TSTP Solution File: SWC109+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC109+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 : Mon Jun 24 16:22:32 EDT 2024
% Result : Theorem 7.64s 1.65s
% Output : CNFRefutation 7.64s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f609)
% 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(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| 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] :
( ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X7] :
( lt(X7,X4)
& memberP(X6,X7)
& ssItem(X7) )
| ? [X8] :
( lt(X4,X8)
& memberP(X5,X8)
& ssItem(X8) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| 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(f121,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) ) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f232,plain,
! [X3,X2] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP6(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f233,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f255,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(f256,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,[],[f255]) ).
fof(f257,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK14(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f258,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK14(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
& ssList(sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0
& ssList(sK15(X0,X1))
& ssList(sK14(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f256,f258,f257]) ).
fof(f318,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f332,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f345,plain,
! [X3,X2] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X7,X4)
| ~ memberP(X6,X7)
| ~ ssItem(X7) )
& ! [X8] :
( ~ lt(X4,X8)
| ~ memberP(X5,X8)
| ~ ssItem(X8) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ sP6(X3,X2) ),
inference(nnf_transformation,[],[f232]) ).
fof(f346,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,X2)
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(X2,X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(X2,nil) = X1
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f345]) ).
fof(f347,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,X2)
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(X2,X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(X2,nil) = X1
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
& ssList(X3) )
& ssItem(sK54(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0,X1] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(X3,X6)
| ~ ssItem(X6) )
& app(app(X3,X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
& ssList(sK55(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0,X1] :
( ? [X4] :
( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(X4,X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),X4) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(X4) )
=> ( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(sK56(X0,X1),X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(sK56(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0,X1] :
( ( ! [X5] :
( ~ lt(X5,sK54(X0,X1))
| ~ memberP(sK56(X0,X1),X5)
| ~ ssItem(X5) )
& ! [X6] :
( ~ lt(sK54(X0,X1),X6)
| ~ memberP(sK55(X0,X1),X6)
| ~ ssItem(X6) )
& app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
& cons(sK54(X0,X1),nil) = X1
& ssList(sK56(X0,X1))
& ssList(sK55(X0,X1))
& ssItem(sK54(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56])],[f346,f349,f348,f347]) ).
fof(f351,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(X1,sK57)
| ~ neq(sK57,nil) )
& neq(X1,nil) )
| ( nil != sK57
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(X1,sK57)
| ~ neq(sK57,nil) )
& neq(X1,nil) )
| ( nil != sK57
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil) )
& neq(sK58,nil) )
| ( nil != sK57
& nil = sK58 ) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
( ? [X2] :
( ? [X3] :
( ( ( ( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil) )
& neq(sK58,nil) )
| ( nil != sK57
& nil = sK58 ) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil) )
& neq(sK58,nil) )
| ( nil != sK57
& nil = sK58 ) )
& ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
( ? [X3] :
( ( ( ( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil) )
& neq(sK58,nil) )
| ( nil != sK57
& nil = sK58 ) )
& ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
=> ( ( ( ( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil) )
& neq(sK58,nil) )
| ( nil != sK57
& nil = sK58 ) )
& ( ( nil = sK59
& nil = sK60 )
| sP6(sK60,sK59) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
( ( ( ( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil) )
& neq(sK58,nil) )
| ( nil != sK57
& nil = sK58 ) )
& ( ( nil = sK59
& nil = sK60 )
| sP6(sK60,sK59) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60)
& ssList(sK59)
& ssList(sK58)
& ssList(sK57) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60])],[f233,f354,f353,f352,f351]) ).
fof(f377,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,[],[f259]) ).
fof(f446,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f448,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f449,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f502,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f555,plain,
! [X0,X1] :
( ssItem(sK54(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f350]) ).
fof(f556,plain,
! [X0,X1] :
( ssList(sK55(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f350]) ).
fof(f557,plain,
! [X0,X1] :
( ssList(sK56(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f350]) ).
fof(f558,plain,
! [X0,X1] :
( cons(sK54(X0,X1),nil) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f350]) ).
fof(f559,plain,
! [X0,X1] :
( app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f350]) ).
fof(f562,plain,
ssList(sK57),
inference(cnf_transformation,[],[f355]) ).
fof(f563,plain,
ssList(sK58),
inference(cnf_transformation,[],[f355]) ).
fof(f566,plain,
sK58 = sK60,
inference(cnf_transformation,[],[f355]) ).
fof(f567,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f355]) ).
fof(f568,plain,
( nil = sK60
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f355]) ).
fof(f569,plain,
( nil = sK59
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f355]) ).
fof(f571,plain,
( neq(sK58,nil)
| nil != sK57 ),
inference(cnf_transformation,[],[f355]) ).
fof(f572,plain,
( ~ segmentP(sK58,sK57)
| ~ neq(sK57,nil)
| nil = sK58 ),
inference(cnf_transformation,[],[f355]) ).
fof(f575,plain,
( ~ segmentP(sK60,sK59)
| ~ neq(sK59,nil)
| nil = sK60 ),
inference(definition_unfolding,[],[f572,f566,f567,f567,f566]) ).
fof(f576,plain,
( neq(sK60,nil)
| nil != sK59 ),
inference(definition_unfolding,[],[f571,f566,f567]) ).
fof(f578,plain,
ssList(sK60),
inference(definition_unfolding,[],[f563,f566]) ).
fof(f579,plain,
ssList(sK59),
inference(definition_unfolding,[],[f562,f567]) ).
fof(f585,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,[],[f377]) ).
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,[],[f585]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f446]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f609]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f448]) ).
cnf(c_142,plain,
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(cnf_transformation,[],[f449]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f502]) ).
cnf(c_248,plain,
( ~ sP6(X0,X1)
| app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f559]) ).
cnf(c_249,plain,
( ~ sP6(X0,X1)
| cons(sK54(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f558]) ).
cnf(c_250,plain,
( ~ sP6(X0,X1)
| ssList(sK56(X0,X1)) ),
inference(cnf_transformation,[],[f557]) ).
cnf(c_251,plain,
( ~ sP6(X0,X1)
| ssList(sK55(X0,X1)) ),
inference(cnf_transformation,[],[f556]) ).
cnf(c_252,plain,
( ~ sP6(X0,X1)
| ssItem(sK54(X0,X1)) ),
inference(cnf_transformation,[],[f555]) ).
cnf(c_254,negated_conjecture,
( ~ neq(sK59,nil)
| ~ segmentP(sK60,sK59)
| nil = sK60 ),
inference(cnf_transformation,[],[f575]) ).
cnf(c_255,negated_conjecture,
( nil != sK59
| neq(sK60,nil) ),
inference(cnf_transformation,[],[f576]) ).
cnf(c_257,negated_conjecture,
( nil = sK59
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_258,negated_conjecture,
( nil = sK60
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_261,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f578]) ).
cnf(c_262,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f579]) ).
cnf(c_3330,plain,
( X0 != sK60
| X1 != sK59
| nil = sK60
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_258]) ).
cnf(c_3331,plain,
( nil = sK60
| ssItem(sK54(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3330]) ).
cnf(c_3338,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_257]) ).
cnf(c_3339,plain,
( nil = sK59
| ssItem(sK54(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3338]) ).
cnf(c_3346,plain,
( X0 != sK60
| X1 != sK59
| nil = sK60
| ssList(sK55(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_251,c_258]) ).
cnf(c_3347,plain,
( nil = sK60
| ssList(sK55(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3346]) ).
cnf(c_3354,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssList(sK55(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_251,c_257]) ).
cnf(c_3355,plain,
( nil = sK59
| ssList(sK55(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3354]) ).
cnf(c_3362,plain,
( X0 != sK60
| X1 != sK59
| nil = sK60
| ssList(sK56(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_250,c_258]) ).
cnf(c_3363,plain,
( nil = sK60
| ssList(sK56(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3362]) ).
cnf(c_3370,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssList(sK56(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_250,c_257]) ).
cnf(c_3371,plain,
( nil = sK59
| ssList(sK56(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3370]) ).
cnf(c_3378,plain,
( X0 != sK60
| X1 != sK59
| cons(sK54(X0,X1),nil) = X1
| nil = sK60 ),
inference(resolution_lifted,[status(thm)],[c_249,c_258]) ).
cnf(c_3379,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK60 ),
inference(unflattening,[status(thm)],[c_3378]) ).
cnf(c_3386,plain,
( X0 != sK60
| X1 != sK59
| cons(sK54(X0,X1),nil) = X1
| nil = sK59 ),
inference(resolution_lifted,[status(thm)],[c_249,c_257]) ).
cnf(c_3387,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK59 ),
inference(unflattening,[status(thm)],[c_3386]) ).
cnf(c_3394,plain,
( X0 != sK60
| X1 != sK59
| app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
| nil = sK60 ),
inference(resolution_lifted,[status(thm)],[c_248,c_258]) ).
cnf(c_3395,plain,
( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
| nil = sK60 ),
inference(unflattening,[status(thm)],[c_3394]) ).
cnf(c_3402,plain,
( X0 != sK60
| X1 != sK59
| app(app(sK55(X0,X1),X1),sK56(X0,X1)) = X0
| nil = sK59 ),
inference(resolution_lifted,[status(thm)],[c_248,c_257]) ).
cnf(c_3403,plain,
( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
| nil = sK59 ),
inference(unflattening,[status(thm)],[c_3402]) ).
cnf(c_3514,plain,
( X0 != sK59
| X1 != nil
| ~ segmentP(sK60,sK59)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| nil = sK60 ),
inference(resolution_lifted,[status(thm)],[c_138,c_254]) ).
cnf(c_3515,plain,
( ~ segmentP(sK60,sK59)
| ~ ssList(nil)
| ~ ssList(sK59)
| nil = sK60
| sK59 = nil ),
inference(unflattening,[status(thm)],[c_3514]) ).
cnf(c_3516,plain,
( ~ segmentP(sK60,sK59)
| nil = sK60
| sK59 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3515,c_262,c_141,c_3515]) ).
cnf(c_3550,plain,
( X0 != nil
| X0 != sK60
| nil != sK59
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_255]) ).
cnf(c_3551,plain,
( nil != sK60
| nil != sK59
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3550]) ).
cnf(c_5167,plain,
app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60,
inference(global_subsumption_just,[status(thm)],[c_3403,c_141,c_3395,c_3403,c_3551]) ).
cnf(c_5169,plain,
app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60,
inference(global_subsumption_just,[status(thm)],[c_3395,c_5167]) ).
cnf(c_5171,plain,
cons(sK54(sK60,sK59),nil) = sK59,
inference(global_subsumption_just,[status(thm)],[c_3387,c_141,c_3379,c_3387,c_3551]) ).
cnf(c_5175,plain,
ssList(sK56(sK60,sK59)),
inference(global_subsumption_just,[status(thm)],[c_3371,c_141,c_3363,c_3371,c_3551]) ).
cnf(c_5177,plain,
ssList(sK56(sK60,sK59)),
inference(global_subsumption_just,[status(thm)],[c_3363,c_5175]) ).
cnf(c_5179,plain,
ssList(sK55(sK60,sK59)),
inference(global_subsumption_just,[status(thm)],[c_3355,c_141,c_3347,c_3355,c_3551]) ).
cnf(c_5181,plain,
ssList(sK55(sK60,sK59)),
inference(global_subsumption_just,[status(thm)],[c_3347,c_5179]) ).
cnf(c_5183,plain,
ssItem(sK54(sK60,sK59)),
inference(global_subsumption_just,[status(thm)],[c_3339,c_141,c_3331,c_3339,c_3551]) ).
cnf(c_5185,plain,
ssItem(sK54(sK60,sK59)),
inference(global_subsumption_just,[status(thm)],[c_3331,c_5183]) ).
cnf(c_13417,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_262]) ).
cnf(c_13418,negated_conjecture,
ssList(sK60),
inference(demodulation,[status(thm)],[c_261]) ).
cnf(c_17733,plain,
( nil != sK59
| ~ ssItem(sK54(sK60,sK59))
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_5171,c_142]) ).
cnf(c_17734,plain,
nil != sK59,
inference(forward_subsumption_resolution,[status(thm)],[c_17733,c_141,c_5185]) ).
cnf(c_31532,plain,
( ~ ssList(app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)))
| ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ ssList(sK59)
| segmentP(sK60,sK59) ),
inference(superposition,[status(thm)],[c_5169,c_67]) ).
cnf(c_31695,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ ssList(sK60)
| ~ ssList(sK59)
| segmentP(sK60,sK59) ),
inference(light_normalisation,[status(thm)],[c_31532,c_5169]) ).
cnf(c_31696,plain,
segmentP(sK60,sK59),
inference(forward_subsumption_resolution,[status(thm)],[c_31695,c_13417,c_13418,c_5181,c_5177]) ).
cnf(c_31869,plain,
( nil = sK60
| nil = sK59 ),
inference(backward_subsumption_resolution,[status(thm)],[c_3516,c_31696]) ).
cnf(c_31872,plain,
nil = sK60,
inference(forward_subsumption_resolution,[status(thm)],[c_31869,c_17734]) ).
cnf(c_32133,plain,
segmentP(nil,sK59),
inference(light_normalisation,[status(thm)],[c_31696,c_31872]) ).
cnf(c_32137,plain,
( ~ ssList(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_32133,c_196]) ).
cnf(c_32138,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_32137,c_17734,c_13417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC109+1 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n013.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 : Thu Jun 20 02:50:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 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
% 7.64/1.65 % SZS status Started for theBenchmark.p
% 7.64/1.65 % SZS status Theorem for theBenchmark.p
% 7.64/1.65
% 7.64/1.65 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.64/1.65
% 7.64/1.65 ------ iProver source info
% 7.64/1.65
% 7.64/1.65 git: date: 2024-06-12 09:56:46 +0000
% 7.64/1.65 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 7.64/1.65 git: non_committed_changes: false
% 7.64/1.65
% 7.64/1.65 ------ Parsing...
% 7.64/1.65 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.64/1.65
% 7.64/1.65 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e
% 7.64/1.65
% 7.64/1.65 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.64/1.65
% 7.64/1.65 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.64/1.65 ------ Proving...
% 7.64/1.65 ------ Problem Properties
% 7.64/1.65
% 7.64/1.65
% 7.64/1.65 clauses 194
% 7.64/1.65 conjectures 2
% 7.64/1.65 EPR 56
% 7.64/1.65 Horn 125
% 7.64/1.65 unary 23
% 7.64/1.65 binary 41
% 7.64/1.65 lits 645
% 7.64/1.65 lits eq 90
% 7.64/1.65 fd_pure 0
% 7.64/1.65 fd_pseudo 0
% 7.64/1.65 fd_cond 21
% 7.64/1.65 fd_pseudo_cond 14
% 7.64/1.65 AC symbols 0
% 7.64/1.65
% 7.64/1.65 ------ Schedule dynamic 5 is on
% 7.64/1.65
% 7.64/1.65 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.64/1.65
% 7.64/1.65
% 7.64/1.65 ------
% 7.64/1.65 Current options:
% 7.64/1.65 ------
% 7.64/1.65
% 7.64/1.65
% 7.64/1.65
% 7.64/1.65
% 7.64/1.65 ------ Proving...
% 7.64/1.65
% 7.64/1.65
% 7.64/1.65 % SZS status Theorem for theBenchmark.p
% 7.64/1.65
% 7.64/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.64/1.66
% 7.64/1.66
%------------------------------------------------------------------------------