TSTP Solution File: SWC396+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC396+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:43:06 EDT 2023
% Result : Theorem 84.00s 12.26s
% Output : CNFRefutation 84.00s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f603)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| 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)
=> ( ( ( ? [X5] :
( ? [X6] :
( ? [X7] :
( neq(nil,X2)
& ? [X8] :
( neq(nil,X2)
& hd(X2) = X8
& cons(X8,nil) = X7
& ssItem(X8) )
& app(X6,X7) = X5
& tl(X2) = X6
& ssList(X7) )
& ssList(X6) )
& X3 != X5
& ssList(X5) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( neq(nil,X2)
& ? [X7] :
( neq(nil,X2)
& hd(X2) = X7
& cons(X7,nil) = X6
& ssItem(X7) )
& app(X5,X6) = X4
& tl(X2) = X5
& ssList(X6) )
& ssList(X5) )
& X3 != X4
& ssList(X4) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ! [X8] :
( ssItem(X8)
=> ( memberP(X1,X8)
| ~ memberP(X0,X8) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f128,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f127]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f131,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f130]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f136]) ).
fof(f140,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f149,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f187,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f188,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f190,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f194,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(X1,X8)
& memberP(X0,X8)
& ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(X1,X8)
& memberP(X0,X8)
& ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f99]) ).
fof(f237,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK8(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK8(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f240,plain,
! [X0,X1] :
( ? [X5] :
( app(sK8(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f238,f240,f239]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f323,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f147]) ).
fof(f324,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f323]) ).
fof(f325,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f325]) ).
fof(f331,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f336,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ( hd(X0) = sK51(X0)
& ssItem(sK51(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f188,f336]) ).
fof(f338,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f190,f338]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(X1,X8)
& memberP(X0,X8)
& ssItem(X8) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(X1,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(X1,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(sK54,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,X2)
| ! [X7] :
( ~ neq(nil,X2)
| hd(X2) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(X2) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ? [X8] :
( ~ memberP(sK54,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = sK55 )
& ? [X8] :
( ~ memberP(sK54,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| X3 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = sK55 )
& ? [X8] :
( ~ memberP(sK54,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK56 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ? [X8] :
( ~ memberP(sK54,X8)
& memberP(sK53,X8)
& ssItem(X8) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X8] :
( ~ memberP(sK54,X8)
& memberP(sK53,X8)
& ssItem(X8) )
=> ( ~ memberP(sK54,sK57)
& memberP(sK53,sK57)
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK55)
| ! [X7] :
( ~ neq(nil,sK55)
| hd(sK55) != X7
| cons(X7,nil) != X6
| ~ ssItem(X7) )
| app(X5,X6) != X4
| tl(sK55) != X5
| ~ ssList(X6) )
| ~ ssList(X5) )
| sK56 = X4
| ~ ssList(X4) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ~ memberP(sK54,sK57)
& memberP(sK53,sK57)
& ssItem(sK57)
& sK53 = sK55
& sK54 = sK56
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f223,f348,f347,f346,f345,f344]) ).
fof(f351,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f358,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f317]) ).
fof(f441,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f442,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f450,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f452,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f454,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f457,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f459,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f467,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f469,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f472,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f496,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f497,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f522,plain,
! [X0] :
( ssItem(sK51(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f523,plain,
! [X0] :
( hd(X0) = sK51(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f524,plain,
! [X0] :
( ssList(sK52(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f525,plain,
! [X0] :
( tl(X0) = sK52(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f527,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f549,plain,
ssList(sK53),
inference(cnf_transformation,[],[f349]) ).
fof(f550,plain,
ssList(sK54),
inference(cnf_transformation,[],[f349]) ).
fof(f553,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f349]) ).
fof(f554,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f349]) ).
fof(f555,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f557,f553]) ).
fof(f562,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f556,f554]) ).
fof(f563,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f564,plain,
ssList(sK55),
inference(definition_unfolding,[],[f549,f554]) ).
fof(f566,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f358]) ).
fof(f584,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f497]) ).
cnf(c_49,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f351]) ).
cnf(c_54,plain,
( ~ ssList(app(X0,cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,cons(X1,X2)),X1) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f440]) ).
cnf(c_140,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| ssList(cons(X0,X1)) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f442]) ).
cnf(c_149,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f450]) ).
cnf(c_151,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f452]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f454]) ).
cnf(c_156,plain,
( ~ leq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f457]) ).
cnf(c_158,plain,
( ~ ssItem(X0)
| leq(X0,X0) ),
inference(cnf_transformation,[],[f459]) ).
cnf(c_166,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f467]) ).
cnf(c_170,plain,
( ~ memberP(cons(X0,X1),X2)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| X0 = X2
| memberP(X1,X2) ),
inference(cnf_transformation,[],[f469]) ).
cnf(c_171,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f472]) ).
cnf(c_195,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(cnf_transformation,[],[f584]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f496]) ).
cnf(c_219,plain,
( ~ ssList(X0)
| hd(X0) = sK51(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f523]) ).
cnf(c_220,plain,
( ~ ssList(X0)
| X0 = nil
| ssItem(sK51(X0)) ),
inference(cnf_transformation,[],[f522]) ).
cnf(c_221,plain,
( ~ ssList(X0)
| tl(X0) = sK52(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f525]) ).
cnf(c_222,plain,
( ~ ssList(X0)
| X0 = nil
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f524]) ).
cnf(c_224,plain,
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| X0 = nil ),
inference(cnf_transformation,[],[f527]) ).
cnf(c_246,negated_conjecture,
( ~ ssList(app(tl(sK55),cons(hd(sK55),nil)))
| ~ ssList(cons(hd(sK55),nil))
| ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(cnf_transformation,[],[f603]) ).
cnf(c_248,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_249,negated_conjecture,
~ memberP(sK56,sK57),
inference(cnf_transformation,[],[f561]) ).
cnf(c_250,negated_conjecture,
memberP(sK55,sK57),
inference(cnf_transformation,[],[f562]) ).
cnf(c_251,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f555]) ).
cnf(c_254,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f563]) ).
cnf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f564]) ).
cnf(c_305,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| nil = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_1030,plain,
( ~ ssList(cons(hd(sK55),nil))
| ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(backward_subsumption_resolution,[status(thm)],[c_246,c_153]) ).
cnf(c_6762,plain,
X0 = X0,
theory(equality) ).
cnf(c_6764,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_6769,plain,
( X0 != X1
| X2 != X3
| ~ memberP(X1,X3)
| memberP(X0,X2) ),
theory(equality) ).
cnf(c_6770,plain,
( X0 != X1
| ~ ssList(X1)
| ssList(X0) ),
theory(equality) ).
cnf(c_10044,plain,
( ~ ssItem(sK57)
| leq(sK57,sK57) ),
inference(instantiation,[status(thm)],[c_158]) ).
cnf(c_10123,plain,
( X0 != sK55
| X1 != sK57
| ~ memberP(sK55,sK57)
| memberP(X0,X1) ),
inference(instantiation,[status(thm)],[c_6769]) ).
cnf(c_10228,plain,
( ~ leq(sK57,sK57)
| ~ ssItem(sK57)
| sK57 = sK57 ),
inference(instantiation,[status(thm)],[c_156]) ).
cnf(c_10484,plain,
( X0 != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_10123]) ).
cnf(c_10486,plain,
( nil != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(nil,sK57) ),
inference(instantiation,[status(thm)],[c_10484]) ).
cnf(c_10572,plain,
( ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(superposition,[status(thm)],[c_140,c_1030]) ).
cnf(c_10650,plain,
( ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(sK56,nil)
| ~ neq(nil,sK55)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_10572,c_141,c_10572]) ).
cnf(c_10651,plain,
( ~ neq(nil,sK55)
| ~ neq(sK56,nil)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56 ),
inference(renaming,[status(thm)],[c_10650]) ).
cnf(c_10961,plain,
( ~ neq(nil,sK55)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssItem(nil)
| ~ ssItem(sK56)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_49,c_10651]) ).
cnf(c_10982,plain,
( ~ neq(nil,sK55)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| ~ ssList(sK56)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_138,c_10651]) ).
cnf(c_11033,plain,
( ~ neq(nil,sK55)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_10961,c_254,c_141,c_10982]) ).
cnf(c_11035,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| ~ ssList(sK55)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK55
| nil = sK56 ),
inference(superposition,[status(thm)],[c_138,c_11033]) ).
cnf(c_11036,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssItem(nil)
| ~ ssItem(sK55)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK55
| nil = sK56 ),
inference(superposition,[status(thm)],[c_49,c_11033]) ).
cnf(c_11039,plain,
( nil = sK55
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55)) ),
inference(global_subsumption_just,[status(thm)],[c_11035,c_255,c_141,c_248,c_11035]) ).
cnf(c_11040,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK55 ),
inference(renaming,[status(thm)],[c_11039]) ).
cnf(c_11041,plain,
( ~ ssList(tl(sK55))
| ~ ssList(sK55)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK55 ),
inference(superposition,[status(thm)],[c_149,c_11040]) ).
cnf(c_11042,plain,
( nil = sK55
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| ~ ssList(tl(sK55)) ),
inference(global_subsumption_just,[status(thm)],[c_11036,c_255,c_11041]) ).
cnf(c_11043,plain,
( ~ ssList(tl(sK55))
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK55 ),
inference(renaming,[status(thm)],[c_11042]) ).
cnf(c_11044,plain,
( ~ ssList(sK55)
| app(tl(sK55),cons(hd(sK55),nil)) = sK56
| nil = sK55 ),
inference(superposition,[status(thm)],[c_151,c_11043]) ).
cnf(c_12052,plain,
( X0 != X1
| sK55 != X1
| X0 = sK55 ),
inference(instantiation,[status(thm)],[c_6764]) ).
cnf(c_12053,plain,
( nil != nil
| sK55 != nil
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_12052]) ).
cnf(c_12179,plain,
( X0 != X1
| sK56 != X1
| sK56 = X0 ),
inference(instantiation,[status(thm)],[c_6764]) ).
cnf(c_12797,plain,
sK56 = sK56,
inference(instantiation,[status(thm)],[c_6762]) ).
cnf(c_12898,plain,
( hd(sK55) = sK51(sK55)
| nil = sK55 ),
inference(superposition,[status(thm)],[c_255,c_219]) ).
cnf(c_13057,plain,
( tl(sK55) = sK52(sK55)
| nil = sK55 ),
inference(superposition,[status(thm)],[c_255,c_221]) ).
cnf(c_13718,plain,
( ~ ssList(sK55)
| nil = sK55
| ssItem(hd(sK55)) ),
inference(superposition,[status(thm)],[c_12898,c_220]) ).
cnf(c_13720,plain,
( ~ ssList(sK55)
| nil = sK55
| ssList(tl(sK55)) ),
inference(superposition,[status(thm)],[c_13057,c_222]) ).
cnf(c_14190,plain,
( ~ ssList(sK55)
| cons(hd(sK55),tl(sK55)) = sK55
| sK55 = nil ),
inference(instantiation,[status(thm)],[c_224]) ).
cnf(c_14946,plain,
( ~ memberP(nil,sK57)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_171]) ).
cnf(c_19810,plain,
( app(X0,cons(X1,X2)) != X3
| ~ ssList(X3)
| ssList(app(X0,cons(X1,X2))) ),
inference(instantiation,[status(thm)],[c_6770]) ).
cnf(c_23222,plain,
( X0 != sK56
| sK56 != sK56
| sK56 = X0 ),
inference(instantiation,[status(thm)],[c_12179]) ).
cnf(c_27974,plain,
( app(tl(sK55),cons(hd(sK55),nil)) != sK56
| ~ ssList(sK56)
| ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(instantiation,[status(thm)],[c_19810]) ).
cnf(c_28448,plain,
( ~ ssList(app(tl(sK55),cons(hd(sK55),nil)))
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssList(nil)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),hd(sK55)) ),
inference(instantiation,[status(thm)],[c_54]) ).
cnf(c_50376,plain,
( app(tl(sK55),cons(hd(sK55),nil)) != sK56
| sK56 != sK56
| sK56 = app(tl(sK55),cons(hd(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_23222]) ).
cnf(c_60889,plain,
( X0 != sK55
| X1 != sK57
| ~ memberP(sK55,sK57)
| memberP(X0,X1) ),
inference(instantiation,[status(thm)],[c_6769]) ).
cnf(c_61298,plain,
( X0 != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_60889]) ).
cnf(c_63854,plain,
( X0 != X1
| sK57 != X1
| sK57 = X0 ),
inference(instantiation,[status(thm)],[c_6764]) ).
cnf(c_70236,plain,
( ~ memberP(cons(X0,X1),sK57)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(sK57)
| X0 = sK57
| memberP(X1,sK57) ),
inference(instantiation,[status(thm)],[c_170]) ).
cnf(c_79172,plain,
( cons(hd(sK55),tl(sK55)) != sK55
| sK57 != sK57
| ~ memberP(sK55,sK57)
| memberP(cons(hd(sK55),tl(sK55)),sK57) ),
inference(instantiation,[status(thm)],[c_61298]) ).
cnf(c_79254,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(X0)
| ssList(cons(hd(sK55),X0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_79258,plain,
( ~ ssItem(hd(sK55))
| ~ ssList(nil)
| ssList(cons(hd(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_79254]) ).
cnf(c_85047,plain,
( ~ memberP(cons(hd(sK55),tl(sK55)),sK57)
| ~ ssItem(hd(sK55))
| ~ ssList(tl(sK55))
| ~ ssItem(sK57)
| hd(sK55) = sK57
| memberP(tl(sK55),sK57) ),
inference(instantiation,[status(thm)],[c_70236]) ).
cnf(c_91292,plain,
( sK56 != X0
| sK57 != X1
| ~ memberP(X0,X1)
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_6769]) ).
cnf(c_91771,plain,
( ~ memberP(X0,sK57)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK57)
| memberP(app(X0,X1),sK57) ),
inference(instantiation,[status(thm)],[c_166]) ).
cnf(c_97072,plain,
( sK56 != app(tl(sK55),cons(hd(sK55),nil))
| sK57 != X0
| ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),X0)
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_91292]) ).
cnf(c_97399,plain,
( ~ memberP(tl(sK55),sK57)
| ~ ssList(tl(sK55))
| ~ ssList(X0)
| ~ ssItem(sK57)
| memberP(app(tl(sK55),X0),sK57) ),
inference(instantiation,[status(thm)],[c_91771]) ).
cnf(c_101393,plain,
( X0 != sK57
| sK57 != sK57
| sK57 = X0 ),
inference(instantiation,[status(thm)],[c_63854]) ).
cnf(c_104905,plain,
( sK56 != app(tl(sK55),cons(hd(sK55),nil))
| sK57 != hd(sK55)
| ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),hd(sK55))
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_97072]) ).
cnf(c_106848,plain,
( hd(sK55) != sK57
| sK57 != sK57
| sK57 = hd(sK55) ),
inference(instantiation,[status(thm)],[c_101393]) ).
cnf(c_116848,plain,
( ~ ssList(cons(hd(sK55),nil))
| ~ memberP(tl(sK55),sK57)
| ~ ssList(tl(sK55))
| ~ ssItem(sK57)
| memberP(app(tl(sK55),cons(hd(sK55),nil)),sK57) ),
inference(instantiation,[status(thm)],[c_97399]) ).
cnf(c_116849,plain,
( sK56 != app(tl(sK55),cons(hd(sK55),nil))
| sK57 != sK57
| ~ memberP(app(tl(sK55),cons(hd(sK55),nil)),sK57)
| memberP(sK56,sK57) ),
inference(instantiation,[status(thm)],[c_97072]) ).
cnf(c_116850,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116849,c_116848,c_106848,c_104905,c_85047,c_79258,c_79172,c_50376,c_28448,c_27974,c_14946,c_14190,c_13720,c_13718,c_12797,c_12053,c_11044,c_10486,c_10228,c_10044,c_305,c_195,c_249,c_250,c_141,c_251,c_254,c_255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC396+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.18/0.36 % Computer : n019.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Mon Aug 28 18:30:28 EDT 2023
% 0.18/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 84.00/12.26 % SZS status Started for theBenchmark.p
% 84.00/12.26 % SZS status Theorem for theBenchmark.p
% 84.00/12.26
% 84.00/12.26 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 84.00/12.26
% 84.00/12.26 ------ iProver source info
% 84.00/12.26
% 84.00/12.26 git: date: 2023-05-31 18:12:56 +0000
% 84.00/12.26 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 84.00/12.26 git: non_committed_changes: false
% 84.00/12.26 git: last_make_outside_of_git: false
% 84.00/12.26
% 84.00/12.26 ------ Parsing...
% 84.00/12.26 ------ Clausification by vclausify_rel & Parsing by iProver...
% 84.00/12.26
% 84.00/12.26 ------ 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
% 84.00/12.26
% 84.00/12.26 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 84.00/12.26
% 84.00/12.26 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 84.00/12.26 ------ Proving...
% 84.00/12.26 ------ Problem Properties
% 84.00/12.26
% 84.00/12.26
% 84.00/12.26 clauses 192
% 84.00/12.26 conjectures 7
% 84.00/12.26 EPR 60
% 84.00/12.26 Horn 122
% 84.00/12.26 unary 21
% 84.00/12.26 binary 44
% 84.00/12.26 lits 645
% 84.00/12.26 lits eq 83
% 84.00/12.26 fd_pure 0
% 84.00/12.26 fd_pseudo 0
% 84.00/12.26 fd_cond 21
% 84.00/12.26 fd_pseudo_cond 16
% 84.00/12.26 AC symbols 0
% 84.00/12.26
% 84.00/12.26 ------ Input Options Time Limit: Unbounded
% 84.00/12.26
% 84.00/12.26
% 84.00/12.26 ------
% 84.00/12.26 Current options:
% 84.00/12.26 ------
% 84.00/12.26
% 84.00/12.26
% 84.00/12.26
% 84.00/12.26
% 84.00/12.26 ------ Proving...
% 84.00/12.26
% 84.00/12.26
% 84.00/12.26 % SZS status Theorem for theBenchmark.p
% 84.00/12.26
% 84.00/12.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 84.00/12.26
% 84.00/12.27
%------------------------------------------------------------------------------