TSTP Solution File: SWC409+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 20:43:12 EDT 2023
% Result : Timeout 299.66s 38.90s
% Output : None
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f597)
% 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/theBenchmark.p',ax3) ).
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(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(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
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(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax91) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ! [X6] :
( ssItem(X6)
=> ( memberP(X0,X6)
| ~ memberP(X1,X6) ) )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(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)
=> ( ( nil = X3
& nil != X2 )
| ! [X6] :
( ssItem(X6)
=> ( memberP(X0,X6)
| ~ memberP(X1,X6) ) )
| ? [X4] :
( ? [X5] :
( app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) != X2
& ssList(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X0,X4)
| ~ memberP(X1,X4) ) )
| ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X3
& app(X6,cons(X5,nil)) != X2
& ssList(X6) )
& ssItem(X5) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
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(f120,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
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(f149,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f187,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f188,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f189,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f190,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f194,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f213]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(X0,X4)
& memberP(X1,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(X0,X4)
& memberP(X1,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f224,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
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(f260,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f224]) ).
fof(f261,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f260]) ).
fof(f262,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK15(X0))
& leq(sK15(X0),X2)
& app(app(X3,cons(sK15(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f263,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK15(X0))
& leq(sK15(X0),X2)
& app(app(X3,cons(sK15(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(X3,cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK16(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f264,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(X3,cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(sK17(X0),cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK17(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f265,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(sK17(X0),cons(sK15(X0),X4)),cons(sK16(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),X5)) = X0
& ssList(X5) )
& ssList(sK18(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f266,plain,
! [X0] :
( ? [X5] :
( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),sK19(X0))) = X0
& ssList(sK19(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f267,plain,
! [X0] :
( ( sP0(X0)
| ( leq(sK16(X0),sK15(X0))
& leq(sK15(X0),sK16(X0))
& app(app(sK17(X0),cons(sK15(X0),sK18(X0))),cons(sK16(X0),sK19(X0))) = X0
& ssList(sK19(X0))
& ssList(sK18(X0))
& ssList(sK17(X0))
& ssItem(sK16(X0))
& ssItem(sK15(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18,sK19])],[f261,f266,f265,f264,f263,f262]) ).
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(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(f342,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f217]) ).
fof(f343,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f342]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(X0,X4)
& memberP(X1,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(X1,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(X1,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(sK54,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X3
| nil = X2 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(sK54,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = X2
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != X3
| nil = sK55 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(sK54,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = sK55
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( nil != X3
| nil = sK55 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(sK54,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != X3
| app(X6,cons(X5,nil)) = sK55
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( nil != sK56
| nil = sK55 )
& ? [X4] :
( ~ memberP(sK53,X4)
& memberP(sK54,X4)
& ssItem(X4) )
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != sK56
| app(X6,cons(X5,nil)) = sK55
| ~ ssList(X6) )
| ~ ssItem(X5) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X4] :
( ~ memberP(sK53,X4)
& memberP(sK54,X4)
& ssItem(X4) )
=> ( ~ memberP(sK53,sK57)
& memberP(sK54,sK57)
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( nil != sK56
| nil = sK55 )
& ~ memberP(sK53,sK57)
& memberP(sK54,sK57)
& ssItem(sK57)
& ! [X5] :
( ! [X6] :
( app(cons(X5,nil),X6) != sK56
| app(X6,cons(X5,nil)) = sK55
| ~ ssList(X6) )
| ~ ssItem(X5) )
& 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(f357,plain,
! [X0,X1] :
( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f374,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f267]) ).
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(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(f466,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f324]) ).
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(f468,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f472,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f149]) ).
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(f530,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f199]) ).
fof(f542,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f546,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f343]) ).
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,
! [X6,X5] :
( app(cons(X5,nil),X6) != sK56
| app(X6,cons(X5,nil)) = sK55
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
memberP(sK54,sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
~ memberP(sK53,sK57),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
~ memberP(sK55,sK57),
inference(definition_unfolding,[],[f558,f554]) ).
fof(f561,plain,
memberP(sK56,sK57),
inference(definition_unfolding,[],[f557,f553]) ).
fof(f562,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f570,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP0(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f374]) ).
cnf(c_55,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0 ),
inference(cnf_transformation,[],[f357]) ).
cnf(c_81,plain,
( ~ sP0(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ leq(X1,X3)
| ~ leq(X3,X1)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f570]) ).
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_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_165,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X2,X0),X1) ),
inference(cnf_transformation,[],[f468]) ).
cnf(c_166,plain,
( ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| memberP(app(X0,X2),X1) ),
inference(cnf_transformation,[],[f467]) ).
cnf(c_167,plain,
( ~ memberP(app(X0,X1),X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| memberP(X0,X2)
| memberP(X1,X2) ),
inference(cnf_transformation,[],[f466]) ).
cnf(c_171,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f472]) ).
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_227,plain,
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
inference(cnf_transformation,[],[f530]) ).
cnf(c_239,plain,
( ~ leq(X0,X1)
| ~ lt(X1,X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| lt(X0,X2) ),
inference(cnf_transformation,[],[f542]) ).
cnf(c_241,plain,
( ~ leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| lt(X0,X1) ),
inference(cnf_transformation,[],[f546]) ).
cnf(c_243,plain,
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f597]) ).
cnf(c_246,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_247,negated_conjecture,
~ memberP(sK55,sK57),
inference(cnf_transformation,[],[f560]) ).
cnf(c_248,negated_conjecture,
memberP(sK56,sK57),
inference(cnf_transformation,[],[f561]) ).
cnf(c_249,negated_conjecture,
ssItem(sK57),
inference(cnf_transformation,[],[f556]) ).
cnf(c_250,negated_conjecture,
( app(cons(X0,nil),X1) != sK56
| ~ ssItem(X0)
| ~ ssList(X1)
| app(X1,cons(X0,nil)) = sK55 ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f562]) ).
cnf(c_8829,plain,
X0 = X0,
theory(equality) ).
cnf(c_8835,plain,
( X0 != X1
| X2 != X3
| ~ memberP(X1,X3)
| memberP(X0,X2) ),
theory(equality) ).
cnf(c_13034,plain,
( ~ memberP(nil,sK57)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_171]) ).
cnf(c_13256,plain,
( ~ ssItem(sK57)
| leq(sK57,sK57) ),
inference(instantiation,[status(thm)],[c_158]) ).
cnf(c_13262,plain,
( ~ lt(sK57,sK57)
| ~ ssItem(sK57) ),
inference(instantiation,[status(thm)],[c_243]) ).
cnf(c_13768,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_219]) ).
cnf(c_14031,plain,
( X0 != sK56
| X1 != sK57
| ~ memberP(sK56,sK57)
| memberP(X0,X1) ),
inference(instantiation,[status(thm)],[c_8835]) ).
cnf(c_14170,plain,
( ~ lt(X0,X1)
| ~ leq(sK57,X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(sK57)
| lt(sK57,X1) ),
inference(instantiation,[status(thm)],[c_239]) ).
cnf(c_14206,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_13768,c_220]) ).
cnf(c_14207,plain,
( nil = sK56
| ssItem(hd(sK56)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14206,c_253]) ).
cnf(c_16530,plain,
( X0 != sK56
| sK57 != sK57
| ~ memberP(sK56,sK57)
| memberP(X0,sK57) ),
inference(instantiation,[status(thm)],[c_14031]) ).
cnf(c_16531,plain,
sK57 = sK57,
inference(instantiation,[status(thm)],[c_8829]) ).
cnf(c_16532,plain,
( nil != sK56
| sK57 != sK57
| ~ memberP(sK56,sK57)
| memberP(nil,sK57) ),
inference(instantiation,[status(thm)],[c_16530]) ).
cnf(c_31411,plain,
( ~ leq(X0,sK57)
| ~ leq(sK57,X0)
| ~ ssItem(X0)
| ~ ssItem(sK57)
| sK57 = X0 ),
inference(instantiation,[status(thm)],[c_156]) ).
cnf(c_40080,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(X0)
| ssList(cons(hd(sK56),X0)) ),
inference(instantiation,[status(thm)],[c_140]) ).
cnf(c_40081,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ssList(cons(hd(sK56),nil)) ),
inference(instantiation,[status(thm)],[c_40080]) ).
cnf(c_72300,plain,
( ~ leq(sK57,X0)
| ~ lt(X0,sK57)
| ~ ssItem(X0)
| ~ ssItem(sK57)
| lt(sK57,sK57) ),
inference(instantiation,[status(thm)],[c_14170]) ).
cnf(c_93359,negated_conjecture,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_246,c_249,c_248,c_13034,c_16532,c_16531]) ).
cnf(c_319883,plain,
( X0 != sK56
| X1 != sK57
| memberP(X0,X1) ),
inference(resolution,[status(thm)],[c_8835,c_248]) ).
cnf(c_319927,plain,
( X0 != sK57
| memberP(sK56,X0) ),
inference(resolution,[status(thm)],[c_319883,c_8829]) ).
cnf(c_320299,plain,
( ~ leq(X0,sK57)
| ~ ssItem(X0)
| ~ ssItem(sK57)
| memberP(sK56,X0)
| lt(X0,sK57) ),
inference(resolution,[status(thm)],[c_319927,c_241]) ).
cnf(c_322669,plain,
( ~ ssItem(X0)
| ~ leq(X0,sK57)
| memberP(sK56,X0)
| lt(X0,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_320299,c_249,c_320299]) ).
cnf(c_322670,plain,
( ~ leq(X0,sK57)
| ~ ssItem(X0)
| memberP(sK56,X0)
| lt(X0,sK57) ),
inference(renaming,[status(thm)],[c_322669]) ).
cnf(c_397504,plain,
( sK55 != X0
| sK57 != X1
| ~ memberP(X0,X1)
| memberP(sK55,sK57) ),
inference(instantiation,[status(thm)],[c_8835]) ).
cnf(c_414748,plain,
( sK55 != sK55
| sK57 != X0
| ~ memberP(sK55,X0)
| memberP(sK55,sK57) ),
inference(instantiation,[status(thm)],[c_397504]) ).
cnf(c_414749,plain,
sK55 = sK55,
inference(instantiation,[status(thm)],[c_8829]) ).
cnf(c_644879,plain,
( ~ ssItem(sK57)
| ~ ssList(sK56)
| app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57))) = sK56 ),
inference(superposition,[status(thm)],[c_248,c_55]) ).
cnf(c_644880,plain,
app(sK8(sK56,sK57),cons(sK57,sK9(sK56,sK57))) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_644879,c_253,c_249]) ).
cnf(c_650714,plain,
( hd(sK56) = sK51(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_219]) ).
cnf(c_650718,plain,
hd(sK56) = sK51(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_650714,c_93359]) ).
cnf(c_650840,plain,
( ~ ssList(sK56)
| nil = sK56
| ssItem(hd(sK56)) ),
inference(superposition,[status(thm)],[c_650718,c_220]) ).
cnf(c_650841,plain,
ssItem(hd(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_650840,c_93359,c_253]) ).
cnf(c_650904,plain,
( tl(sK56) = sK52(sK56)
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_221]) ).
cnf(c_650908,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_650904,c_93359]) ).
cnf(c_651216,plain,
( cons(hd(sK56),tl(sK56)) = sK56
| nil = sK56 ),
inference(superposition,[status(thm)],[c_253,c_224]) ).
cnf(c_651220,plain,
cons(hd(sK56),tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_651216,c_93359]) ).
cnf(c_651466,plain,
( ~ ssList(sK56)
| nil = sK56
| ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_650908,c_222]) ).
cnf(c_651467,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_651466,c_93359,c_253]) ).
cnf(c_651839,plain,
( ~ ssList(X0)
| app(cons(hd(sK56),nil),X0) = cons(hd(sK56),X0) ),
inference(superposition,[status(thm)],[c_650841,c_227]) ).
cnf(c_654180,plain,
( ~ sP0(app(sK56,cons(X0,X1)))
| ~ ssList(sK8(sK56,sK57))
| ~ ssList(sK9(sK56,sK57))
| ~ leq(X0,sK57)
| ~ leq(sK57,X0)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_644880,c_81]) ).
cnf(c_654263,plain,
( ~ sP0(app(sK56,cons(X0,X1)))
| ~ ssList(sK8(sK56,sK57))
| ~ ssList(sK9(sK56,sK57))
| ~ leq(X0,sK57)
| ~ leq(sK57,X0)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_654180,c_249]) ).
cnf(c_841275,plain,
app(cons(hd(sK56),nil),tl(sK56)) = cons(hd(sK56),tl(sK56)),
inference(superposition,[status(thm)],[c_651467,c_651839]) ).
cnf(c_841278,plain,
app(cons(hd(sK56),nil),tl(sK56)) = sK56,
inference(light_normalisation,[status(thm)],[c_841275,c_651220]) ).
cnf(c_882933,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ memberP(sK56,X0)
| ~ ssList(tl(sK56))
| ~ ssItem(X0)
| memberP(cons(hd(sK56),nil),X0)
| memberP(tl(sK56),X0) ),
inference(superposition,[status(thm)],[c_841278,c_167]) ).
cnf(c_882944,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56))
| app(tl(sK56),cons(hd(sK56),nil)) = sK55 ),
inference(superposition,[status(thm)],[c_841278,c_250]) ).
cnf(c_882951,plain,
app(tl(sK56),cons(hd(sK56),nil)) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_882944,c_651467,c_650841]) ).
cnf(c_882974,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ memberP(sK56,X0)
| ~ ssItem(X0)
| memberP(cons(hd(sK56),nil),X0)
| memberP(tl(sK56),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_882933,c_651467]) ).
cnf(c_940795,plain,
( ~ memberP(cons(hd(sK56),nil),X0)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(tl(sK56))
| ~ ssItem(X0)
| memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_882951,c_165]) ).
cnf(c_940798,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ memberP(tl(sK56),X0)
| ~ ssList(tl(sK56))
| ~ ssItem(X0)
| memberP(sK55,X0) ),
inference(superposition,[status(thm)],[c_882951,c_166]) ).
cnf(c_940824,plain,
( ~ ssList(cons(hd(sK56),nil))
| ~ memberP(tl(sK56),X0)
| ~ ssItem(X0)
| memberP(sK55,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_940798,c_651467]) ).
cnf(c_940851,plain,
( ~ memberP(cons(hd(sK56),nil),X0)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssItem(X0)
| memberP(sK55,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_940795,c_651467]) ).
cnf(c_942571,plain,
( ~ ssItem(X0)
| ~ leq(sK57,X0)
| ~ leq(X0,sK57) ),
inference(global_subsumption_just,[status(thm)],[c_654263,c_249,c_141,c_248,c_247,c_13034,c_13262,c_14207,c_16532,c_16531,c_31411,c_40081,c_72300,c_322670,c_414748,c_414749,c_882974,c_940824,c_940851]) ).
cnf(c_942572,plain,
( ~ leq(X0,sK57)
| ~ leq(sK57,X0)
| ~ ssItem(X0) ),
inference(renaming,[status(thm)],[c_942571]) ).
cnf(c_942580,plain,
( ~ leq(sK57,sK57)
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_158,c_942572]) ).
cnf(c_942581,plain,
~ leq(sK57,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_942580,c_249]) ).
cnf(c_942582,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_942581,c_13256,c_249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC409+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 17:19:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 299.66/38.90 % SZS status Started for theBenchmark.p
% 299.66/38.90 % SZS status Theorem for theBenchmark.p
% 299.66/38.90
% 299.66/38.90 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 299.66/38.90
% 299.66/38.90 ------ iProver source info
% 299.66/38.90
% 299.66/38.90 git: date: 2023-05-31 18:12:56 +0000
% 299.66/38.90 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 299.66/38.90 git: non_committed_changes: false
% 299.66/38.90 git: last_make_outside_of_git: false
% 299.66/38.90
% 299.66/38.90 ------ Parsing...
% 299.66/38.90 ------ Clausification by vclausify_rel & Parsing by iProver...
% 299.66/38.90
% 299.66/38.90 ------ 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
% 299.66/38.90
% 299.66/38.90 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 299.66/38.90
% 299.66/38.90 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 299.66/38.90 ------ Proving...
% 299.66/38.90 ------ Problem Properties
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 clauses 187
% 299.66/38.90 conjectures 7
% 299.66/38.90 EPR 55
% 299.66/38.90 Horn 119
% 299.66/38.90 unary 21
% 299.66/38.90 binary 41
% 299.66/38.90 lits 629
% 299.66/38.90 lits eq 82
% 299.66/38.90 fd_pure 0
% 299.66/38.90 fd_pseudo 0
% 299.66/38.90 fd_cond 21
% 299.66/38.90 fd_pseudo_cond 14
% 299.66/38.90 AC symbols 0
% 299.66/38.90
% 299.66/38.90 ------ Schedule dynamic 5 is on
% 299.66/38.90
% 299.66/38.90 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 ------
% 299.66/38.90 Current options:
% 299.66/38.90 ------
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 ------ Proving...
% 299.66/38.90 Proof_search_loop: time out after: 10571 full_loop iterations
% 299.66/38.90
% 299.66/38.90 ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 ------
% 299.66/38.90 Current options:
% 299.66/38.90 ------
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 ------ Proving...
% 299.66/38.90 Proof_search_loop: time out after: 12261 full_loop iterations
% 299.66/38.90
% 299.66/38.90 ------ Option_1: Negative Selections Time Limit: 35.
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 ------
% 299.66/38.90 Current options:
% 299.66/38.90 ------
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 ------ Proving...
% 299.66/38.90
% 299.66/38.90
% 299.66/38.90 % SZS status Theorem for theBenchmark.p
% 299.66/38.90
% 299.66/38.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 299.66/38.90
% 299.66/38.92
%------------------------------------------------------------------------------