%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC295+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 : n003.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 03:09:11 PM UTC 2026
% Result : Theorem 50.26s 12.06s
% Output : CNFRefutation 50.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 32
% Syntax : Number of formulae : 296 ( 72 unt; 4 def)
% Number of atoms : 1232 ( 347 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1189 ( 467 ~; 518 |; 121 &)
% ( 14 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 349 ( 0 sgn 311 !; 38 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
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(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
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(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
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(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax41) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax46) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax65) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax67) ).
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(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
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(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(app(X0,X1)) = hd(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X8,X9)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ! [X7] :
( ssItem(X7)
=> ( ( lt(X4,X7)
| ~ memberP(X6,X7) )
& ( lt(X7,X4)
| ~ memberP(X5,X7) ) ) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
| 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)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X8,X9)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ! [X7] :
( ssItem(X7)
=> ( ( lt(X4,X7)
| ~ memberP(X6,X7) )
& ( lt(X7,X4)
| ~ memberP(X5,X7) ) ) )
| app(app(X5,cons(X4,nil)),X6) != X0 ) ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
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(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f131,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ) ),
inference(ennf_transformation,[],[f25]) ).
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(f151,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f152,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f151]) ).
fof(f158,plain,
! [X0] :
( ~ ssList(X0)
| ( frontsegP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f180,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f181,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f67]) ).
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(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
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(f202,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| nil = X0
| hd(app(X0,X1)) = hd(X0) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f203,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| nil = X0
| hd(app(X0,X1)) = hd(X0) ) ),
inference(flattening,[],[f202]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ leq(X8,X9)
| ~ memberP(X3,X9)
| X8 = X9
| ~ ssItem(X9) )
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssItem(X7)
& ( ( ~ lt(X4,X7)
& memberP(X6,X7) )
| ( ~ lt(X7,X4)
& memberP(X5,X7) ) ) )
& app(app(X5,cons(X4,nil)),X6) = X0 ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil = X2
& nil = X3 )
| ? [X8] :
( ssItem(X8)
& ! [X9] :
( ~ leq(X8,X9)
| ~ memberP(X3,X9)
| X8 = X9
| ~ ssItem(X9) )
& memberP(X3,X8)
& cons(X8,nil) = X2 ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& ? [X7] :
( ssItem(X7)
& ( ( ~ lt(X4,X7)
& memberP(X6,X7) )
| ( ~ lt(X7,X4)
& memberP(X5,X7) ) ) )
& app(app(X5,cons(X4,nil)),X6) = X0 ) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
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(f240,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f241,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f240]) ).
fof(f242,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f241]) ).
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(f283,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ frontsegP(nil,X0)
| nil = X0 )
& ( nil != X0
| frontsegP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f158]) ).
fof(f286,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ totalorderedP(cons(X0,X1))
| ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 )
& ( ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 )
| totalorderedP(cons(X0,X1)) ) ) ) ),
inference(nnf_transformation,[],[f181]) ).
fof(f287,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ totalorderedP(cons(X0,X1))
| ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 )
& ( ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 )
| totalorderedP(cons(X0,X1)) ) ) ) ),
inference(flattening,[],[f286]) ).
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)
& ( ( nil = sK55
& nil = sK56 )
| ( ssItem(sK61)
& ! [X9] :
( ~ leq(sK61,X9)
| ~ memberP(sK56,X9)
| sK61 = X9
| ~ ssItem(X9) )
& memberP(sK56,sK61)
& sK55 = cons(sK61,nil) ) )
& ssItem(sK57)
& ssList(sK58)
& ssList(sK59)
& ssItem(sK60)
& ( ( ~ lt(sK57,sK60)
& memberP(sK59,sK60) )
| ( ~ lt(sK60,sK57)
& memberP(sK58,sK60) ) )
& sK53 = app(app(sK58,cons(sK57,nil)),sK59)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59),skolemize(X7,sK60),skolemize(X8,sK61)],[f222]) ).
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(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
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(f398,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
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(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(f422,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f152]) ).
fof(f429,plain,
! [X0] :
( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f283]) ).
fof(f451,plain,
! [X0] :
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f180]) ).
fof(f454,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(cons(X0,X1))
| totalorderedP(X1)
| nil = X1 ),
inference(cnf_transformation,[],[f287]) ).
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(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
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(f483,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil = sK55
| ssItem(sK61) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( nil = sK56
| ssItem(sK61) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( nil = sK55
| sK55 = cons(sK61,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
ssItem(sK60),
inference(cnf_transformation,[],[f296]) ).
fof(f515,plain,
( memberP(sK59,sK60)
| memberP(sK58,sK60) ),
inference(cnf_transformation,[],[f296]) ).
fof(f516,plain,
sK53 = app(app(sK58,cons(sK57,nil)),sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f517,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f519,plain,
sK55 = app(app(sK58,cons(sK57,nil)),sK59),
inference(definition_unfolding,[],[f516,f517]) ).
fof(f521,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f517]) ).
fof(f523,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(f525,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
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,[],[f523]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f525]) ).
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_150,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X0,X1)) = X1 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f400]) ).
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_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_174,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f422]) ).
tcf(c_182,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f429]) ).
tcf(c_203,plain,
! [X0: $i] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f451]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i] :
( totalorderedP(X1)
| ( X1 = nil )
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ totalorderedP(cons(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
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_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
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_233,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ( hd(app(X0,X1)) = hd(X0) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f483]) ).
tcf(c_246,negated_conjecture,
app(app(sK58,cons(sK57,nil)),sK59) = sK55,
inference(cnf_transformation,[],[f519]) ).
tcf(c_247,negated_conjecture,
( memberP(sK59,sK60)
| memberP(sK58,sK60) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_251,negated_conjecture,
ssItem(sK60),
inference(cnf_transformation,[],[f511]) ).
tcf(c_252,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f510]) ).
tcf(c_253,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f509]) ).
tcf(c_254,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f508]) ).
tcf(c_256,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK61,nil) = sK55 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_261,negated_conjecture,
( ssItem(sK61)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_262,negated_conjecture,
( ssItem(sK61)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_266,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f521]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_9042,definition,
iPr_def_10 = cons(sK61,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9043,definition,
iPr_def_11 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_9044,definition,
iPr_def_12 = app(sK58,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_9045,definition,
iPr_def_13 = app(iPr_def_12,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_9046,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_266]) ).
tcf(c_9048,negated_conjecture,
( ssItem(sK61)
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_262]) ).
tcf(c_9049,negated_conjecture,
( ssItem(sK61)
| ( nil = sK56 ) ),
inference(demodulation,[status(thm)],[c_261]) ).
tcf(c_9054,negated_conjecture,
( ( iPr_def_10 = sK55 )
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_256,c_9042]) ).
tcf(c_9056,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_9057,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_9058,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_9064,negated_conjecture,
iPr_def_13 = sK55,
inference(demodulation,[status(thm)],[c_246,c_9043,c_9044,c_9045]) ).
tcf(c_9065,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_9071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_12004,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_9046,c_9064]) ).
tcf(c_12005,plain,
( ssItem(sK61)
| ( nil = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_9048,c_9064]) ).
tcf(c_12035,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_9054,c_9064]) ).
tcf(c_12331,plain,
( totalorderedP(iPr_def_10)
| ~ ssItem(sK61) ),
inference(superposition,[status(thm)],[c_9042,c_203]) ).
tcf(c_12345,plain,
( totalorderedP(iPr_def_10)
| ( nil = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_12005,c_12331]) ).
tcf(c_12418,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,nil))) ),
inference(superposition,[status(thm)],[c_9043,c_54]) ).
tcf(c_12428,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_12418,c_9043]) ).
tcf(c_12429,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12428,c_141,c_9056]) ).
tcf(c_12518,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(sK58)
| ~ ssList(app(sK58,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_9044,c_12429]) ).
tcf(c_12519,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12)
| ~ ssList(sK58) ),
inference(light_normalisation,[status(thm)],[c_12518,c_9044]) ).
tcf(c_12520,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12519,c_9057]) ).
tcf(c_12958,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_9043,c_140]) ).
tcf(c_12959,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK61) ),
inference(superposition,[status(thm)],[c_9042,c_140]) ).
tcf(c_12964,plain,
( ssList(iPr_def_10)
| ~ ssItem(sK61) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12959,c_141]) ).
tcf(c_12967,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_12958,c_141,c_9056]) ).
tcf(c_12980,plain,
app(nil,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_12967,c_155]) ).
tcf(c_12985,plain,
( ssList(iPr_def_10)
| ( nil = sK56 ) ),
inference(superposition,[status(thm)],[c_9049,c_12964]) ).
tcf(c_13091,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_9044,c_153]) ).
tcf(c_13108,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_13091,c_12967,c_9057]) ).
tcf(c_13124,plain,
memberP(iPr_def_12,sK57),
inference(backward_subsumption_resolution,[status(thm)],[c_12520,c_13108]) ).
tcf(c_13129,plain,
app(iPr_def_12,nil) = iPr_def_12,
inference(superposition,[status(thm)],[c_13108,c_232]) ).
tcf(c_13458,plain,
! [X0: $i] :
( ( iPr_def_10 = iPr_def_13 )
| ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_12035,c_182]) ).
tcf(c_13633,plain,
( ~ ssItem(sK60)
| ~ memberP(nil,sK60) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_13755,plain,
( frontsegP(iPr_def_13,iPr_def_12)
| ~ ssList(iPr_def_12)
| ~ ssList(sK59) ),
inference(superposition,[status(thm)],[c_9045,c_390]) ).
tcf(c_13795,plain,
frontsegP(iPr_def_13,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_13755,c_13108,c_9058]) ).
tcf(c_13910,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_9043,c_142]) ).
tcf(c_13917,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_13910,c_141,c_9056]) ).
tcf(c_13947,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_13795,c_13458]) ).
tcf(c_13948,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13947,c_13108]) ).
tcf(c_14409,plain,
( ( nil = iPr_def_13 )
| ( hd(iPr_def_13) = sK51(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_12004,c_220]) ).
tcf(c_14609,plain,
( ( nil = iPr_def_12 )
| ( tl(iPr_def_12) = sK52(iPr_def_12) ) ),
inference(superposition,[status(thm)],[c_13108,c_222]) ).
tcf(c_14612,plain,
( ( nil = iPr_def_10 )
| ( nil = sK56 )
| ( tl(iPr_def_10) = sK52(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_12985,c_222]) ).
tcf(c_14767,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sK58,sK60)
| ( X1 != sK60 )
| ( X0 != sK58 ) ),
inference(instantiation,[status(thm)],[c_9071]) ).
tcf(c_16556,plain,
( ssItem(hd(iPr_def_13))
| ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_14409,c_219]) ).
tcf(c_16557,plain,
( ssItem(hd(iPr_def_13))
| ( nil = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16556,c_12004]) ).
tcf(c_16601,plain,
( ( nil = iPr_def_13 )
| ( cons(hd(iPr_def_13),tl(iPr_def_13)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_12004,c_224]) ).
tcf(c_16602,plain,
( ( nil = iPr_def_12 )
| ( cons(hd(iPr_def_12),tl(iPr_def_12)) = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13108,c_224]) ).
tcf(c_17671,plain,
( ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK58)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_9044,c_230]) ).
tcf(c_17707,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_17671,c_13917,c_12967,c_9057]) ).
tcf(c_17709,plain,
iPr_def_10 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_13948,c_17707]) ).
tcf(c_17713,plain,
frontsegP(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_13795,c_17709]) ).
tcf(c_17726,plain,
( totalorderedP(iPr_def_10)
| ( nil = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_12345,c_17709]) ).
tcf(c_17727,plain,
app(iPr_def_12,sK59) = iPr_def_10,
inference(demodulation,[status(thm)],[c_9045,c_17709]) ).
tcf(c_17730,plain,
( ssItem(sK61)
| ( nil = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_12005,c_17709]) ).
tcf(c_17732,plain,
ssList(iPr_def_10),
inference(demodulation,[status(thm)],[c_12004,c_17709]) ).
tcf(c_17851,plain,
( ( nil = iPr_def_10 )
| ( tl(iPr_def_10) = sK52(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_17732,c_222]) ).
tcf(c_18381,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ frontsegP(iPr_def_12,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17713,c_174]) ).
tcf(c_18382,plain,
( ( iPr_def_10 = iPr_def_12 )
| ~ frontsegP(iPr_def_12,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18381,c_13108,c_17732]) ).
tcf(c_19290,plain,
! [X0: $i] :
( ( nil = iPr_def_12 )
| ( hd(app(iPr_def_12,X0)) = hd(iPr_def_12) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_13108,c_233]) ).
tcf(c_19303,plain,
! [X0: $i] :
( ( hd(app(iPr_def_12,X0)) = hd(iPr_def_12) )
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19290,c_17707]) ).
tcf(c_19532,plain,
! [X0: $i] :
( memberP(X0,sK60)
| ~ memberP(sK58,sK60)
| ( sK60 != sK60 )
| ( X0 != sK58 ) ),
inference(instantiation,[status(thm)],[c_14767]) ).
tcf(c_19533,plain,
sK60 = sK60,
inference(instantiation,[status(thm)],[c_9065]) ).
tcf(c_19534,plain,
( memberP(nil,sK60)
| ~ memberP(sK58,sK60)
| ( sK60 != sK60 )
| ( nil != sK58 ) ),
inference(instantiation,[status(thm)],[c_19532]) ).
tcf(c_19712,plain,
tl(iPr_def_12) = sK52(iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_14609,c_14609,c_17707]) ).
tcf(c_19714,plain,
( ssList(tl(iPr_def_12))
| ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_19712,c_221]) ).
tcf(c_19715,plain,
ssList(tl(iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_19714,c_17707,c_13108]) ).
tcf(c_20286,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ( nil != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17727,c_231]) ).
tcf(c_20292,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_17727,c_165]) ).
tcf(c_20296,plain,
nil != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_20286,c_17707,c_13108,c_9058]) ).
tcf(c_20305,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20292,c_13108,c_9058]) ).
tcf(c_20313,plain,
totalorderedP(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_17726,c_20296]) ).
tcf(c_20390,plain,
tl(iPr_def_10) = sK52(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_14612,c_17851,c_20296]) ).
tcf(c_20392,plain,
( ssList(tl(iPr_def_10))
| ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_20390,c_221]) ).
tcf(c_20393,plain,
ssList(tl(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_20392,c_20296,c_17732]) ).
tcf(c_20731,plain,
ssItem(sK61),
inference(global_subsumption_just,[status(thm)],[c_17730,c_17730,c_20296]) ).
tcf(c_20739,plain,
! [X0: $i] :
( ( app(cons(sK61,nil),X0) = cons(sK61,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_20731,c_227]) ).
tcf(c_20740,plain,
! [X0: $i] :
( ( tl(cons(sK61,X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_20731,c_152]) ).
tcf(c_20741,plain,
! [X0: $i] :
( ( hd(cons(sK61,X0)) = sK61 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_20731,c_150]) ).
tcf(c_20746,plain,
! [X0: $i] :
( ( cons(sK61,X0) = app(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_20739,c_9042]) ).
tcf(c_20759,plain,
( memberP(iPr_def_10,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_13124,c_20305]) ).
tcf(c_20762,plain,
memberP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_20759,c_9056]) ).
tcf(c_24769,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_9042,c_170]) ).
tcf(c_24776,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24769,c_141,c_20731]) ).
tcf(c_25248,plain,
! [X0: $i] :
( ( X0 = sK58 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK58)
| ~ ssList(X0)
| ( app(X0,iPr_def_11) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_9044,c_225]) ).
tcf(c_25345,plain,
! [X0: $i] :
( ( X0 = sK58 )
| ~ ssList(X0)
| ( app(X0,iPr_def_11) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25248,c_12967,c_9057]) ).
tcf(c_25738,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sK59,sK60)
| ( X1 != sK60 )
| ( X0 != sK59 ) ),
inference(instantiation,[status(thm)],[c_9071]) ).
tcf(c_25899,plain,
! [X0: $i] :
( ( X0 = sK59 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ~ ssList(X0)
| ( app(iPr_def_12,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17727,c_226]) ).
tcf(c_25993,plain,
! [X0: $i] :
( ( X0 = sK59 )
| ~ ssList(X0)
| ( app(iPr_def_12,X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25899,c_13108,c_9058]) ).
tcf(c_29662,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( tl(cons(sK61,X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_9049,c_152]) ).
tcf(c_30951,plain,
( ssItem(hd(iPr_def_10))
| ( nil = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_16557,c_17709]) ).
tcf(c_30952,plain,
ssItem(hd(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_30951,c_20296]) ).
tcf(c_32456,plain,
( ( nil = sK58 )
| ~ ssList(nil)
| ( iPr_def_11 != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_12980,c_25345]) ).
tcf(c_32457,plain,
( ( nil = sK58 )
| ( iPr_def_11 != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32456,c_141]) ).
tcf(c_32936,plain,
( ( nil = sK59 )
| ~ ssList(nil)
| ( iPr_def_10 != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_13129,c_25993]) ).
tcf(c_32938,plain,
( ( nil = sK59 )
| ( iPr_def_10 != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32936,c_141]) ).
tcf(c_42399,plain,
! [X0: $i] :
( memberP(X0,sK60)
| ~ memberP(sK59,sK60)
| ( sK60 != sK60 )
| ( X0 != sK59 ) ),
inference(instantiation,[status(thm)],[c_25738]) ).
tcf(c_42400,plain,
( memberP(nil,sK60)
| ~ memberP(sK59,sK60)
| ( sK60 != sK60 )
| ( nil != sK59 ) ),
inference(instantiation,[status(thm)],[c_42399]) ).
tcf(c_46545,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( tl(cons(sK61,X0)) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_29662,c_20740]) ).
tcf(c_46546,plain,
! [X0: $i] :
( ( tl(cons(sK61,X0)) = X0 )
| ~ ssList(X0) ),
inference(renaming,[status(thm)],[c_46545]) ).
tcf(c_46579,plain,
tl(cons(sK61,nil)) = nil,
inference(superposition,[status(thm)],[c_141,c_46546]) ).
tcf(c_46592,plain,
tl(iPr_def_10) = nil,
inference(light_normalisation,[status(thm)],[c_46579,c_9042]) ).
tcf(c_48172,plain,
( ( nil = iPr_def_10 )
| ( cons(hd(iPr_def_10),tl(iPr_def_10)) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_16601,c_17709]) ).
tcf(c_48173,plain,
cons(hd(iPr_def_10),tl(iPr_def_10)) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_48172,c_20296]) ).
tcf(c_48205,plain,
( totalorderedP(tl(iPr_def_10))
| ( tl(iPr_def_10) = nil )
| ~ totalorderedP(iPr_def_10)
| ~ ssList(tl(iPr_def_10))
| ~ ssItem(hd(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_48173,c_207]) ).
tcf(c_48234,plain,
( totalorderedP(tl(iPr_def_10))
| ( tl(iPr_def_10) = nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48205,c_20313,c_20393,c_30952]) ).
tcf(c_48628,plain,
tl(iPr_def_10) = nil,
inference(global_subsumption_just,[status(thm)],[c_48234,c_46592]) ).
tcf(c_48632,plain,
cons(hd(iPr_def_10),nil) = iPr_def_10,
inference(demodulation,[status(thm)],[c_48173,c_48628]) ).
tcf(c_48936,plain,
cons(hd(iPr_def_12),tl(iPr_def_12)) = iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_16602,c_16602,c_17707]) ).
tcf(c_53844,plain,
hd(cons(sK61,nil)) = sK61,
inference(superposition,[status(thm)],[c_141,c_20741]) ).
tcf(c_53870,plain,
hd(iPr_def_10) = sK61,
inference(light_normalisation,[status(thm)],[c_53844,c_9042]) ).
tcf(c_53971,plain,
cons(sK61,nil) = iPr_def_10,
inference(demodulation,[status(thm)],[c_48632,c_53870]) ).
tcf(c_128163,plain,
hd(app(iPr_def_12,sK59)) = hd(iPr_def_12),
inference(superposition,[status(thm)],[c_9058,c_19303]) ).
tcf(c_128226,plain,
hd(iPr_def_12) = sK61,
inference(light_normalisation,[status(thm)],[c_128163,c_17727,c_53870]) ).
tcf(c_128371,plain,
cons(sK61,tl(iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_48936,c_128226]) ).
tcf(c_128988,plain,
cons(sK61,sK59) = app(iPr_def_10,sK59),
inference(superposition,[status(thm)],[c_9058,c_20746]) ).
tcf(c_129003,plain,
cons(sK61,tl(iPr_def_12)) = app(iPr_def_10,tl(iPr_def_12)),
inference(superposition,[status(thm)],[c_19715,c_20746]) ).
tcf(c_129052,plain,
app(iPr_def_10,tl(iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_129003,c_128371]) ).
tcf(c_129692,plain,
! [X0: $i] :
( memberP(cons(sK61,sK59),X0)
| ~ ssList(iPr_def_10)
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_128988,c_165]) ).
tcf(c_129732,plain,
! [X0: $i] :
( memberP(cons(sK61,sK59),X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129692,c_17732,c_9058]) ).
tcf(c_132846,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ( X0 = sK61 )
| ~ ssList(sK59)
| ~ ssItem(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_129732,c_170]) ).
tcf(c_132847,plain,
! [X0: $i] :
( memberP(sK59,X0)
| ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_132846,c_9058,c_20731]) ).
tcf(c_133974,plain,
( frontsegP(iPr_def_12,iPr_def_10)
| ~ ssList(iPr_def_10)
| ~ ssList(tl(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_129052,c_390]) ).
tcf(c_133990,plain,
frontsegP(iPr_def_12,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_133974,c_17732,c_19715]) ).
tcf(c_134032,plain,
iPr_def_10 = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_18382,c_133990]) ).
tcf(c_134177,plain,
( ( nil = sK58 )
| ( iPr_def_10 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_32457,c_134032]) ).
tcf(c_136328,plain,
! [X0: $i] :
( ~ memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ( X0 = sK61 ) ),
inference(global_subsumption_just,[status(thm)],[c_132847,c_171,c_24776]) ).
tcf(c_136329,plain,
! [X0: $i] :
( ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(renaming,[status(thm)],[c_136328]) ).
tcf(c_136339,plain,
( ( sK57 = sK61 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_20762,c_136329]) ).
tcf(c_136341,plain,
sK57 = sK61,
inference(forward_subsumption_resolution,[status(thm)],[c_136339,c_9056]) ).
tcf(c_136582,plain,
cons(sK61,nil) = iPr_def_11,
inference(demodulation,[status(thm)],[c_9043,c_136341]) ).
tcf(c_136584,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_136582,c_53971]) ).
tcf(c_136986,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_136584,c_134177,c_133990,c_42400,c_32938,c_19533,c_19534,c_18382,c_13633,c_247,c_251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC295+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/3.57 % Computer : n003.cluster.edu
% 0.10/3.57 % Model : x86_64 x86_64
% 0.10/3.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/3.57 % Memory : 8046.5625MB
% 0.10/3.57 % OS : Linux 6.8.0-71-generic
% 0.10/3.57 % CPULimit : 300
% 0.10/3.57 % WCLimit : 300
% 0.10/3.57 % DateTime : Thu Sep 24 17:30:10 UTC 2026
% 0.10/3.57 % CPUTime :
% 0.10/3.57 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/3.62 Running first-order theorem proving
% 0.15/3.62 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
% 0.15/3.63
% 0.15/3.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/3.63
% 0.15/3.63 % Detected problem language: tptp
% 0.15/3.64 % Proving...
% 50.26/12.06 % SZS status Started for theBenchmark.p
% 50.26/12.06 % SZS status Theorem for theBenchmark.p
% 50.26/12.06
% 50.26/12.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.26/12.06
% 50.26/12.06 % ------ iProver source info
% 50.26/12.06
% 50.26/12.06 % git: date: 2026-07-19 20:42:38 +0200
% 50.26/12.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.26/12.06 % git: non_committed_changes: false
% 50.26/12.06
% 50.26/12.06 % ------ Parsing...
% 50.26/12.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.26/12.06
% 50.26/12.06 % ------ 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: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 50.26/12.06
% 50.26/12.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.26/12.06
% 50.26/12.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 50.26/12.06 % ------ Proving...
% 50.26/12.06 % ------ Problem Properties
% 50.26/12.06
% 50.26/12.06 %
% 50.26/12.06 % clauses 203
% 50.26/12.06 % conjectures 19
% 50.26/12.06 % EPR 68
% 50.26/12.06 % Horn 126
% 50.26/12.06 % unary 27
% 50.26/12.06 % binary 50
% 50.26/12.06 % lits 659
% 50.26/12.06 % lits eq 95
% 50.26/12.06 % fd_pure 0
% 50.26/12.06 % fd_pseudo 0
% 50.26/12.06 % fd_cond 23
% 50.26/12.06 % fd_pseudo_cond 14
% 50.26/12.06 % AC symbols 0
% 50.26/12.06
% 50.26/12.06 % ------ Schedule dynamic 5 is on
% 50.26/12.06
% 50.26/12.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 50.26/12.06
% 50.26/12.06
% 50.26/12.06 % ------
% 50.26/12.06 % Current options:
% 50.26/12.06 % ------
% 50.26/12.06
% 50.26/12.06
% 50.26/12.06 %
% 50.26/12.06
% 50.26/12.06 % ------ Proving...
% 50.26/12.06 %
% 50.26/12.06
% 50.26/12.06 % SZS status Theorem for theBenchmark.p
% 50.26/12.06
% 50.26/12.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.26/12.07
% 50.26/12.07
%------------------------------------------------------------------------------