TSTP Solution File: SWC067+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 : Fri May 3 03:11:06 EDT 2024
% Result : Theorem 10.27s 2.14s
% Output : CNFRefutation 10.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X14] :
( segmentP(X0,X14)
& segmentP(X1,X14)
& neq(X14,nil)
& ssList(X14) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X14] :
( segmentP(X0,X14)
& segmentP(X1,X14)
& neq(X14,nil)
& ssList(X14) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( lt(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( lt(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ strictorderedP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( lt(X9,X7)
& app(X10,cons(X9,nil)) = X2
& ssList(X10) )
& ssItem(X9) )
& app(cons(X7,nil),X8) = X6
& ssList(X8) )
& ssItem(X7) )
| ? [X11] :
( ? [X12] :
( ? [X13] :
( ? [X14] :
( lt(X11,X13)
& app(cons(X13,nil),X14) = X2
& ssList(X14) )
& ssItem(X13) )
& app(X12,cons(X11,nil)) = X5
& ssList(X12) )
& ssItem(X11) )
| ~ strictorderedP(X2)
| app(app(X5,X2),X6) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f173,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f255,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f254]) ).
fof(f256,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK13(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK13(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK13(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
& ssList(sK14(X0,X1))
& ssList(sK13(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f255,f257,f256]) ).
fof(f317,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f340,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f341,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f340]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != X2
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != X2
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != X2
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(X2)
& app(app(X5,X2),X6) = X3
& ssList(X6) )
& ssList(X5) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK55
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& app(app(X5,sK55),X6) = X3
& ssList(X6) )
& ssList(X5) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK55
| nil = X3 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& app(app(X5,sK55),X6) = X3
& ssList(X6) )
& ssList(X5) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK55
| nil = sK56 )
& ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& app(app(X5,sK55),X6) = sK56
& ssList(X6) )
& ssList(X5) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != X5
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& app(app(X5,sK55),X6) = sK56
& ssList(X6) )
& ssList(X5) )
=> ( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != sK57
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& sK56 = app(app(sK57,sK55),X6)
& ssList(X6) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ? [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != X6
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != sK57
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& sK56 = app(app(sK57,sK55),X6)
& ssList(X6) )
=> ( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != sK58
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != sK57
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( nil != sK55
| nil = sK56 )
& ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ lt(X9,X7)
| app(X10,cons(X9,nil)) != sK55
| ~ ssList(X10) )
| ~ ssItem(X9) )
| app(cons(X7,nil),X8) != sK58
| ~ ssList(X8) )
| ~ ssItem(X7) )
& ! [X11] :
( ! [X12] :
( ! [X13] :
( ! [X14] :
( ~ lt(X11,X13)
| app(cons(X13,nil),X14) != sK55
| ~ ssList(X14) )
| ~ ssItem(X13) )
| app(X12,cons(X11,nil)) != sK57
| ~ ssList(X12) )
| ~ ssItem(X11) )
& strictorderedP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& ssList(sK58)
& ssList(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,sK58])],[f223,f349,f348,f347,f346,f345,f344]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f441,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f317]) ).
fof(f443,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f455,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f494,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f533,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f534,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f550,plain,
ssList(sK53),
inference(cnf_transformation,[],[f350]) ).
fof(f551,plain,
ssList(sK54),
inference(cnf_transformation,[],[f350]) ).
fof(f554,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f350]) ).
fof(f555,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f350]) ).
fof(f556,plain,
ssList(sK57),
inference(cnf_transformation,[],[f350]) ).
fof(f557,plain,
ssList(sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f558,plain,
sK56 = app(app(sK57,sK55),sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f562,plain,
( nil != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f350]) ).
fof(f564,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f350]) ).
fof(f565,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK54 ),
inference(cnf_transformation,[],[f350]) ).
fof(f568,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK56 ),
inference(definition_unfolding,[],[f565,f555,f554,f554]) ).
fof(f569,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f564,f554,f555]) ).
fof(f571,plain,
ssList(sK56),
inference(definition_unfolding,[],[f551,f554]) ).
fof(f572,plain,
ssList(sK55),
inference(definition_unfolding,[],[f550,f555]) ).
fof(f578,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f372]) ).
cnf(c_67,plain,
( ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(cnf_transformation,[],[f578]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f602]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f443]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f455]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f494]) ).
cnf(c_230,plain,
( app(X0,X1) != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = nil ),
inference(cnf_transformation,[],[f534]) ).
cnf(c_231,plain,
( app(X0,X1) != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X1 = nil ),
inference(cnf_transformation,[],[f533]) ).
cnf(c_247,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| nil = sK56 ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_250,negated_conjecture,
( nil != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_254,negated_conjecture,
app(app(sK57,sK55),sK58) = sK56,
inference(cnf_transformation,[],[f558]) ).
cnf(c_255,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f557]) ).
cnf(c_256,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f556]) ).
cnf(c_259,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f571]) ).
cnf(c_260,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f572]) ).
cnf(c_3825,plain,
( X0 != X1
| X2 != nil
| ~ segmentP(sK55,X1)
| ~ segmentP(sK56,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2
| nil = sK56 ),
inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).
cnf(c_3826,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil
| nil = sK56 ),
inference(unflattening,[status(thm)],[c_3825]) ).
cnf(c_3828,plain,
( ~ ssList(X0)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| X0 = nil
| nil = sK56 ),
inference(global_subsumption_just,[status(thm)],[c_3826,c_141,c_3826]) ).
cnf(c_3829,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| X0 = nil
| nil = sK56 ),
inference(renaming,[status(thm)],[c_3828]) ).
cnf(c_3877,plain,
( X0 != nil
| X0 != sK56
| nil != sK55
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_248]) ).
cnf(c_3878,plain,
( nil != sK55
| nil != sK56
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3877]) ).
cnf(c_3879,plain,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_3878,c_141,c_250,c_3878]) ).
cnf(c_9094,plain,
app(sK57,sK55) = sP0_iProver_def,
definition ).
cnf(c_9095,plain,
app(sP0_iProver_def,sK58) = sP1_iProver_def,
definition ).
cnf(c_9096,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_260]) ).
cnf(c_9097,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_259]) ).
cnf(c_9098,negated_conjecture,
ssList(sK57),
inference(demodulation,[status(thm)],[c_256]) ).
cnf(c_9099,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_255]) ).
cnf(c_9100,negated_conjecture,
sP1_iProver_def = sK56,
inference(demodulation,[status(thm)],[c_254,c_9094,c_9095]) ).
cnf(c_11999,plain,
ssList(sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_9097,c_9100]) ).
cnf(c_12028,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sP1_iProver_def,X0)
| ~ ssList(X0)
| X0 = nil
| nil = sP1_iProver_def ),
inference(light_normalisation,[status(thm)],[c_3829,c_9100]) ).
cnf(c_12123,plain,
( ~ segmentP(sP1_iProver_def,sK55)
| ~ ssList(sK55)
| nil = sK55
| nil = sP1_iProver_def ),
inference(superposition,[status(thm)],[c_192,c_12028]) ).
cnf(c_12124,plain,
( ~ segmentP(sP1_iProver_def,sK55)
| nil = sP1_iProver_def ),
inference(forward_subsumption_resolution,[status(thm)],[c_12123,c_3879,c_9096]) ).
cnf(c_12555,plain,
( ~ ssList(sK55)
| ~ ssList(sK57)
| ssList(sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_9094,c_153]) ).
cnf(c_12567,plain,
ssList(sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_12555,c_9098,c_9096]) ).
cnf(c_17187,plain,
( nil != sP1_iProver_def
| ~ ssList(sK58)
| ~ ssList(sP0_iProver_def)
| nil = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_9095,c_230]) ).
cnf(c_17201,plain,
( nil != sP1_iProver_def
| nil = sP0_iProver_def ),
inference(forward_subsumption_resolution,[status(thm)],[c_17187,c_12567,c_9099]) ).
cnf(c_17216,plain,
( nil != sP0_iProver_def
| ~ ssList(sK55)
| ~ ssList(sK57)
| nil = sK55 ),
inference(superposition,[status(thm)],[c_9094,c_231]) ).
cnf(c_17234,plain,
nil != sP0_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_17216,c_3879,c_9098,c_9096]) ).
cnf(c_17511,plain,
nil != sP1_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_17201,c_17201,c_17234]) ).
cnf(c_17517,plain,
~ segmentP(sP1_iProver_def,sK55),
inference(backward_subsumption_resolution,[status(thm)],[c_12124,c_17511]) ).
cnf(c_26357,plain,
( ~ ssList(app(app(sK57,sK55),X0))
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(sK57)
| segmentP(app(sP0_iProver_def,X0),sK55) ),
inference(superposition,[status(thm)],[c_9094,c_67]) ).
cnf(c_26470,plain,
( ~ ssList(app(sP0_iProver_def,X0))
| ~ ssList(X0)
| ~ ssList(sK55)
| ~ ssList(sK57)
| segmentP(app(sP0_iProver_def,X0),sK55) ),
inference(light_normalisation,[status(thm)],[c_26357,c_9094]) ).
cnf(c_26471,plain,
( ~ ssList(app(sP0_iProver_def,X0))
| ~ ssList(X0)
| segmentP(app(sP0_iProver_def,X0),sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26470,c_9098,c_9096]) ).
cnf(c_31707,plain,
( ~ ssList(app(sP0_iProver_def,sK58))
| ~ ssList(sK58)
| segmentP(sP1_iProver_def,sK55) ),
inference(superposition,[status(thm)],[c_9095,c_26471]) ).
cnf(c_31716,plain,
( ~ ssList(sK58)
| ~ ssList(sP1_iProver_def)
| segmentP(sP1_iProver_def,sK55) ),
inference(light_normalisation,[status(thm)],[c_31707,c_9095]) ).
cnf(c_31717,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_31716,c_17517,c_11999,c_9099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC067+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 23:34:03 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.27/2.14 % SZS status Started for theBenchmark.p
% 10.27/2.14 % SZS status Theorem for theBenchmark.p
% 10.27/2.14
% 10.27/2.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.27/2.14
% 10.27/2.14 ------ iProver source info
% 10.27/2.14
% 10.27/2.14 git: date: 2024-05-02 19:28:25 +0000
% 10.27/2.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.27/2.14 git: non_committed_changes: false
% 10.27/2.14
% 10.27/2.14 ------ Parsing...
% 10.27/2.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.27/2.14
% 10.27/2.14 ------ 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
% 10.27/2.14
% 10.27/2.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.27/2.14
% 10.27/2.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.27/2.14 ------ Proving...
% 10.27/2.14 ------ Problem Properties
% 10.27/2.14
% 10.27/2.14
% 10.27/2.14 clauses 193
% 10.27/2.14 conjectures 8
% 10.27/2.14 EPR 58
% 10.27/2.14 Horn 124
% 10.27/2.14 unary 25
% 10.27/2.14 binary 40
% 10.27/2.14 lits 649
% 10.27/2.14 lits eq 89
% 10.27/2.14 fd_pure 0
% 10.27/2.14 fd_pseudo 0
% 10.27/2.14 fd_cond 22
% 10.27/2.14 fd_pseudo_cond 14
% 10.27/2.14 AC symbols 0
% 10.27/2.14
% 10.27/2.14 ------ Schedule dynamic 5 is on
% 10.27/2.14
% 10.27/2.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.27/2.14
% 10.27/2.14
% 10.27/2.14 ------
% 10.27/2.14 Current options:
% 10.27/2.14 ------
% 10.27/2.14
% 10.27/2.14
% 10.27/2.14
% 10.27/2.14
% 10.27/2.14 ------ Proving...
% 10.27/2.14
% 10.27/2.14
% 10.27/2.14 % SZS status Theorem for theBenchmark.p
% 10.27/2.14
% 10.27/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 10.27/2.14
%------------------------------------------------------------------------------