TSTP Solution File: SWC045+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWC045+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n003.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 20:55:53 EDT 2023
% Result : Theorem 28.09s 4.41s
% Output : Refutation 28.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 41
% Syntax : Number of formulae : 265 ( 12 unt; 0 def)
% Number of atoms : 1359 ( 223 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 1919 ( 825 ~; 822 |; 190 &)
% ( 17 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-2 aty)
% Number of variables : 476 (; 391 !; 85 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f111631,plain,
$false,
inference(avatar_sat_refutation,[],[f5026,f5185,f50356,f108051,f108187,f111630]) ).
fof(f111630,plain,
( ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(avatar_contradiction_clause,[],[f111629]) ).
fof(f111629,plain,
( $false
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f111628,f575]) ).
fof(f575,plain,
ssList(sK0),
inference(forward_demodulation,[],[f340,f344]) ).
fof(f344,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
( ! [X4] :
( ( ( ~ memberP(sK2,X4)
| ( segmentP(sK3,app(app(cons(X4,nil),sK4(X4)),cons(X4,nil)))
& ssList(sK4(X4)) ) )
& ( ! [X6] :
( ~ segmentP(sK3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(sK2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = sK2
& sK1 = sK3
& nil = sK1
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f100,f228,f227,f226,f225,f224]) ).
fof(f224,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = X2
& sK1 = X3
& nil = sK1
& ssList(X3) )
& ssList(X2) )
& ssList(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = X2
& sK1 = X3
& nil = sK1
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(sK2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(sK2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = sK2
& sK1 = X3
& nil = sK1
& ssList(X3) )
& ssList(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f227,plain,
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(sK2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(sK2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = sK2
& sK1 = X3
& nil = sK1
& ssList(X3) )
=> ( ! [X4] :
( ( ( ~ memberP(sK2,X4)
| ? [X5] :
( segmentP(sK3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(sK3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(sK2,X4) ) )
| ~ ssItem(X4) )
& nil != sK0
& sK0 = sK2
& sK1 = sK3
& nil = sK1
& ssList(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
! [X4] :
( ? [X5] :
( segmentP(sK3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
=> ( segmentP(sK3,app(app(cons(X4,nil),sK4(X4)),cons(X4,nil)))
& ssList(sK4(X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ( ( ~ memberP(X2,X4)
| ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) ) )
& ( ! [X6] :
( ~ segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6) )
| memberP(X2,X4) ) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ( ( memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
| ( ? [X6] :
( segmentP(X3,app(app(cons(X4,nil),X6),cons(X4,nil)))
& ssList(X6) )
& ~ memberP(X2,X4) ) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ( ( memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
| ( ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
& ~ memberP(X2,X4) ) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ( ( memberP(X2,X4)
& ! [X5] :
( ssList(X5)
=> ~ segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil))) ) )
| ( ? [X5] :
( segmentP(X3,app(app(cons(X4,nil),X5),cons(X4,nil)))
& ssList(X5) )
& ~ memberP(X2,X4) ) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',co1) ).
fof(f340,plain,
ssList(sK2),
inference(cnf_transformation,[],[f229]) ).
fof(f111628,plain,
( ~ ssList(sK0)
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f111626,f345]) ).
fof(f345,plain,
nil != sK0,
inference(cnf_transformation,[],[f229]) ).
fof(f111626,plain,
( nil = sK0
| ~ ssList(sK0)
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(resolution,[],[f111619,f416]) ).
fof(f416,plain,
! [X0] :
( ssItem(sK6(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( ( cons(sK6(X0),sK5(X0)) = X0
& ssItem(sK6(X0))
& ssList(sK5(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f150,f246,f245]) ).
fof(f245,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK5(X0)) = X0
& ssItem(X2) )
& ssList(sK5(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f246,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK5(X0)) = X0
& ssItem(X2) )
=> ( cons(sK6(X0),sK5(X0)) = X0
& ssItem(sK6(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax20) ).
fof(f111619,plain,
( ~ ssItem(sK6(sK0))
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f111618,f575]) ).
fof(f111618,plain,
( ~ ssList(sK0)
| ~ ssItem(sK6(sK0))
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f111610,f345]) ).
fof(f111610,plain,
( nil = sK0
| ~ ssList(sK0)
| ~ ssItem(sK6(sK0))
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(resolution,[],[f111530,f1915]) ).
fof(f1915,plain,
! [X0] :
( ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f1914,f357]) ).
fof(f357,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax17) ).
fof(f1914,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK0,X0)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f1911]) ).
fof(f1911,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[],[f1903,f492]) ).
fof(f492,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax16) ).
fof(f1903,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ memberP(sK0,X0) ),
inference(subsumption_resolution,[],[f1902,f547]) ).
fof(f547,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f427]) ).
fof(f427,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK9(X0),nil) = X0
& ssItem(sK9(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f253,f254]) ).
fof(f254,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK9(X0),nil) = X0
& ssItem(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f252]) ).
fof(f252,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,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax4) ).
fof(f1902,plain,
! [X0] :
( ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ singletonP(cons(X0,nil)) ),
inference(duplicate_literal_removal,[],[f1899]) ).
fof(f1899,plain,
! [X0] :
( ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[],[f1854,f425]) ).
fof(f425,plain,
! [X0] :
( ssItem(sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1854,plain,
! [X0] :
( ~ ssItem(sK9(cons(X0,nil)))
| ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(duplicate_literal_removal,[],[f1847]) ).
fof(f1847,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssItem(sK9(cons(X0,nil))) ),
inference(resolution,[],[f1739,f806]) ).
fof(f806,plain,
! [X0] :
( ssList(sK4(sK9(cons(X0,nil))))
| ~ memberP(sK0,X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssItem(sK9(cons(X0,nil))) ),
inference(resolution,[],[f783,f577]) ).
fof(f577,plain,
! [X0] :
( ~ memberP(sK0,X0)
| ssList(sK4(X0))
| ~ ssItem(X0) ),
inference(superposition,[],[f347,f344]) ).
fof(f347,plain,
! [X4] :
( ~ memberP(sK2,X4)
| ssList(sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f229]) ).
fof(f783,plain,
! [X0] :
( memberP(sK0,sK9(cons(X0,nil)))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f782,f547]) ).
fof(f782,plain,
! [X0] :
( memberP(sK0,sK9(cons(X0,nil)))
| ~ singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f749,f577]) ).
fof(f749,plain,
! [X0] :
( memberP(sK0,sK9(cons(X0,nil)))
| ~ ssList(sK4(X0))
| ~ singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(resolution,[],[f655,f605]) ).
fof(f605,plain,
! [X0] :
( segmentP(nil,app(app(cons(X0,nil),sK4(X0)),cons(X0,nil)))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f604,f344]) ).
fof(f604,plain,
! [X0] :
( segmentP(nil,app(app(cons(X0,nil),sK4(X0)),cons(X0,nil)))
| ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f580,f342]) ).
fof(f342,plain,
nil = sK1,
inference(cnf_transformation,[],[f229]) ).
fof(f580,plain,
! [X0] :
( segmentP(sK1,app(app(cons(X0,nil),sK4(X0)),cons(X0,nil)))
| ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(superposition,[],[f348,f343]) ).
fof(f343,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f229]) ).
fof(f348,plain,
! [X4] :
( segmentP(sK3,app(app(cons(X4,nil),sK4(X4)),cons(X4,nil)))
| ~ memberP(sK2,X4)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f229]) ).
fof(f655,plain,
! [X0,X1] :
( ~ segmentP(nil,app(app(X0,X1),X0))
| memberP(sK0,sK9(X0))
| ~ ssList(X1)
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f654,f344]) ).
fof(f654,plain,
! [X0,X1] :
( ~ segmentP(nil,app(app(X0,X1),X0))
| ~ ssList(X1)
| memberP(sK2,sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f653,f342]) ).
fof(f653,plain,
! [X0,X1] :
( ~ segmentP(sK1,app(app(X0,X1),X0))
| ~ ssList(X1)
| memberP(sK2,sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f652,f343]) ).
fof(f652,plain,
! [X0,X1] :
( ~ segmentP(sK3,app(app(X0,X1),X0))
| ~ ssList(X1)
| memberP(sK2,sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f629,f425]) ).
fof(f629,plain,
! [X0,X1] :
( ~ segmentP(sK3,app(app(X0,X1),X0))
| ~ ssList(X1)
| memberP(sK2,sK9(X0))
| ~ ssItem(sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(superposition,[],[f346,f426]) ).
fof(f426,plain,
! [X0] :
( cons(sK9(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f346,plain,
! [X6,X4] :
( ~ segmentP(sK3,app(app(cons(X4,nil),X6),cons(X4,nil)))
| ~ ssList(X6)
| memberP(sK2,X4)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f229]) ).
fof(f1739,plain,
! [X0] :
( ~ ssList(sK4(sK9(cons(X0,nil))))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f1738,f547]) ).
fof(f1738,plain,
! [X0] :
( ~ singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssList(sK4(sK9(cons(X0,nil))))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(duplicate_literal_removal,[],[f1733]) ).
fof(f1733,plain,
! [X0] :
( ~ singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssList(sK4(sK9(cons(X0,nil))))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK0,X0)
| ~ ssItem(X0) ),
inference(resolution,[],[f1732,f783]) ).
fof(f1732,plain,
! [X0] :
( ~ memberP(sK0,sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0)
| ~ ssList(sK4(sK9(X0))) ),
inference(duplicate_literal_removal,[],[f1725]) ).
fof(f1725,plain,
! [X0] :
( ~ memberP(sK0,sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0)
| ~ ssList(sK4(sK9(X0)))
| ~ ssList(X0) ),
inference(resolution,[],[f1724,f502]) ).
fof(f502,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax26) ).
fof(f1724,plain,
! [X0] :
( ~ ssList(app(X0,sK4(sK9(X0))))
| ~ memberP(sK0,sK9(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1723,f425]) ).
fof(f1723,plain,
! [X0] :
( ~ ssItem(sK9(X0))
| ~ memberP(sK0,sK9(X0))
| ~ ssList(app(X0,sK4(sK9(X0))))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f1712,f502]) ).
fof(f1712,plain,
! [X0] :
( ~ ssList(app(app(X0,sK4(sK9(X0))),X0))
| ~ ssItem(sK9(X0))
| ~ memberP(sK0,sK9(X0))
| ~ ssList(app(X0,sK4(sK9(X0))))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(superposition,[],[f1196,f426]) ).
fof(f1196,plain,
! [X26] :
( ~ ssList(app(app(cons(X26,nil),sK4(X26)),cons(X26,nil)))
| ~ ssItem(X26)
| ~ memberP(sK0,X26)
| ~ ssList(app(cons(X26,nil),sK4(X26))) ),
inference(subsumption_resolution,[],[f1195,f358]) ).
fof(f358,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax38) ).
fof(f1195,plain,
! [X26] :
( memberP(nil,X26)
| ~ ssList(app(cons(X26,nil),sK4(X26)))
| ~ ssItem(X26)
| ~ memberP(sK0,X26)
| ~ ssList(app(app(cons(X26,nil),sK4(X26)),cons(X26,nil))) ),
inference(subsumption_resolution,[],[f1151,f357]) ).
fof(f1151,plain,
! [X26] :
( memberP(nil,X26)
| ~ ssList(nil)
| ~ ssList(app(cons(X26,nil),sK4(X26)))
| ~ ssItem(X26)
| ~ memberP(sK0,X26)
| ~ ssList(app(app(cons(X26,nil),sK4(X26)),cons(X26,nil))) ),
inference(duplicate_literal_removal,[],[f1124]) ).
fof(f1124,plain,
! [X26] :
( memberP(nil,X26)
| ~ ssList(nil)
| ~ ssList(app(cons(X26,nil),sK4(X26)))
| ~ ssItem(X26)
| ~ ssList(nil)
| ~ memberP(sK0,X26)
| ~ ssItem(X26)
| ~ ssList(app(app(cons(X26,nil),sK4(X26)),cons(X26,nil))) ),
inference(superposition,[],[f559,f603]) ).
fof(f603,plain,
! [X2] :
( nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(subsumption_resolution,[],[f602,f357]) ).
fof(f602,plain,
! [X2] :
( ~ ssList(nil)
| nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f601,f342]) ).
fof(f601,plain,
! [X2] :
( ~ ssList(sK1)
| nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f600,f343]) ).
fof(f600,plain,
! [X2] :
( nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(subsumption_resolution,[],[f599,f411]) ).
fof(f411,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax57) ).
fof(f599,plain,
! [X2] :
( ~ segmentP(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil)),nil)
| nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f598,f342]) ).
fof(f598,plain,
! [X2] :
( ~ segmentP(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil)),sK1)
| nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f597,f343]) ).
fof(f597,plain,
! [X2] :
( nil = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ segmentP(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil)),sK3)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f596,f342]) ).
fof(f596,plain,
! [X2] :
( sK1 = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ memberP(sK0,X2)
| ~ ssItem(X2)
| ~ segmentP(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil)),sK3)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f595,f343]) ).
fof(f595,plain,
! [X2] :
( ~ memberP(sK0,X2)
| ~ ssItem(X2)
| sK3 = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ segmentP(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil)),sK3)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(forward_demodulation,[],[f579,f344]) ).
fof(f579,plain,
! [X2] :
( ~ memberP(sK2,X2)
| ~ ssItem(X2)
| sK3 = app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))
| ~ segmentP(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil)),sK3)
| ~ ssList(sK3)
| ~ ssList(app(app(cons(X2,nil),sK4(X2)),cons(X2,nil))) ),
inference(resolution,[],[f348,f508]) ).
fof(f508,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax54) ).
fof(f559,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f501]) ).
fof(f501,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK44(X0,X1),cons(X1,sK45(X0,X1))) = X0
& ssList(sK45(X0,X1))
& ssList(sK44(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f315,f317,f316]) ).
fof(f316,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK44(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK44(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0,X1] :
( ? [X5] :
( app(sK44(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK44(X0,X1),cons(X1,sK45(X0,X1))) = X0
& ssList(sK45(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f314]) ).
fof(f314,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax3) ).
fof(f111530,plain,
( ! [X126] :
( memberP(X126,sK6(X126))
| nil = X126
| ~ ssList(X126) )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f111529,f416]) ).
fof(f111529,plain,
( ! [X126] :
( memberP(X126,sK6(X126))
| ~ ssItem(sK6(X126))
| nil = X126
| ~ ssList(X126) )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f111146,f419]) ).
fof(f419,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax24) ).
fof(f111146,plain,
( ! [X126] :
( memberP(X126,sK6(X126))
| ~ ssList(tl(X126))
| ~ ssItem(sK6(X126))
| nil = X126
| ~ ssList(X126) )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(superposition,[],[f568,f110712]) ).
fof(f110712,plain,
( ! [X1] :
( cons(sK6(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1) )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(duplicate_literal_removal,[],[f110445]) ).
fof(f110445,plain,
( ! [X1] :
( cons(sK6(X1),tl(X1)) = X1
| nil = X1
| ~ ssList(X1)
| ~ ssList(X1)
| nil = X1 )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(superposition,[],[f417,f110410]) ).
fof(f110410,plain,
( ! [X0] :
( tl(X0) = sK5(X0)
| ~ ssList(X0)
| nil = X0 )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(duplicate_literal_removal,[],[f110397]) ).
fof(f110397,plain,
( ! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X0)
| tl(X0) = sK5(X0)
| nil = X0 )
| ~ spl52_10
| ~ spl52_12
| ~ spl52_55 ),
inference(resolution,[],[f110396,f55610]) ).
fof(f55610,plain,
( ! [X3] :
( ~ segmentP(sK5(X3),tl(X3))
| ~ ssList(X3)
| tl(X3) = sK5(X3)
| nil = X3 )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55609,f415]) ).
fof(f415,plain,
! [X0] :
( ssList(sK5(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f55609,plain,
( ! [X3] :
( nil = X3
| ~ ssList(X3)
| tl(X3) = sK5(X3)
| ~ segmentP(sK5(X3),tl(X3))
| ~ ssList(sK5(X3)) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55603,f419]) ).
fof(f55603,plain,
( ! [X3] :
( nil = X3
| ~ ssList(X3)
| tl(X3) = sK5(X3)
| ~ segmentP(sK5(X3),tl(X3))
| ~ ssList(tl(X3))
| ~ ssList(sK5(X3)) )
| ~ spl52_10
| ~ spl52_12 ),
inference(resolution,[],[f55586,f508]) ).
fof(f55586,plain,
( ! [X3] :
( segmentP(tl(X3),sK5(X3))
| nil = X3
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55585,f415]) ).
fof(f55585,plain,
( ! [X3] :
( segmentP(tl(X3),sK5(X3))
| ~ ssList(sK5(X3))
| nil = X3
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55575,f416]) ).
fof(f55575,plain,
( ! [X3] :
( segmentP(tl(X3),sK5(X3))
| ~ ssItem(sK6(X3))
| ~ ssList(sK5(X3))
| nil = X3
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f55513,f417]) ).
fof(f55513,plain,
( ! [X14,X13] :
( segmentP(tl(cons(X13,X14)),X14)
| ~ ssItem(X13)
| ~ ssList(X14) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55512,f492]) ).
fof(f55512,plain,
( ! [X14,X13] :
( segmentP(tl(cons(X13,X14)),X14)
| ~ ssItem(X13)
| ~ ssList(X14)
| ~ ssList(cons(X13,X14)) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55489,f357]) ).
fof(f55489,plain,
( ! [X14,X13] :
( segmentP(tl(cons(X13,X14)),X14)
| ~ ssList(nil)
| ~ ssItem(X13)
| ~ ssList(X14)
| ~ ssList(cons(X13,X14)) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f55039,f413]) ).
fof(f413,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax84) ).
fof(f55039,plain,
( ! [X2,X0,X1] :
( segmentP(tl(app(cons(X0,X1),X2)),X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55038,f492]) ).
fof(f55038,plain,
( ! [X2,X0,X1] :
( segmentP(tl(app(cons(X0,X1),X2)),X1)
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f55013,f493]) ).
fof(f493,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax21) ).
fof(f55013,plain,
( ! [X2,X0,X1] :
( segmentP(tl(app(cons(X0,X1),X2)),X1)
| ~ ssList(X2)
| nil = cons(X0,X1)
| ~ ssList(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f53592,f495]) ).
fof(f495,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax25) ).
fof(f53592,plain,
( ! [X36,X37] :
( segmentP(tl(app(X36,X37)),tl(X36))
| ~ ssList(X37)
| nil = X36
| ~ ssList(X36) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f53567,f419]) ).
fof(f53567,plain,
( ! [X36,X37] :
( segmentP(tl(app(X36,X37)),tl(X36))
| ~ ssList(X37)
| ~ ssList(tl(X36))
| nil = X36
| ~ ssList(X36) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f53561]) ).
fof(f53561,plain,
( ! [X36,X37] :
( segmentP(tl(app(X36,X37)),tl(X36))
| ~ ssList(X37)
| ~ ssList(tl(X36))
| nil = X36
| ~ ssList(X37)
| ~ ssList(X36) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f53464,f504]) ).
fof(f504,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax86) ).
fof(f53464,plain,
( ! [X3,X4] :
( segmentP(app(X3,X4),X3)
| ~ ssList(X4)
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f53451]) ).
fof(f53451,plain,
( ! [X3,X4] :
( segmentP(app(X3,X4),X3)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X3)
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f52676,f414]) ).
fof(f414,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax28) ).
fof(f52676,plain,
( ! [X495,X494] :
( segmentP(app(app(nil,X494),X495),app(nil,X494))
| ~ ssList(X495)
| ~ ssList(app(nil,X494))
| ~ ssList(X494) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f52675,f502]) ).
fof(f52675,plain,
( ! [X495,X494] :
( segmentP(app(app(nil,X494),X495),app(nil,X494))
| ~ ssList(X495)
| ~ ssList(app(nil,X494))
| ~ ssList(app(app(nil,X494),X495))
| ~ ssList(X494) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f52094,f357]) ).
fof(f52094,plain,
( ! [X495,X494] :
( segmentP(app(app(nil,X494),X495),app(nil,X494))
| ~ ssList(X495)
| ~ ssList(nil)
| ~ ssList(app(nil,X494))
| ~ ssList(app(app(nil,X494),X495))
| ~ ssList(X494) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f563,f51436]) ).
fof(f51436,plain,
( ! [X173] :
( app(nil,X173) = app(nil,app(nil,X173))
| ~ ssList(X173) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f51412,f357]) ).
fof(f51412,plain,
( ! [X173] :
( app(nil,X173) = app(nil,app(nil,X173))
| ~ ssList(X173)
| ~ ssList(nil) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f50757]) ).
fof(f50757,plain,
( ! [X173] :
( app(nil,X173) = app(nil,app(nil,X173))
| ~ ssList(X173)
| ~ ssList(nil)
| ~ ssList(nil) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f527,f50458]) ).
fof(f50458,plain,
( nil = app(nil,nil)
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f50408,f5147]) ).
fof(f5147,plain,
( ssList(app(nil,nil))
| ~ spl52_10 ),
inference(avatar_component_clause,[],[f5146]) ).
fof(f5146,plain,
( spl52_10
<=> ssList(app(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_10])]) ).
fof(f50408,plain,
( nil = app(nil,nil)
| ~ ssList(app(nil,nil))
| ~ spl52_12 ),
inference(resolution,[],[f5155,f490]) ).
fof(f490,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax58) ).
fof(f5155,plain,
( segmentP(nil,app(nil,nil))
| ~ spl52_12 ),
inference(avatar_component_clause,[],[f5154]) ).
fof(f5154,plain,
( spl52_12
<=> segmentP(nil,app(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_12])]) ).
fof(f527,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax82) ).
fof(f563,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,[],[f520]) ).
fof(f520,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,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK48(X0,X1),X1),sK49(X0,X1)) = X0
& ssList(sK49(X0,X1))
& ssList(sK48(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f329,f331,f330]) ).
fof(f330,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK48(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK48(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f331,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK48(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK48(X0,X1),X1),sK49(X0,X1)) = X0
& ssList(sK49(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,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,[],[f328]) ).
fof(f328,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,[],[f202]) ).
fof(f202,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(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/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax7) ).
fof(f110396,plain,
( ! [X4] :
( segmentP(sK5(X4),tl(X4))
| nil = X4
| ~ ssList(X4) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f110395,f415]) ).
fof(f110395,plain,
( ! [X4] :
( segmentP(sK5(X4),tl(X4))
| ~ ssList(sK5(X4))
| nil = X4
| ~ ssList(X4) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f110373,f416]) ).
fof(f110373,plain,
( ! [X4] :
( segmentP(sK5(X4),tl(X4))
| ~ ssItem(sK6(X4))
| ~ ssList(sK5(X4))
| nil = X4
| ~ ssList(X4) )
| ~ spl52_55 ),
inference(superposition,[],[f110223,f417]) ).
fof(f110223,plain,
( ! [X8,X9] :
( segmentP(X9,tl(cons(X8,X9)))
| ~ ssItem(X8)
| ~ ssList(X9) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f110176,f492]) ).
fof(f110176,plain,
( ! [X8,X9] :
( segmentP(X9,tl(cons(X8,X9)))
| ~ ssItem(X8)
| ~ ssList(X9)
| ~ ssList(cons(X8,X9)) )
| ~ spl52_55 ),
inference(superposition,[],[f109754,f413]) ).
fof(f109754,plain,
( ! [X0,X1] :
( segmentP(X1,tl(app(cons(X0,X1),nil)))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f109753,f492]) ).
fof(f109753,plain,
( ! [X0,X1] :
( segmentP(X1,tl(app(cons(X0,X1),nil)))
| ~ ssList(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f109710,f493]) ).
fof(f109710,plain,
( ! [X0,X1] :
( segmentP(X1,tl(app(cons(X0,X1),nil)))
| nil = cons(X0,X1)
| ~ ssList(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl52_55 ),
inference(superposition,[],[f108565,f495]) ).
fof(f108565,plain,
( ! [X14] :
( segmentP(tl(X14),tl(app(X14,nil)))
| nil = X14
| ~ ssList(X14) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f108564,f419]) ).
fof(f108564,plain,
( ! [X14] :
( segmentP(tl(X14),tl(app(X14,nil)))
| ~ ssList(tl(X14))
| nil = X14
| ~ ssList(X14) )
| ~ spl52_55 ),
inference(subsumption_resolution,[],[f108482,f357]) ).
fof(f108482,plain,
( ! [X14] :
( segmentP(tl(X14),tl(app(X14,nil)))
| ~ ssList(tl(X14))
| nil = X14
| ~ ssList(nil)
| ~ ssList(X14) )
| ~ spl52_55 ),
inference(superposition,[],[f108050,f504]) ).
fof(f108050,plain,
( ! [X1174] :
( segmentP(X1174,app(X1174,nil))
| ~ ssList(X1174) )
| ~ spl52_55 ),
inference(avatar_component_clause,[],[f108049]) ).
fof(f108049,plain,
( spl52_55
<=> ! [X1174] :
( segmentP(X1174,app(X1174,nil))
| ~ ssList(X1174) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_55])]) ).
fof(f417,plain,
! [X0] :
( cons(sK6(X0),sK5(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f568,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f541]) ).
fof(f541,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f389]) ).
fof(f389,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f235]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax37) ).
fof(f108187,plain,
~ spl52_53,
inference(avatar_contradiction_clause,[],[f108186]) ).
fof(f108186,plain,
( $false
| ~ spl52_53 ),
inference(subsumption_resolution,[],[f108177,f357]) ).
fof(f108177,plain,
( ~ ssList(nil)
| ~ spl52_53 ),
inference(duplicate_literal_removal,[],[f108168]) ).
fof(f108168,plain,
( ~ ssList(nil)
| ~ ssList(nil)
| ~ spl52_53 ),
inference(resolution,[],[f108043,f409]) ).
fof(f409,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax45) ).
fof(f108043,plain,
( ! [X921] :
( ~ frontsegP(nil,X921)
| ~ ssList(X921) )
| ~ spl52_53 ),
inference(avatar_component_clause,[],[f108042]) ).
fof(f108042,plain,
( spl52_53
<=> ! [X921] :
( ~ ssList(X921)
| ~ frontsegP(nil,X921) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_53])]) ).
fof(f108051,plain,
( spl52_53
| spl52_55
| ~ spl52_10
| ~ spl52_12 ),
inference(avatar_split_clause,[],[f107554,f5154,f5146,f108049,f108042]) ).
fof(f107554,plain,
( ! [X1175,X1174] :
( segmentP(X1174,app(X1174,nil))
| ~ ssList(X1175)
| ~ ssList(X1174)
| ~ frontsegP(nil,X1175) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f104036]) ).
fof(f104036,plain,
( ! [X1175,X1174] :
( segmentP(X1174,app(X1174,nil))
| ~ ssList(X1175)
| ~ ssList(X1174)
| ~ ssList(X1174)
| ~ frontsegP(nil,X1175)
| ~ ssList(X1175) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f76279,f103528]) ).
fof(f103528,plain,
( ! [X2,X3] :
( app(X3,X2) = X3
| ~ ssList(X3)
| ~ frontsegP(nil,X2)
| ~ ssList(X2) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f102818]) ).
fof(f102818,plain,
( ! [X2,X3] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(nil,X2)
| ~ ssList(X3)
| app(X3,X2) = X3
| ~ ssList(X2) )
| ~ spl52_10
| ~ spl52_12 ),
inference(resolution,[],[f102691,f53587]) ).
fof(f53587,plain,
( ! [X4,X5] :
( ~ segmentP(X5,app(X5,X4))
| ~ ssList(X5)
| app(X5,X4) = X5
| ~ ssList(X4) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f53583,f502]) ).
fof(f53583,plain,
( ! [X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| app(X5,X4) = X5
| ~ segmentP(X5,app(X5,X4))
| ~ ssList(app(X5,X4)) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f53532]) ).
fof(f53532,plain,
( ! [X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| app(X5,X4) = X5
| ~ segmentP(X5,app(X5,X4))
| ~ ssList(app(X5,X4))
| ~ ssList(X5) )
| ~ spl52_10
| ~ spl52_12 ),
inference(resolution,[],[f53464,f508]) ).
fof(f102691,plain,
( ! [X10,X11] :
( segmentP(X10,app(X10,X11))
| ~ ssList(X11)
| ~ ssList(X10)
| ~ frontsegP(nil,X11) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f102675,f357]) ).
fof(f102675,plain,
( ! [X10,X11] :
( segmentP(X10,app(X10,X11))
| ~ ssList(X11)
| ~ ssList(X10)
| ~ frontsegP(nil,X11)
| ~ ssList(nil) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f102556]) ).
fof(f102556,plain,
( ! [X10,X11] :
( segmentP(X10,app(X10,X11))
| ~ ssList(X11)
| ~ ssList(X10)
| ~ frontsegP(nil,X11)
| ~ ssList(nil)
| ~ ssList(X10) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f76275,f413]) ).
fof(f76275,plain,
( ! [X2,X3,X4] :
( segmentP(app(X4,X3),app(X4,X2))
| ~ ssList(X2)
| ~ ssList(X4)
| ~ frontsegP(X3,X2)
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f76271,f514]) ).
fof(f514,plain,
! [X0,X1] :
( ssList(sK47(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK47(X0,X1)) = X0
& ssList(sK47(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f325,f326]) ).
fof(f326,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK47(X0,X1)) = X0
& ssList(sK47(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f324]) ).
fof(f324,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax5) ).
fof(f76271,plain,
( ! [X2,X3,X4] :
( segmentP(app(X4,X3),app(X4,X2))
| ~ ssList(sK47(X3,X2))
| ~ ssList(X2)
| ~ ssList(X4)
| ~ frontsegP(X3,X2)
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f76149]) ).
fof(f76149,plain,
( ! [X2,X3,X4] :
( segmentP(app(X4,X3),app(X4,X2))
| ~ ssList(sK47(X3,X2))
| ~ ssList(X2)
| ~ ssList(X4)
| ~ frontsegP(X3,X2)
| ~ ssList(X2)
| ~ ssList(X3) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f53590,f515]) ).
fof(f515,plain,
! [X0,X1] :
( app(X1,sK47(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f53590,plain,
( ! [X18,X19,X20] :
( segmentP(app(X18,app(X19,X20)),app(X18,X19))
| ~ ssList(X20)
| ~ ssList(X19)
| ~ ssList(X18) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f53572,f502]) ).
fof(f53572,plain,
( ! [X18,X19,X20] :
( segmentP(app(X18,app(X19,X20)),app(X18,X19))
| ~ ssList(X20)
| ~ ssList(app(X18,X19))
| ~ ssList(X19)
| ~ ssList(X18) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f53546]) ).
fof(f53546,plain,
( ! [X18,X19,X20] :
( segmentP(app(X18,app(X19,X20)),app(X18,X19))
| ~ ssList(X20)
| ~ ssList(app(X18,X19))
| ~ ssList(X20)
| ~ ssList(X19)
| ~ ssList(X18) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f53464,f527]) ).
fof(f76279,plain,
( ! [X60,X61] :
( segmentP(app(X61,X60),app(X61,nil))
| ~ ssList(X60)
| ~ ssList(X61) )
| ~ spl52_10
| ~ spl52_12 ),
inference(subsumption_resolution,[],[f76259,f357]) ).
fof(f76259,plain,
( ! [X60,X61] :
( segmentP(app(X61,X60),app(X61,nil))
| ~ ssList(X60)
| ~ ssList(nil)
| ~ ssList(X61) )
| ~ spl52_10
| ~ spl52_12 ),
inference(duplicate_literal_removal,[],[f76173]) ).
fof(f76173,plain,
( ! [X60,X61] :
( segmentP(app(X61,X60),app(X61,nil))
| ~ ssList(X60)
| ~ ssList(nil)
| ~ ssList(X61)
| ~ ssList(X60) )
| ~ spl52_10
| ~ spl52_12 ),
inference(superposition,[],[f53590,f414]) ).
fof(f50356,plain,
( ~ spl52_2
| spl52_12 ),
inference(avatar_contradiction_clause,[],[f50355]) ).
fof(f50355,plain,
( $false
| ~ spl52_2
| spl52_12 ),
inference(subsumption_resolution,[],[f50354,f357]) ).
fof(f50354,plain,
( ~ ssList(nil)
| ~ spl52_2
| spl52_12 ),
inference(subsumption_resolution,[],[f50347,f1175]) ).
fof(f1175,plain,
( segmentP(nil,nil)
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f1173,plain,
( spl52_2
<=> segmentP(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).
fof(f50347,plain,
( ~ segmentP(nil,nil)
| ~ ssList(nil)
| spl52_12 ),
inference(superposition,[],[f5156,f413]) ).
fof(f5156,plain,
( ~ segmentP(nil,app(nil,nil))
| spl52_12 ),
inference(avatar_component_clause,[],[f5154]) ).
fof(f5185,plain,
spl52_10,
inference(avatar_contradiction_clause,[],[f5184]) ).
fof(f5184,plain,
( $false
| spl52_10 ),
inference(subsumption_resolution,[],[f5174,f357]) ).
fof(f5174,plain,
( ~ ssList(nil)
| spl52_10 ),
inference(duplicate_literal_removal,[],[f5173]) ).
fof(f5173,plain,
( ~ ssList(nil)
| ~ ssList(nil)
| spl52_10 ),
inference(superposition,[],[f5148,f413]) ).
fof(f5148,plain,
( ~ ssList(app(nil,nil))
| spl52_10 ),
inference(avatar_component_clause,[],[f5146]) ).
fof(f5026,plain,
spl52_2,
inference(avatar_contradiction_clause,[],[f5025]) ).
fof(f5025,plain,
( $false
| spl52_2 ),
inference(subsumption_resolution,[],[f5020,f357]) ).
fof(f5020,plain,
( ~ ssList(nil)
| spl52_2 ),
inference(resolution,[],[f1174,f410]) ).
fof(f410,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644',ax55) ).
fof(f1174,plain,
( ~ segmentP(nil,nil)
| spl52_2 ),
inference(avatar_component_clause,[],[f1173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC045+1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n003.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 : Mon Aug 28 17:14:10 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.btPxF5SmoQ/Vampire---4.8_2644
% 0.22/0.36 % (2751)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (2755)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.42 % (2757)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.42 % (2758)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.42 % (2752)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.42 % (2754)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.42 % (2753)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.42 % (2756)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 28.09/4.40 % (2758)First to succeed.
% 28.09/4.41 % (2758)Refutation found. Thanks to Tanya!
% 28.09/4.41 % SZS status Theorem for Vampire---4
% 28.09/4.41 % SZS output start Proof for Vampire---4
% See solution above
% 28.09/4.42 % (2758)------------------------------
% 28.09/4.42 % (2758)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 28.09/4.42 % (2758)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 28.09/4.42 % (2758)Termination reason: Refutation
% 28.09/4.42
% 28.09/4.42 % (2758)Memory used [KB]: 100936
% 28.09/4.42 % (2758)Time elapsed: 3.980 s
% 28.09/4.42 % (2758)------------------------------
% 28.09/4.42 % (2758)------------------------------
% 28.09/4.42 % (2751)Success in time 4.052 s
% 28.09/4.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------