%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX029+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:45:42 PM UTC 2026
% Result : Theorem 11.55s 4.15s
% Output : Refutation 23.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 46
% Syntax : Number of formulae : 349 ( 46 unt; 20 def)
% Number of atoms : 1011 ( 360 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1154 ( 492 ~; 524 |; 94 &)
% ( 24 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 21 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-3 aty)
% Number of variables : 365 ( 0 sgn 308 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( s(X0) = s(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id4) ).
fof(f7,axiom,
! [X0,X1] : nil != cons(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id7) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( cons(X0,X1) = cons(X2,X3)
=> X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id8) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( cons(X0,X1) = cons(X2,X3)
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id9) ).
fof(f73,axiom,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
<=> ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X1 = cons(X3,X5)
& split_succeeds(X4,X2,X5) )
| ( X0 = nil
& X1 = nil
& X2 = nil ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id73) ).
fof(f94,axiom,
! [X0,X1,X2] :
( delete_succeeds(X0,X1,X2)
<=> ( ? [X3,X4,X5] :
( X1 = cons(X3,X4)
& X2 = cons(X3,X5)
& delete_succeeds(X0,X4,X5) )
| X1 = cons(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id94) ).
fof(f106,axiom,
! [X0] :
( list_succeeds(X0)
<=> ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2) )
| X0 = nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id106) ).
fof(f121,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
<=> ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@<_succeeds'(X2,X3) )
| ? [X4] :
( X0 = '0'
& X1 = s(X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id121) ).
fof(f181,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
=> ? [X2] : X1 = s(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:successor)') ).
fof(f183,axiom,
! [X0,X1] :
( '@<_succeeds'(X0,X1)
=> '@<_succeeds'(X0,s(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:weakening)') ).
fof(f187,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@<_succeeds'(X0,s(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:one)') ).
fof(f210,axiom,
! [X0,X1] :
( nat_succeeds(X0)
=> '@<_succeeds'(X0,'@+'(X0,s(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(less:plus:second)_009') ).
fof(f232,axiom,
! [X0,X1] :
( list_succeeds(cons(X0,X1))
=> list_succeeds(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(list:cons)') ).
fof(f248,axiom,
! [X0] : '**'(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:nil)') ).
fof(f249,axiom,
! [X0,X1,X2] :
( list_succeeds(X1)
=> '**'(cons(X0,X1),X2) = cons(X0,'**'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:cons)') ).
fof(f255,axiom,
! [X0] :
( list_succeeds(X0)
=> '**'(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:nil)_015') ).
fof(f261,axiom,
lh(nil) = '0',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:nil)') ).
fof(f262,axiom,
! [X0,X1] :
( list_succeeds(X1)
=> lh(cons(X0,X1)) = s(lh(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:cons)') ).
fof(f263,axiom,
! [X0] :
( list_succeeds(X0)
=> nat_succeeds(lh(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:types)') ).
fof(f264,axiom,
! [X0] :
( ( list_succeeds(X0)
& lh(X0) = '0' )
=> X0 = nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:zero)') ).
fof(f265,axiom,
! [X0,X1] :
( ( list_succeeds(X1)
& lh(X1) = s(X0) )
=> ? [X2,X3] : X1 = cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(lh:successor)') ).
fof(f266,axiom,
! [X0,X1] :
( ( list_succeeds(X0)
& list_succeeds(X1) )
=> lh('**'(X0,X1)) = '@+'(lh(X0),lh(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(app:lh)') ).
fof(f303,axiom,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
& list_succeeds(X1) )
=> lh(X1) = s(lh(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom-(delete:length)') ).
fof(f365,axiom,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
=> ( list_succeeds(X0)
& list_succeeds(X1)
& list_succeeds(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(split:types)') ).
fof(f366,axiom,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
=> lh(X0) = '@+'(lh(X1),lh(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(split:length)') ).
fof(f374,conjecture,
! [X0,X1,X2,X3,X4] :
( split_succeeds(cons(X0,cons(X1,X2)),X3,X4)
=> ( '@<_succeeds'(lh(X3),lh(cons(X0,cons(X1,X2))))
& '@<_succeeds'(lh(X4),lh(cons(X0,cons(X1,X2)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(split:length:less)') ).
fof(f375,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( split_succeeds(cons(X0,cons(X1,X2)),X3,X4)
=> ( '@<_succeeds'(lh(X3),lh(cons(X0,cons(X1,X2))))
& '@<_succeeds'(lh(X4),lh(cons(X0,cons(X1,X2)))) ) ),
inference(negated_conjecture,[status(cth)],[f374]) ).
fof(f409,plain,
! [X0,X1] :
( X0 = X1
| s(X0) != s(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f410,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| cons(X0,X1) != cons(X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f411,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| cons(X0,X1) != cons(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f550,plain,
! [X0,X1] :
( ? [X2] : X1 = s(X2)
| ~ '@<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f181]) ).
fof(f553,plain,
! [X0,X1] :
( '@<_succeeds'(X0,s(X1))
| ~ '@<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f183]) ).
fof(f558,plain,
! [X0] :
( '@<_succeeds'(X0,s(X0))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f187]) ).
fof(f593,plain,
! [X0,X1] :
( '@<_succeeds'(X0,'@+'(X0,s(X1)))
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f210]) ).
fof(f629,plain,
! [X0,X1] :
( list_succeeds(X1)
| ~ list_succeeds(cons(X0,X1)) ),
inference(ennf_transformation,[],[f232]) ).
fof(f654,plain,
! [X0,X1,X2] :
( '**'(cons(X0,X1),X2) = cons(X0,'**'(X1,X2))
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f249]) ).
fof(f665,plain,
! [X0] :
( '**'(X0,nil) = X0
| ~ list_succeeds(X0) ),
inference(ennf_transformation,[],[f255]) ).
fof(f672,plain,
! [X0,X1] :
( lh(cons(X0,X1)) = s(lh(X1))
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f262]) ).
fof(f673,plain,
! [X0] :
( nat_succeeds(lh(X0))
| ~ list_succeeds(X0) ),
inference(ennf_transformation,[],[f263]) ).
fof(f674,plain,
! [X0] :
( X0 = nil
| ~ list_succeeds(X0)
| '0' != lh(X0) ),
inference(ennf_transformation,[],[f264]) ).
fof(f675,plain,
! [X0] :
( X0 = nil
| ~ list_succeeds(X0)
| '0' != lh(X0) ),
inference(flattening,[],[f674]) ).
fof(f676,plain,
! [X0,X1] :
( ? [X2,X3] : X1 = cons(X2,X3)
| ~ list_succeeds(X1)
| s(X0) != lh(X1) ),
inference(ennf_transformation,[],[f265]) ).
fof(f677,plain,
! [X0,X1] :
( ? [X2,X3] : X1 = cons(X2,X3)
| ~ list_succeeds(X1)
| s(X0) != lh(X1) ),
inference(flattening,[],[f676]) ).
fof(f678,plain,
! [X0,X1] :
( lh('**'(X0,X1)) = '@+'(lh(X0),lh(X1))
| ~ list_succeeds(X0)
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f266]) ).
fof(f679,plain,
! [X0,X1] :
( lh('**'(X0,X1)) = '@+'(lh(X0),lh(X1))
| ~ list_succeeds(X0)
| ~ list_succeeds(X1) ),
inference(flattening,[],[f678]) ).
fof(f735,plain,
! [X0,X1,X2] :
( lh(X1) = s(lh(X2))
| ~ delete_succeeds(X0,X1,X2)
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f303]) ).
fof(f736,plain,
! [X0,X1,X2] :
( lh(X1) = s(lh(X2))
| ~ delete_succeeds(X0,X1,X2)
| ~ list_succeeds(X1) ),
inference(flattening,[],[f735]) ).
fof(f833,plain,
! [X0,X1,X2] :
( ( list_succeeds(X0)
& list_succeeds(X1)
& list_succeeds(X2) )
| ~ split_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f365]) ).
fof(f834,plain,
! [X0,X1,X2] :
( lh(X0) = '@+'(lh(X1),lh(X2))
| ~ split_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f366]) ).
fof(f846,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ '@<_succeeds'(lh(X3),lh(cons(X0,cons(X1,X2))))
| ~ '@<_succeeds'(lh(X4),lh(cons(X0,cons(X1,X2)))) )
& split_succeeds(cons(X0,cons(X1,X2)),X3,X4) ),
inference(ennf_transformation,[],[f375]) ).
fof(f911,plain,
! [X0,X1,X2] :
( ( split_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X1
| ~ split_succeeds(X4,X2,X5) )
& ( nil != X0
| nil != X1
| nil != X2 ) ) )
& ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X1 = cons(X3,X5)
& split_succeeds(X4,X2,X5) )
| ( X0 = nil
& X1 = nil
& X2 = nil )
| ~ split_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f912,plain,
! [X0,X1,X2] :
( ( split_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X1
| ~ split_succeeds(X4,X2,X5) )
& ( nil != X0
| nil != X1
| nil != X2 ) ) )
& ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X1 = cons(X3,X5)
& split_succeeds(X4,X2,X5) )
| ( X0 = nil
& X1 = nil
& X2 = nil )
| ~ split_succeeds(X0,X1,X2) ) ),
inference(flattening,[],[f911]) ).
fof(f913,plain,
! [X0,X1,X2] :
( ( split_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X1
| ~ split_succeeds(X4,X2,X5) )
& ( nil != X0
| nil != X1
| nil != X2 ) ) )
& ( ? [X6,X7,X8] :
( cons(X6,X7) = X0
& cons(X6,X8) = X1
& split_succeeds(X7,X2,X8) )
| ( X0 = nil
& X1 = nil
& X2 = nil )
| ~ split_succeeds(X0,X1,X2) ) ),
inference(rectify,[],[f912]) ).
fof(f914,plain,
! [X0,X1,X2] :
( ( split_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X1
| ~ split_succeeds(X4,X2,X5) )
& ( nil != X0
| nil != X1
| nil != X2 ) ) )
& ( ( cons(sK62(X0,X1,X2),sK63(X0,X1,X2)) = X0
& cons(sK62(X0,X1,X2),sK64(X0,X1,X2)) = X1
& split_succeeds(sK63(X0,X1,X2),X2,sK64(X0,X1,X2)) )
| ( X0 = nil
& X1 = nil
& X2 = nil )
| ~ split_succeeds(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62,sK63,sK64]),skolemize(X6,sK62(X0,X1,X2)),skolemize(X7,sK63(X0,X1,X2)),skolemize(X8,sK64(X0,X1,X2))],[f913]) ).
fof(f987,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ? [X3,X4,X5] :
( X1 = cons(X3,X4)
& X2 = cons(X3,X5)
& delete_succeeds(X0,X4,X5) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f988,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ? [X3,X4,X5] :
( X1 = cons(X3,X4)
& X2 = cons(X3,X5)
& delete_succeeds(X0,X4,X5) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(flattening,[],[f987]) ).
fof(f989,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ? [X6,X7,X8] :
( cons(X6,X7) = X1
& cons(X6,X8) = X2
& delete_succeeds(X0,X7,X8) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(rectify,[],[f988]) ).
fof(f990,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ( cons(sK124(X0,X1,X2),sK125(X0,X1,X2)) = X1
& cons(sK124(X0,X1,X2),sK126(X0,X1,X2)) = X2
& delete_succeeds(X0,sK125(X0,X1,X2),sK126(X0,X1,X2)) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124,sK125,sK126]),skolemize(X6,sK124(X0,X1,X2)),skolemize(X7,sK125(X0,X1,X2)),skolemize(X8,sK126(X0,X1,X2))],[f989]) ).
fof(f1031,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f1032,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(flattening,[],[f1031]) ).
fof(f1033,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ? [X3,X4] :
( cons(X3,X4) = X0
& list_succeeds(X4) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(rectify,[],[f1032]) ).
fof(f1034,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ( cons(sK159(X0),sK160(X0)) = X0
& list_succeeds(sK160(X0)) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159,sK160]),skolemize(X3,sK159(X0)),skolemize(X4,sK160(X0))],[f1033]) ).
fof(f1086,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@<_succeeds'(X2,X3) )
| ? [X4] :
( X0 = '0'
& X1 = s(X4) )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f1087,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ? [X2,X3] :
( X0 = s(X2)
& X1 = s(X3)
& '@<_succeeds'(X2,X3) )
| ? [X4] :
( X0 = '0'
& X1 = s(X4) )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(flattening,[],[f1086]) ).
fof(f1088,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ? [X5,X6] :
( s(X5) = X0
& s(X6) = X1
& '@<_succeeds'(X5,X6) )
| ? [X7] :
( X0 = '0'
& s(X7) = X1 )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(rectify,[],[f1087]) ).
fof(f1089,plain,
! [X0,X1] :
( ( '@<_succeeds'(X0,X1)
| ( ! [X2,X3] :
( s(X2) != X0
| s(X3) != X1
| ~ '@<_succeeds'(X2,X3) )
& ! [X4] :
( '0' != X0
| s(X4) != X1 ) ) )
& ( ( s(sK189(X0,X1)) = X0
& s(sK190(X0,X1)) = X1
& '@<_succeeds'(sK189(X0,X1),sK190(X0,X1)) )
| ( X0 = '0'
& s(sK191(X0,X1)) = X1 )
| ~ '@<_succeeds'(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189,sK190,sK191]),skolemize(X5,sK189(X0,X1)),skolemize(X6,sK190(X0,X1)),skolemize(X7,sK191(X0,X1))],[f1088]) ).
fof(f1110,plain,
! [X0,X1] :
( s(sK202(X1)) = X1
| ~ '@<_succeeds'(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(X2,sK202(X1))],[f550]) ).
fof(f1118,plain,
! [X0,X1] :
( cons(sK209(X1),sK210(X1)) = X1
| ~ list_succeeds(X1)
| s(X0) != lh(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209,sK210]),skolemize(X2,sK209(X1)),skolemize(X3,sK210(X1))],[f677]) ).
fof(f1136,plain,
( ( ~ '@<_succeeds'(lh(sK226),lh(cons(sK223,cons(sK224,sK225))))
| ~ '@<_succeeds'(lh(sK227),lh(cons(sK223,cons(sK224,sK225)))) )
& split_succeeds(cons(sK223,cons(sK224,sK225)),sK226,sK227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223,sK224,sK225,sK226,sK227]),skolemize(X0,sK223),skolemize(X1,sK224),skolemize(X2,sK225),skolemize(X3,sK226),skolemize(X4,sK227)],[f846]) ).
fof(f1140,plain,
! [X0,X1] :
( s(X0) != s(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f409]) ).
fof(f1143,plain,
! [X0,X1] : nil != cons(X0,X1),
inference(cnf_transformation,[],[f7]) ).
fof(f1144,plain,
! [X2,X3,X0,X1] :
( cons(X0,X1) != cons(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f410]) ).
fof(f1145,plain,
! [X2,X3,X0,X1] :
( cons(X0,X1) != cons(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f411]) ).
fof(f1299,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| nil = X1
| split_succeeds(sK63(X0,X1,X2),X2,sK64(X0,X1,X2)) ),
inference(cnf_transformation,[],[f914]) ).
fof(f1300,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| nil = X0
| split_succeeds(sK63(X0,X1,X2),X2,sK64(X0,X1,X2)) ),
inference(cnf_transformation,[],[f914]) ).
fof(f1301,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| nil = X2
| cons(sK62(X0,X1,X2),sK64(X0,X1,X2)) = X1 ),
inference(cnf_transformation,[],[f914]) ).
fof(f1303,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| nil = X0
| cons(sK62(X0,X1,X2),sK64(X0,X1,X2)) = X1 ),
inference(cnf_transformation,[],[f914]) ).
fof(f1304,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| nil = X2
| cons(sK62(X0,X1,X2),sK63(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f914]) ).
fof(f1306,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| nil = X0
| cons(sK62(X0,X1,X2),sK63(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f914]) ).
fof(f1458,plain,
! [X2,X0,X1] :
( delete_succeeds(X0,X1,X2)
| cons(X0,X2) != X1 ),
inference(cnf_transformation,[],[f990]) ).
fof(f1521,plain,
! [X0] :
( ~ list_succeeds(X0)
| nil = X0
| cons(sK159(X0),sK160(X0)) = X0 ),
inference(cnf_transformation,[],[f1034]) ).
fof(f1522,plain,
! [X0] :
( list_succeeds(X0)
| nil != X0 ),
inference(cnf_transformation,[],[f1034]) ).
fof(f1602,plain,
! [X0,X1] :
( '@<_succeeds'(sK189(X0,X1),sK190(X0,X1))
| '0' = X0
| ~ '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1089]) ).
fof(f1606,plain,
! [X0,X1] :
( ~ '@<_succeeds'(X0,X1)
| '0' = X0
| s(sK189(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f1089]) ).
fof(f1607,plain,
! [X0,X1,X4] :
( '@<_succeeds'(X0,X1)
| '0' != X0
| s(X4) != X1 ),
inference(cnf_transformation,[],[f1089]) ).
fof(f1686,plain,
! [X0,X1] :
( ~ '@<_succeeds'(X0,X1)
| s(sK202(X1)) = X1 ),
inference(cnf_transformation,[],[f1110]) ).
fof(f1688,plain,
! [X0,X1] :
( ~ '@<_succeeds'(X0,X1)
| '@<_succeeds'(X0,s(X1)) ),
inference(cnf_transformation,[],[f553]) ).
fof(f1692,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,s(X0)) ),
inference(cnf_transformation,[],[f558]) ).
fof(f1715,plain,
! [X0,X1] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,'@+'(X0,s(X1))) ),
inference(cnf_transformation,[],[f593]) ).
fof(f1737,plain,
! [X0,X1] :
( ~ list_succeeds(cons(X0,X1))
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f629]) ).
fof(f1755,plain,
! [X0] : '**'(nil,X0) = X0,
inference(cnf_transformation,[],[f248]) ).
fof(f1756,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X1)
| '**'(cons(X0,X1),X2) = cons(X0,'**'(X1,X2)) ),
inference(cnf_transformation,[],[f654]) ).
fof(f1763,plain,
! [X0] :
( ~ list_succeeds(X0)
| '**'(X0,nil) = X0 ),
inference(cnf_transformation,[],[f665]) ).
fof(f1770,plain,
'0' = lh(nil),
inference(cnf_transformation,[],[f261]) ).
fof(f1771,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| lh(cons(X0,X1)) = s(lh(X1)) ),
inference(cnf_transformation,[],[f672]) ).
fof(f1772,plain,
! [X0] :
( ~ list_succeeds(X0)
| nat_succeeds(lh(X0)) ),
inference(cnf_transformation,[],[f673]) ).
fof(f1773,plain,
! [X0] :
( ~ list_succeeds(X0)
| nil = X0
| '0' != lh(X0) ),
inference(cnf_transformation,[],[f675]) ).
fof(f1774,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| cons(sK209(X1),sK210(X1)) = X1
| s(X0) != lh(X1) ),
inference(cnf_transformation,[],[f1118]) ).
fof(f1775,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| ~ list_succeeds(X0)
| lh('**'(X0,X1)) = '@+'(lh(X0),lh(X1)) ),
inference(cnf_transformation,[],[f679]) ).
fof(f1812,plain,
! [X2,X0,X1] :
( ~ delete_succeeds(X0,X1,X2)
| lh(X1) = s(lh(X2))
| ~ list_succeeds(X1) ),
inference(cnf_transformation,[],[f736]) ).
fof(f1887,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| list_succeeds(X2) ),
inference(cnf_transformation,[],[f833]) ).
fof(f1888,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f833]) ).
fof(f1889,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| list_succeeds(X0) ),
inference(cnf_transformation,[],[f833]) ).
fof(f1890,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| lh(X0) = '@+'(lh(X1),lh(X2)) ),
inference(cnf_transformation,[],[f834]) ).
fof(f1898,plain,
split_succeeds(cons(sK223,cons(sK224,sK225)),sK226,sK227),
inference(cnf_transformation,[],[f1136]) ).
fof(f1899,plain,
( ~ '@<_succeeds'(lh(sK226),lh(cons(sK223,cons(sK224,sK225))))
| ~ '@<_succeeds'(lh(sK227),lh(cons(sK223,cons(sK224,sK225)))) ),
inference(cnf_transformation,[],[f1136]) ).
fof(f2009,plain,
! [X2,X0] : delete_succeeds(X0,cons(X0,X2),X2),
inference(equality_resolution,[],[f1458]) ).
fof(f2041,plain,
list_succeeds(nil),
inference(equality_resolution,[],[f1522]) ).
fof(f2079,plain,
! [X1,X4] :
( '@<_succeeds'('0',X1)
| s(X4) != X1 ),
inference(equality_resolution,[],[f1607]) ).
fof(f2080,plain,
! [X4] : '@<_succeeds'('0',s(X4)),
inference(equality_resolution,[],[f2079]) ).
fof(f2100,definition,
( spl228_1
<=> '@<_succeeds'(lh(sK227),lh(cons(sK223,cons(sK224,sK225)))) ),
introduced(definition,[new_symbols(definition,[spl228_1])],[avatar_definition]) ).
fof(f2101,plain,
( ~ '@<_succeeds'(lh(sK227),lh(cons(sK223,cons(sK224,sK225))))
| spl228_1 ),
inference(avatar_component_clause,[],[f2100]) ).
fof(f2103,definition,
( spl228_2
<=> '@<_succeeds'(lh(sK226),lh(cons(sK223,cons(sK224,sK225)))) ),
introduced(definition,[new_symbols(definition,[spl228_2])],[avatar_definition]) ).
fof(f2104,plain,
( ~ '@<_succeeds'(lh(sK226),lh(cons(sK223,cons(sK224,sK225))))
| spl228_2 ),
inference(avatar_component_clause,[],[f2103]) ).
fof(f2105,plain,
( ~ spl228_1
| ~ spl228_2 ),
inference(avatar_split_clause,[],[f1899,f2103,f2100]) ).
fof(f2128,plain,
lh(cons(sK223,cons(sK224,sK225))) = '@+'(lh(sK226),lh(sK227)),
inference(resolution,[],[f1890,f1898]) ).
fof(f2130,plain,
( nil = sK227
| cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
inference(resolution,[],[f1304,f1898]) ).
fof(f2132,definition,
( spl228_3
<=> cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
introduced(definition,[new_symbols(definition,[spl228_3])],[avatar_definition]) ).
fof(f2133,plain,
( cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227))
| ~ spl228_3 ),
inference(avatar_component_clause,[],[f2132]) ).
fof(f2135,definition,
( spl228_4
<=> nil = sK227 ),
introduced(definition,[new_symbols(definition,[spl228_4])],[avatar_definition]) ).
fof(f2136,plain,
( nil = sK227
| ~ spl228_4 ),
inference(avatar_component_clause,[],[f2135]) ).
fof(f2137,plain,
( spl228_3
| spl228_4 ),
inference(avatar_split_clause,[],[f2130,f2135,f2132]) ).
fof(f2138,plain,
( nil = sK227
| sK226 = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
inference(resolution,[],[f1301,f1898]) ).
fof(f2140,definition,
( spl228_5
<=> sK226 = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
introduced(definition,[new_symbols(definition,[spl228_5])],[avatar_definition]) ).
fof(f2141,plain,
( sK226 = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227))
| ~ spl228_5 ),
inference(avatar_component_clause,[],[f2140]) ).
fof(f2142,plain,
( spl228_5
| spl228_4 ),
inference(avatar_split_clause,[],[f2138,f2135,f2140]) ).
fof(f2144,plain,
( split_succeeds(cons(sK223,cons(sK224,sK225)),sK226,nil)
| ~ spl228_4 ),
inference(superposition,[],[f1898,f2136]) ).
fof(f2150,plain,
list_succeeds(cons(sK223,cons(sK224,sK225))),
inference(resolution,[],[f1889,f1898]) ).
fof(f2152,plain,
list_succeeds(sK226),
inference(resolution,[],[f1888,f1898]) ).
fof(f2153,plain,
list_succeeds(sK227),
inference(resolution,[],[f1887,f1898]) ).
fof(f2166,plain,
( nil = cons(sK223,cons(sK224,sK225))
| cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,nil),sK63(cons(sK223,cons(sK224,sK225)),sK226,nil))
| ~ spl228_4 ),
inference(resolution,[],[f2144,f1306]) ).
fof(f2172,plain,
( cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,nil),sK63(cons(sK223,cons(sK224,sK225)),sK226,nil))
| ~ spl228_4 ),
inference(forward_subsumption_resolution,[],[f2166,f1143]) ).
fof(f2174,definition,
( spl228_6
<=> cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,nil),sK63(cons(sK223,cons(sK224,sK225)),sK226,nil)) ),
introduced(definition,[new_symbols(definition,[spl228_6])],[avatar_definition]) ).
fof(f2175,plain,
( cons(sK223,cons(sK224,sK225)) = cons(sK62(cons(sK223,cons(sK224,sK225)),sK226,nil),sK63(cons(sK223,cons(sK224,sK225)),sK226,nil))
| ~ spl228_6 ),
inference(avatar_component_clause,[],[f2174]) ).
fof(f2180,plain,
( spl228_6
| ~ spl228_4 ),
inference(avatar_split_clause,[],[f2172,f2135,f2174]) ).
fof(f2183,plain,
! [X0] : lh(cons(X0,sK227)) = s(lh(sK227)),
inference(resolution,[],[f2153,f1771]) ).
fof(f2187,plain,
( ! [X0,X1] :
( cons(X0,X1) != cons(sK223,cons(sK224,sK225))
| sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227) = X0 )
| ~ spl228_3 ),
inference(superposition,[],[f1145,f2133]) ).
fof(f2192,plain,
( ! [X0,X1] :
( cons(X0,X1) != cons(sK223,cons(sK224,sK225))
| sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227) = X1 )
| ~ spl228_3 ),
inference(superposition,[],[f1144,f2133]) ).
fof(f2193,plain,
( ! [X0,X1] :
( cons(X0,X1) != sK226
| sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227) = X1 )
| ~ spl228_5 ),
inference(superposition,[],[f1144,f2141]) ).
fof(f2202,plain,
( nil != sK226
| ~ spl228_5 ),
inference(superposition,[],[f1143,f2141]) ).
fof(f2203,plain,
! [X0] :
( ~ list_succeeds(X0)
| lh('**'(X0,sK227)) = '@+'(lh(X0),lh(sK227)) ),
inference(resolution,[],[f1775,f2153]) ).
fof(f2207,plain,
( sK223 = sK62(cons(sK223,cons(sK224,sK225)),sK226,sK227)
| ~ spl228_3 ),
inference(equality_resolution,[],[f2187]) ).
fof(f2208,plain,
( sK226 = cons(sK223,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227))
| ~ spl228_3
| ~ spl228_5 ),
inference(superposition,[],[f2141,f2207]) ).
fof(f2215,plain,
( cons(sK224,sK225) = sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227)
| ~ spl228_3 ),
inference(equality_resolution,[],[f2192]) ).
fof(f2224,definition,
( spl228_8
<=> split_succeeds(cons(sK224,sK225),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
introduced(definition,[new_symbols(definition,[spl228_8])],[avatar_definition]) ).
fof(f2225,plain,
( split_succeeds(cons(sK224,sK225),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227))
| ~ spl228_8 ),
inference(avatar_component_clause,[],[f2224]) ).
fof(f2275,plain,
( ! [X0,X1] :
( cons(X0,X1) != cons(sK223,cons(sK224,sK225))
| sK63(cons(sK223,cons(sK224,sK225)),sK226,nil) = X1 )
| ~ spl228_6 ),
inference(superposition,[],[f1144,f2175]) ).
fof(f2335,plain,
( ! [X0,X1] :
( cons(X0,X1) != sK226
| sK223 = X0 )
| ~ spl228_3
| ~ spl228_5 ),
inference(superposition,[],[f1145,f2208]) ).
fof(f2376,plain,
( nil = sK226
| split_succeeds(sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
inference(resolution,[],[f1299,f1898]) ).
fof(f2381,plain,
( split_succeeds(sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227))
| ~ spl228_5 ),
inference(forward_subsumption_resolution,[],[f2376,f2202]) ).
fof(f2386,plain,
( nil = cons(sK223,cons(sK224,sK225))
| split_succeeds(sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227)) ),
inference(resolution,[],[f1300,f1898]) ).
fof(f2391,plain,
split_succeeds(sK63(cons(sK223,cons(sK224,sK225)),sK226,sK227),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227)),
inference(forward_subsumption_resolution,[],[f2386,f1143]) ).
fof(f2399,plain,
nat_succeeds(lh(sK227)),
inference(resolution,[],[f1772,f2153]) ).
fof(f2400,plain,
nat_succeeds(lh(sK226)),
inference(resolution,[],[f1772,f2152]) ).
fof(f2407,plain,
'@<_succeeds'(lh(sK226),s(lh(sK226))),
inference(resolution,[],[f2400,f1692]) ).
fof(f2453,definition,
( spl228_12
<=> '@<_succeeds'('0',lh(sK226)) ),
introduced(definition,[new_symbols(definition,[spl228_12])],[avatar_definition]) ).
fof(f2454,plain,
( '@<_succeeds'('0',lh(sK226))
| ~ spl228_12 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f2490,plain,
list_succeeds(cons(sK224,sK225)),
inference(resolution,[],[f1737,f2150]) ).
fof(f2508,plain,
list_succeeds(sK225),
inference(resolution,[],[f2490,f1737]) ).
fof(f2510,plain,
! [X0] : lh(cons(X0,cons(sK224,sK225))) = s(lh(cons(sK224,sK225))),
inference(resolution,[],[f2490,f1771]) ).
fof(f2521,plain,
! [X0,X1] : '**'(cons(X0,sK225),X1) = cons(X0,'**'(sK225,X1)),
inference(resolution,[],[f2508,f1756]) ).
fof(f2522,plain,
! [X0] : lh(cons(X0,sK225)) = s(lh(sK225)),
inference(resolution,[],[f2508,f1771]) ).
fof(f2523,plain,
nat_succeeds(lh(sK225)),
inference(resolution,[],[f2508,f1772]) ).
fof(f2541,plain,
'@+'(lh(sK226),lh(sK227)) = s(lh(cons(sK224,sK225))),
inference(superposition,[],[f2128,f2510]) ).
fof(f2542,plain,
( ~ '@<_succeeds'(lh(sK227),s(lh(cons(sK224,sK225))))
| spl228_1 ),
inference(superposition,[],[f2101,f2510]) ).
fof(f2543,plain,
( ~ '@<_succeeds'(lh(sK227),s(s(lh(sK225))))
| spl228_1 ),
inference(forward_demodulation,[],[f2542,f2522]) ).
fof(f2544,plain,
'@+'(lh(sK226),lh(sK227)) = s(s(lh(sK225))),
inference(forward_demodulation,[],[f2541,f2522]) ).
fof(f2548,plain,
( ~ '@<_succeeds'(lh(nil),s(s(lh(sK225))))
| spl228_1
| ~ spl228_4 ),
inference(forward_demodulation,[],[f2543,f2136]) ).
fof(f2553,plain,
( ~ '@<_succeeds'('0',s(s(lh(sK225))))
| spl228_1
| ~ spl228_4 ),
inference(forward_demodulation,[],[f2548,f1770]) ).
fof(f2558,plain,
( $false
| spl228_1
| ~ spl228_4 ),
inference(forward_subsumption_resolution,[],[f2553,f2080]) ).
fof(f2559,plain,
( spl228_1
| ~ spl228_4 ),
inference(avatar_contradiction_clause,[],[f2558]) ).
fof(f2579,plain,
( split_succeeds(cons(sK224,sK225),sK227,sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227))
| ~ spl228_3
| ~ spl228_5 ),
inference(forward_demodulation,[],[f2381,f2215]) ).
fof(f2630,plain,
( cons(sK224,sK225) = sK63(cons(sK223,cons(sK224,sK225)),sK226,nil)
| ~ spl228_6 ),
inference(equality_resolution,[],[f2275]) ).
fof(f2641,plain,
'@<_succeeds'(lh(sK227),s(lh(sK227))),
inference(resolution,[],[f2399,f1692]) ).
fof(f2724,plain,
( ~ '@<_succeeds'(lh(sK226),'@+'(lh(sK226),lh(sK227)))
| spl228_2 ),
inference(forward_demodulation,[],[f2104,f2128]) ).
fof(f2897,plain,
( lh(sK226) = s(sK202(lh(sK226)))
| ~ spl228_12 ),
inference(resolution,[],[f2454,f1686]) ).
fof(f2903,plain,
! [X0] :
( sK225 = cons(sK209(sK225),sK210(sK225))
| s(X0) != lh(sK225) ),
inference(resolution,[],[f1774,f2508]) ).
fof(f2915,definition,
( spl228_21
<=> ! [X0] : s(X0) != lh(sK225) ),
introduced(definition,[new_symbols(definition,[spl228_21])],[avatar_definition]) ).
fof(f2916,plain,
( ! [X0] : s(X0) != lh(sK225)
| ~ spl228_21 ),
inference(avatar_component_clause,[],[f2915]) ).
fof(f2918,definition,
( spl228_22
<=> sK225 = cons(sK209(sK225),sK210(sK225)) ),
introduced(definition,[new_symbols(definition,[spl228_22])],[avatar_definition]) ).
fof(f2919,plain,
( sK225 = cons(sK209(sK225),sK210(sK225))
| ~ spl228_22 ),
inference(avatar_component_clause,[],[f2918]) ).
fof(f2920,plain,
( spl228_21
| spl228_22 ),
inference(avatar_split_clause,[],[f2903,f2918,f2915]) ).
fof(f3040,plain,
sK227 = '**'(sK227,nil),
inference(resolution,[],[f1763,f2153]) ).
fof(f3113,plain,
! [X0] : '@<_succeeds'(lh(sK226),'@+'(lh(sK226),s(X0))),
inference(resolution,[],[f1715,f2400]) ).
fof(f3114,plain,
! [X0] : '@<_succeeds'(lh(sK227),'@+'(lh(sK227),s(X0))),
inference(resolution,[],[f1715,f2399]) ).
fof(f3457,plain,
! [X0] :
( ~ list_succeeds(X0)
| '@+'(lh(X0),lh(nil)) = lh('**'(X0,nil)) ),
inference(resolution,[],[f2041,f1775]) ).
fof(f3476,plain,
! [X0] :
( ~ list_succeeds(X0)
| '@+'(lh(X0),'0') = lh('**'(X0,nil)) ),
inference(forward_demodulation,[],[f3457,f1770]) ).
fof(f3508,plain,
'@+'(lh(sK227),'0') = lh('**'(sK227,nil)),
inference(resolution,[],[f3476,f2153]) ).
fof(f3672,plain,
( nil = sK226
| sK226 = cons(sK159(sK226),sK160(sK226)) ),
inference(resolution,[],[f1521,f2152]) ).
fof(f3674,plain,
( sK226 = cons(sK159(sK226),sK160(sK226))
| ~ spl228_5 ),
inference(forward_subsumption_resolution,[],[f3672,f2202]) ).
fof(f3679,definition,
( spl228_40
<=> nil = sK225 ),
introduced(definition,[new_symbols(definition,[spl228_40])],[avatar_definition]) ).
fof(f3680,plain,
( nil = sK225
| ~ spl228_40 ),
inference(avatar_component_clause,[],[f3679]) ).
fof(f3805,plain,
( sK226 != sK226
| sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227) = sK160(sK226)
| ~ spl228_5 ),
inference(superposition,[],[f2193,f3674]) ).
fof(f3808,plain,
( sK226 != sK226
| sK223 = sK159(sK226)
| ~ spl228_3
| ~ spl228_5 ),
inference(superposition,[],[f2335,f3674]) ).
fof(f3812,plain,
( sK223 = sK159(sK226)
| ~ spl228_3
| ~ spl228_5 ),
inference(trivial_inequality_removal,[],[f3808]) ).
fof(f3826,plain,
( sK226 = cons(sK223,sK160(sK226))
| ~ spl228_3
| ~ spl228_5 ),
inference(superposition,[],[f3674,f3812]) ).
fof(f3953,plain,
'@<_succeeds'(lh(sK225),s(lh(sK225))),
inference(resolution,[],[f2523,f1692]) ).
fof(f4098,plain,
( nil = sK225
| '0' != lh(sK225) ),
inference(resolution,[],[f1773,f2508]) ).
fof(f4099,plain,
( nil = sK226
| '0' != lh(sK226) ),
inference(resolution,[],[f1773,f2152]) ).
fof(f4100,plain,
( nil = sK227
| '0' != lh(sK227) ),
inference(resolution,[],[f1773,f2153]) ).
fof(f4101,plain,
( '0' != lh(sK226)
| ~ spl228_5 ),
inference(forward_subsumption_resolution,[],[f4099,f2202]) ).
fof(f4120,plain,
'@+'(lh(cons(sK224,sK225)),lh(sK227)) = lh('**'(cons(sK224,sK225),sK227)),
inference(resolution,[],[f2203,f2490]) ).
fof(f4124,plain,
'@+'(lh(sK226),lh(sK227)) = lh('**'(sK226,sK227)),
inference(resolution,[],[f2203,f2152]) ).
fof(f4131,plain,
'@+'(lh(cons(sK224,sK225)),lh(sK227)) = lh(cons(sK224,'**'(sK225,sK227))),
inference(forward_demodulation,[],[f4120,f2521]) ).
fof(f4501,plain,
! [X0,X1] :
( ~ list_succeeds(cons(X0,X1))
| lh(cons(X0,X1)) = s(lh(X1)) ),
inference(resolution,[],[f2009,f1812]) ).
fof(f4554,plain,
( ~ list_succeeds(sK226)
| lh(sK226) = s(lh(sK160(sK226)))
| ~ spl228_3
| ~ spl228_5 ),
inference(superposition,[],[f4501,f3826]) ).
fof(f4557,plain,
( lh(sK226) = s(lh(sK160(sK226)))
| ~ spl228_3
| ~ spl228_5 ),
inference(forward_subsumption_resolution,[],[f4554,f2152]) ).
fof(f4586,plain,
( ! [X0] :
( s(X0) != lh(sK226)
| lh(sK160(sK226)) = X0 )
| ~ spl228_3
| ~ spl228_5 ),
inference(superposition,[],[f1140,f4557]) ).
fof(f4885,plain,
( '0' = lh(sK226)
| lh(sK226) = s(sK189(lh(sK226),s(lh(sK226)))) ),
inference(resolution,[],[f1606,f2407]) ).
fof(f4897,plain,
( lh(sK226) = s(sK189(lh(sK226),s(lh(sK226))))
| ~ spl228_5 ),
inference(forward_subsumption_resolution,[],[f4885,f4101]) ).
fof(f4900,plain,
( ! [X0] :
( s(X0) != lh(sK226)
| sK189(lh(sK226),s(lh(sK226))) = X0 )
| ~ spl228_5 ),
inference(superposition,[],[f1140,f4897]) ).
fof(f4905,plain,
( '@<_succeeds'('0',lh(sK226))
| ~ spl228_5 ),
inference(superposition,[],[f2080,f4897]) ).
fof(f4964,definition,
( spl228_47
<=> '0' = lh(sK225) ),
introduced(definition,[new_symbols(definition,[spl228_47])],[avatar_definition]) ).
fof(f4966,plain,
( ~ spl228_47
| spl228_40 ),
inference(avatar_split_clause,[],[f4098,f3679,f4964]) ).
fof(f5176,plain,
( ~ list_succeeds(sK225)
| lh(sK225) = s(lh(sK210(sK225)))
| ~ spl228_22 ),
inference(superposition,[],[f4501,f2919]) ).
fof(f5177,plain,
( lh(sK225) = s(lh(sK210(sK225)))
| ~ spl228_22 ),
inference(forward_subsumption_resolution,[],[f5176,f2508]) ).
fof(f5216,plain,
( '@<_succeeds'(lh(sK226),'@+'(lh(sK226),lh(sK225)))
| ~ spl228_22 ),
inference(superposition,[],[f3113,f5177]) ).
fof(f5328,plain,
( '0' = lh(sK225)
| lh(sK225) = s(sK189(lh(sK225),s(lh(sK225)))) ),
inference(resolution,[],[f3953,f1606]) ).
fof(f5524,plain,
( lh(sK226) != lh(sK226)
| sK202(lh(sK226)) = sK189(lh(sK226),s(lh(sK226)))
| ~ spl228_5
| ~ spl228_12 ),
inference(superposition,[],[f4900,f2897]) ).
fof(f5613,plain,
( '0' = lh(sK226)
| lh(sK226) = s(sK189(lh(sK226),'@+'(lh(sK226),lh(sK225))))
| ~ spl228_22 ),
inference(resolution,[],[f5216,f1606]) ).
fof(f5619,plain,
( lh(sK226) = s(sK189(lh(sK226),'@+'(lh(sK226),lh(sK225))))
| ~ spl228_5
| ~ spl228_22 ),
inference(forward_subsumption_resolution,[],[f5613,f4101]) ).
fof(f5621,plain,
( ! [X0] :
( s(X0) != lh(sK226)
| sK189(lh(sK226),'@+'(lh(sK226),lh(sK225))) = X0 )
| ~ spl228_5
| ~ spl228_22 ),
inference(superposition,[],[f1140,f5619]) ).
fof(f5895,definition,
( spl228_88
<=> '0' = sK202(lh(sK226)) ),
introduced(definition,[new_symbols(definition,[spl228_88])],[avatar_definition]) ).
fof(f5896,plain,
( '0' = sK202(lh(sK226))
| ~ spl228_88 ),
inference(avatar_component_clause,[],[f5895]) ).
fof(f6074,plain,
( lh(sK226) != lh(sK226)
| lh(sK160(sK226)) = sK189(lh(sK226),'@+'(lh(sK226),lh(sK225)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_22 ),
inference(superposition,[],[f5621,f4557]) ).
fof(f6082,plain,
( lh(sK226) != lh(sK226)
| sK202(lh(sK226)) = sK189(lh(sK226),'@+'(lh(sK226),lh(sK225)))
| ~ spl228_5
| ~ spl228_12
| ~ spl228_22 ),
inference(superposition,[],[f5621,f2897]) ).
fof(f6088,plain,
( lh(sK160(sK226)) = sK189(lh(sK226),'@+'(lh(sK226),lh(sK225)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_22 ),
inference(trivial_inequality_removal,[],[f6074]) ).
fof(f6310,definition,
( spl228_109
<=> '@<_succeeds'(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226)))) ),
introduced(definition,[new_symbols(definition,[spl228_109])],[avatar_definition]) ).
fof(f6311,plain,
( '@<_succeeds'(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226))))
| ~ spl228_109 ),
inference(avatar_component_clause,[],[f6310]) ).
fof(f6551,plain,
( sK64(cons(sK223,cons(sK224,sK225)),sK226,sK227) = sK160(sK226)
| ~ spl228_5 ),
inference(trivial_inequality_removal,[],[f3805]) ).
fof(f6565,plain,
( spl228_12
| ~ spl228_5 ),
inference(avatar_split_clause,[],[f4905,f2140,f2453]) ).
fof(f6568,plain,
( spl228_8
| ~ spl228_3
| ~ spl228_5 ),
inference(avatar_split_clause,[],[f2579,f2140,f2132,f2224]) ).
fof(f6604,plain,
( split_succeeds(cons(sK224,sK225),sK227,sK160(sK226))
| ~ spl228_5
| ~ spl228_8 ),
inference(forward_demodulation,[],[f2225,f6551]) ).
fof(f6664,plain,
lh(sK227) = '@+'(lh(sK227),'0'),
inference(forward_demodulation,[],[f3508,f3040]) ).
fof(f6672,definition,
( spl228_122
<=> '0' = lh(sK227) ),
introduced(definition,[new_symbols(definition,[spl228_122])],[avatar_definition]) ).
fof(f6673,plain,
( '0' != lh(sK227)
| spl228_122 ),
inference(avatar_component_clause,[],[f6672]) ).
fof(f6674,plain,
( ~ spl228_122
| spl228_4 ),
inference(avatar_split_clause,[],[f4100,f2135,f6672]) ).
fof(f6678,plain,
lh(cons(sK224,'**'(sK225,sK227))) = '@+'(s(lh(sK225)),lh(sK227)),
inference(forward_demodulation,[],[f4131,f2522]) ).
fof(f6851,definition,
( spl228_131
<=> '@<_succeeds'(lh(sK227),s('0')) ),
introduced(definition,[new_symbols(definition,[spl228_131])],[avatar_definition]) ).
fof(f6852,plain,
( '@<_succeeds'(lh(sK227),s('0'))
| ~ spl228_131 ),
inference(avatar_component_clause,[],[f6851]) ).
fof(f6878,plain,
( sK202(lh(sK226)) = sK189(lh(sK226),'@+'(lh(sK226),lh(sK225)))
| ~ spl228_5
| ~ spl228_12
| ~ spl228_22 ),
inference(trivial_inequality_removal,[],[f6082]) ).
fof(f6879,plain,
( sK202(lh(sK226)) = sK189(lh(sK226),s(lh(sK226)))
| ~ spl228_5
| ~ spl228_12 ),
inference(trivial_inequality_removal,[],[f5524]) ).
fof(f6943,plain,
( sK202(lh(sK226)) = lh(sK160(sK226))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_12
| ~ spl228_22 ),
inference(forward_demodulation,[],[f6088,f6878]) ).
fof(f7140,plain,
( ~ '@<_succeeds'(lh(sK226),s(s(lh(sK225))))
| spl228_2 ),
inference(superposition,[],[f2724,f2544]) ).
fof(f7176,plain,
! [X0] :
( '0' = lh(sK227)
| lh(sK227) = s(sK189(lh(sK227),'@+'(lh(sK227),s(X0)))) ),
inference(resolution,[],[f3114,f1606]) ).
fof(f7185,plain,
( ! [X0] : lh(sK227) = s(sK189(lh(sK227),'@+'(lh(sK227),s(X0))))
| spl228_122 ),
inference(forward_subsumption_resolution,[],[f7176,f6673]) ).
fof(f7329,plain,
s(s(lh(sK225))) = lh('**'(sK226,sK227)),
inference(superposition,[],[f2544,f4124]) ).
fof(f8983,plain,
( lh(sK226) = s(sK202(lh(sK226)))
| ~ spl228_12 ),
inference(resolution,[],[f2454,f1686]) ).
fof(f9253,plain,
( lh(cons(sK224,sK225)) = '@+'(lh(sK227),lh(sK160(sK226)))
| ~ spl228_5
| ~ spl228_8 ),
inference(resolution,[],[f6604,f1890]) ).
fof(f9271,plain,
( lh(cons(sK224,sK225)) = '@+'(lh(sK227),sK202(lh(sK226)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22 ),
inference(forward_demodulation,[],[f9253,f6943]) ).
fof(f10499,plain,
( '@<_succeeds'(lh(sK226),'@+'(lh(sK226),lh(sK227)))
| spl228_122 ),
inference(superposition,[],[f3113,f7185]) ).
fof(f10555,plain,
( '@<_succeeds'(lh(sK226),lh('**'(sK226,sK227)))
| spl228_122 ),
inference(forward_demodulation,[],[f10499,f4124]) ).
fof(f10584,plain,
( '@<_succeeds'(lh(sK226),s(s(lh(sK225))))
| spl228_122 ),
inference(forward_demodulation,[],[f10555,f7329]) ).
fof(f12145,definition,
( spl228_305
<=> lh(sK227) = s(lh(sK225)) ),
introduced(definition,[new_symbols(definition,[spl228_305])],[avatar_definition]) ).
fof(f12146,plain,
( lh(sK227) = s(lh(sK225))
| ~ spl228_305 ),
inference(avatar_component_clause,[],[f12145]) ).
fof(f12819,plain,
( s(lh(sK225)) = '@+'(lh(sK227),sK202(lh(sK226)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22 ),
inference(forward_demodulation,[],[f9271,f2522]) ).
fof(f13118,plain,
( $false
| spl228_2
| spl228_122 ),
inference(forward_subsumption_resolution,[],[f10584,f7140]) ).
fof(f13119,plain,
( spl228_2
| spl228_122 ),
inference(avatar_contradiction_clause,[],[f13118]) ).
fof(f14144,plain,
( s(lh(sK225)) = '@+'(lh(sK227),lh(sK160(sK226)))
| ~ spl228_5
| ~ spl228_8 ),
inference(forward_demodulation,[],[f9253,f2522]) ).
fof(f14226,definition,
( spl228_469
<=> '@<_succeeds'(lh(sK227),s(lh(sK225))) ),
introduced(definition,[new_symbols(definition,[spl228_469])],[avatar_definition]) ).
fof(f14227,plain,
( '@<_succeeds'(lh(sK227),s(lh(sK225)))
| ~ spl228_469 ),
inference(avatar_component_clause,[],[f14226]) ).
fof(f15576,plain,
( ~ '@<_succeeds'(lh(sK227),s(s(lh(nil))))
| spl228_1
| ~ spl228_40 ),
inference(superposition,[],[f2543,f3680]) ).
fof(f15702,plain,
( ~ '@<_succeeds'(lh(sK227),s(s('0')))
| spl228_1
| ~ spl228_40 ),
inference(forward_demodulation,[],[f15576,f1770]) ).
fof(f16795,definition,
( spl228_523
<=> s('0') = lh(sK226) ),
introduced(definition,[new_symbols(definition,[spl228_523])],[avatar_definition]) ).
fof(f16796,plain,
( s('0') = lh(sK226)
| ~ spl228_523 ),
inference(avatar_component_clause,[],[f16795]) ).
fof(f18893,plain,
( '0' = lh(sK225)
| ~ spl228_21 ),
inference(forward_subsumption_resolution,[],[f5328,f2916]) ).
fof(f19880,plain,
( '@<_succeeds'(lh(sK227),s(s(lh(sK225))))
| ~ spl228_469 ),
inference(resolution,[],[f14227,f1688]) ).
fof(f19882,plain,
( $false
| spl228_1
| ~ spl228_469 ),
inference(forward_subsumption_resolution,[],[f19880,f2543]) ).
fof(f19883,plain,
( spl228_1
| ~ spl228_469 ),
inference(avatar_contradiction_clause,[],[f19882]) ).
fof(f23503,plain,
( '0' = sK202(lh(sK226))
| sK202(lh(sK226)) = s(sK189(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226)))))
| ~ spl228_109 ),
inference(resolution,[],[f6311,f1606]) ).
fof(f23511,definition,
( spl228_661
<=> sK202(lh(sK226)) = s(sK189(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226))))) ),
introduced(definition,[new_symbols(definition,[spl228_661])],[avatar_definition]) ).
fof(f23512,plain,
( sK202(lh(sK226)) = s(sK189(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226)))))
| ~ spl228_661 ),
inference(avatar_component_clause,[],[f23511]) ).
fof(f23513,plain,
( spl228_661
| spl228_88
| ~ spl228_109 ),
inference(avatar_split_clause,[],[f23503,f6310,f5895,f23511]) ).
fof(f25260,plain,
( s(lh(sK225)) = '@+'(lh(sK227),'0')
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| ~ spl228_88 ),
inference(superposition,[],[f12819,f5896]) ).
fof(f25262,plain,
( lh(sK227) = s(lh(sK225))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| ~ spl228_88 ),
inference(forward_demodulation,[],[f25260,f6664]) ).
fof(f25263,plain,
( spl228_305
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| ~ spl228_88 ),
inference(avatar_split_clause,[],[f25262,f5895,f2918,f2453,f2224,f2140,f2132,f12145]) ).
fof(f25265,plain,
( ~ '@<_succeeds'(lh(sK227),s(lh(sK227)))
| spl228_1
| ~ spl228_305 ),
inference(superposition,[],[f2543,f12146]) ).
fof(f25376,plain,
( $false
| spl228_1
| ~ spl228_305 ),
inference(forward_subsumption_resolution,[],[f25265,f2641]) ).
fof(f25377,plain,
( spl228_1
| ~ spl228_305 ),
inference(avatar_contradiction_clause,[],[f25376]) ).
fof(f25427,plain,
( spl228_47
| ~ spl228_21 ),
inference(avatar_split_clause,[],[f18893,f2915,f4964]) ).
fof(f26190,plain,
( lh(cons(sK224,'**'(nil,sK227))) = '@+'(s(lh(nil)),lh(sK227))
| ~ spl228_40 ),
inference(superposition,[],[f6678,f3680]) ).
fof(f26293,plain,
( '@+'(s('0'),lh(sK227)) = lh(cons(sK224,'**'(nil,sK227)))
| ~ spl228_40 ),
inference(forward_demodulation,[],[f26190,f1770]) ).
fof(f26357,plain,
( '@+'(s('0'),lh(sK227)) = lh(cons(sK224,sK227))
| ~ spl228_40 ),
inference(forward_demodulation,[],[f26293,f1755]) ).
fof(f26387,plain,
( s(lh(sK227)) = '@+'(s('0'),lh(sK227))
| ~ spl228_40 ),
inference(forward_demodulation,[],[f26357,f2183]) ).
fof(f26633,plain,
( ~ '@<_succeeds'(lh(sK227),s('0'))
| spl228_131 ),
inference(avatar_component_clause,[],[f6851]) ).
fof(f27896,plain,
( lh(sK226) != lh(sK226)
| sK202(lh(sK226)) = lh(sK160(sK226))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_12 ),
inference(superposition,[],[f4586,f8983]) ).
fof(f27939,plain,
( sK202(lh(sK226)) = lh(sK160(sK226))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_12 ),
inference(trivial_inequality_removal,[],[f27896]) ).
fof(f27967,plain,
( s(lh(sK225)) = '@+'(lh(sK227),sK202(lh(sK226)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12 ),
inference(superposition,[],[f14144,f27939]) ).
fof(f27974,plain,
( s('0') = lh(sK226)
| ~ spl228_12
| ~ spl228_88 ),
inference(superposition,[],[f8983,f5896]) ).
fof(f27994,plain,
( spl228_523
| ~ spl228_12
| ~ spl228_88 ),
inference(avatar_split_clause,[],[f27974,f5895,f2453,f16795]) ).
fof(f29785,plain,
( s(s(lh(sK225))) = '@+'(s('0'),lh(sK227))
| ~ spl228_523 ),
inference(superposition,[],[f2544,f16796]) ).
fof(f29945,plain,
( s(lh(sK227)) = s(s(lh(sK225)))
| ~ spl228_40
| ~ spl228_523 ),
inference(forward_demodulation,[],[f29785,f26387]) ).
fof(f29981,plain,
( s(lh(sK227)) = s(s(lh(nil)))
| ~ spl228_40
| ~ spl228_523 ),
inference(forward_demodulation,[],[f29945,f3680]) ).
fof(f29990,plain,
( s(lh(sK227)) = s(s('0'))
| ~ spl228_40
| ~ spl228_523 ),
inference(forward_demodulation,[],[f29981,f1770]) ).
fof(f30364,plain,
( '@<_succeeds'(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226))))
| '0' = lh(sK226)
| ~ '@<_succeeds'(lh(sK226),s(lh(sK226)))
| ~ spl228_5
| ~ spl228_12 ),
inference(superposition,[],[f1602,f6879]) ).
fof(f39311,plain,
( '@<_succeeds'(lh(sK227),s(s('0')))
| ~ spl228_40
| ~ spl228_523 ),
inference(superposition,[],[f2641,f29990]) ).
fof(f39546,plain,
( $false
| spl228_1
| ~ spl228_40
| ~ spl228_523 ),
inference(forward_subsumption_resolution,[],[f39311,f15702]) ).
fof(f39547,plain,
( spl228_1
| ~ spl228_40
| ~ spl228_523 ),
inference(avatar_contradiction_clause,[],[f39546]) ).
fof(f39728,plain,
( s(lh(nil)) = '@+'(lh(sK227),sK202(lh(sK226)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_40 ),
inference(forward_demodulation,[],[f27967,f3680]) ).
fof(f40478,plain,
( s('0') = '@+'(lh(sK227),sK202(lh(sK226)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_40 ),
inference(forward_demodulation,[],[f39728,f1770]) ).
fof(f47077,plain,
( '@<_succeeds'(lh(sK227),'@+'(lh(sK227),sK202(lh(sK226))))
| ~ spl228_661 ),
inference(superposition,[],[f3114,f23512]) ).
fof(f47162,plain,
( '@<_succeeds'(lh(sK227),s('0'))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_40
| ~ spl228_661 ),
inference(forward_demodulation,[],[f47077,f40478]) ).
fof(f47186,plain,
( $false
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_40
| spl228_131
| ~ spl228_661 ),
inference(forward_subsumption_resolution,[],[f47162,f26633]) ).
fof(f47187,plain,
( ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_40
| spl228_131
| ~ spl228_661 ),
inference(avatar_contradiction_clause,[],[f47186]) ).
fof(f47207,plain,
( '@<_succeeds'(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226))))
| ~ '@<_succeeds'(lh(sK226),s(lh(sK226)))
| ~ spl228_5
| ~ spl228_12 ),
inference(forward_subsumption_resolution,[],[f30364,f4101]) ).
fof(f47210,plain,
( '@<_succeeds'(sK202(lh(sK226)),sK190(lh(sK226),s(lh(sK226))))
| ~ spl228_5
| ~ spl228_12 ),
inference(forward_subsumption_resolution,[],[f47207,f2407]) ).
fof(f47213,plain,
( spl228_109
| ~ spl228_5
| ~ spl228_12 ),
inference(avatar_split_clause,[],[f47210,f2453,f2140,f6310]) ).
fof(f47570,plain,
( '@<_succeeds'(lh(sK227),s(s('0')))
| ~ spl228_131 ),
inference(resolution,[],[f6852,f1688]) ).
fof(f47576,plain,
( $false
| spl228_1
| ~ spl228_40
| ~ spl228_131 ),
inference(forward_subsumption_resolution,[],[f47570,f15702]) ).
fof(f47577,plain,
( spl228_1
| ~ spl228_40
| ~ spl228_131 ),
inference(avatar_contradiction_clause,[],[f47576]) ).
fof(f49050,plain,
( '@<_succeeds'(lh(sK227),s(lh(sK225)))
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| ~ spl228_661 ),
inference(forward_demodulation,[],[f47077,f12819]) ).
fof(f49810,plain,
( spl228_469
| ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| ~ spl228_661 ),
inference(avatar_split_clause,[],[f49050,f23511,f2918,f2453,f2224,f2140,f2132,f14226]) ).
fof(f53627,plain,
( split_succeeds(sK63(cons(sK223,cons(sK224,sK225)),sK226,nil),nil,sK64(cons(sK223,cons(sK224,sK225)),sK226,nil))
| ~ spl228_4 ),
inference(forward_demodulation,[],[f2391,f2136]) ).
fof(f53706,plain,
( split_succeeds(cons(sK224,sK225),nil,sK64(cons(sK223,cons(sK224,sK225)),sK226,nil))
| ~ spl228_4
| ~ spl228_6 ),
inference(forward_demodulation,[],[f53627,f2630]) ).
fof(f55006,plain,
( nil = cons(sK224,sK225)
| nil = cons(sK62(cons(sK224,sK225),nil,sK64(cons(sK223,cons(sK224,sK225)),sK226,nil)),sK64(cons(sK224,sK225),nil,sK64(cons(sK223,cons(sK224,sK225)),sK226,nil)))
| ~ spl228_4
| ~ spl228_6 ),
inference(resolution,[],[f53706,f1303]) ).
fof(f55034,plain,
( nil = cons(sK224,sK225)
| ~ spl228_4
| ~ spl228_6 ),
inference(forward_subsumption_resolution,[],[f55006,f1143]) ).
fof(f55041,plain,
( $false
| ~ spl228_4
| ~ spl228_6 ),
inference(forward_subsumption_resolution,[],[f55034,f1143]) ).
fof(f55042,plain,
( ~ spl228_4
| ~ spl228_6 ),
inference(avatar_contradiction_clause,[],[f55041]) ).
cnf(s1,plain,
( ~ spl228_1
| ~ spl228_2 ),
inference(sat_conversion,[],[f2105]) ).
cnf(s2,plain,
( spl228_3
| spl228_4 ),
inference(sat_conversion,[],[f2137]) ).
cnf(s3,plain,
( spl228_4
| spl228_5 ),
inference(sat_conversion,[],[f2142]) ).
cnf(s5,plain,
( ~ spl228_4
| spl228_6 ),
inference(sat_conversion,[],[f2180]) ).
cnf(s9,plain,
( spl228_1
| ~ spl228_4 ),
inference(sat_conversion,[],[f2559]) ).
cnf(s25,plain,
( spl228_21
| spl228_22 ),
inference(sat_conversion,[],[f2920]) ).
cnf(s43,plain,
( spl228_40
| ~ spl228_47 ),
inference(sat_conversion,[],[f4966]) ).
cnf(s107,plain,
( ~ spl228_5
| spl228_12 ),
inference(sat_conversion,[],[f6565]) ).
cnf(s108,plain,
( ~ spl228_3
| ~ spl228_5
| spl228_8 ),
inference(sat_conversion,[],[f6568]) ).
cnf(s120,plain,
( spl228_4
| ~ spl228_122 ),
inference(sat_conversion,[],[f6674]) ).
cnf(s590,plain,
( spl228_2
| spl228_122 ),
inference(sat_conversion,[],[f13119]) ).
cnf(s1367,plain,
( spl228_1
| ~ spl228_469 ),
inference(sat_conversion,[],[f19883]) ).
cnf(s1542,plain,
( spl228_88
| ~ spl228_109
| spl228_661 ),
inference(sat_conversion,[],[f23513]) ).
cnf(s1613,plain,
( ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| ~ spl228_88
| spl228_305 ),
inference(sat_conversion,[],[f25263]) ).
cnf(s1616,plain,
( spl228_1
| ~ spl228_305 ),
inference(sat_conversion,[],[f25377]) ).
cnf(s1623,plain,
( ~ spl228_21
| spl228_47 ),
inference(sat_conversion,[],[f25427]) ).
cnf(s1701,plain,
( ~ spl228_12
| ~ spl228_88
| spl228_523 ),
inference(sat_conversion,[],[f27994]) ).
cnf(s2057,plain,
( spl228_1
| ~ spl228_40
| ~ spl228_523 ),
inference(sat_conversion,[],[f39547]) ).
cnf(s2651,plain,
( ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_40
| spl228_131
| ~ spl228_661 ),
inference(sat_conversion,[],[f47187]) ).
cnf(s2654,plain,
( ~ spl228_5
| ~ spl228_12
| spl228_109 ),
inference(sat_conversion,[],[f47213]) ).
cnf(s2657,plain,
( spl228_1
| ~ spl228_40
| ~ spl228_131 ),
inference(sat_conversion,[],[f47577]) ).
cnf(s2985,plain,
( ~ spl228_3
| ~ spl228_5
| ~ spl228_8
| ~ spl228_12
| ~ spl228_22
| spl228_469
| ~ spl228_661 ),
inference(sat_conversion,[],[f49810]) ).
cnf(s3306,plain,
( ~ spl228_4
| ~ spl228_6 ),
inference(sat_conversion,[],[f55042]) ).
cnf(s3312,plain,
( ~ spl228_22
| spl228_1 ),
inference(rat,[],[s1542,s1613,s2985,s1616,s1367,s108,s2,s2654,s107,s3,s9]) ).
cnf(s3313,plain,
spl228_1,
inference(rat,[],[s1542,s1701,s2651,s2057,s2657,s43,s1623,s25,s3312,s2654,s108,s107,s2,s3,s9]) ).
cnf(s3314,plain,
~ spl228_2,
inference(rat,[],[s1,s3313]) ).
cnf(s3315,plain,
spl228_122,
inference(rat,[],[s590,s3314]) ).
cnf(s3321,plain,
spl228_4,
inference(rat,[],[s120,s3315]) ).
cnf(s3323,plain,
~ spl228_6,
inference(rat,[],[s3306,s3321]) ).
cnf(s3334,plain,
$false,
inference(rat,[],[s5,s3323,s3321]) ).
fof(f55045,plain,
$false,
inference(avatar_sat_refutation,[],[s3334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX029+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n016.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Mon Sep 28 14:56:49 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running first-order theorem proving
% 0.24/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.10/3.90 % (3683897)Detected formulas, will run a generic FOF schedule.
% 21.10/3.90 % (3683916)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2723400051:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 21.10/3.90 % (3683918)dis-21_1_sil=8000:lcm=predicate:random_seed=1992051725:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 21.10/3.90 % (3683917)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3904467208:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 21.10/3.90 % (3683914)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=117650397:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 21.10/3.90 % (3683915)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2327602060:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 21.10/3.90 % (3683912)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2404314077:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 21.10/3.90 % (3683916)Instruction limit reached!
% 21.10/3.90 % (3683916)------------------------------
% 21.10/3.90 % (3683916)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.10/3.90 % (3683916)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.10/3.90 % (3683916)CaDiCaL version: 2.1.3
% 21.10/3.90 % (3683916)Termination reason: Instruction limit
% 21.10/3.90 % (3683916)Termination phase: Saturation
% 21.10/3.90 % (3683916)Time elapsed: 0.081 s
% 21.10/3.90 % (3683916)Peak memory usage: 89 MB
% 21.10/3.90 % (3683916)Instructions burned: 119 (million)
% 21.10/3.90 % (3683913)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=939727996:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 21.10/3.90 % (3683915)Instruction limit reached!
% 21.10/3.90 % (3683915)------------------------------
% 21.10/3.90 % (3683915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.10/3.90 % (3683915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.10/3.90 % (3683915)CaDiCaL version: 2.1.3
% 21.10/3.90 % (3683915)Termination reason: Instruction limit
% 21.10/3.90 % (3683915)Termination phase: Saturation
% 21.10/3.90 % (3683915)Time elapsed: 0.119 s
% 21.10/3.90 % (3683915)Peak memory usage: 89 MB
% 21.10/3.90 % (3683915)Instructions burned: 109 (million)
% 21.10/3.90 % (3683918)Instruction limit reached!
% 21.10/3.90 % (3683918)------------------------------
% 21.10/3.90 % (3683918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.10/3.90 % (3683918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.10/3.90 % (3683918)CaDiCaL version: 2.1.3
% 21.10/3.90 % (3683918)Termination reason: Instruction limit
% 21.10/3.90 % (3683918)Termination phase: Saturation
% 21.10/3.90 % (3683918)Time elapsed: 0.124 s
% 21.10/3.90 % (3683918)Peak memory usage: 90 MB
% 21.10/3.90 % (3683918)Instructions burned: 129 (million)
% 21.10/3.90 % (3683917)Instruction limit reached!
% 21.10/3.90 % (3683917)------------------------------
% 21.10/3.90 % (3683917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.10/3.90 % (3683917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.10/3.90 % (3683917)CaDiCaL version: 2.1.3
% 21.10/3.90 % (3683917)Termination reason: Instruction limit
% 21.10/3.90 % (3683917)Termination phase: Saturation
% 21.10/3.90 % (3683917)Time elapsed: 0.155 s
% 21.10/3.90 % (3683917)Peak memory usage: 91 MB
% 21.10/3.90 % (3683917)Instructions burned: 139 (million)
% 21.10/3.90 % (3683927)lrs+10_1_sil=8000:sp=occurrence:random_seed=1129640766:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 21.10/3.90 % (3683929)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3216095145:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 21.10/3.90 % (3683930)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2557929854:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 21.10/3.90 % (3683931)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3566626895:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 21.10/3.90 % (3683929)Instruction limit reached!
% 11.55/4.15 % (3683929)------------------------------
% 11.55/4.15 % (3683929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683929)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683929)Termination reason: Instruction limit
% 11.55/4.15 % (3683929)Termination phase: Saturation
% 11.55/4.15 % (3683929)Time elapsed: 0.124 s
% 11.55/4.15 % (3683929)Peak memory usage: 91 MB
% 11.55/4.15 % (3683929)Instructions burned: 157 (million)
% 11.55/4.15 % (3683927)Instruction limit reached!
% 11.55/4.15 % (3683927)------------------------------
% 11.55/4.15 % (3683927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683927)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683927)Termination reason: Instruction limit
% 11.55/4.15 % (3683927)Termination phase: Saturation
% 11.55/4.15 % (3683927)Time elapsed: 0.324 s
% 11.55/4.15 % (3683927)Peak memory usage: 92 MB
% 11.55/4.15 % (3683927)Instructions burned: 285 (million)
% 11.55/4.15 % (3683938)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=129502609:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 11.55/4.15 % (3683931)Instruction limit reached!
% 11.55/4.15 % (3683931)------------------------------
% 11.55/4.15 % (3683931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683931)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683931)Termination reason: Instruction limit
% 11.55/4.15 % (3683931)Termination phase: Saturation
% 11.55/4.15 % (3683931)Time elapsed: 0.236 s
% 11.55/4.15 % (3683931)Peak memory usage: 94 MB
% 11.55/4.15 % (3683931)Instructions burned: 249 (million)
% 11.55/4.15 % (3683930)Instruction limit reached!
% 11.55/4.15 % (3683930)------------------------------
% 11.55/4.15 % (3683930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683930)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683930)Termination reason: Instruction limit
% 11.55/4.15 % (3683930)Termination phase: Saturation
% 11.55/4.15 % (3683930)Time elapsed: 0.353 s
% 11.55/4.15 % (3683930)Peak memory usage: 92 MB
% 11.55/4.15 % (3683930)Instructions burned: 326 (million)
% 11.55/4.15 % (3683939)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2008243743:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 11.55/4.15 % (3683938)Instruction limit reached!
% 11.55/4.15 % (3683938)------------------------------
% 11.55/4.15 % (3683938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683938)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683938)Termination reason: Instruction limit
% 11.55/4.15 % (3683938)Termination phase: Saturation
% 11.55/4.15 % (3683938)Time elapsed: 0.197 s
% 11.55/4.15 % (3683938)Peak memory usage: 90 MB
% 11.55/4.15 % (3683938)Instructions burned: 295 (million)
% 11.55/4.15 % (3683941)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=250565528:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 11.55/4.15 % (3683944)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1897129158:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 11.55/4.15 % (3683942)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3852839166:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 11.55/4.15 % (3683941)Instruction limit reached!
% 11.55/4.15 % (3683941)------------------------------
% 11.55/4.15 % (3683941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683941)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683941)Termination reason: Instruction limit
% 11.55/4.15 % (3683941)Termination phase: Saturation
% 11.55/4.15 % (3683941)Time elapsed: 0.120 s
% 11.55/4.15 % (3683941)Peak memory usage: 91 MB
% 11.55/4.15 % (3683941)Instructions burned: 113 (million)
% 11.55/4.15 % (3683944)Instruction limit reached!
% 11.55/4.15 % (3683944)------------------------------
% 11.55/4.15 % (3683944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683944)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683944)Termination reason: Instruction limit
% 11.55/4.15 % (3683944)Termination phase: Saturation
% 11.55/4.15 % (3683944)Time elapsed: 0.116 s
% 11.55/4.15 % (3683944)Peak memory usage: 89 MB
% 11.55/4.15 % (3683944)Instructions burned: 114 (million)
% 11.55/4.15 % (3683942)Instruction limit reached!
% 11.55/4.15 % (3683942)------------------------------
% 11.55/4.15 % (3683942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683942)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683942)Termination reason: Instruction limit
% 11.55/4.15 % (3683942)Termination phase: Saturation
% 11.55/4.15 % (3683942)Time elapsed: 0.118 s
% 11.55/4.15 % (3683942)Peak memory usage: 90 MB
% 11.55/4.15 % (3683942)Instructions burned: 127 (million)
% 11.55/4.15 % (3683948)lrs+10_1_sil=8000:sp=occurrence:random_seed=2237360197:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 11.55/4.15 % (3683949)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3427642716:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 11.55/4.15 % (3683950)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=550279082:i=5202:ss=axioms:sgt=16_2987 on theBenchmark for (2987ds/5202Mi)
% 11.55/4.15 % (3683949)Instruction limit reached!
% 11.55/4.15 % (3683949)------------------------------
% 11.55/4.15 % (3683949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683949)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683949)Termination reason: Instruction limit
% 11.55/4.15 % (3683949)Termination phase: Saturation
% 11.55/4.15 % (3683949)Time elapsed: 0.444 s
% 11.55/4.15 % (3683949)Peak memory usage: 93 MB
% 11.55/4.15 % (3683949)Instructions burned: 438 (million)
% 11.55/4.15 % (3683958)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2381846148:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2981 on theBenchmark for (2981ds/134Mi)
% 11.55/4.15 % (3683958)Instruction limit reached!
% 11.55/4.15 % (3683958)------------------------------
% 11.55/4.15 % (3683958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683958)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683958)Termination reason: Instruction limit
% 11.55/4.15 % (3683958)Termination phase: Saturation
% 11.55/4.15 % (3683958)Time elapsed: 0.107 s
% 11.55/4.15 % (3683958)Peak memory usage: 91 MB
% 11.55/4.15 % (3683958)Instructions burned: 134 (million)
% 11.55/4.15 % (3683948)Instruction limit reached!
% 11.55/4.15 % (3683948)------------------------------
% 11.55/4.15 % (3683948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683948)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683948)Termination reason: Instruction limit
% 11.55/4.15 % (3683948)Termination phase: Saturation
% 11.55/4.15 % (3683948)Time elapsed: 0.948 s
% 11.55/4.15 % (3683948)Peak memory usage: 100 MB
% 11.55/4.15 % (3683948)Instructions burned: 907 (million)
% 11.55/4.15 % (3683960)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3064548656:st=8:i=592:sd=3:ep=RST:ss=axioms_2978 on theBenchmark for (2978ds/592Mi)
% 11.55/4.15 % (3683961)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4165695377:st=3:i=13193:sd=3:ss=axioms_2976 on theBenchmark for (2976ds/13193Mi)
% 11.55/4.15 % (3683960)Instruction limit reached!
% 11.55/4.15 % (3683960)------------------------------
% 11.55/4.15 % (3683960)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683960)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683960)Termination reason: Instruction limit
% 11.55/4.15 % (3683960)Termination phase: Saturation
% 11.55/4.15 % (3683960)Time elapsed: 0.486 s
% 11.55/4.15 % (3683960)Peak memory usage: 94 MB
% 11.55/4.15 % (3683960)Instructions burned: 592 (million)
% 11.55/4.15 % (3683913)First to succeed.
% 11.55/4.15 % (3683913)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3683897"
% 11.55/4.15 % (3683964)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=4007191545:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2971 on theBenchmark for (2971ds/125Mi)
% 11.55/4.15 % (3683964)Instruction limit reached!
% 11.55/4.15 % (3683964)------------------------------
% 11.55/4.15 % (3683964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.55/4.15 % (3683964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.55/4.15 % (3683964)CaDiCaL version: 2.1.3
% 11.55/4.15 % (3683964)Termination reason: Instruction limit
% 11.55/4.15 % (3683964)Termination phase: Saturation
% 11.55/4.15 % (3683964)Time elapsed: 0.135 s
% 11.55/4.15 % (3683964)Peak memory usage: 91 MB
% 11.55/4.15 % (3683964)Instructions burned: 126 (million)
% 11.55/4.15 % (3683913)Refutation found. Thanks to Tanya!
% 11.55/4.15 % SZS status Theorem for theBenchmark
% 11.55/4.15 % SZS output start Proof for theBenchmark
% See solution above
% 23.94/4.30 % (3683913)------------------------------
% 23.94/4.30 % (3683913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 23.94/4.30 % (3683913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 23.94/4.30 % (3683913)CaDiCaL version: 2.1.3
% 23.94/4.30 % (3683913)Termination reason: Refutation
% 23.94/4.30 % (3683913)Time elapsed: 2.754 s
% 23.94/4.30 % (3683913)Peak memory usage: 168 MB
% 23.94/4.30 % (3683913)Instructions burned: 4937 (million)
% 23.94/4.30 % (3683913)------------------------------
% 23.94/4.30 % (3683913)------------------------------
% 23.94/4.30 % (3683897)Success in time 3.286 s
% 23.94/4.30 % Vampire exiting
%------------------------------------------------------------------------------