%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC284+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 : n008.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 03:09:08 PM UTC 2026
% Result : Theorem 134.64s 21.70s
% Output : CNFRefutation 134.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 21
% Syntax : Number of formulae : 265 ( 76 unt; 4 def)
% Number of atoms : 1010 ( 228 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 965 ( 407 ~; 434 |; 73 &)
% ( 12 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 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 : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 235 ( 0 sgn 215 !; 20 ?; 74 :)
% 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(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(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax31) ).
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(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(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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ! [X8] :
( ~ memberP(X3,X8)
| cons(X8,nil) != X2
| ~ ssItem(X8) ) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ! [X7] :
( ssItem(X7)
=> ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ! [X8] :
( ~ memberP(X3,X8)
| cons(X8,nil) != X2
| ~ ssItem(X8) ) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ! [X7] :
( ssItem(X7)
=> ( ( leq(X4,X7)
| ~ memberP(X6,X7) )
& ( leq(X7,X4)
| ~ memberP(X5,X7) ) ) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(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(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(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f139,plain,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
inference(ennf_transformation,[],[f31]) ).
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(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(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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ~ neq(X3,nil)
| ? [X8] :
( memberP(X3,X8)
& cons(X8,nil) = X2
& ssItem(X8) ) )
& ( nil != X3
| nil = X2 )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ? [X7] :
( ssItem(X7)
& ( ( ~ leq(X4,X7)
& memberP(X6,X7) )
| ( ~ leq(X7,X4)
& memberP(X5,X7) ) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f233,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(f234,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,[],[f233]) ).
fof(f235,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))],[f234]) ).
fof(f272,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f276,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(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(flattening,[],[f276]) ).
fof(f278,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(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(flattening,[],[f278]) ).
fof(f284,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
fof(f289,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)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f200]) ).
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(flattening,[],[f291]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ( ~ neq(sK56,nil)
| ( memberP(sK56,sK61)
& sK55 = cons(sK61,nil)
& ssItem(sK61) ) )
& ( nil != sK56
| nil = sK55 )
& ssItem(sK57)
& ssList(sK58)
& ssItem(sK60)
& ( ( ~ leq(sK57,sK60)
& memberP(sK59,sK60) )
| ( ~ leq(sK60,sK57)
& memberP(sK58,sK60) ) )
& sK53 = app(app(sK58,cons(sK57,nil)),sK59)
& ssList(sK59)
& sK53 = sK55
& sK54 = sK56
& ssList(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)],[f221]) ).
fof(f304,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,[],[f235]) ).
fof(f386,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f389,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f397,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f400,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f405,plain,
! [X0] :
( ~ ssItem(X0)
| leq(X0,X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f413,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X2,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f414,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ memberP(X1,X0)
| memberP(app(X1,X2),X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f415,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f279]) ).
fof(f418,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f442,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f284]) ).
fof(f443,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f468,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK51(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f289]) ).
fof(f476,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f478,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f292]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f292]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f496,plain,
ssList(sK54),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( ~ neq(sK56,nil)
| sK55 = cons(sK61,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| ssItem(sK61) ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
ssList(sK58),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
ssItem(sK60),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
( ~ leq(sK57,sK60)
| ~ leq(sK60,sK57) ),
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
( memberP(sK59,sK60)
| memberP(sK58,sK60) ),
inference(cnf_transformation,[],[f295]) ).
fof(f509,plain,
sK53 = app(app(sK58,cons(sK57,nil)),sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
ssList(sK59),
inference(cnf_transformation,[],[f295]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f512,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f514,plain,
sK55 = app(app(sK58,cons(sK57,nil)),sK59),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f515,plain,
ssList(sK56),
inference(definition_unfolding,[],[f496,f512]) ).
fof(f516,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f511]) ).
fof(f518,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,[],[f304]) ).
fof(f536,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f443]) ).
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,[],[f518]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f389]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f400]) ).
tcf(c_158,plain,
! [X0: $i] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f405]) ).
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,[],[f414]) ).
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,[],[f413]) ).
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,[],[f415]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f418]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f536]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f442]) ).
tcf(c_219,plain,
! [X0: $i] :
( ssItem(sK51(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f469]) ).
tcf(c_220,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(X0) = sK51(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f468]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
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,[],[f479]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f478]) ).
tcf(c_247,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f510]) ).
tcf(c_248,negated_conjecture,
app(app(sK58,cons(sK57,nil)),sK59) = sK55,
inference(cnf_transformation,[],[f514]) ).
tcf(c_249,negated_conjecture,
( memberP(sK58,sK60)
| memberP(sK59,sK60) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_252,negated_conjecture,
( ~ leq(sK60,sK57)
| ~ leq(sK57,sK60) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_253,negated_conjecture,
ssItem(sK60),
inference(cnf_transformation,[],[f504]) ).
tcf(c_254,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f503]) ).
tcf(c_255,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f502]) ).
tcf(c_256,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_257,negated_conjecture,
( ssItem(sK61)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_258,negated_conjecture,
( ( cons(sK61,nil) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f499]) ).
tcf(c_261,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f515]) ).
tcf(c_262,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f516]) ).
tcf(c_312,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_3286,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(sK61,nil) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_258]) ).
tcf(c_3287,plain,
( ( sK56 = nil )
| ( cons(sK61,nil) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3286]) ).
tcf(c_3288,plain,
( ( sK56 = nil )
| ( cons(sK61,nil) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_3287,c_261,c_141,c_3287]) ).
tcf(c_3296,plain,
! [X0: $i,X1: $i] :
( ssItem(sK61)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK56 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_257]) ).
tcf(c_3297,plain,
( ssItem(sK61)
| ( sK56 = nil )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3296]) ).
tcf(c_3298,plain,
( ssItem(sK61)
| ( sK56 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3297,c_261,c_141,c_3297]) ).
tcf(c_8967,definition,
iPr_def_10 = cons(sK61,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8968,definition,
iPr_def_11 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8969,definition,
iPr_def_12 = app(sK58,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8970,definition,
iPr_def_13 = app(iPr_def_12,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8971,plain,
( ssItem(sK61)
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3298]) ).
tcf(c_8972,plain,
( ( iPr_def_10 = sK55 )
| ( sK56 = nil ) ),
inference(demodulation,[status(thm)],[c_3288,c_8967]) ).
tcf(c_8974,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_262]) ).
tcf(c_8975,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(demodulation,[status(thm)],[c_256]) ).
tcf(c_8976,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_255]) ).
tcf(c_8977,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8978,negated_conjecture,
ssItem(sK60),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_8979,negated_conjecture,
( ~ leq(sK60,sK57)
| ~ leq(sK57,sK60) ),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_8982,negated_conjecture,
( memberP(sK58,sK60)
| memberP(sK59,sK60) ),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_8983,negated_conjecture,
iPr_def_13 = sK55,
inference(demodulation,[status(thm)],[c_248,c_8968,c_8969,c_8970]) ).
tcf(c_8984,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_8985,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_261]) ).
tcf(c_8988,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_11869,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_8974,c_8983]) ).
tcf(c_11884,plain,
( ( nil = iPr_def_13 )
| ( nil != sK56 ) ),
inference(light_normalisation,[status(thm)],[c_8975,c_8983]) ).
tcf(c_11899,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_8972,c_8983]) ).
tcf(c_11907,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_11899,c_11884]) ).
tcf(c_12152,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_8968,c_54]) ).
tcf(c_12162,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_12152,c_8968]) ).
tcf(c_12163,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_12162,c_141,c_8976]) ).
tcf(c_12244,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(sK58)
| ~ ssList(app(sK58,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8969,c_12163]) ).
tcf(c_12245,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12)
| ~ ssList(sK58) ),
inference(light_normalisation,[status(thm)],[c_12244,c_8969]) ).
tcf(c_12246,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12245,c_8977]) ).
tcf(c_12775,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8968,c_140]) ).
tcf(c_12776,plain,
( ssList(iPr_def_10)
| ~ ssList(nil)
| ~ ssItem(sK61) ),
inference(superposition,[status(thm)],[c_8967,c_140]) ).
tcf(c_12781,plain,
( ssList(iPr_def_10)
| ~ ssItem(sK61) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12776,c_141]) ).
tcf(c_12784,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_12775,c_141,c_8976]) ).
tcf(c_12822,plain,
( ssList(iPr_def_10)
| ( nil = sK56 ) ),
inference(superposition,[status(thm)],[c_8971,c_12781]) ).
tcf(c_12883,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_8969,c_153]) ).
tcf(c_12903,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12883,c_12784,c_8977]) ).
tcf(c_13567,plain,
( leq(sK60,sK60)
| ~ ssItem(sK60) ),
inference(instantiation,[status(thm)],[c_158]) ).
tcf(c_13749,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8968,c_142]) ).
tcf(c_13756,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_13749,c_141,c_8976]) ).
tcf(c_14378,plain,
( ( nil = iPr_def_13 )
| ( hd(iPr_def_13) = sK51(iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_11869,c_220]) ).
tcf(c_14381,plain,
( ( nil = iPr_def_10 )
| ( nil = sK56 )
| ( hd(iPr_def_10) = sK51(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_12822,c_220]) ).
tcf(c_16068,plain,
ssList(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_8974,c_8983]) ).
tcf(c_16083,plain,
( ( nil = iPr_def_13 )
| ( nil != sK56 ) ),
inference(light_normalisation,[status(thm)],[c_8975,c_8983]) ).
tcf(c_16098,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_8972,c_8983]) ).
tcf(c_16106,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( nil = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_16098,c_16083]) ).
tcf(c_16554,plain,
( ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK58)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8969,c_230]) ).
tcf(c_16591,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_16554,c_13756,c_12784,c_8977]) ).
tcf(c_16620,plain,
( ( iPr_def_10 = iPr_def_13 )
| ( cons(sK57,iPr_def_13) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_16106,c_8968]) ).
tcf(c_16843,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ( iPr_def_10 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_16620,c_54]) ).
tcf(c_16855,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_11),sK57)
| ( iPr_def_10 = iPr_def_13 )
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,iPr_def_13))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16843,c_16068,c_8976]) ).
tcf(c_17193,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8970,c_231]) ).
tcf(c_17226,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_17193,c_16591,c_12903,c_8984]) ).
tcf(c_17227,plain,
iPr_def_10 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_11907,c_17226]) ).
tcf(c_17228,plain,
nil != sK56,
inference(backward_subsumption_resolution,[status(thm)],[c_11884,c_17226]) ).
tcf(c_17239,plain,
app(iPr_def_12,sK59) = iPr_def_10,
inference(demodulation,[status(thm)],[c_8970,c_17227]) ).
tcf(c_17241,plain,
ssList(iPr_def_10),
inference(demodulation,[status(thm)],[c_11869,c_17227]) ).
tcf(c_17387,plain,
nil != iPr_def_10,
inference(light_normalisation,[status(thm)],[c_17226,c_17227]) ).
tcf(c_17486,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58)
| ~ ssItem(X0)
| ~ memberP(sK58,X0) ),
inference(superposition,[status(thm)],[c_8969,c_165]) ).
tcf(c_17507,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssItem(X0)
| ~ memberP(sK58,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17486,c_12784,c_8977]) ).
tcf(c_17806,plain,
iPr_def_10 = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_16855,c_17227]) ).
tcf(c_17808,plain,
app(iPr_def_12,sK59) = iPr_def_10,
inference(demodulation,[status(thm)],[c_8970,c_17806]) ).
tcf(c_17820,plain,
( ( nil = iPr_def_10 )
| ( nil != sK56 ) ),
inference(demodulation,[status(thm)],[c_16083,c_17806]) ).
tcf(c_17871,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_17820,c_17228]) ).
tcf(c_18697,plain,
hd(iPr_def_13) = sK51(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_14378,c_14378,c_17226]) ).
tcf(c_18699,plain,
hd(iPr_def_10) = sK51(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_18697,c_17227]) ).
tcf(c_18700,plain,
( ssItem(hd(iPr_def_10))
| ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_18699,c_219]) ).
tcf(c_18701,plain,
ssItem(hd(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_18700,c_17387,c_17241]) ).
tcf(c_19109,plain,
( memberP(iPr_def_12,sK60)
| memberP(sK59,sK60)
| ~ ssItem(sK60) ),
inference(superposition,[status(thm)],[c_8982,c_17507]) ).
tcf(c_19110,plain,
( memberP(iPr_def_12,sK60)
| memberP(sK59,sK60) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19109,c_8978]) ).
tcf(c_19418,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8968,c_140]) ).
tcf(c_19422,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_19418,c_141,c_8976]) ).
tcf(c_19955,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_8969,c_153]) ).
tcf(c_19969,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_19955,c_19422,c_8977]) ).
tcf(c_21144,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_17239,c_165]) ).
tcf(c_21146,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(superposition,[status(thm)],[c_17239,c_166]) ).
tcf(c_21147,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21146,c_12903,c_8984]) ).
tcf(c_21152,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21144,c_12903,c_8984]) ).
tcf(c_21456,plain,
( memberP(iPr_def_12,sK60)
| memberP(iPr_def_10,sK60)
| ~ ssItem(sK60) ),
inference(superposition,[status(thm)],[c_19110,c_21147]) ).
tcf(c_21458,plain,
( memberP(iPr_def_12,sK60)
| memberP(iPr_def_10,sK60) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21456,c_8978]) ).
tcf(c_21935,plain,
( memberP(iPr_def_10,sK60)
| ~ ssItem(sK60) ),
inference(superposition,[status(thm)],[c_21458,c_21152]) ).
tcf(c_21936,plain,
memberP(iPr_def_10,sK60),
inference(forward_subsumption_resolution,[status(thm)],[c_21935,c_8978]) ).
tcf(c_23998,plain,
( ~ ssList(nil)
| ~ ssItem(sK57)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8968,c_142]) ).
tcf(c_24003,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_23998,c_141,c_8976]) ).
tcf(c_43130,plain,
( ( nil = iPr_def_11 )
| ~ ssList(iPr_def_11)
| ~ ssList(sK58)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_8969,c_230]) ).
tcf(c_43157,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_43130,c_24003,c_19422,c_8977]) ).
tcf(c_46544,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ( nil != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17808,c_231]) ).
tcf(c_46571,plain,
nil != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_46544,c_43157,c_19969,c_8984]) ).
tcf(c_118560,plain,
ssList(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_8974,c_8983,c_17227]) ).
tcf(c_118676,plain,
app(iPr_def_12,sK59) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_8970,c_17227]) ).
tcf(c_118687,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_8968,c_54]) ).
tcf(c_118695,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_118687,c_8968]) ).
tcf(c_118696,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_118695,c_141,c_8976]) ).
tcf(c_118738,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(sK58)
| ~ ssList(app(sK58,iPr_def_11)) ),
inference(superposition,[status(thm)],[c_8969,c_118696]) ).
tcf(c_118739,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12)
| ~ ssList(sK58) ),
inference(light_normalisation,[status(thm)],[c_118738,c_8969]) ).
tcf(c_118740,plain,
( memberP(iPr_def_12,sK57)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_118739,c_8977]) ).
tcf(c_118743,plain,
memberP(iPr_def_12,sK57),
inference(global_subsumption_just,[status(thm)],[c_118740,c_12246,c_12903]) ).
tcf(c_119150,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_8968,c_140]) ).
tcf(c_119154,plain,
ssList(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_119150,c_141,c_8976]) ).
tcf(c_119328,plain,
( ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58) ),
inference(superposition,[status(thm)],[c_8969,c_153]) ).
tcf(c_119347,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_119328,c_119154,c_8977]) ).
tcf(c_120292,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( hd(cons(sK61,X0)) = sK61 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8971,c_150]) ).
tcf(c_120301,plain,
! [X0: $i] :
( ( hd(cons(sK61,X0)) = sK61 )
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_120292,c_17871]) ).
tcf(c_120371,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( sK56 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_8988]) ).
tcf(c_120372,plain,
( ( nil = sK56 )
| ( sK56 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_120371]) ).
tcf(c_120904,plain,
( ( nil = iPr_def_10 )
| ( hd(iPr_def_10) = sK51(iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_118560,c_220]) ).
tcf(c_122796,plain,
ssItem(sK61),
inference(global_subsumption_just,[status(thm)],[c_8971,c_261,c_141,c_195,c_312,c_3297,c_17228,c_120372]) ).
tcf(c_122957,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( app(cons(sK61,nil),X0) = cons(sK61,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8971,c_227]) ).
tcf(c_122972,plain,
! [X0: $i] :
( ( nil = sK56 )
| ( cons(sK61,X0) = app(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_122957,c_8967]) ).
tcf(c_122973,plain,
! [X0: $i] :
( ( cons(sK61,X0) = app(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_122972,c_17871]) ).
tcf(c_123866,plain,
hd(iPr_def_10) = sK51(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_120904,c_14381,c_17228,c_46571]) ).
tcf(c_123868,plain,
( ssItem(hd(iPr_def_10))
| ( nil = iPr_def_10 )
| ~ ssList(iPr_def_10) ),
inference(superposition,[status(thm)],[c_123866,c_219]) ).
tcf(c_123869,plain,
( ssItem(hd(iPr_def_10))
| ( nil = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_123868,c_118560]) ).
tcf(c_124148,plain,
ssItem(hd(iPr_def_10)),
inference(global_subsumption_just,[status(thm)],[c_123869,c_18701]) ).
tcf(c_124445,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssList(iPr_def_11)
| ~ ssList(sK58)
| ~ ssItem(X0)
| ~ memberP(sK58,X0) ),
inference(superposition,[status(thm)],[c_8969,c_165]) ).
tcf(c_124446,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_118676,c_165]) ).
tcf(c_124480,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_124446,c_119347,c_8984]) ).
tcf(c_124484,plain,
! [X0: $i] :
( memberP(iPr_def_12,X0)
| ~ ssItem(X0)
| ~ memberP(sK58,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_124445,c_119154,c_8977]) ).
tcf(c_124522,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sK59)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(superposition,[status(thm)],[c_118676,c_166]) ).
tcf(c_124556,plain,
! [X0: $i] :
( memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ~ memberP(sK59,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_124522,c_119347,c_8984]) ).
tcf(c_126264,plain,
( memberP(iPr_def_10,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_118743,c_124480]) ).
tcf(c_126265,plain,
memberP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_126264,c_8976]) ).
tcf(c_126747,plain,
( memberP(iPr_def_12,sK60)
| memberP(sK59,sK60)
| ~ ssItem(sK60) ),
inference(superposition,[status(thm)],[c_8982,c_124484]) ).
tcf(c_126748,plain,
( memberP(iPr_def_12,sK60)
| memberP(sK59,sK60) ),
inference(forward_subsumption_resolution,[status(thm)],[c_126747,c_8978]) ).
tcf(c_126765,plain,
( memberP(iPr_def_12,sK60)
| memberP(iPr_def_10,sK60)
| ~ ssItem(sK60) ),
inference(superposition,[status(thm)],[c_126748,c_124556]) ).
tcf(c_126767,plain,
( memberP(iPr_def_12,sK60)
| memberP(iPr_def_10,sK60) ),
inference(forward_subsumption_resolution,[status(thm)],[c_126765,c_8978]) ).
tcf(c_126773,plain,
memberP(iPr_def_10,sK60),
inference(global_subsumption_just,[status(thm)],[c_126767,c_21936]) ).
tcf(c_147877,plain,
hd(cons(sK61,nil)) = sK61,
inference(superposition,[status(thm)],[c_141,c_120301]) ).
tcf(c_147896,plain,
hd(iPr_def_10) = sK61,
inference(light_normalisation,[status(thm)],[c_147877,c_8967]) ).
tcf(c_147993,plain,
ssItem(sK61),
inference(demodulation,[status(thm)],[c_124148,c_147896]) ).
tcf(c_183593,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssList(nil)
| ~ ssItem(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_8967,c_170]) ).
tcf(c_183605,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_183593,c_141,c_122796]) ).
tcf(c_203359,plain,
cons(sK61,sK56) = app(iPr_def_10,sK56),
inference(superposition,[status(thm)],[c_8985,c_122973]) ).
tcf(c_203892,plain,
! [X0: $i] :
( memberP(cons(sK61,sK56),X0)
| ~ ssList(iPr_def_10)
| ~ ssList(sK56)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_203359,c_165]) ).
tcf(c_203924,plain,
! [X0: $i] :
( memberP(cons(sK61,sK56),X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_203892,c_118560,c_8985]) ).
tcf(c_217941,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( X0 = sK61 )
| ~ ssList(sK56)
| ~ ssItem(sK61)
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_203924,c_170]) ).
tcf(c_217942,plain,
! [X0: $i] :
( memberP(sK56,X0)
| ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_217941,c_8985,c_147993]) ).
tcf(c_221305,plain,
! [X0: $i] :
( ~ memberP(iPr_def_10,X0)
| ~ ssItem(X0)
| ( X0 = sK61 ) ),
inference(global_subsumption_just,[status(thm)],[c_217942,c_171,c_183605]) ).
tcf(c_221306,plain,
! [X0: $i] :
( ( X0 = sK61 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(renaming,[status(thm)],[c_221305]) ).
tcf(c_221315,plain,
( ( sK60 = sK61 )
| ~ ssItem(sK60) ),
inference(superposition,[status(thm)],[c_126773,c_221306]) ).
tcf(c_221316,plain,
( ( sK57 = sK61 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_126265,c_221306]) ).
tcf(c_221319,plain,
sK57 = sK61,
inference(forward_subsumption_resolution,[status(thm)],[c_221316,c_8976]) ).
tcf(c_221320,plain,
sK60 = sK61,
inference(forward_subsumption_resolution,[status(thm)],[c_221315,c_8978]) ).
tcf(c_222118,plain,
sK57 = sK60,
inference(demodulation,[status(thm)],[c_221319,c_221320]) ).
tcf(c_222403,plain,
~ leq(sK60,sK60),
inference(demodulation,[status(thm)],[c_8979,c_222118]) ).
tcf(c_222471,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_222403,c_13567,c_253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC284+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 17:25:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 134.64/21.70 % SZS status Started for theBenchmark.p
% 134.64/21.70 % SZS status Theorem for theBenchmark.p
% 134.64/21.70
% 134.64/21.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 134.64/21.70
% 134.64/21.70 % ------ iProver source info
% 134.64/21.70
% 134.64/21.70 % git: date: 2026-07-19 20:42:38 +0200
% 134.64/21.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 134.64/21.70 % git: non_committed_changes: false
% 134.64/21.70
% 134.64/21.70 % ------ Parsing...
% 134.64/21.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 134.64/21.70
% 134.64/21.70 % ------ 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: 5 0s sf_e pe_s pe_e %
% 134.64/21.70
% 134.64/21.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 134.64/21.70
% 134.64/21.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 134.64/21.70 % ------ Proving...
% 134.64/21.70 % ------ Problem Properties
% 134.64/21.70
% 134.64/21.70 %
% 134.64/21.70 % clauses 199
% 134.64/21.70 % conjectures 12
% 134.64/21.70 % EPR 64
% 134.64/21.70 % Horn 127
% 134.64/21.70 % unary 27
% 134.64/21.70 % binary 48
% 134.64/21.70 % lits 645
% 134.64/21.70 % lits eq 89
% 134.64/21.70 % fd_pure 0
% 134.64/21.70 % fd_pseudo 0
% 134.64/21.70 % fd_cond 21
% 134.64/21.70 % fd_pseudo_cond 14
% 134.64/21.70 % AC symbols 0
% 134.64/21.70
% 134.64/21.70 % ------ Schedule dynamic 5 is on
% 134.64/21.70
% 134.64/21.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 134.64/21.70
% 134.64/21.70
% 134.64/21.70 % ------
% 134.64/21.70 % Current options:
% 134.64/21.70 % ------
% 134.64/21.70
% 134.64/21.70
% 134.64/21.70 %
% 134.64/21.70
% 134.64/21.70 % ------ Proving...
% 134.64/21.70 % Proof_search_loop: time out after: 5179 full_loop iterations
% 134.64/21.70
% 134.64/21.70 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 134.64/21.70
% 134.64/21.70
% 134.64/21.70 % ------
% 134.64/21.70 % Current options:
% 134.64/21.70 % ------
% 134.64/21.70
% 134.64/21.70
% 134.64/21.70 %
% 134.64/21.70
% 134.64/21.70 % ------ Proving...
% 134.64/21.70 %
% 134.64/21.70
% 134.64/21.70 % SZS status Theorem for theBenchmark.p
% 134.64/21.70
% 134.64/21.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 134.64/21.71
% 134.64/21.71
%------------------------------------------------------------------------------