ssItem(sK10(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
fof(f246,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(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) ) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f247,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f277,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f146]) ).
fof(f278,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0) )
& ( ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) )
| memberP(app(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f277]) ).
fof(f279,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f147]) ).
fof(f280,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ! [X2] :
( ~ ssList(X2)
| ( ( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 )
& ( ( ~ memberP(X2,X0)
& X0 != X1 )
| memberP(cons(X1,X2),X0) ) ) ) ) ),
inference(flattening,[],[f279]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
fof(f290,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(X1,sK51(X0))],[f187]) ).
fof(f291,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f292,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f200]) ).
fof(f293,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f292]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| singletonP(sK55) )
& ssItem(sK57)
& ssItem(sK58)
& ssList(sK59)
& ssList(sK60)
& ~ neq(sK57,sK58)
& sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60)
& segmentP(sK56,sK55)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60)],[f222]) ).
fof(f298,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f306,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sK10(X0),nil) = X0 ),
inference(cnf_transformation,[],[f239]) ).
fof(f307,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sK10(X0)) ),
inference(cnf_transformation,[],[f239]) ).
fof(f318,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f390,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| cons(X2,X0) != cons(X3,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X3)
| cons(X2,X0) != cons(X3,X1)
| X2 = X3 ),
inference(cnf_transformation,[],[f122]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f280]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f439,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f171]) ).
fof(f442,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f175]) ).
fof(f443,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f444,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f290]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f475,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X2,X1) != app(X0,X1)
| X0 = X2 ),
inference(cnf_transformation,[],[f195]) ).
fof(f476,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X1,X2) != app(X1,X0)
| X0 = X2 ),
inference(cnf_transformation,[],[f197]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f293]) ).
fof(f480,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f293]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| singletonP(sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
ssList(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
~ neq(sK57,sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK55 = app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60),
inference(definition_unfolding,[],[f506,f508]) ).
fof(f511,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f509]) ).
fof(f512,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f508]) ).
fof(f514,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f305]) ).
fof(f518,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f318]) ).
fof(f532,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_59,plain,
! [X0: $i] :
( ssItem(sK10(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f518]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ( cons(X0,X1) != cons(X2,X3) ) ),
inference(cnf_transformation,[],[f392]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ( cons(X0,X1) != cons(X2,X3) ) ),
inference(cnf_transformation,[],[f391]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f415]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f414]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f416]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f439]) ).
tcf(c_194,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f532]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f475]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X0,X2) ) ),
inference(cnf_transformation,[],[f476]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f480]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f479]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f507]) ).
tcf(c_247,negated_conjecture,
app(app(app(sK59,cons(sK57,nil)),cons(sK58,nil)),sK60) = sK55,
inference(cnf_transformation,[],[f510]) ).
tcf(c_248,negated_conjecture,
~ neq(sK57,sK58),
inference(cnf_transformation,[],[f505]) ).
tcf(c_249,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f504]) ).
tcf(c_250,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f503]) ).
tcf(c_251,negated_conjecture,
ssItem(sK58),
inference(cnf_transformation,[],[f502]) ).
tcf(c_252,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f501]) ).
tcf(c_253,negated_conjecture,
( singletonP(sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_256,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f511]) ).
tcf(c_257,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f512]) ).
tcf(c_307,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_3263,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ( X1 != sK58 )
| ( X0 != sK57 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_248]) ).
tcf(c_3264,plain,
( ( sK57 = sK58 )
| ~ ssItem(sK58)
| ~ ssItem(sK57) ),
inference(unflattening,[status(thm)],[c_3263]) ).
tcf(c_3265,plain,
sK57 = sK58,
inference(global_subsumption_just,[status(thm)],[c_3264,c_252,c_251,c_3264]) ).
tcf(c_3270,plain,
! [X0: $i,X1: $i] :
( singletonP(sK55)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_253]) ).
tcf(c_3271,plain,
( singletonP(sK55)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3270]) ).
tcf(c_3272,plain,
( singletonP(sK55)
| ( sK56 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3271,c_256,c_141,c_3271]) ).
tcf(c_6655,plain,
app(app(app(sK59,cons(sK57,nil)),cons(sK57,nil)),sK60) = sK55,
inference(light_normalisation,[status(thm)],[c_247,c_3265]) ).
tcf(c_13066,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_13067,definition,
iPr_def_11 = app(sK59,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_13068,definition,
iPr_def_12 = app(iPr_def_11,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_13069,definition,
iPr_def_13 = app(iPr_def_12,sK60),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_13070,plain,
iPr_def_13 = sK55,
inference(demodulation,[status(thm)],[c_6655,c_13066,c_13067,c_13068,c_13069]) ).
tcf(c_13071,plain,
( singletonP(sK55)
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3272]) ).
tcf(c_13073,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_13075,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_13076,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_13077,negated_conjecture,
ssList(sK60),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_13078,negated_conjecture,
segmentP(sK56,sK55),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_13079,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_13081,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_13086,plain,
! [X0: $i,X1: $i] :
( ssList(X0)
| ~ ssList(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_13087,plain,
! [X0: $i,X1: $i] :
( singletonP(X0)
| ~ singletonP(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_13090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_15906,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_13073,c_13070]) ).
tcf(c_15908,plain,
( singletonP(iPr_def_13)
| ( nil = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_13071,c_13070]) ).
tcf(c_16037,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,nil))) ),
inference(superposition,[status(thm)],[c_13066,c_54]) ).
tcf(c_16038,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_16037,c_13066]) ).
tcf(c_16039,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16038,c_141,c_13075]) ).
tcf(c_16356,plain,
app(sK59,nil) = sK59,
inference(superposition,[status(thm)],[c_13076,c_232]) ).
tcf(c_16424,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_13066,c_140]) ).
tcf(c_16427,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_16424,c_141,c_13075]) ).
tcf(c_16450,plain,
app(nil,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_16427,c_155]) ).
tcf(c_16451,plain,
( memberP(iPr_def_10,sK57)
| ~ ssList(nil)
| ~ ssList(app(nil,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_16450,c_16039]) ).
tcf(c_16452,plain,
( memberP(iPr_def_10,sK57)
| ~ ssList(iPr_def_10)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_16451,c_16450]) ).
tcf(c_16453,plain,
memberP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_16452,c_16427,c_141]) ).
tcf(c_16584,plain,
( ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_13067,c_153]) ).
tcf(c_16585,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_13068,c_153]) ).
tcf(c_16599,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16585,c_16427]) ).
tcf(c_16602,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_16584,c_16427,c_13076]) ).
tcf(c_16603,plain,
ssList(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_16599,c_16602]) ).
tcf(c_16615,plain,
app(iPr_def_11,nil) = iPr_def_11,
inference(superposition,[status(thm)],[c_16602,c_232]) ).
tcf(c_17423,plain,
! [X0: $i] :
( singletonP(X0)
| ~ singletonP(sK55)
| ( X0 != sK55 ) ),
inference(instantiation,[status(thm)],[c_13087]) ).
tcf(c_17601,plain,
( ( nil = sK56 )
| ( cons(sK10(iPr_def_13),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_15908,c_60]) ).
tcf(c_17602,plain,
( ( nil = sK56 )
| ( cons(sK10(iPr_def_13),nil) = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17601,c_15906]) ).
tcf(c_17611,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13066,c_142]) ).
tcf(c_17612,plain,
nil != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_17611,c_141,c_13075]) ).
tcf(c_17876,plain,
! [X0: $i,X1: $i] :
( memberP(app(X1,X0),sK57)
| ~ ssItem(sK57)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_166]) ).
tcf(c_20843,plain,
( ( nil = iPr_def_10 )
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13068,c_230]) ).
tcf(c_20876,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_20843,c_17612,c_16602,c_16427]) ).
tcf(c_20890,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK60)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_13069,c_231]) ).
tcf(c_20919,plain,
( ( nil = iPr_def_12 )
| ( nil != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20890,c_16603,c_13077]) ).
tcf(c_21004,plain,
! [X0: $i] :
( ( X0 = sK55 )
| ~ ssList(sK55)
| ~ ssList(X0)
| ~ segmentP(sK55,X0)
| ~ segmentP(X0,sK55) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_21011,plain,
( ( nil = sK55 )
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ segmentP(sK55,nil)
| ~ segmentP(nil,sK55) ),
inference(instantiation,[status(thm)],[c_21004]) ).
tcf(c_21048,plain,
( singletonP(iPr_def_13)
| ~ singletonP(sK55)
| ( iPr_def_13 != sK55 ) ),
inference(instantiation,[status(thm)],[c_17423]) ).
tcf(c_29283,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( nil = sK56 )
| ( sK10(iPr_def_13) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK10(iPr_def_13))
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_17602,c_170]) ).
tcf(c_29309,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( nil = sK56 )
| ( sK10(iPr_def_13) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK10(iPr_def_13))
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29283,c_141]) ).
tcf(c_29787,plain,
! [X0: $i] :
( ( X0 = sK59 )
| ~ ssList(iPr_def_10)
| ~ ssList(sK59)
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13067,c_225]) ).
tcf(c_29925,plain,
! [X0: $i] :
( ( X0 = sK59 )
| ~ ssList(X0)
| ( app(X0,iPr_def_10) != iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29787,c_16427,c_13076]) ).
tcf(c_31021,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(sK59)
| ~ ssList(nil)
| ~ ssList(X0)
| ( app(sK59,X0) != sK59 ) ),
inference(superposition,[status(thm)],[c_16356,c_226]) ).
tcf(c_31119,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ( app(sK59,X0) != sK59 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31021,c_13076,c_141]) ).
tcf(c_31765,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59)
| ~ ssList(X0)
| ~ ssList(app(app(sK59,iPr_def_10),X0)) ),
inference(superposition,[status(thm)],[c_13067,c_67]) ).
tcf(c_31927,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_11,X0)) ),
inference(light_normalisation,[status(thm)],[c_31765,c_13067]) ).
tcf(c_31928,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_11,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31927,c_16427,c_13076]) ).
tcf(c_36967,plain,
( segmentP(iPr_def_11,iPr_def_10)
| ~ ssList(nil)
| ~ ssList(app(iPr_def_11,nil)) ),
inference(superposition,[status(thm)],[c_16615,c_31928]) ).
tcf(c_36973,plain,
( segmentP(iPr_def_11,iPr_def_10)
| ~ ssList(iPr_def_11)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_36967,c_16615]) ).
tcf(c_36974,plain,
segmentP(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_36973,c_16602,c_141]) ).
tcf(c_37037,plain,
( ( sK59 = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ( iPr_def_11 != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13068,c_29925]) ).
tcf(c_37047,plain,
( ( sK59 = iPr_def_11 )
| ( iPr_def_11 != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37037,c_16602]) ).
tcf(c_37078,plain,
( ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10)
| ( sK59 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_13067,c_31119]) ).
tcf(c_37084,plain,
sK59 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_37078,c_17612,c_16427]) ).
tcf(c_40330,plain,
( segmentP(sK55,nil)
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_194]) ).
tcf(c_52403,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(iPr_def_10)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ memberP(iPr_def_10,sK57) ),
inference(instantiation,[status(thm)],[c_17876]) ).
tcf(c_228953,plain,
( ssList(iPr_def_13)
| ~ ssList(sK55) ),
inference(resolution,[status(thm)],[c_13086,c_13070]) ).
tcf(c_250575,plain,
! [X0: $i] :
( singletonP(sK55)
| ( X0 = sK56 )
| ( X0 != nil ) ),
inference(resolution,[status(thm)],[c_13081,c_13071]) ).
tcf(c_250576,plain,
( singletonP(sK55)
| ( nil = sK56 )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_250575]) ).
tcf(c_250585,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ( X0 != sK55 ) ),
inference(resolution,[status(thm)],[c_13081,c_13070]) ).
tcf(c_250586,plain,
( ( nil = iPr_def_13 )
| ( nil != sK55 ) ),
inference(instantiation,[status(thm)],[c_250585]) ).
tcf(c_275626,plain,
! [X0: $i,X1: $i] :
( segmentP(X0,X1)
| ( X1 != sK55 )
| ( X0 != sK56 ) ),
inference(resolution,[status(thm)],[c_13090,c_13078]) ).
tcf(c_277902,plain,
! [X0: $i] :
( segmentP(X0,sK55)
| ( X0 != sK56 ) ),
inference(resolution,[status(thm)],[c_275626,c_13079]) ).
tcf(c_277903,plain,
( segmentP(nil,sK55)
| ( nil != sK56 ) ),
inference(instantiation,[status(thm)],[c_277902]) ).
tcf(c_310937,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13066,c_142]) ).
tcf(c_310938,plain,
nil != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_310937,c_141,c_13075]) ).
tcf(c_357086,plain,
( ssItem(sK10(iPr_def_13))
| ~ singletonP(iPr_def_13)
| ~ ssList(iPr_def_13) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_362586,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_428081,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_362586]) ).
tcf(c_428092,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_13073,c_13070]) ).
tcf(c_428689,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,nil))) ),
inference(superposition,[status(thm)],[c_13066,c_54]) ).
tcf(c_428696,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_428689,c_13066]) ).
tcf(c_428697,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428696,c_141,c_13075]) ).
tcf(c_428923,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_13067,c_428081]) ).
tcf(c_428924,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428923,c_13076]) ).
tcf(c_429152,plain,
singletonP(sK55),
inference(global_subsumption_just,[status(thm)],[c_13071,c_257,c_141,c_195,c_307,c_20876,c_20919,c_21011,c_40330,c_250576,c_250586,c_277903]) ).
tcf(c_429154,plain,
singletonP(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_429152,c_13070]) ).
tcf(c_429155,plain,
( ( cons(sK10(iPr_def_13),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_429154,c_60]) ).
tcf(c_429156,plain,
cons(sK10(iPr_def_13),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_429155,c_428092]) ).
tcf(c_429443,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_13066,c_140]) ).
tcf(c_429449,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_429443,c_141,c_13075]) ).
tcf(c_429506,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK57 )
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13066,c_143]) ).
tcf(c_429509,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK57 )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_429506,c_141,c_13075]) ).
tcf(c_429526,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13066,c_144]) ).
tcf(c_429529,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_429526,c_141,c_13075]) ).
tcf(c_430252,plain,
( ssList(iPr_def_11)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_13067,c_153]) ).
tcf(c_430253,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_13068,c_153]) ).
tcf(c_430265,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430253,c_429449]) ).
tcf(c_430268,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_430252,c_429449,c_13076]) ).
tcf(c_430269,plain,
ssList(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_430265,c_430268]) ).
tcf(c_430558,plain,
app(nil,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_430268,c_155]) ).
tcf(c_430559,plain,
app(nil,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_430269,c_155]) ).
tcf(c_430844,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sK60)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_13069,c_165]) ).
tcf(c_430849,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430844,c_430269,c_13077]) ).
tcf(c_430912,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_11)
| ~ ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_430558,c_428081]) ).
tcf(c_430915,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430912,c_430268,c_141]) ).
tcf(c_431024,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_430559,c_428081]) ).
tcf(c_431027,plain,
! [X0: $i] :
( segmentP(app(iPr_def_12,X0),iPr_def_12)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_431024,c_430269,c_141]) ).
tcf(c_431053,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK10(iPr_def_13) = X0 )
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK10(iPr_def_13))
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_429156,c_170]) ).
tcf(c_431059,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( sK10(iPr_def_13) = X0 )
| ~ ssItem(X0)
| ~ ssItem(sK10(iPr_def_13))
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_431053,c_141]) ).
tcf(c_432021,plain,
( ( nil = iPr_def_10 )
| ( hd(iPr_def_10) = sK51(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_429449,c_220]) ).
tcf(c_432022,plain,
hd(iPr_def_10) = sK51(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_432021,c_310938]) ).
tcf(c_432210,plain,
( ssItem(hd(iPr_def_10))
| ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_432022,c_219]) ).
tcf(c_432211,plain,
ssItem(hd(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_432210,c_310938,c_429449]) ).
tcf(c_432314,plain,
( ( nil = iPr_def_10 )
| ( tl(iPr_def_10) = sK52(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_429449,c_222]) ).
tcf(c_432315,plain,
tl(iPr_def_10) = sK52(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_432314,c_310938]) ).
tcf(c_432528,plain,
( ssList(tl(iPr_def_10))
| ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_432315,c_221]) ).
tcf(c_432529,plain,
ssList(tl(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_432528,c_310938,c_429449]) ).
tcf(c_432599,plain,
( ( nil = iPr_def_10 )
| ( cons(hd(iPr_def_10),tl(iPr_def_10)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_429449,c_224]) ).
tcf(c_432601,plain,
cons(hd(iPr_def_10),tl(iPr_def_10)) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_432599,c_310938]) ).
tcf(c_439307,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_428697,c_252,c_16427,c_16453,c_52403]) ).
tcf(c_439314,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_13068,c_439307]) ).
tcf(c_439318,plain,
memberP(iPr_def_12,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_439314,c_430268]) ).
tcf(c_440774,plain,
( segmentP(iPr_def_12,iPr_def_11)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_13068,c_430915]) ).
tcf(c_440780,plain,
segmentP(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_440774,c_429449]) ).
tcf(c_440824,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ segmentP(iPr_def_11,iPr_def_12) ),
inference(superposition,[status(thm)],[c_440780,c_191]) ).
tcf(c_440827,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ segmentP(iPr_def_11,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_440824,c_430269,c_430268]) ).
tcf(c_441422,plain,
! [X0: $i] :
( segmentP(app(iPr_def_11,X0),iPr_def_10)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_428924,c_16427,c_428924]) ).
tcf(c_441429,plain,
( segmentP(iPr_def_12,iPr_def_10)
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_13068,c_441422]) ).
tcf(c_441435,plain,
segmentP(iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_441429,c_429449]) ).
tcf(c_441470,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ segmentP(iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_441435,c_191]) ).
tcf(c_441473,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ segmentP(iPr_def_10,iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_441470,c_430269,c_429449]) ).
tcf(c_441521,plain,
( segmentP(iPr_def_13,iPr_def_12)
| ~ ssList(sK60) ),
inference(superposition,[status(thm)],[c_13069,c_431027]) ).
tcf(c_441527,plain,
segmentP(iPr_def_13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_441521,c_13077]) ).
tcf(c_445324,plain,
( ( hd(iPr_def_10) = sK57 )
| ~ ssList(tl(iPr_def_10))
| ~ ssItem(hd(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_432601,c_429509]) ).
tcf(c_445328,plain,
hd(iPr_def_10) = sK57,
inference(forward_subsumption_resolution,[status(thm)],[c_445324,c_432529,c_432211]) ).
tcf(c_445337,plain,
cons(sK57,tl(iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_432601,c_445328]) ).
tcf(c_445436,plain,
( ( tl(iPr_def_10) = nil )
| ~ ssItem(sK57)
| ~ ssList(tl(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_445337,c_429529]) ).
tcf(c_445461,plain,
tl(iPr_def_10) = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_445436,c_13075,c_432529]) ).
tcf(c_445521,plain,
cons(sK57,nil) = iPr_def_10,
inference(demodulation,[status(thm)],[c_445337,c_445461]) ).
tcf(c_465173,plain,
~ segmentP(iPr_def_11,iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_440827,c_37047,c_37084,c_440827]) ).
tcf(c_484817,plain,
( memberP(iPr_def_13,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_439318,c_430849]) ).
tcf(c_484818,plain,
memberP(iPr_def_13,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_484817,c_13075]) ).
tcf(c_492971,plain,
! [X0: $i] :
( ~ memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ( sK10(iPr_def_13) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_431059,c_257,c_141,c_195,c_171,c_307,c_13070,c_20876,c_20919,c_21011,c_21048,c_29309,c_40330,c_228953,c_250576,c_250586,c_277903,c_357086]) ).
tcf(c_492972,plain,
! [X0: $i] :
( ( sK10(iPr_def_13) = X0 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_13,X0) ),
inference(renaming,[status(thm)],[c_492971]) ).
tcf(c_492981,plain,
( ( sK10(iPr_def_13) = sK57 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_484818,c_492972]) ).
tcf(c_492982,plain,
sK10(iPr_def_13) = sK57,
inference(forward_subsumption_resolution,[status(thm)],[c_492981,c_13075]) ).
tcf(c_493000,plain,
cons(sK57,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_429156,c_492982]) ).
tcf(c_493001,plain,
iPr_def_10 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_493000,c_445521]) ).
tcf(c_493034,plain,
segmentP(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_441527,c_493001]) ).
tcf(c_493062,plain,
iPr_def_10 = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_441473,c_493034]) ).
tcf(c_493078,plain,
~ segmentP(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_465173,c_493062]) ).
tcf(c_493262,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_493078,c_36974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC170+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/15.60 % Computer : n002.cluster.edu
% 0.10/15.60 % Model : x86_64 x86_64
% 0.10/15.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.60 % Memory : 8046.5625MB
% 0.10/15.60 % OS : Linux 6.8.0-71-generic
% 0.10/15.60 % CPULimit : 300
% 0.10/15.60 % WCLimit : 300
% 0.10/15.60 % DateTime : Thu Sep 24 16:49:51 UTC 2026
% 0.10/15.61 % CPUTime :
% 0.10/15.61 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/15.64 Running first-order theorem proving
% 0.10/15.64 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.65
% 0.10/15.65 % ======== iProver multi-core TPTP/SMT =========
% 0.10/15.65
% 0.10/15.65 % Detected problem language: tptp
% 0.10/15.67 % Proving...
% 127.00/45.75 % SZS status Started for theBenchmark.p
% 127.00/45.75 % SZS status Theorem for theBenchmark.p
% 127.00/45.75
% 127.00/45.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 127.00/45.75
% 127.00/45.75 % ------ iProver source info
% 127.00/45.75
% 127.00/45.75 % git: date: 2026-07-19 20:42:38 +0200
% 127.00/45.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 127.00/45.75 % git: non_committed_changes: false
% 127.00/45.75
% 127.00/45.75 % ------ Parsing...
% 127.00/45.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 127.00/45.75
% 127.00/45.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 3 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 127.00/45.75
% 127.00/45.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 127.00/45.75
% 127.00/45.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 127.00/45.75 % ------ Proving...
% 127.00/45.75 % ------ Problem Properties
% 127.00/45.75
% 127.00/45.75 %
% 127.00/45.75 % clauses 193
% 127.00/45.75 % conjectures 6
% 127.00/45.75 % EPR 58
% 127.00/45.75 % Horn 124
% 127.00/45.75 % unary 28
% 127.00/45.75 % binary 41
% 127.00/45.75 % lits 632
% 127.00/45.75 % lits eq 85
% 127.00/45.75 % fd_pure 0
% 127.00/45.75 % fd_pseudo 0
% 127.00/45.75 % fd_cond 21
% 127.00/45.75 % fd_pseudo_cond 14
% 127.00/45.75 % AC symbols 0
% 127.00/45.75
% 127.00/45.75 % ------ Schedule dynamic 5 is on
% 127.00/45.75
% 127.00/45.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 127.00/45.75
% 127.00/45.75
% 127.00/45.75 % ------
% 127.00/45.75 % Current options:
% 127.00/45.75 % ------
% 127.00/45.75
% 127.00/45.75
% 127.00/45.75 %
% 127.00/45.75
% 127.00/45.75 % ------ Proving...
% 127.00/45.75 % Proof_search_loop: time out after: 9080 full_loop iterations
% 127.00/45.75
% 127.00/45.75 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 127.00/45.75
% 127.00/45.75
% 127.00/45.75 % ------
% 127.00/45.75 % Current options:
% 127.00/45.75 % ------
% 127.00/45.75
% 127.00/45.75
% 127.00/45.75 %
% 127.00/45.75
% 127.00/45.75 % ------ Proving...
% 127.00/45.75 % Proof_search_loop: time out after: 10340 full_loop iterations
% 127.00/45.75
% 127.00/45.75 % ------ Option_1: Negative Selections Time Limit: 35.
% 127.00/45.75
% 127.00/45.75
% 127.00/45.75 % ------
% 127.00/45.75 % Current options:
% 127.00/45.75 % ------
% 127.00/45.75
% 127.00/45.75
% 127.00/45.75 %
% 127.00/45.75
% 127.00/45.75 % ------ Proving...
% 127.00/45.75 %
% 127.00/45.75
% 127.00/45.75 % SZS status Theorem for theBenchmark.p
% 127.00/45.75
% 127.00/45.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 127.00/45.76
% 127.00/45.76
%------------------------------------------------------------------------------