TSTP Solution File: SWC389+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC389+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 03:12:18 EDT 2024
% Result : Theorem 9.99s 2.20s
% Output : CNFRefutation 9.99s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f605)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
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(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(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( singletonP(X0)
| ~ neq(X1,nil) )
& segmentP(X1,X0) )
| ( ( 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] :
( ( ( singletonP(X0)
| ~ neq(X1,nil) )
& segmentP(X1,X0) )
| ( ( 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] :
( ( ( singletonP(X0)
| ~ neq(X1,nil) )
& segmentP(X1,X0) )
| ( ( 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(f101,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
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(f133,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f176,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ singletonP(X0)
& neq(X1,nil) )
| ~ segmentP(X1,X0) )
& ( ( 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] :
( ( ( ~ singletonP(X0)
& neq(X1,nil) )
| ~ segmentP(X1,X0) )
& ( ( 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(f243,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f101]) ).
fof(f244,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f243]) ).
fof(f245,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f246,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK11(X0),nil) = X0
& ssItem(sK11(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f244,f245]) ).
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(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] :
( ( ( ~ singletonP(X0)
& neq(X1,nil) )
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( ~ singletonP(sK57)
& neq(X1,nil) )
| ~ segmentP(X1,sK57) )
& ( ( 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] :
( ( ( ~ singletonP(sK57)
& neq(X1,nil) )
| ~ segmentP(X1,sK57) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( ~ singletonP(sK57)
& neq(sK58,nil) )
| ~ segmentP(sK58,sK57) )
& ( ( 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] :
( ( ( ~ singletonP(sK57)
& neq(sK58,nil) )
| ~ segmentP(sK58,sK57) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( ~ singletonP(sK57)
& neq(sK58,nil) )
| ~ segmentP(sK58,sK57) )
& ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
& ssList(sK59) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
( ? [X3] :
( ( ( ~ singletonP(sK57)
& neq(sK58,nil) )
| ~ segmentP(sK58,sK57) )
& ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
=> ( ( ( ~ singletonP(sK57)
& neq(sK58,nil) )
| ~ segmentP(sK58,sK57) )
& ( ( nil = sK59
& nil = sK60 )
| sP6(sK60,sK59) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
( ( ( ~ singletonP(sK57)
& neq(sK58,nil) )
| ~ segmentP(sK58,sK57) )
& ( ( 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(f367,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
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(f448,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f460,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f501,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f176]) ).
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(f570,plain,
( neq(sK58,nil)
| ~ segmentP(sK58,sK57) ),
inference(cnf_transformation,[],[f355]) ).
fof(f571,plain,
( ~ singletonP(sK57)
| ~ segmentP(sK58,sK57) ),
inference(cnf_transformation,[],[f355]) ).
fof(f572,plain,
( ~ singletonP(sK59)
| ~ segmentP(sK60,sK59) ),
inference(definition_unfolding,[],[f571,f567,f566,f567]) ).
fof(f573,plain,
( neq(sK60,nil)
| ~ segmentP(sK60,sK59) ),
inference(definition_unfolding,[],[f570,f566,f566,f567]) ).
fof(f574,plain,
ssList(sK60),
inference(definition_unfolding,[],[f563,f566]) ).
fof(f575,plain,
ssList(sK59),
inference(definition_unfolding,[],[f562,f567]) ).
fof(f578,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f367]) ).
fof(f581,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_58,plain,
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f578]) ).
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,[],[f581]) ).
cnf(c_139,plain,
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f605]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f448]) ).
cnf(c_153,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f460]) ).
cnf(c_194,plain,
( ~ ssList(X0)
| segmentP(X0,nil) ),
inference(cnf_transformation,[],[f501]) ).
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_253,negated_conjecture,
( ~ segmentP(sK60,sK59)
| ~ singletonP(sK59) ),
inference(cnf_transformation,[],[f572]) ).
cnf(c_254,negated_conjecture,
( ~ segmentP(sK60,sK59)
| neq(sK60,nil) ),
inference(cnf_transformation,[],[f573]) ).
cnf(c_255,negated_conjecture,
( nil = sK59
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_256,negated_conjecture,
( nil = sK60
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_259,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f574]) ).
cnf(c_260,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f575]) ).
cnf(c_3330,plain,
( X0 != nil
| X0 != sK60
| ~ segmentP(sK60,sK59)
| ~ ssList(X0) ),
inference(resolution_lifted,[status(thm)],[c_139,c_254]) ).
cnf(c_3331,plain,
( nil != sK60
| ~ segmentP(sK60,sK59)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3330]) ).
cnf(c_3332,plain,
( ~ segmentP(sK60,sK59)
| nil != sK60 ),
inference(global_subsumption_just,[status(thm)],[c_3331,c_141,c_3331]) ).
cnf(c_3333,plain,
( nil != sK60
| ~ segmentP(sK60,sK59) ),
inference(renaming,[status(thm)],[c_3332]) ).
cnf(c_3344,plain,
( X0 != sK60
| X1 != sK59
| nil = sK60
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_256]) ).
cnf(c_3345,plain,
( nil = sK60
| ssItem(sK54(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3344]) ).
cnf(c_3368,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssList(sK55(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_251,c_255]) ).
cnf(c_3369,plain,
( nil = sK59
| ssList(sK55(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3368]) ).
cnf(c_3384,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssList(sK56(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_250,c_255]) ).
cnf(c_3385,plain,
( nil = sK59
| ssList(sK56(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3384]) ).
cnf(c_3392,plain,
( X0 != sK60
| X1 != sK59
| cons(sK54(X0,X1),nil) = X1
| nil = sK60 ),
inference(resolution_lifted,[status(thm)],[c_249,c_256]) ).
cnf(c_3393,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK60 ),
inference(unflattening,[status(thm)],[c_3392]) ).
cnf(c_3416,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_255]) ).
cnf(c_3417,plain,
( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
| nil = sK59 ),
inference(unflattening,[status(thm)],[c_3416]) ).
cnf(c_9275,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_260]) ).
cnf(c_9277,negated_conjecture,
( ~ segmentP(sK60,sK59)
| ~ singletonP(sK59) ),
inference(demodulation,[status(thm)],[c_253]) ).
cnf(c_9278,plain,
X0 = X0,
theory(equality) ).
cnf(c_9280,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_9289,plain,
( X0 != X1
| X2 != X3
| ~ segmentP(X1,X3)
| segmentP(X0,X2) ),
theory(equality) ).
cnf(c_12376,plain,
( ~ ssItem(sK54(sK60,sK59))
| ~ ssList(sK59)
| nil = sK60
| singletonP(cons(sK54(sK60,sK59),nil)) ),
inference(superposition,[status(thm)],[c_3393,c_58]) ).
cnf(c_12377,plain,
( ~ ssItem(sK54(sK60,sK59))
| nil = sK60
| singletonP(cons(sK54(sK60,sK59),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12376,c_9275]) ).
cnf(c_12417,plain,
( nil = sK60
| singletonP(cons(sK54(sK60,sK59),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_12377,c_3345,c_12377]) ).
cnf(c_12424,plain,
( nil = sK60
| singletonP(sK59) ),
inference(superposition,[status(thm)],[c_3393,c_12417]) ).
cnf(c_14453,plain,
( sK59 != X0
| sK60 != X1
| ~ segmentP(X1,X0)
| segmentP(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_9289]) ).
cnf(c_15050,plain,
sK59 = sK59,
inference(instantiation,[status(thm)],[c_9278]) ).
cnf(c_15052,plain,
( X0 != X1
| sK59 != X1
| sK59 = X0 ),
inference(instantiation,[status(thm)],[c_9280]) ).
cnf(c_16594,negated_conjecture,
~ segmentP(sK60,sK59),
inference(global_subsumption_just,[status(thm)],[c_9277,c_253,c_3333,c_12424]) ).
cnf(c_19292,plain,
( sK59 != X0
| sK60 != sK60
| ~ segmentP(sK60,X0)
| segmentP(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_14453]) ).
cnf(c_19293,plain,
sK60 = sK60,
inference(instantiation,[status(thm)],[c_9278]) ).
cnf(c_19294,plain,
( sK59 != nil
| sK60 != sK60
| ~ segmentP(sK60,nil)
| segmentP(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_19292]) ).
cnf(c_24280,plain,
( ~ ssList(sK60)
| segmentP(sK60,nil) ),
inference(instantiation,[status(thm)],[c_194]) ).
cnf(c_24310,plain,
( ~ ssList(app(X0,X1))
| ~ ssList(X2)
| ssList(app(app(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_153]) ).
cnf(c_27804,plain,
( X0 != sK59
| sK59 != sK59
| sK59 = X0 ),
inference(instantiation,[status(thm)],[c_15052]) ).
cnf(c_27805,plain,
( nil != sK59
| sK59 != sK59
| sK59 = nil ),
inference(instantiation,[status(thm)],[c_27804]) ).
cnf(c_30415,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(app(app(X0,X1),X2),X1) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_153,c_67,c_24310]) ).
cnf(c_30426,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ ssList(sK59)
| nil = sK59
| segmentP(sK60,sK59) ),
inference(superposition,[status(thm)],[c_3417,c_30415]) ).
cnf(c_30554,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| nil = sK59
| segmentP(sK60,sK59) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30426,c_9275]) ).
cnf(c_30772,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_30554,c_27805,c_24280,c_19293,c_19294,c_16594,c_15050,c_3385,c_3369,c_259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC389+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 2 23:33:43 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 9.99/2.20 % SZS status Started for theBenchmark.p
% 9.99/2.20 % SZS status Theorem for theBenchmark.p
% 9.99/2.20
% 9.99/2.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 9.99/2.20
% 9.99/2.20 ------ iProver source info
% 9.99/2.20
% 9.99/2.20 git: date: 2024-05-02 19:28:25 +0000
% 9.99/2.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 9.99/2.20 git: non_committed_changes: false
% 9.99/2.20
% 9.99/2.20 ------ Parsing...
% 9.99/2.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.99/2.20
% 9.99/2.20 ------ 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
% 9.99/2.20
% 9.99/2.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.99/2.20
% 9.99/2.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.99/2.20 ------ Proving...
% 9.99/2.20 ------ Problem Properties
% 9.99/2.20
% 9.99/2.20
% 9.99/2.20 clauses 198
% 9.99/2.20 conjectures 3
% 9.99/2.20 EPR 53
% 9.99/2.20 Horn 120
% 9.99/2.20 unary 18
% 9.99/2.20 binary 52
% 9.99/2.20 lits 660
% 9.99/2.21 lits eq 97
% 9.99/2.21 fd_pure 0
% 9.99/2.21 fd_pseudo 0
% 9.99/2.21 fd_cond 21
% 9.99/2.21 fd_pseudo_cond 14
% 9.99/2.21 AC symbols 0
% 9.99/2.21
% 9.99/2.21 ------ Schedule dynamic 5 is on
% 9.99/2.21
% 9.99/2.21 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.99/2.21
% 9.99/2.21
% 9.99/2.21 ------
% 9.99/2.21 Current options:
% 9.99/2.21 ------
% 9.99/2.21
% 9.99/2.21
% 9.99/2.21
% 9.99/2.21
% 9.99/2.21 ------ Proving...
% 9.99/2.21
% 9.99/2.21
% 9.99/2.21 % SZS status Theorem for theBenchmark.p
% 9.99/2.21
% 9.99/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.99/2.21
% 9.99/2.21
%------------------------------------------------------------------------------