TSTP Solution File: SWC076+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWC076+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 : Thu Aug 31 20:40:48 EDT 2023
% Result : Theorem 6.97s 1.64s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 79 ( 20 unt; 0 def)
% Number of atoms : 647 ( 232 equ)
% Maximal formula atoms : 56 ( 8 avg)
% Number of connectives : 930 ( 362 ~; 310 |; 220 &)
% ( 6 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn; 164 !; 81 ?)
% 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(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
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] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( app(X12,cons(X10,nil)) = X2
& ssList(X12) )
& app(cons(X10,nil),X11) = X6
& ssList(X11) )
& ssItem(X10) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( app(cons(X7,nil),X9) = X2
& ssList(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X2)
| app(app(X5,X2),X6) != X3 ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| 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)
=> ( ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( ? [X10] :
( ? [X11] :
( ? [X12] :
( app(X12,cons(X10,nil)) = X2
& ssList(X12) )
& app(cons(X10,nil),X11) = X6
& ssList(X11) )
& ssItem(X10) )
| ? [X7] :
( ? [X8] :
( ? [X9] :
( app(cons(X7,nil),X9) = X2
& ssList(X9) )
& app(X8,cons(X7,nil)) = X5
& ssList(X8) )
& ssItem(X7) )
| ~ equalelemsP(X2)
| app(app(X5,X2),X6) != X3 ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X2
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ? [X9] :
( ? [X10] :
( ? [X11] :
( app(cons(X9,nil),X11) = X2
& ssList(X11) )
& app(X10,cons(X9,nil)) = X4
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| ? [X12] :
( segmentP(X0,X12)
& segmentP(X1,X12)
& neq(X12,nil)
& ssList(X12) )
| 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(f173,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(X0,X12)
| ~ segmentP(X1,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(X0,X12)
| ~ segmentP(X1,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& 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(f331,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f344,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X0
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(X0,X12)
| ~ segmentP(X1,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != sK53
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(X1,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK53) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != sK53
| nil != X1 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(X1,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != sK53
| nil != sK54 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK54) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
( ? [X2] :
( ? [X3] :
( ( nil != sK53
| nil != sK54 )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = X2
& sK54 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& app(app(X4,sK55),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
& ssList(sK55) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
( ? [X3] :
( ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = X3 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& app(app(X4,sK55),X5) = X3
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = sK55
& sK54 = X3
& ssList(X3) )
=> ( ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = sK56 )
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& app(app(X4,sK55),X5) = sK56
& ssList(X5) )
& ssList(X4) )
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& app(app(X4,sK55),X5) = sK56
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK57
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& sK56 = app(app(sK57,sK55),X5)
& ssList(X5) )
& ssList(sK57) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK57
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& sK56 = app(app(sK57,sK55),X5)
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK58
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK57
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& ssList(sK58) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
( ( nil != sK53
| nil != sK54 )
& ( nil != sK55
| nil = sK56 )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK55
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK58
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK55
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK57
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& sK56 = app(app(sK57,sK55),sK58)
& ssList(sK58)
& ssList(sK57)
& ! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) )
& 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(f494,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f497,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f498,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f331]) ).
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,
! [X12] :
( ~ segmentP(sK53,X12)
| ~ segmentP(sK54,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) ),
inference(cnf_transformation,[],[f350]) ).
fof(f557,plain,
ssList(sK57),
inference(cnf_transformation,[],[f350]) ).
fof(f558,plain,
ssList(sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f559,plain,
sK56 = app(app(sK57,sK55),sK58),
inference(cnf_transformation,[],[f350]) ).
fof(f563,plain,
( nil != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f350]) ).
fof(f564,plain,
( nil != sK53
| nil != sK54 ),
inference(cnf_transformation,[],[f350]) ).
fof(f565,plain,
( nil != sK55
| nil != sK56 ),
inference(definition_unfolding,[],[f564,f555,f554]) ).
fof(f566,plain,
! [X12] :
( ~ segmentP(sK55,X12)
| ~ segmentP(sK56,X12)
| ~ neq(X12,nil)
| ~ ssList(X12) ),
inference(definition_unfolding,[],[f556,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]) ).
fof(f588,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f498]) ).
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_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f494]) ).
cnf(c_195,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(cnf_transformation,[],[f588]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f497]) ).
cnf(c_246,negated_conjecture,
( nil != sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f565]) ).
cnf(c_247,negated_conjecture,
( nil != sK55
| nil = sK56 ),
inference(cnf_transformation,[],[f563]) ).
cnf(c_251,negated_conjecture,
app(app(sK57,sK55),sK58) = sK56,
inference(cnf_transformation,[],[f559]) ).
cnf(c_252,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f558]) ).
cnf(c_253,negated_conjecture,
ssList(sK57),
inference(cnf_transformation,[],[f557]) ).
cnf(c_254,negated_conjecture,
( ~ neq(X0,nil)
| ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f566]) ).
cnf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f567]) ).
cnf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f568]) ).
cnf(c_308,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| nil = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_373,negated_conjecture,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_247,c_247,c_246]) ).
cnf(c_3270,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_254]) ).
cnf(c_3271,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| X0 = nil ),
inference(unflattening,[status(thm)],[c_3270]) ).
cnf(c_3273,plain,
( ~ ssList(X0)
| ~ segmentP(sK56,X0)
| ~ segmentP(sK55,X0)
| X0 = nil ),
inference(global_subsumption_just,[status(thm)],[c_3271,c_141,c_3271]) ).
cnf(c_3274,plain,
( ~ segmentP(sK55,X0)
| ~ segmentP(sK56,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(renaming,[status(thm)],[c_3273]) ).
cnf(c_8998,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_13810,plain,
( nil != X0
| sK55 != X0
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_8998]) ).
cnf(c_13811,plain,
( nil != nil
| sK55 != nil
| nil = sK55 ),
inference(instantiation,[status(thm)],[c_13810]) ).
cnf(c_14370,plain,
( ~ segmentP(sK55,sK55)
| ~ segmentP(sK56,sK55)
| ~ ssList(sK55)
| sK55 = nil ),
inference(instantiation,[status(thm)],[c_3274]) ).
cnf(c_23895,plain,
( ~ ssList(sK55)
| segmentP(sK55,sK55) ),
inference(instantiation,[status(thm)],[c_192]) ).
cnf(c_27257,plain,
( ~ ssList(app(app(sK57,sK55),sK58))
| ~ ssList(sK55)
| ~ ssList(sK58)
| ~ ssList(sK57)
| segmentP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_251,c_67]) ).
cnf(c_27304,plain,
( ~ ssList(sK55)
| ~ ssList(sK56)
| ~ ssList(sK58)
| ~ ssList(sK57)
| segmentP(sK56,sK55) ),
inference(light_normalisation,[status(thm)],[c_27257,c_251]) ).
cnf(c_27305,plain,
segmentP(sK56,sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_27304,c_253,c_252,c_257,c_258]) ).
cnf(c_27530,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_27305,c_23895,c_14370,c_13811,c_373,c_308,c_195,c_141,c_258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC076+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 15:41:52 EDT 2023
% 0.12/0.34 % 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.97/1.64 % SZS status Started for theBenchmark.p
% 6.97/1.64 % SZS status Theorem for theBenchmark.p
% 6.97/1.64
% 6.97/1.64 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 6.97/1.64
% 6.97/1.64 ------ iProver source info
% 6.97/1.64
% 6.97/1.64 git: date: 2023-05-31 18:12:56 +0000
% 6.97/1.64 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 6.97/1.64 git: non_committed_changes: false
% 6.97/1.64 git: last_make_outside_of_git: false
% 6.97/1.64
% 6.97/1.64 ------ Parsing...
% 6.97/1.64 ------ Clausification by vclausify_rel & Parsing by iProver...
% 6.97/1.64
% 6.97/1.64 ------ 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
% 6.97/1.64
% 6.97/1.64 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 6.97/1.64
% 6.97/1.64 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.97/1.64 ------ Proving...
% 6.97/1.64 ------ Problem Properties
% 6.97/1.64
% 6.97/1.64
% 6.97/1.64 clauses 190
% 6.97/1.64 conjectures 9
% 6.97/1.64 EPR 56
% 6.97/1.64 Horn 122
% 6.97/1.64 unary 23
% 6.97/1.64 binary 40
% 6.97/1.64 lits 639
% 6.97/1.64 lits eq 85
% 6.97/1.64 fd_pure 0
% 6.97/1.64 fd_pseudo 0
% 6.97/1.64 fd_cond 22
% 6.97/1.64 fd_pseudo_cond 14
% 6.97/1.64 AC symbols 0
% 6.97/1.64
% 6.97/1.64 ------ Schedule dynamic 5 is on
% 6.97/1.64
% 6.97/1.64 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.97/1.64
% 6.97/1.64
% 6.97/1.64 ------
% 6.97/1.64 Current options:
% 6.97/1.64 ------
% 6.97/1.64
% 6.97/1.64
% 6.97/1.64
% 6.97/1.64
% 6.97/1.64 ------ Proving...
% 6.97/1.64
% 6.97/1.64
% 6.97/1.64 % SZS status Theorem for theBenchmark.p
% 6.97/1.64
% 6.97/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.97/1.64
% 6.97/1.64
%------------------------------------------------------------------------------