TSTP Solution File: SWC336+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SWC336+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 03:12:03 EDT 2024
% Result : Theorem 20.00s 3.66s
% Output : CNFRefutation 20.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 32
% Syntax : Number of formulae : 176 ( 27 unt; 0 def)
% Number of atoms : 886 ( 214 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 1134 ( 424 ~; 411 |; 237 &)
% ( 7 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 366 ( 0 sgn 189 !; 98 ?)
% 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(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( totalorderedP(X0)
& 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] :
( ( totalorderedP(X0)
& 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] :
( ( totalorderedP(X0)
& 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(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(f111,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f112,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f111]) ).
fof(f135,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f169,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f171]) ).
fof(f173,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f181,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f202,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(X0)
| ~ 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] :
( ( ~ totalorderedP(X0)
| ~ 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(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(f287,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ totalorderedP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f112]) ).
fof(f288,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ totalorderedP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f287]) ).
fof(f289,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK31(X0),X2)
& app(app(X3,cons(sK31(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK31(X0),X2)
& app(app(X3,cons(sK31(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK31(X0),sK32(X0))
& app(app(X3,cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f291,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK31(X0),sK32(X0))
& app(app(X3,cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK31(X0),sK32(X0))
& app(app(sK33(X0),cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK31(X0),sK32(X0))
& app(app(sK33(X0),cons(sK31(X0),X4)),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK31(X0),sK32(X0))
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),X5)) = X0
& ssList(X5) )
& ssList(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK31(X0),sK32(X0))
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK31(X0),sK32(X0))
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ( ~ leq(sK31(X0),sK32(X0))
& app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
& ssList(sK35(X0))
& ssList(sK34(X0))
& ssList(sK33(X0))
& ssItem(sK32(X0))
& ssItem(sK31(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ totalorderedP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34,sK35])],[f288,f293,f292,f291,f290,f289]) ).
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] :
( ( ~ totalorderedP(X0)
| ~ 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] :
( ( ~ totalorderedP(sK57)
| ~ 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] :
( ( ~ totalorderedP(sK57)
| ~ segmentP(X1,sK57) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ~ totalorderedP(sK57)
| ~ 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] :
( ( ~ totalorderedP(sK57)
| ~ segmentP(sK58,sK57) )
& ( ( nil = X2
& nil = X3 )
| sP6(X3,X2) )
& sK57 = X2
& sK58 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ~ totalorderedP(sK57)
| ~ 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] :
( ( ~ totalorderedP(sK57)
| ~ segmentP(sK58,sK57) )
& ( ( nil = sK59
& nil = X3 )
| sP6(X3,sK59) )
& sK57 = sK59
& sK58 = X3
& ssList(X3) )
=> ( ( ~ totalorderedP(sK57)
| ~ segmentP(sK58,sK57) )
& ( ( nil = sK59
& nil = sK60 )
| sP6(sK60,sK59) )
& sK57 = sK59
& sK58 = sK60
& ssList(sK60) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
( ( ~ totalorderedP(sK57)
| ~ 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(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(f420,plain,
! [X0] :
( totalorderedP(X0)
| app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f448,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f462,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f497,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f498,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f499,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f173]) ).
fof(f500,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f502,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f503,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f510,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f511,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f541,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f202]) ).
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,
( ~ totalorderedP(sK57)
| ~ segmentP(sK58,sK57) ),
inference(cnf_transformation,[],[f355]) ).
fof(f571,plain,
( ~ totalorderedP(sK59)
| ~ segmentP(sK60,sK59) ),
inference(definition_unfolding,[],[f570,f567,f566,f567]) ).
fof(f572,plain,
ssList(sK60),
inference(definition_unfolding,[],[f563,f566]) ).
fof(f573,plain,
ssList(sK59),
inference(definition_unfolding,[],[f562,f567]) ).
fof(f579,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]) ).
fof(f593,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f503]) ).
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,[],[f579]) ).
cnf(c_108,plain,
( ~ ssList(X0)
| app(app(sK33(X0),cons(sK31(X0),sK34(X0))),cons(sK32(X0),sK35(X0))) = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f420]) ).
cnf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f448]) ).
cnf(c_155,plain,
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f462]) ).
cnf(c_190,plain,
( ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(X0,X2) ),
inference(cnf_transformation,[],[f497]) ).
cnf(c_191,plain,
( ~ segmentP(X0,X1)
| ~ segmentP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f498]) ).
cnf(c_192,plain,
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f499]) ).
cnf(c_193,plain,
( ~ segmentP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| segmentP(app(app(X2,X0),X3),X1) ),
inference(cnf_transformation,[],[f500]) ).
cnf(c_195,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(cnf_transformation,[],[f593]) ).
cnf(c_196,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[],[f502]) ).
cnf(c_203,plain,
( ~ ssItem(X0)
| totalorderedP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f510]) ).
cnf(c_204,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f511]) ).
cnf(c_232,plain,
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f541]) ).
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)
| ~ totalorderedP(sK59) ),
inference(cnf_transformation,[],[f571]) ).
cnf(c_254,negated_conjecture,
( nil = sK59
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f569]) ).
cnf(c_255,negated_conjecture,
( nil = sK60
| sP6(sK60,sK59) ),
inference(cnf_transformation,[],[f568]) ).
cnf(c_258,negated_conjecture,
ssList(sK60),
inference(cnf_transformation,[],[f572]) ).
cnf(c_259,negated_conjecture,
ssList(sK59),
inference(cnf_transformation,[],[f573]) ).
cnf(c_312,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| nil = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_3310,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssItem(sK54(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_252,c_254]) ).
cnf(c_3311,plain,
( nil = sK59
| ssItem(sK54(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3310]) ).
cnf(c_3326,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssList(sK55(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_251,c_254]) ).
cnf(c_3327,plain,
( nil = sK59
| ssList(sK55(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3326]) ).
cnf(c_3342,plain,
( X0 != sK60
| X1 != sK59
| nil = sK59
| ssList(sK56(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_250,c_254]) ).
cnf(c_3343,plain,
( nil = sK59
| ssList(sK56(sK60,sK59)) ),
inference(unflattening,[status(thm)],[c_3342]) ).
cnf(c_3358,plain,
( X0 != sK60
| X1 != sK59
| cons(sK54(X0,X1),nil) = X1
| nil = sK59 ),
inference(resolution_lifted,[status(thm)],[c_249,c_254]) ).
cnf(c_3359,plain,
( cons(sK54(sK60,sK59),nil) = sK59
| nil = sK59 ),
inference(unflattening,[status(thm)],[c_3358]) ).
cnf(c_3366,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_255]) ).
cnf(c_3367,plain,
( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
| nil = sK60 ),
inference(unflattening,[status(thm)],[c_3366]) ).
cnf(c_3374,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_254]) ).
cnf(c_3375,plain,
( app(app(sK55(sK60,sK59),sK59),sK56(sK60,sK59)) = sK60
| nil = sK59 ),
inference(unflattening,[status(thm)],[c_3374]) ).
cnf(c_9208,negated_conjecture,
ssList(sK59),
inference(demodulation,[status(thm)],[c_259]) ).
cnf(c_9209,negated_conjecture,
ssList(sK60),
inference(demodulation,[status(thm)],[c_258]) ).
cnf(c_9210,negated_conjecture,
( ~ segmentP(sK60,sK59)
| ~ totalorderedP(sK59) ),
inference(demodulation,[status(thm)],[c_253]) ).
cnf(c_9211,plain,
X0 = X0,
theory(equality) ).
cnf(c_9213,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_9222,plain,
( X0 != X1
| X2 != X3
| ~ segmentP(X1,X3)
| segmentP(X0,X2) ),
theory(equality) ).
cnf(c_9228,plain,
( X0 != X1
| ~ totalorderedP(X1)
| totalorderedP(X0) ),
theory(equality) ).
cnf(c_12410,plain,
( ~ ssItem(sK54(sK60,sK59))
| nil = sK59
| totalorderedP(sK59) ),
inference(superposition,[status(thm)],[c_3359,c_203]) ).
cnf(c_12814,plain,
app(nil,sK59) = sK59,
inference(superposition,[status(thm)],[c_9208,c_155]) ).
cnf(c_12908,plain,
app(sK60,nil) = sK60,
inference(superposition,[status(thm)],[c_9209,c_232]) ).
cnf(c_12909,plain,
app(sK59,nil) = sK59,
inference(superposition,[status(thm)],[c_9208,c_232]) ).
cnf(c_14007,plain,
( sK59 != X0
| ~ totalorderedP(X0)
| totalorderedP(sK59) ),
inference(instantiation,[status(thm)],[c_9228]) ).
cnf(c_14008,plain,
( sK59 != nil
| ~ totalorderedP(nil)
| totalorderedP(sK59) ),
inference(instantiation,[status(thm)],[c_14007]) ).
cnf(c_16049,plain,
( ~ segmentP(X0,sK59)
| ~ segmentP(sK60,X0)
| ~ ssList(X0)
| ~ ssList(sK59)
| ~ ssList(sK60)
| segmentP(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_190]) ).
cnf(c_16052,plain,
( ~ segmentP(nil,sK59)
| ~ segmentP(sK60,nil)
| ~ ssList(nil)
| ~ ssList(sK59)
| ~ ssList(sK60)
| segmentP(sK60,sK59) ),
inference(instantiation,[status(thm)],[c_16049]) ).
cnf(c_20340,plain,
( X0 != X1
| sK59 != X2
| ~ segmentP(X1,X2)
| segmentP(X0,sK59) ),
inference(instantiation,[status(thm)],[c_9222]) ).
cnf(c_20341,plain,
( nil != nil
| sK59 != nil
| ~ segmentP(nil,nil)
| segmentP(nil,sK59) ),
inference(instantiation,[status(thm)],[c_20340]) ).
cnf(c_20384,plain,
( ~ segmentP(nil,sK59)
| ~ ssList(sK59)
| sK59 = nil ),
inference(instantiation,[status(thm)],[c_196]) ).
cnf(c_20396,plain,
sK59 = sK59,
inference(instantiation,[status(thm)],[c_9211]) ).
cnf(c_20398,plain,
( X0 != X1
| sK59 != X1
| sK59 = X0 ),
inference(instantiation,[status(thm)],[c_9213]) ).
cnf(c_26188,plain,
( app(app(sK33(sK59),cons(sK31(sK59),sK34(sK59))),cons(sK32(sK59),sK35(sK59))) = sK59
| totalorderedP(sK59) ),
inference(superposition,[status(thm)],[c_9208,c_108]) ).
cnf(c_29594,plain,
( ~ ssList(app(app(nil,sK59),X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK59)
| segmentP(app(sK59,X0),sK59) ),
inference(superposition,[status(thm)],[c_12814,c_67]) ).
cnf(c_29663,plain,
( ~ ssList(app(sK59,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK59)
| segmentP(app(sK59,X0),sK59) ),
inference(light_normalisation,[status(thm)],[c_29594,c_12814]) ).
cnf(c_29664,plain,
( ~ ssList(app(sK59,X0))
| ~ ssList(X0)
| segmentP(app(sK59,X0),sK59) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29663,c_9208,c_141]) ).
cnf(c_31400,plain,
( ~ ssList(app(sK59,nil))
| ~ ssList(nil)
| segmentP(sK59,sK59) ),
inference(superposition,[status(thm)],[c_12909,c_29664]) ).
cnf(c_31405,plain,
( ~ ssList(nil)
| ~ ssList(sK59)
| segmentP(sK59,sK59) ),
inference(light_normalisation,[status(thm)],[c_31400,c_12909]) ).
cnf(c_31406,plain,
segmentP(sK59,sK59),
inference(forward_subsumption_resolution,[status(thm)],[c_31405,c_9208,c_141]) ).
cnf(c_31605,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ segmentP(sK59,X0)
| ~ ssList(X0)
| ~ ssList(sK59)
| nil = sK59
| segmentP(sK60,X0) ),
inference(superposition,[status(thm)],[c_3375,c_193]) ).
cnf(c_31606,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ segmentP(sK59,X0)
| ~ ssList(X0)
| ~ ssList(sK59)
| nil = sK60
| segmentP(sK60,X0) ),
inference(superposition,[status(thm)],[c_3367,c_193]) ).
cnf(c_31620,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(sK60)
| segmentP(app(sK60,X1),X0) ),
inference(superposition,[status(thm)],[c_12908,c_193]) ).
cnf(c_31621,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(sK59)
| segmentP(app(sK59,X1),X0) ),
inference(superposition,[status(thm)],[c_12909,c_193]) ).
cnf(c_31670,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(sK59,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31621,c_9208,c_141]) ).
cnf(c_31675,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(sK60,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31620,c_9209,c_141]) ).
cnf(c_31739,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ segmentP(sK59,X0)
| ~ ssList(X0)
| nil = sK60
| segmentP(sK60,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31606,c_9208]) ).
cnf(c_31746,plain,
( ~ ssList(sK56(sK60,sK59))
| ~ ssList(sK55(sK60,sK59))
| ~ segmentP(sK59,X0)
| ~ ssList(X0)
| nil = sK59
| segmentP(sK60,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31605,c_9208]) ).
cnf(c_35459,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(sK59,X0) ),
inference(superposition,[status(thm)],[c_12909,c_31670]) ).
cnf(c_35464,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| segmentP(sK59,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35459,c_141]) ).
cnf(c_35498,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(sK60,X0) ),
inference(superposition,[status(thm)],[c_12908,c_31675]) ).
cnf(c_35503,plain,
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| segmentP(sK60,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35498,c_141]) ).
cnf(c_35525,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| segmentP(sK60,nil) ),
inference(instantiation,[status(thm)],[c_35503]) ).
cnf(c_37293,plain,
( ~ ssList(nil)
| segmentP(sK59,nil) ),
inference(superposition,[status(thm)],[c_192,c_35464]) ).
cnf(c_37296,plain,
segmentP(sK59,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_37293,c_141]) ).
cnf(c_37299,plain,
( ~ segmentP(nil,sK59)
| ~ ssList(nil)
| ~ ssList(sK59)
| nil = sK59 ),
inference(superposition,[status(thm)],[c_37296,c_191]) ).
cnf(c_37300,plain,
( ~ segmentP(nil,sK59)
| nil = sK59 ),
inference(forward_subsumption_resolution,[status(thm)],[c_37299,c_9208,c_141]) ).
cnf(c_37305,plain,
~ segmentP(nil,sK59),
inference(global_subsumption_just,[status(thm)],[c_37300,c_259,c_258,c_204,c_141,c_195,c_253,c_14008,c_16052,c_20384,c_35525]) ).
cnf(c_38973,plain,
( X0 != sK59
| sK59 != sK59
| sK59 = X0 ),
inference(instantiation,[status(thm)],[c_20398]) ).
cnf(c_38974,plain,
( nil != sK59
| sK59 != sK59
| sK59 = nil ),
inference(instantiation,[status(thm)],[c_38973]) ).
cnf(c_45438,plain,
totalorderedP(sK59),
inference(global_subsumption_just,[status(thm)],[c_26188,c_259,c_258,c_204,c_141,c_195,c_253,c_312,c_3311,c_12410,c_14008,c_16052,c_20341,c_20384,c_20396,c_35525,c_38974]) ).
cnf(c_45440,plain,
~ segmentP(sK60,sK59),
inference(backward_subsumption_resolution,[status(thm)],[c_9210,c_45438]) ).
cnf(c_59765,plain,
( ~ ssList(X0)
| ~ segmentP(sK59,X0)
| segmentP(sK60,X0) ),
inference(global_subsumption_just,[status(thm)],[c_31739,c_141,c_195,c_312,c_3327,c_3343,c_20341,c_20396,c_31746,c_37305,c_38974]) ).
cnf(c_59766,plain,
( ~ segmentP(sK59,X0)
| ~ ssList(X0)
| segmentP(sK60,X0) ),
inference(renaming,[status(thm)],[c_59765]) ).
cnf(c_59775,plain,
( ~ ssList(sK59)
| segmentP(sK60,sK59) ),
inference(superposition,[status(thm)],[c_31406,c_59766]) ).
cnf(c_59777,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_59775,c_45440,c_9208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SWC336+1 : TPTP v8.1.2. Released v2.4.0.
% 0.09/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n002.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 May 2 23:46:27 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 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
% 20.00/3.66 % SZS status Started for theBenchmark.p
% 20.00/3.66 % SZS status Theorem for theBenchmark.p
% 20.00/3.66
% 20.00/3.66 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.00/3.66
% 20.00/3.66 ------ iProver source info
% 20.00/3.66
% 20.00/3.66 git: date: 2024-05-02 19:28:25 +0000
% 20.00/3.66 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.00/3.66 git: non_committed_changes: false
% 20.00/3.66
% 20.00/3.66 ------ Parsing...
% 20.00/3.66 ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.00/3.66
% 20.00/3.66 ------ 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: 5 0s sf_e pe_s pe_e
% 20.00/3.66
% 20.00/3.66 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 20.00/3.66
% 20.00/3.66 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.00/3.66 ------ Proving...
% 20.00/3.66 ------ Problem Properties
% 20.00/3.66
% 20.00/3.66
% 20.00/3.66 clauses 197
% 20.00/3.66 conjectures 3
% 20.00/3.66 EPR 52
% 20.00/3.66 Horn 119
% 20.00/3.66 unary 18
% 20.00/3.66 binary 51
% 20.00/3.66 lits 658
% 20.00/3.66 lits eq 96
% 20.00/3.66 fd_pure 0
% 20.00/3.66 fd_pseudo 0
% 20.00/3.66 fd_cond 21
% 20.00/3.66 fd_pseudo_cond 14
% 20.00/3.66 AC symbols 0
% 20.00/3.66
% 20.00/3.66 ------ Schedule dynamic 5 is on
% 20.00/3.66
% 20.00/3.66 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 20.00/3.66
% 20.00/3.66
% 20.00/3.66 ------
% 20.00/3.66 Current options:
% 20.00/3.66 ------
% 20.00/3.66
% 20.00/3.66
% 20.00/3.66
% 20.00/3.66
% 20.00/3.66 ------ Proving...
% 20.00/3.66
% 20.00/3.66
% 20.00/3.66 % SZS status Theorem for theBenchmark.p
% 20.00/3.66
% 20.00/3.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.00/3.66
% 20.00/3.67
%------------------------------------------------------------------------------