TSTP Solution File: SWC063+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC063+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 03:11:05 EDT 2024
% Result : Theorem 13.66s 2.64s
% Output : CNFRefutation 13.66s
% 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(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
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(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2
| ~ ssList(X6) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(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(f120,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
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(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
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 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f253,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(f254,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,[],[f253]) ).
fof(f255,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(f256,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(f257,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])],[f254,f256,f255]) ).
fof(f316,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f339,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(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(flattening,[],[f339]) ).
fof(f343,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(X0,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& 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 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) )
| ( nil != sK53
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& 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 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X2] :
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = X2
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = X2 )
& 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 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = sK55 )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X3] :
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(X3,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = X3
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != X3
| nil = sK55 )
& 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 ) )
& ( ~ neq(sK56,nil)
| ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = sK56
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X5] :
( ? [X6] :
( app(X6,cons(X5,nil)) = sK56
& app(cons(X5,nil),X6) = sK55
& ssList(X6) )
& ssItem(X5) )
=> ( ? [X6] :
( sK56 = app(X6,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),X6)
& ssList(X6) )
& ssItem(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X6] :
( sK56 = app(X6,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),X6)
& ssList(X6) )
=> ( sK56 = app(sK58,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ( ( ! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ( sK56 = app(sK58,cons(sK57,nil))
& sK55 = app(cons(sK57,nil),sK58)
& ssList(sK58)
& ssItem(sK57) ) )
& ( nil != sK56
| nil = sK55 )
& 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])],[f222,f348,f347,f346,f345,f344,f343]) ).
fof(f371,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,[],[f257]) ).
fof(f440,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f316]) ).
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(f443,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f456,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f493,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f533,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f535,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
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,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f349]) ).
fof(f556,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f349]) ).
fof(f557,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f558,plain,
( ~ neq(sK56,nil)
| sK55 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f349]) ).
fof(f559,plain,
( ~ neq(sK56,nil)
| sK56 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f349]) ).
fof(f560,plain,
( neq(sK54,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f349]) ).
fof(f561,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f349]) ).
fof(f562,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK54 ),
inference(cnf_transformation,[],[f349]) ).
fof(f563,plain,
! [X4] :
( ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK53 ),
inference(cnf_transformation,[],[f349]) ).
fof(f564,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil != sK55 ),
inference(definition_unfolding,[],[f563,f554,f553,f554]) ).
fof(f565,plain,
! [X4] :
( ~ segmentP(sK55,X4)
| ~ segmentP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| nil = sK56 ),
inference(definition_unfolding,[],[f562,f554,f553,f553]) ).
fof(f566,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f561,f553,f554]) ).
fof(f567,plain,
( neq(sK56,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f560,f553,f553]) ).
fof(f568,plain,
ssList(sK56),
inference(definition_unfolding,[],[f550,f553]) ).
fof(f569,plain,
ssList(sK55),
inference(definition_unfolding,[],[f549,f554]) ).
fof(f575,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,[],[f371]) ).
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,[],[f575]) ).
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_142,plain,
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f443]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f456]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f493]) ).
cnf(c_230,plain,
( app(X0,X1) != nil
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = nil ),
inference(cnf_transformation,[],[f533]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f535]) ).
cnf(c_246,negated_conjecture,
( nil != sK55
| ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f564]) ).
cnf(c_247,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| nil = sK56 ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_249,negated_conjecture,
( nil = sK56
| neq(sK56,nil) ),
inference(cnf_transformation,[],[f567]) ).
cnf(c_250,negated_conjecture,
( ~ neq(sK56,nil)
| app(sK58,cons(sK57,nil)) = sK56 ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_251,negated_conjecture,
( ~ neq(sK56,nil)
| app(cons(sK57,nil),sK58) = sK55 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_252,negated_conjecture,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_253,negated_conjecture,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_254,negated_conjecture,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f568]) ).
cnf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f569]) ).
cnf(c_367,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_248,c_254]) ).
cnf(c_369,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_249,c_248,c_254]) ).
cnf(c_377,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_249,c_248,c_254]) ).
cnf(c_387,negated_conjecture,
app(cons(sK57,nil),sK58) = sK55,
inference(global_subsumption_just,[status(thm)],[c_251,c_249,c_248,c_254,c_251]) ).
cnf(c_389,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK56,
inference(global_subsumption_just,[status(thm)],[c_250,c_250,c_377]) ).
cnf(c_397,plain,
( ~ ssList(X0)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| ~ neq(X0,nil) ),
inference(global_subsumption_just,[status(thm)],[c_247,c_254,c_247,c_246]) ).
cnf(c_398,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(renaming,[status(thm)],[c_397]) ).
cnf(c_399,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_246,c_398]) ).
cnf(c_3250,plain,
( X0 != X1
| X2 != nil
| ~ segmentP(sK55,X1)
| ~ segmentP(sK56,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2 ),
inference(resolution_lifted,[status(thm)],[c_138,c_399]) ).
cnf(c_3251,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil ),
inference(unflattening,[status(thm)],[c_3250]) ).
cnf(c_3253,plain,
( ~ ssList(X0)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| X0 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3251,c_141,c_3251]) ).
cnf(c_3254,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(renaming,[status(thm)],[c_3253]) ).
cnf(c_8907,plain,
cons(sK57,nil) = sP0_iProver_def,
definition ).
cnf(c_8908,plain,
app(sK58,sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_8909,plain,
app(sP0_iProver_def,sK58) = sP2_iProver_def,
definition ).
cnf(c_8910,negated_conjecture,
sP1_iProver_def = sK56,
inference(demodulation,[status(thm)],[c_389,c_8907,c_8908]) ).
cnf(c_8911,negated_conjecture,
sP2_iProver_def = sK55,
inference(demodulation,[status(thm)],[c_387,c_8909]) ).
cnf(c_8912,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_369]) ).
cnf(c_8913,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_367]) ).
cnf(c_8914,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_258]) ).
cnf(c_8915,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_257]) ).
cnf(c_11751,plain,
ssList(sP2_iProver_def),
inference(light_normalisation,[status(thm)],[c_8914,c_8911]) ).
cnf(c_11752,plain,
ssList(sP1_iProver_def),
inference(light_normalisation,[status(thm)],[c_8915,c_8910]) ).
cnf(c_11757,plain,
( ~ segmentP(sP1_iProver_def,X0)
| ~ segmentP(sP2_iProver_def,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(light_normalisation,[status(thm)],[c_3254,c_8910,c_8911]) ).
cnf(c_11850,plain,
( ~ segmentP(sP1_iProver_def,sP2_iProver_def)
| ~ ssList(sP2_iProver_def)
| nil = sP2_iProver_def ),
inference(superposition,[status(thm)],[c_192,c_11757]) ).
cnf(c_11851,plain,
( ~ segmentP(sP1_iProver_def,sP2_iProver_def)
| nil = sP2_iProver_def ),
inference(forward_subsumption_resolution,[status(thm)],[c_11850,c_11751]) ).
cnf(c_12141,plain,
app(nil,sK58) = sK58,
inference(superposition,[status(thm)],[c_8912,c_155]) ).
cnf(c_12221,plain,
app(sP2_iProver_def,nil) = sP2_iProver_def,
inference(superposition,[status(thm)],[c_11751,c_232]) ).
cnf(c_12222,plain,
app(sP1_iProver_def,nil) = sP1_iProver_def,
inference(superposition,[status(thm)],[c_11752,c_232]) ).
cnf(c_12280,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| ssList(sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_8907,c_140]) ).
cnf(c_12283,plain,
ssList(sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_12280,c_141,c_8913]) ).
cnf(c_12291,plain,
app(sP0_iProver_def,nil) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_12283,c_232]) ).
cnf(c_12292,plain,
app(nil,sP0_iProver_def) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_12283,c_155]) ).
cnf(c_13589,plain,
( nil != sP0_iProver_def
| ~ ssItem(sK57)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_8907,c_142]) ).
cnf(c_13590,plain,
nil != sP0_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_13589,c_141,c_8913]) ).
cnf(c_17223,plain,
( nil != sP2_iProver_def
| ~ ssList(sK58)
| ~ ssList(sP0_iProver_def)
| nil = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_8909,c_230]) ).
cnf(c_17258,plain,
nil != sP2_iProver_def,
inference(forward_subsumption_resolution,[status(thm)],[c_17223,c_13590,c_12283,c_8912]) ).
cnf(c_17279,plain,
~ segmentP(sP1_iProver_def,sP2_iProver_def),
inference(backward_subsumption_resolution,[status(thm)],[c_11851,c_17258]) ).
cnf(c_28196,plain,
( ~ ssList(app(app(sK58,sP0_iProver_def),X0))
| ~ ssList(X0)
| ~ ssList(sK58)
| ~ ssList(sP0_iProver_def)
| segmentP(app(sP1_iProver_def,X0),sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_8908,c_67]) ).
cnf(c_28197,plain,
( ~ ssList(app(app(sP0_iProver_def,sK58),X0))
| ~ ssList(X0)
| ~ ssList(sK58)
| ~ ssList(sP0_iProver_def)
| segmentP(app(sP2_iProver_def,X0),sK58) ),
inference(superposition,[status(thm)],[c_8909,c_67]) ).
cnf(c_28200,plain,
( ~ ssList(app(app(nil,sK58),X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK58)
| segmentP(app(sK58,X0),sK58) ),
inference(superposition,[status(thm)],[c_12141,c_67]) ).
cnf(c_28303,plain,
( ~ ssList(app(sK58,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK58)
| segmentP(app(sK58,X0),sK58) ),
inference(light_normalisation,[status(thm)],[c_28200,c_12141]) ).
cnf(c_28304,plain,
( ~ ssList(app(sK58,X0))
| ~ ssList(X0)
| segmentP(app(sK58,X0),sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28303,c_8912,c_141]) ).
cnf(c_28313,plain,
( ~ ssList(app(sP2_iProver_def,X0))
| ~ ssList(X0)
| ~ ssList(sK58)
| ~ ssList(sP0_iProver_def)
| segmentP(app(sP2_iProver_def,X0),sK58) ),
inference(light_normalisation,[status(thm)],[c_28197,c_8909]) ).
cnf(c_28314,plain,
( ~ ssList(app(sP2_iProver_def,X0))
| ~ ssList(X0)
| segmentP(app(sP2_iProver_def,X0),sK58) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28313,c_12283,c_8912]) ).
cnf(c_28318,plain,
( ~ ssList(app(sP1_iProver_def,X0))
| ~ ssList(X0)
| ~ ssList(sK58)
| ~ ssList(sP0_iProver_def)
| segmentP(app(sP1_iProver_def,X0),sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_28196,c_8908]) ).
cnf(c_28319,plain,
( ~ ssList(app(sP1_iProver_def,X0))
| ~ ssList(X0)
| segmentP(app(sP1_iProver_def,X0),sP0_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28318,c_12283,c_8912]) ).
cnf(c_32032,plain,
( ~ ssList(app(sK58,sP0_iProver_def))
| ~ ssList(sP0_iProver_def)
| segmentP(sP1_iProver_def,sK58) ),
inference(superposition,[status(thm)],[c_8908,c_28304]) ).
cnf(c_32043,plain,
( ~ ssList(sP0_iProver_def)
| ~ ssList(sP1_iProver_def)
| segmentP(sP1_iProver_def,sK58) ),
inference(light_normalisation,[status(thm)],[c_32032,c_8908]) ).
cnf(c_32044,plain,
segmentP(sP1_iProver_def,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_32043,c_11752,c_12283]) ).
cnf(c_32160,plain,
( ~ ssList(app(sP2_iProver_def,nil))
| ~ ssList(nil)
| segmentP(sP2_iProver_def,sK58) ),
inference(superposition,[status(thm)],[c_12221,c_28314]) ).
cnf(c_32165,plain,
( ~ ssList(nil)
| ~ ssList(sP2_iProver_def)
| segmentP(sP2_iProver_def,sK58) ),
inference(light_normalisation,[status(thm)],[c_32160,c_12221]) ).
cnf(c_32166,plain,
segmentP(sP2_iProver_def,sK58),
inference(forward_subsumption_resolution,[status(thm)],[c_32165,c_11751,c_141]) ).
cnf(c_32190,plain,
( ~ ssList(app(sP1_iProver_def,nil))
| ~ ssList(nil)
| segmentP(sP1_iProver_def,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_12222,c_28319]) ).
cnf(c_32195,plain,
( ~ ssList(nil)
| ~ ssList(sP1_iProver_def)
| segmentP(sP1_iProver_def,sP0_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_32190,c_12222]) ).
cnf(c_32196,plain,
segmentP(sP1_iProver_def,sP0_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_32195,c_11752,c_141]) ).
cnf(c_33414,plain,
( ~ segmentP(sP1_iProver_def,sK58)
| ~ ssList(sK58)
| nil = sK58 ),
inference(superposition,[status(thm)],[c_32166,c_11757]) ).
cnf(c_33415,plain,
nil = sK58,
inference(forward_subsumption_resolution,[status(thm)],[c_33414,c_8912,c_32044]) ).
cnf(c_33507,plain,
app(sP0_iProver_def,nil) = sP2_iProver_def,
inference(demodulation,[status(thm)],[c_8909,c_33415]) ).
cnf(c_33508,plain,
app(nil,sP0_iProver_def) = sP1_iProver_def,
inference(demodulation,[status(thm)],[c_8908,c_33415]) ).
cnf(c_33514,plain,
sP0_iProver_def = sP1_iProver_def,
inference(light_normalisation,[status(thm)],[c_33508,c_12292]) ).
cnf(c_33533,plain,
~ segmentP(sP0_iProver_def,sP2_iProver_def),
inference(demodulation,[status(thm)],[c_17279,c_33514]) ).
cnf(c_33601,plain,
sP0_iProver_def = sP2_iProver_def,
inference(light_normalisation,[status(thm)],[c_33507,c_12291]) ).
cnf(c_33685,plain,
segmentP(sP0_iProver_def,sP0_iProver_def),
inference(light_normalisation,[status(thm)],[c_32196,c_33514]) ).
cnf(c_33988,plain,
~ segmentP(sP0_iProver_def,sP0_iProver_def),
inference(light_normalisation,[status(thm)],[c_33533,c_33601]) ).
cnf(c_33989,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_33988,c_33685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC063+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 23:33:48 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 13.66/2.64 % SZS status Started for theBenchmark.p
% 13.66/2.64 % SZS status Theorem for theBenchmark.p
% 13.66/2.64
% 13.66/2.64 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 13.66/2.64
% 13.66/2.64 ------ iProver source info
% 13.66/2.64
% 13.66/2.64 git: date: 2024-05-02 19:28:25 +0000
% 13.66/2.64 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 13.66/2.64 git: non_committed_changes: false
% 13.66/2.64
% 13.66/2.64 ------ Parsing...
% 13.66/2.64 ------ Clausification by vclausify_rel & Parsing by iProver...
% 13.66/2.64
% 13.66/2.64 ------ 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
% 13.66/2.64
% 13.66/2.64 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 13.66/2.64
% 13.66/2.64 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 13.66/2.64 ------ Proving...
% 13.66/2.64 ------ Problem Properties
% 13.66/2.64
% 13.66/2.64
% 13.66/2.64 clauses 192
% 13.66/2.64 conjectures 6
% 13.66/2.64 EPR 58
% 13.66/2.64 Horn 124
% 13.66/2.64 unary 26
% 13.66/2.64 binary 41
% 13.66/2.64 lits 634
% 13.66/2.64 lits eq 85
% 13.66/2.64 fd_pure 0
% 13.66/2.64 fd_pseudo 0
% 13.66/2.64 fd_cond 22
% 13.66/2.64 fd_pseudo_cond 14
% 13.66/2.64 AC symbols 0
% 13.66/2.64
% 13.66/2.64 ------ Schedule dynamic 5 is on
% 13.66/2.64
% 13.66/2.64 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 13.66/2.64
% 13.66/2.64
% 13.66/2.64 ------
% 13.66/2.64 Current options:
% 13.66/2.64 ------
% 13.66/2.64
% 13.66/2.64
% 13.66/2.64
% 13.66/2.64
% 13.66/2.64 ------ Proving...
% 13.66/2.64
% 13.66/2.64
% 13.66/2.64 % SZS status Theorem for theBenchmark.p
% 13.66/2.64
% 13.66/2.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.66/2.64
% 13.66/2.64
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