TSTP Solution File: SWC118+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC118+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 03:11:17 EDT 2024
% Result : Theorem 7.88s 1.69s
% Output : CNFRefutation 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 24 unt; 0 def)
% Number of atoms : 652 ( 229 equ)
% Maximal formula atoms : 60 ( 9 avg)
% Number of connectives : 957 ( 377 ~; 321 |; 225 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 272 ( 0 sgn 173 !; 84 ?)
% 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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(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] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(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] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(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)
=> ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X8,X6)
& app(X9,cons(X8,nil)) = X2
& ssList(X9) )
& ssItem(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X10,X12)
& app(cons(X12,nil),X13) = X2
& ssList(X13) )
& ssItem(X12) )
& app(X11,cons(X10,nil)) = X4
& ssList(X11) )
& ssItem(X10) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != 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(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& 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(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(X1,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != sK54 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != sK54 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != X2
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != X2
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& app(app(X4,sK55),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& app(app(X4,sK55),X5) = X3
& ssList(X5) )
& ssList(X4) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = sK56 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& app(app(X4,sK55),X5) = sK56
& ssList(X5) )
& ssList(X4) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != X4
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& app(app(X4,sK55),X5) = sK56
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK57
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& sK56 = app(app(sK57,sK55),X5)
& ssList(X5) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK57
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& sK56 = app(app(sK57,sK55),X5)
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != sK58
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK57
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
( ( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) )
& ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = sK56 )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ leq(X8,X6)
| app(X9,cons(X8,nil)) != sK55
| ~ ssList(X9) )
| ~ ssItem(X8) )
| app(cons(X6,nil),X7) != sK58
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X10] :
( ! [X11] :
( ! [X12] :
( ! [X13] :
( ~ leq(X10,X12)
| app(cons(X12,nil),X13) != sK55
| ~ ssList(X13) )
| ~ ssItem(X12) )
| app(X11,cons(X10,nil)) != sK57
| ~ ssList(X11) )
| ~ ssItem(X10) )
& totalorderedP(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(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(f563,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f350]) ).
fof(f564,plain,
( ~ segmentP(sK54,sK53)
| ~ neq(sK53,nil) ),
inference(cnf_transformation,[],[f350]) ).
fof(f565,plain,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(definition_unfolding,[],[f564,f554,f555,f555]) ).
fof(f566,plain,
( nil != sK55
| nil != sK56 ),
inference(definition_unfolding,[],[f563,f555,f554]) ).
fof(f567,plain,
ssList(sK56),
inference(definition_unfolding,[],[f551,f554]) ).
fof(f568,plain,
ssList(sK55),
inference(definition_unfolding,[],[f550,f555]) ).
fof(f574,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,[],[f574]) ).
cnf(c_138,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f441]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f443]) ).
cnf(c_246,negated_conjecture,
( ~ neq(sK55,nil)
| ~ segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_247,negated_conjecture,
( nil != sK56
| nil != sK55 ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_248,negated_conjecture,
( nil != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f562]) ).
cnf(c_252,negated_conjecture,
app(app(sK57,sK55),sK58) = sK56,
inference(cnf_transformation,[],[f558]) ).
cnf(c_253,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f557]) ).
cnf(c_254,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f556]) ).
cnf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f567]) ).
cnf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f568]) ).
cnf(c_373,negated_conjecture,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_248,c_248,c_247]) ).
cnf(c_377,negated_conjecture,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_247,c_373]) ).
cnf(c_507,plain,
( ~ segmentP(sK56,sK55)
| ~ neq(sK55,nil) ),
inference(prop_impl_just,[status(thm)],[c_246]) ).
cnf(c_508,plain,
( ~ neq(sK55,nil)
| ~ segmentP(sK56,sK55) ),
inference(renaming,[status(thm)],[c_507]) ).
cnf(c_799,plain,
( X0 != sK55
| X1 != nil
| ~ segmentP(sK56,sK55)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_138,c_508]) ).
cnf(c_800,plain,
( ~ segmentP(sK56,sK55)
| ~ ssList(nil)
| ~ ssList(sK55)
| sK55 = nil ),
inference(unflattening,[status(thm)],[c_799]) ).
cnf(c_801,plain,
( ~ segmentP(sK56,sK55)
| sK55 = nil ),
inference(global_subsumption_just,[status(thm)],[c_800,c_258,c_141,c_800]) ).
cnf(c_2460,plain,
( ~ segmentP(sK56,sK55)
| sK55 = nil ),
inference(prop_impl_just,[status(thm)],[c_801]) ).
cnf(c_4089,plain,
( ~ segmentP(sK56,sK55)
| sK55 = nil ),
inference(subtyping,[status(esa)],[c_2460]) ).
cnf(c_4099,negated_conjecture,
nil != sK55,
inference(subtyping,[status(esa)],[c_377]) ).
cnf(c_4107,negated_conjecture,
app(app(sK57,sK55),sK58) = sK56,
inference(subtyping,[status(esa)],[c_252]) ).
cnf(c_4264,plain,
( ~ ssList(app(app(X0_13,X1_13),X2_13))
| ~ ssList(X0_13)
| ~ ssList(X1_13)
| ~ ssList(X2_13)
| segmentP(app(app(X0_13,X1_13),X2_13),X1_13) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_4480,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_4482,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_4605,plain,
nil = nil,
inference(instantiation,[status(thm)],[c_4480]) ).
cnf(c_5721,plain,
( nil != X0_13
| sK55 != X0_13
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_4482]) ).
cnf(c_5722,plain,
( nil != nil
| sK55 != nil
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_5721]) ).
cnf(c_13210,plain,
( ~ ssList(app(app(sK57,sK55),sK58))
| ~ ssList(sK55)
| ~ ssList(sK58)
| ~ ssList(sK57)
| segmentP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_4107,c_4264]) ).
cnf(c_13240,plain,
( ~ ssList(sK56)
| ~ ssList(sK55)
| ~ ssList(sK58)
| ~ ssList(sK57)
| segmentP(sK56,sK55) ),
inference(demodulation,[status(thm)],[c_13210,c_4107]) ).
cnf(c_13300,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13240,c_5722,c_4099,c_4089,c_4605,c_253,c_254,c_257,c_258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWC118+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 23:31:40 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 7.88/1.69 % SZS status Started for theBenchmark.p
% 7.88/1.69 % SZS status Theorem for theBenchmark.p
% 7.88/1.69
% 7.88/1.69 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.88/1.69
% 7.88/1.69 ------ iProver source info
% 7.88/1.69
% 7.88/1.69 git: date: 2024-05-02 19:28:25 +0000
% 7.88/1.69 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.88/1.69 git: non_committed_changes: false
% 7.88/1.69
% 7.88/1.69 ------ Parsing...
% 7.88/1.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.88/1.69
% 7.88/1.69 ------ Preprocessing... sup_sim: 0 pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 pe_s pe_e
% 7.88/1.69
% 7.88/1.69 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 4 0s scvd_e snvd_s sp: 0 0s snvd_e
% 7.88/1.69
% 7.88/1.69 ------ Preprocessing...
% 7.88/1.69 ------ Proving...
% 7.88/1.69 ------ Problem Properties
% 7.88/1.69
% 7.88/1.69
% 7.88/1.69 clauses 194
% 7.88/1.69 conjectures 13
% 7.88/1.69 EPR 58
% 7.88/1.69 Horn 124
% 7.88/1.69 unary 23
% 7.88/1.69 binary 41
% 7.88/1.69 lits 649
% 7.88/1.69 lits eq 85
% 7.88/1.69 fd_pure 0
% 7.88/1.69 fd_pseudo 0
% 7.88/1.69 fd_cond 21
% 7.88/1.69 fd_pseudo_cond 14
% 7.88/1.69 AC symbols 0
% 7.88/1.69
% 7.88/1.69 ------ Input Options Time Limit: Unbounded
% 7.88/1.69
% 7.88/1.69
% 7.88/1.69 ------
% 7.88/1.69 Current options:
% 7.88/1.69 ------
% 7.88/1.69
% 7.88/1.69
% 7.88/1.69
% 7.88/1.69
% 7.88/1.69 ------ Proving...
% 7.88/1.69
% 7.88/1.69
% 7.88/1.69 % SZS status Theorem for theBenchmark.p
% 7.88/1.69
% 7.88/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.88/1.69
% 7.88/1.69
%------------------------------------------------------------------------------