%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX025+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 : n015.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 7.00s 1.84s
% Output : Refutation 8.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 201 ( 23 unt; 16 def)
% Number of atoms : 745 ( 212 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 907 ( 363 ~; 413 |; 92 &)
% ( 18 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 296 ( 0 sgn 239 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : nil != cons(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id5) ).
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(f42,axiom,
! [X0,X1,X2] :
( append_succeeds(X0,X1,X2)
<=> ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5) )
| ( X0 = nil
& X2 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id42) ).
fof(f159,axiom,
! [X0,X1,X2] :
( list_succeeds(X0)
=> ( '**'(X0,X1) = X2
<=> append_succeeds(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','(**)/2') ).
fof(f165,axiom,
! [X0,X1] :
( list_succeeds(cons(X0,X1))
=> list_succeeds(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(list:cons)') ).
fof(f171,axiom,
! [X0,X1,X2] :
( append_succeeds(X0,X1,X2)
=> list_succeeds(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(append:types:1)') ).
fof(f181,axiom,
! [X0] : '**'(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(app:nil)') ).
fof(f222,axiom,
! [X0,X1,X2,X3] :
( ( append_succeeds(X1,X2,X3)
& list_succeeds(X3) )
=> X2 != cons(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(append:cons:different)') ).
fof(f223,axiom,
! [X0,X1] :
( ( append_succeeds(X0,X1,X1)
& list_succeeds(X1) )
=> X0 = nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(append:equal:nil)') ).
fof(f224,axiom,
( ! [X0,X1,X2] :
( ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5)
& ! [X6] :
( ( list_succeeds(X5)
& append_succeeds(X6,X1,X5) )
=> X4 = X6 ) )
| ( X0 = nil
& X2 = X1 ) )
=> ! [X6] :
( ( list_succeeds(X2)
& append_succeeds(X6,X1,X2) )
=> X0 = X6 ) )
=> ! [X0,X1,X2] :
( append_succeeds(X0,X1,X2)
=> ! [X6] :
( ( list_succeeds(X2)
& append_succeeds(X6,X1,X2) )
=> X0 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
fof(f225,conjecture,
! [X0,X1,X2,X3] :
( ( append_succeeds(X0,X1,X2)
& append_succeeds(X3,X1,X2)
& list_succeeds(X2) )
=> X0 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(append:uniqueness:1)') ).
fof(f226,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( append_succeeds(X0,X1,X2)
& append_succeeds(X3,X1,X2)
& list_succeeds(X2) )
=> X0 = X3 ),
inference(negated_conjecture,[status(cth)],[f225]) ).
fof(f247,plain,
( ! [X0,X1,X2] :
( ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5)
& ! [X6] :
( ( list_succeeds(X5)
& append_succeeds(X6,X1,X5) )
=> X4 = X6 ) )
| ( X0 = nil
& X2 = X1 ) )
=> ! [X7] :
( ( list_succeeds(X2)
& append_succeeds(X7,X1,X2) )
=> X0 = X7 ) )
=> ! [X8,X9,X10] :
( append_succeeds(X8,X9,X10)
=> ! [X11] :
( ( list_succeeds(X10)
& append_succeeds(X11,X9,X10) )
=> X8 = X11 ) ) ),
inference(rectify,[],[f224]) ).
fof(f249,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| cons(X0,X1) != cons(X2,X3) ),
inference(ennf_transformation,[],[f8]) ).
fof(f250,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| cons(X0,X1) != cons(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f426,plain,
! [X0,X1,X2] :
( ( '**'(X0,X1) = X2
<=> append_succeeds(X0,X1,X2) )
| ~ list_succeeds(X0) ),
inference(ennf_transformation,[],[f159]) ).
fof(f429,plain,
! [X0,X1] :
( list_succeeds(X1)
| ~ list_succeeds(cons(X0,X1)) ),
inference(ennf_transformation,[],[f165]) ).
fof(f438,plain,
! [X0,X1,X2] :
( list_succeeds(X0)
| ~ append_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f171]) ).
fof(f512,plain,
! [X0,X1,X2,X3] :
( X2 != cons(X0,X3)
| ~ append_succeeds(X1,X2,X3)
| ~ list_succeeds(X3) ),
inference(ennf_transformation,[],[f222]) ).
fof(f513,plain,
! [X0,X1,X2,X3] :
( X2 != cons(X0,X3)
| ~ append_succeeds(X1,X2,X3)
| ~ list_succeeds(X3) ),
inference(flattening,[],[f512]) ).
fof(f514,plain,
! [X0,X1] :
( X0 = nil
| ~ append_succeeds(X0,X1,X1)
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f223]) ).
fof(f515,plain,
! [X0,X1] :
( X0 = nil
| ~ append_succeeds(X0,X1,X1)
| ~ list_succeeds(X1) ),
inference(flattening,[],[f514]) ).
fof(f516,plain,
( ! [X8,X9,X10] :
( ! [X11] :
( X8 = X11
| ~ list_succeeds(X10)
| ~ append_succeeds(X11,X9,X10) )
| ~ append_succeeds(X8,X9,X10) )
| ? [X0,X1,X2] :
( ? [X7] :
( X0 != X7
& list_succeeds(X2)
& append_succeeds(X7,X1,X2) )
& ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5)
& ! [X6] :
( X4 = X6
| ~ list_succeeds(X5)
| ~ append_succeeds(X6,X1,X5) ) )
| ( X0 = nil
& X2 = X1 ) ) ) ),
inference(ennf_transformation,[],[f247]) ).
fof(f517,plain,
( ! [X8,X9,X10] :
( ! [X11] :
( X8 = X11
| ~ list_succeeds(X10)
| ~ append_succeeds(X11,X9,X10) )
| ~ append_succeeds(X8,X9,X10) )
| ? [X0,X1,X2] :
( ? [X7] :
( X0 != X7
& list_succeeds(X2)
& append_succeeds(X7,X1,X2) )
& ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5)
& ! [X6] :
( X4 = X6
| ~ list_succeeds(X5)
| ~ append_succeeds(X6,X1,X5) ) )
| ( X0 = nil
& X2 = X1 ) ) ) ),
inference(flattening,[],[f516]) ).
fof(f518,plain,
? [X0,X1,X2,X3] :
( X0 != X3
& append_succeeds(X0,X1,X2)
& append_succeeds(X3,X1,X2)
& list_succeeds(X2) ),
inference(ennf_transformation,[],[f226]) ).
fof(f519,plain,
? [X0,X1,X2,X3] :
( X0 != X3
& append_succeeds(X0,X1,X2)
& append_succeeds(X3,X1,X2)
& list_succeeds(X2) ),
inference(flattening,[],[f518]) ).
fof(f520,definition,
! [X0,X2,X1] :
( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5)
& ! [X6] :
( X4 = X6
| ~ list_succeeds(X5)
| ~ append_succeeds(X6,X1,X5) ) )
| ( X0 = nil
& X2 = X1 )
| ~ sP0(X0,X2,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f521,plain,
( ! [X8,X9,X10] :
( ! [X11] :
( X8 = X11
| ~ list_succeeds(X10)
| ~ append_succeeds(X11,X9,X10) )
| ~ append_succeeds(X8,X9,X10) )
| ? [X0,X1,X2] :
( ? [X7] :
( X0 != X7
& list_succeeds(X2)
& append_succeeds(X7,X1,X2) )
& sP0(X0,X2,X1) ) ),
inference(definition_folding,[],[f517,f520]) ).
fof(f547,plain,
! [X0,X1,X2] :
( ( append_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X2
| ~ append_succeeds(X4,X1,X5) )
& ( nil != X0
| X1 != X2 ) ) )
& ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5) )
| ( X0 = nil
& X2 = X1 )
| ~ append_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f548,plain,
! [X0,X1,X2] :
( ( append_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X2
| ~ append_succeeds(X4,X1,X5) )
& ( nil != X0
| X1 != X2 ) ) )
& ( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5) )
| ( X0 = nil
& X2 = X1 )
| ~ append_succeeds(X0,X1,X2) ) ),
inference(flattening,[],[f547]) ).
fof(f549,plain,
! [X0,X1,X2] :
( ( append_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X2
| ~ append_succeeds(X4,X1,X5) )
& ( nil != X0
| X1 != X2 ) ) )
& ( ? [X6,X7,X8] :
( cons(X6,X7) = X0
& cons(X6,X8) = X2
& append_succeeds(X7,X1,X8) )
| ( X0 = nil
& X2 = X1 )
| ~ append_succeeds(X0,X1,X2) ) ),
inference(rectify,[],[f548]) ).
fof(f550,plain,
! [X0,X1,X2] :
( ( append_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X0
| cons(X3,X5) != X2
| ~ append_succeeds(X4,X1,X5) )
& ( nil != X0
| X1 != X2 ) ) )
& ( ( cons(sK19(X0,X1,X2),sK20(X0,X1,X2)) = X0
& cons(sK19(X0,X1,X2),sK21(X0,X1,X2)) = X2
& append_succeeds(sK20(X0,X1,X2),X1,sK21(X0,X1,X2)) )
| ( X0 = nil
& X2 = X1 )
| ~ append_succeeds(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X6,sK19(X0,X1,X2)),skolemize(X7,sK20(X0,X1,X2)),skolemize(X8,sK21(X0,X1,X2))],[f549]) ).
fof(f653,plain,
! [X0,X1,X2] :
( ( ( '**'(X0,X1) = X2
| ~ append_succeeds(X0,X1,X2) )
& ( append_succeeds(X0,X1,X2)
| '**'(X0,X1) != X2 ) )
| ~ list_succeeds(X0) ),
inference(nnf_transformation,[],[f426]) ).
fof(f663,plain,
! [X0,X2,X1] :
( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& X2 = cons(X3,X5)
& append_succeeds(X4,X1,X5)
& ! [X6] :
( X4 = X6
| ~ list_succeeds(X5)
| ~ append_succeeds(X6,X1,X5) ) )
| ( X0 = nil
& X2 = X1 )
| ~ sP0(X0,X2,X1) ),
inference(nnf_transformation,[],[f520]) ).
fof(f664,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( X0 = cons(X3,X4)
& cons(X3,X5) = X1
& append_succeeds(X4,X2,X5)
& ! [X6] :
( X4 = X6
| ~ list_succeeds(X5)
| ~ append_succeeds(X6,X2,X5) ) )
| ( X0 = nil
& X2 = X1 )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f663]) ).
fof(f665,plain,
! [X0,X1,X2] :
( ( cons(sK91(X0,X1,X2),sK92(X0,X1,X2)) = X0
& cons(sK91(X0,X1,X2),sK93(X0,X1,X2)) = X1
& append_succeeds(sK92(X0,X1,X2),X2,sK93(X0,X1,X2))
& ! [X6] :
( sK92(X0,X1,X2) = X6
| ~ list_succeeds(sK93(X0,X1,X2))
| ~ append_succeeds(X6,X2,sK93(X0,X1,X2)) ) )
| ( X0 = nil
& X2 = X1 )
| ~ sP0(X0,X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91,sK92,sK93]),skolemize(X3,sK91(X0,X1,X2)),skolemize(X4,sK92(X0,X1,X2)),skolemize(X5,sK93(X0,X1,X2))],[f664]) ).
fof(f666,plain,
( ! [X0,X1,X2] :
( ! [X3] :
( X0 = X3
| ~ list_succeeds(X2)
| ~ append_succeeds(X3,X1,X2) )
| ~ append_succeeds(X0,X1,X2) )
| ? [X4,X5,X6] :
( ? [X7] :
( X4 != X7
& list_succeeds(X6)
& append_succeeds(X7,X5,X6) )
& sP0(X4,X6,X5) ) ),
inference(rectify,[],[f521]) ).
fof(f667,plain,
( ! [X0,X1,X2] :
( ! [X3] :
( X0 = X3
| ~ list_succeeds(X2)
| ~ append_succeeds(X3,X1,X2) )
| ~ append_succeeds(X0,X1,X2) )
| ( sK94 != sK97
& list_succeeds(sK96)
& append_succeeds(sK97,sK95,sK96)
& sP0(sK94,sK96,sK95) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94,sK95,sK96,sK97]),skolemize(X4,sK94),skolemize(X5,sK95),skolemize(X6,sK96),skolemize(X7,sK97)],[f666]) ).
fof(f668,plain,
( sK98 != sK101
& append_succeeds(sK98,sK99,sK100)
& append_succeeds(sK101,sK99,sK100)
& list_succeeds(sK100) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98,sK99,sK100,sK101]),skolemize(X0,sK98),skolemize(X1,sK99),skolemize(X2,sK100),skolemize(X3,sK101)],[f519]) ).
fof(f673,plain,
! [X0,X1] : nil != cons(X0,X1),
inference(cnf_transformation,[],[f5]) ).
fof(f676,plain,
! [X2,X3,X0,X1] :
( cons(X0,X1) != cons(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f249]) ).
fof(f677,plain,
! [X2,X3,X0,X1] :
( cons(X0,X1) != cons(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f250]) ).
fof(f741,plain,
! [X2,X0,X1] :
( append_succeeds(sK20(X0,X1,X2),X1,sK21(X0,X1,X2))
| X1 = X2
| ~ append_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f550]) ).
fof(f744,plain,
! [X2,X0,X1] :
( ~ append_succeeds(X0,X1,X2)
| nil = X0
| cons(sK19(X0,X1,X2),sK21(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f550]) ).
fof(f745,plain,
! [X2,X0,X1] :
( ~ append_succeeds(X0,X1,X2)
| X1 = X2
| cons(sK19(X0,X1,X2),sK20(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f550]) ).
fof(f746,plain,
! [X2,X0,X1] :
( ~ append_succeeds(X0,X1,X2)
| nil = X0
| cons(sK19(X0,X1,X2),sK20(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f550]) ).
fof(f975,plain,
! [X2,X0,X1] :
( '**'(X0,X1) = X2
| ~ append_succeeds(X0,X1,X2)
| ~ list_succeeds(X0) ),
inference(cnf_transformation,[],[f653]) ).
fof(f984,plain,
! [X0,X1] :
( ~ list_succeeds(cons(X0,X1))
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f429]) ).
fof(f990,plain,
! [X2,X0,X1] :
( ~ append_succeeds(X0,X1,X2)
| list_succeeds(X0) ),
inference(cnf_transformation,[],[f438]) ).
fof(f1002,plain,
! [X0] : '**'(nil,X0) = X0,
inference(cnf_transformation,[],[f181]) ).
fof(f1045,plain,
! [X2,X3,X0,X1] :
( cons(X0,X3) != X2
| ~ append_succeeds(X1,X2,X3)
| ~ list_succeeds(X3) ),
inference(cnf_transformation,[],[f513]) ).
fof(f1046,plain,
! [X0,X1] :
( ~ append_succeeds(X0,X1,X1)
| nil = X0
| ~ list_succeeds(X1) ),
inference(cnf_transformation,[],[f515]) ).
fof(f1047,plain,
! [X2,X0,X1,X6] :
( ~ append_succeeds(X6,X2,sK93(X0,X1,X2))
| ~ list_succeeds(sK93(X0,X1,X2))
| sK92(X0,X1,X2) = X6
| X1 = X2
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f665]) ).
fof(f1050,plain,
! [X2,X0,X1] :
( append_succeeds(sK92(X0,X1,X2),X2,sK93(X0,X1,X2))
| nil = X0
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f665]) ).
fof(f1051,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| X1 = X2
| cons(sK91(X0,X1,X2),sK93(X0,X1,X2)) = X1 ),
inference(cnf_transformation,[],[f665]) ).
fof(f1052,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| nil = X0
| cons(sK91(X0,X1,X2),sK93(X0,X1,X2)) = X1 ),
inference(cnf_transformation,[],[f665]) ).
fof(f1053,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| X1 = X2
| cons(sK91(X0,X1,X2),sK92(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f665]) ).
fof(f1055,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ list_succeeds(X2)
| ~ append_succeeds(X3,X1,X2)
| ~ append_succeeds(X0,X1,X2)
| sP0(sK94,sK96,sK95) ),
inference(cnf_transformation,[],[f667]) ).
fof(f1056,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ list_succeeds(X2)
| ~ append_succeeds(X3,X1,X2)
| ~ append_succeeds(X0,X1,X2)
| append_succeeds(sK97,sK95,sK96) ),
inference(cnf_transformation,[],[f667]) ).
fof(f1057,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ list_succeeds(X2)
| ~ append_succeeds(X3,X1,X2)
| ~ append_succeeds(X0,X1,X2)
| list_succeeds(sK96) ),
inference(cnf_transformation,[],[f667]) ).
fof(f1058,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ list_succeeds(X2)
| ~ append_succeeds(X3,X1,X2)
| ~ append_succeeds(X0,X1,X2)
| sK94 != sK97 ),
inference(cnf_transformation,[],[f667]) ).
fof(f1059,plain,
list_succeeds(sK100),
inference(cnf_transformation,[],[f668]) ).
fof(f1060,plain,
append_succeeds(sK101,sK99,sK100),
inference(cnf_transformation,[],[f668]) ).
fof(f1061,plain,
append_succeeds(sK98,sK99,sK100),
inference(cnf_transformation,[],[f668]) ).
fof(f1062,plain,
sK98 != sK101,
inference(cnf_transformation,[],[f668]) ).
fof(f1150,plain,
! [X3,X0,X1] :
( ~ append_succeeds(X1,cons(X0,X3),X3)
| ~ list_succeeds(X3) ),
inference(equality_resolution,[],[f1045]) ).
fof(f1152,definition,
( spl102_1
<=> sP0(sK94,sK96,sK95) ),
introduced(definition,[new_symbols(definition,[spl102_1])],[avatar_definition]) ).
fof(f1154,plain,
( sP0(sK94,sK96,sK95)
| ~ spl102_1 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f1156,definition,
( spl102_2
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| ~ append_succeeds(X0,X1,X2)
| ~ append_succeeds(X3,X1,X2)
| ~ list_succeeds(X2) ) ),
introduced(definition,[new_symbols(definition,[spl102_2])],[avatar_definition]) ).
fof(f1157,plain,
( ! [X2,X3,X0,X1] :
( ~ append_succeeds(X3,X1,X2)
| ~ append_succeeds(X0,X1,X2)
| X0 = X3
| ~ list_succeeds(X2) )
| ~ spl102_2 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1158,plain,
( spl102_1
| spl102_2 ),
inference(avatar_split_clause,[],[f1055,f1156,f1152]) ).
fof(f1160,definition,
( spl102_3
<=> append_succeeds(sK97,sK95,sK96) ),
introduced(definition,[new_symbols(definition,[spl102_3])],[avatar_definition]) ).
fof(f1162,plain,
( append_succeeds(sK97,sK95,sK96)
| ~ spl102_3 ),
inference(avatar_component_clause,[],[f1160]) ).
fof(f1163,plain,
( spl102_3
| spl102_2 ),
inference(avatar_split_clause,[],[f1056,f1156,f1160]) ).
fof(f1165,definition,
( spl102_4
<=> list_succeeds(sK96) ),
introduced(definition,[new_symbols(definition,[spl102_4])],[avatar_definition]) ).
fof(f1167,plain,
( list_succeeds(sK96)
| ~ spl102_4 ),
inference(avatar_component_clause,[],[f1165]) ).
fof(f1168,plain,
( spl102_4
| spl102_2 ),
inference(avatar_split_clause,[],[f1057,f1156,f1165]) ).
fof(f1170,definition,
( spl102_5
<=> sK94 = sK97 ),
introduced(definition,[new_symbols(definition,[spl102_5])],[avatar_definition]) ).
fof(f1172,plain,
( sK94 != sK97
| spl102_5 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f1173,plain,
( ~ spl102_5
| spl102_2 ),
inference(avatar_split_clause,[],[f1058,f1156,f1170]) ).
fof(f1175,plain,
! [X2,X0,X1] :
( ~ append_succeeds(X0,X1,X2)
| '**'(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f975,f990]) ).
fof(f1176,plain,
( ! [X0] :
( ~ append_succeeds(X0,sK99,sK100)
| sK101 = X0
| ~ list_succeeds(sK100) )
| ~ spl102_2 ),
inference(resolution,[],[f1060,f1157]) ).
fof(f1177,plain,
( ! [X0] :
( ~ append_succeeds(X0,sK99,sK100)
| sK101 = X0 )
| ~ spl102_2 ),
inference(forward_subsumption_resolution,[],[f1176,f1059]) ).
fof(f1179,plain,
( sK98 = sK101
| ~ spl102_2 ),
inference(resolution,[],[f1061,f1177]) ).
fof(f1182,plain,
( $false
| ~ spl102_2 ),
inference(forward_subsumption_resolution,[],[f1179,f1062]) ).
fof(f1183,plain,
~ spl102_2,
inference(avatar_contradiction_clause,[],[f1182]) ).
fof(f1192,plain,
( sK96 = '**'(sK97,sK95)
| ~ spl102_3 ),
inference(resolution,[],[f1175,f1162]) ).
fof(f1207,plain,
( nil = sK97
| sK96 = cons(sK19(sK97,sK95,sK96),sK21(sK97,sK95,sK96))
| ~ spl102_3 ),
inference(resolution,[],[f744,f1162]) ).
fof(f1209,definition,
( spl102_6
<=> sK96 = cons(sK19(sK97,sK95,sK96),sK21(sK97,sK95,sK96)) ),
introduced(definition,[new_symbols(definition,[spl102_6])],[avatar_definition]) ).
fof(f1211,plain,
( sK96 = cons(sK19(sK97,sK95,sK96),sK21(sK97,sK95,sK96))
| ~ spl102_6 ),
inference(avatar_component_clause,[],[f1209]) ).
fof(f1213,definition,
( spl102_7
<=> nil = sK97 ),
introduced(definition,[new_symbols(definition,[spl102_7])],[avatar_definition]) ).
fof(f1214,plain,
( nil != sK97
| spl102_7 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f1215,plain,
( nil = sK97
| ~ spl102_7 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f1216,plain,
( spl102_6
| spl102_7
| ~ spl102_3 ),
inference(avatar_split_clause,[],[f1207,f1160,f1213,f1209]) ).
fof(f1235,plain,
( sK96 = '**'(nil,sK95)
| ~ spl102_3
| ~ spl102_7 ),
inference(superposition,[],[f1192,f1215]) ).
fof(f1238,plain,
( sK95 = sK96
| ~ spl102_3
| ~ spl102_7 ),
inference(forward_demodulation,[],[f1235,f1002]) ).
fof(f1241,plain,
( sP0(sK94,sK96,sK96)
| ~ spl102_1
| ~ spl102_3
| ~ spl102_7 ),
inference(superposition,[],[f1154,f1238]) ).
fof(f1246,plain,
( nil = sK97
| sK97 = cons(sK19(sK97,sK95,sK96),sK20(sK97,sK95,sK96))
| ~ spl102_3 ),
inference(resolution,[],[f746,f1162]) ).
fof(f1268,plain,
( sK95 = sK96
| sK97 = cons(sK19(sK97,sK95,sK96),sK20(sK97,sK95,sK96))
| ~ spl102_3 ),
inference(resolution,[],[f745,f1162]) ).
fof(f1304,plain,
( sK95 = sK96
| sK96 = cons(sK91(sK94,sK96,sK95),sK93(sK94,sK96,sK95))
| ~ spl102_1 ),
inference(resolution,[],[f1051,f1154]) ).
fof(f1306,plain,
( nil != sK94
| spl102_5
| ~ spl102_7 ),
inference(superposition,[],[f1172,f1215]) ).
fof(f1319,plain,
( sK95 = sK96
| sK94 = cons(sK91(sK94,sK96,sK95),sK92(sK94,sK96,sK95))
| ~ spl102_1 ),
inference(resolution,[],[f1053,f1154]) ).
fof(f1339,plain,
( nil = sK94
| sK96 = cons(sK91(sK94,sK96,sK96),sK93(sK94,sK96,sK96))
| ~ spl102_1
| ~ spl102_3
| ~ spl102_7 ),
inference(resolution,[],[f1052,f1241]) ).
fof(f1340,plain,
( sK96 = cons(sK91(sK94,sK96,sK96),sK93(sK94,sK96,sK96))
| ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_7 ),
inference(forward_subsumption_resolution,[],[f1339,f1306]) ).
fof(f1357,plain,
( ! [X0] :
( ~ append_succeeds(X0,sK96,sK93(sK94,sK96,sK96))
| ~ list_succeeds(sK93(sK94,sK96,sK96)) )
| ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_7 ),
inference(superposition,[],[f1150,f1340]) ).
fof(f1359,definition,
( spl102_16
<=> list_succeeds(sK93(sK94,sK96,sK96)) ),
introduced(definition,[new_symbols(definition,[spl102_16])],[avatar_definition]) ).
fof(f1361,plain,
( ~ list_succeeds(sK93(sK94,sK96,sK96))
| spl102_16 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f1363,definition,
( spl102_17
<=> ! [X0] : ~ append_succeeds(X0,sK96,sK93(sK94,sK96,sK96)) ),
introduced(definition,[new_symbols(definition,[spl102_17])],[avatar_definition]) ).
fof(f1364,plain,
( ! [X0] : ~ append_succeeds(X0,sK96,sK93(sK94,sK96,sK96))
| ~ spl102_17 ),
inference(avatar_component_clause,[],[f1363]) ).
fof(f1365,plain,
( ~ spl102_16
| spl102_17
| ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_7 ),
inference(avatar_split_clause,[],[f1357,f1213,f1170,f1160,f1152,f1363,f1359]) ).
fof(f1522,plain,
( ~ list_succeeds(sK96)
| list_succeeds(sK93(sK94,sK96,sK96))
| ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_7 ),
inference(superposition,[],[f984,f1340]) ).
fof(f1531,plain,
( list_succeeds(sK93(sK94,sK96,sK96))
| ~ spl102_1
| ~ spl102_3
| ~ spl102_4
| spl102_5
| ~ spl102_7 ),
inference(forward_subsumption_resolution,[],[f1522,f1167]) ).
fof(f1541,plain,
( $false
| ~ spl102_1
| ~ spl102_3
| ~ spl102_4
| spl102_5
| ~ spl102_7
| spl102_16 ),
inference(forward_subsumption_resolution,[],[f1531,f1361]) ).
fof(f1542,plain,
( ~ spl102_1
| ~ spl102_3
| ~ spl102_4
| spl102_5
| ~ spl102_7
| spl102_16 ),
inference(avatar_contradiction_clause,[],[f1541]) ).
fof(f1543,plain,
( sK97 = cons(sK19(sK97,sK95,sK96),sK20(sK97,sK95,sK96))
| ~ spl102_3
| spl102_7 ),
inference(forward_subsumption_resolution,[],[f1246,f1214]) ).
fof(f1545,definition,
( spl102_26
<=> sK97 = cons(sK19(sK97,sK95,sK96),sK20(sK97,sK95,sK96)) ),
introduced(definition,[new_symbols(definition,[spl102_26])],[avatar_definition]) ).
fof(f1547,plain,
( sK97 = cons(sK19(sK97,sK95,sK96),sK20(sK97,sK95,sK96))
| ~ spl102_26 ),
inference(avatar_component_clause,[],[f1545]) ).
fof(f1549,definition,
( spl102_27
<=> sK95 = sK96 ),
introduced(definition,[new_symbols(definition,[spl102_27])],[avatar_definition]) ).
fof(f1550,plain,
( sK95 != sK96
| spl102_27 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1551,plain,
( sK95 = sK96
| ~ spl102_27 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f1552,plain,
( spl102_26
| spl102_27
| ~ spl102_3 ),
inference(avatar_split_clause,[],[f1268,f1160,f1549,f1545]) ).
fof(f1554,definition,
( spl102_28
<=> sK96 = cons(sK91(sK94,sK96,sK95),sK93(sK94,sK96,sK95)) ),
introduced(definition,[new_symbols(definition,[spl102_28])],[avatar_definition]) ).
fof(f1556,plain,
( sK96 = cons(sK91(sK94,sK96,sK95),sK93(sK94,sK96,sK95))
| ~ spl102_28 ),
inference(avatar_component_clause,[],[f1554]) ).
fof(f1557,plain,
( spl102_28
| spl102_27
| ~ spl102_1 ),
inference(avatar_split_clause,[],[f1304,f1152,f1549,f1554]) ).
fof(f1559,definition,
( spl102_29
<=> sK94 = cons(sK91(sK94,sK96,sK95),sK92(sK94,sK96,sK95)) ),
introduced(definition,[new_symbols(definition,[spl102_29])],[avatar_definition]) ).
fof(f1561,plain,
( sK94 = cons(sK91(sK94,sK96,sK95),sK92(sK94,sK96,sK95))
| ~ spl102_29 ),
inference(avatar_component_clause,[],[f1559]) ).
fof(f1562,plain,
( spl102_29
| spl102_27
| ~ spl102_1 ),
inference(avatar_split_clause,[],[f1319,f1152,f1549,f1559]) ).
fof(f1564,definition,
( spl102_30
<=> nil = sK94 ),
introduced(definition,[new_symbols(definition,[spl102_30])],[avatar_definition]) ).
fof(f1565,plain,
( nil != sK94
| spl102_30 ),
inference(avatar_component_clause,[],[f1564]) ).
fof(f1566,plain,
( nil = sK94
| ~ spl102_30 ),
inference(avatar_component_clause,[],[f1564]) ).
fof(f1569,plain,
( spl102_26
| ~ spl102_3
| spl102_7 ),
inference(avatar_split_clause,[],[f1543,f1213,f1160,f1545]) ).
fof(f1592,plain,
( ! [X0,X1] :
( cons(X0,X1) != sK96
| sK93(sK94,sK96,sK95) = X1 )
| ~ spl102_28 ),
inference(superposition,[],[f676,f1556]) ).
fof(f1594,plain,
( ! [X0,X1] :
( cons(X0,X1) != sK96
| sK91(sK94,sK96,sK95) = X0 )
| ~ spl102_28 ),
inference(superposition,[],[f677,f1556]) ).
fof(f1595,plain,
( ~ list_succeeds(sK96)
| list_succeeds(sK93(sK94,sK96,sK95))
| ~ spl102_28 ),
inference(superposition,[],[f984,f1556]) ).
fof(f1598,definition,
( spl102_34
<=> list_succeeds(sK93(sK94,sK96,sK95)) ),
introduced(definition,[new_symbols(definition,[spl102_34])],[avatar_definition]) ).
fof(f1599,plain,
( list_succeeds(sK93(sK94,sK96,sK95))
| ~ spl102_34 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f1605,plain,
( list_succeeds(sK93(sK94,sK96,sK95))
| ~ spl102_4
| ~ spl102_28 ),
inference(forward_subsumption_resolution,[],[f1595,f1167]) ).
fof(f1606,plain,
( spl102_34
| ~ spl102_4
| ~ spl102_28 ),
inference(avatar_split_clause,[],[f1605,f1554,f1165,f1598]) ).
fof(f1609,plain,
( sP0(sK94,sK96,sK96)
| ~ spl102_1
| ~ spl102_27 ),
inference(superposition,[],[f1154,f1551]) ).
fof(f1610,plain,
( append_succeeds(sK97,sK96,sK96)
| ~ spl102_3
| ~ spl102_27 ),
inference(superposition,[],[f1162,f1551]) ).
fof(f1621,plain,
( nil = sK97
| ~ list_succeeds(sK96)
| ~ spl102_3
| ~ spl102_27 ),
inference(resolution,[],[f1610,f1046]) ).
fof(f1636,plain,
( ~ list_succeeds(sK96)
| ~ spl102_3
| spl102_7
| ~ spl102_27 ),
inference(forward_subsumption_resolution,[],[f1621,f1214]) ).
fof(f1637,plain,
( $false
| ~ spl102_3
| ~ spl102_4
| spl102_7
| ~ spl102_27 ),
inference(forward_subsumption_resolution,[],[f1636,f1167]) ).
fof(f1638,plain,
( ~ spl102_3
| ~ spl102_4
| spl102_7
| ~ spl102_27 ),
inference(avatar_contradiction_clause,[],[f1637]) ).
fof(f1642,plain,
( $false
| spl102_5
| ~ spl102_7
| ~ spl102_30 ),
inference(forward_subsumption_resolution,[],[f1306,f1566]) ).
fof(f1643,plain,
( spl102_5
| ~ spl102_7
| ~ spl102_30 ),
inference(avatar_contradiction_clause,[],[f1642]) ).
fof(f1704,plain,
( nil = cons(sK19(nil,sK95,sK96),sK20(nil,sK95,sK96))
| ~ spl102_7
| ~ spl102_26 ),
inference(superposition,[],[f1547,f1215]) ).
fof(f1721,plain,
( $false
| ~ spl102_7
| ~ spl102_26 ),
inference(forward_subsumption_resolution,[],[f1704,f673]) ).
fof(f1722,plain,
( ~ spl102_7
| ~ spl102_26 ),
inference(avatar_contradiction_clause,[],[f1721]) ).
fof(f1919,plain,
( nil = sK94
| ~ sP0(sK94,sK96,sK96)
| ~ spl102_17 ),
inference(resolution,[],[f1364,f1050]) ).
fof(f1921,plain,
( ~ sP0(sK94,sK96,sK96)
| ~ spl102_17
| spl102_30 ),
inference(forward_subsumption_resolution,[],[f1919,f1565]) ).
fof(f1922,plain,
( $false
| ~ spl102_1
| ~ spl102_17
| ~ spl102_27
| spl102_30 ),
inference(forward_subsumption_resolution,[],[f1921,f1609]) ).
fof(f1923,plain,
( ~ spl102_1
| ~ spl102_17
| ~ spl102_27
| spl102_30 ),
inference(avatar_contradiction_clause,[],[f1922]) ).
fof(f1977,plain,
( sK96 != sK96
| sK21(sK97,sK95,sK96) = sK93(sK94,sK96,sK95)
| ~ spl102_6
| ~ spl102_28 ),
inference(superposition,[],[f1592,f1211]) ).
fof(f1980,plain,
( sK21(sK97,sK95,sK96) = sK93(sK94,sK96,sK95)
| ~ spl102_6
| ~ spl102_28 ),
inference(trivial_inequality_removal,[],[f1977]) ).
fof(f1991,plain,
( append_succeeds(sK20(sK97,sK95,sK96),sK95,sK93(sK94,sK96,sK95))
| sK95 = sK96
| ~ append_succeeds(sK97,sK95,sK96)
| ~ spl102_6
| ~ spl102_28 ),
inference(superposition,[],[f741,f1980]) ).
fof(f1992,plain,
( append_succeeds(sK20(sK97,sK95,sK96),sK95,sK93(sK94,sK96,sK95))
| ~ append_succeeds(sK97,sK95,sK96)
| ~ spl102_6
| spl102_27
| ~ spl102_28 ),
inference(forward_subsumption_resolution,[],[f1991,f1550]) ).
fof(f1993,plain,
( append_succeeds(sK20(sK97,sK95,sK96),sK95,sK93(sK94,sK96,sK95))
| ~ spl102_3
| ~ spl102_6
| spl102_27
| ~ spl102_28 ),
inference(forward_subsumption_resolution,[],[f1992,f1162]) ).
fof(f1995,plain,
( ~ list_succeeds(sK93(sK94,sK96,sK95))
| sK20(sK97,sK95,sK96) = sK92(sK94,sK96,sK95)
| sK95 = sK96
| ~ sP0(sK94,sK96,sK95)
| ~ spl102_3
| ~ spl102_6
| spl102_27
| ~ spl102_28 ),
inference(resolution,[],[f1993,f1047]) ).
fof(f2027,plain,
( sK20(sK97,sK95,sK96) = sK92(sK94,sK96,sK95)
| sK95 = sK96
| ~ sP0(sK94,sK96,sK95)
| ~ spl102_3
| ~ spl102_6
| spl102_27
| ~ spl102_28
| ~ spl102_34 ),
inference(forward_subsumption_resolution,[],[f1995,f1599]) ).
fof(f2029,plain,
( sK20(sK97,sK95,sK96) = sK92(sK94,sK96,sK95)
| ~ sP0(sK94,sK96,sK95)
| ~ spl102_3
| ~ spl102_6
| spl102_27
| ~ spl102_28
| ~ spl102_34 ),
inference(forward_subsumption_resolution,[],[f2027,f1550]) ).
fof(f2031,plain,
( sK20(sK97,sK95,sK96) = sK92(sK94,sK96,sK95)
| ~ spl102_1
| ~ spl102_3
| ~ spl102_6
| spl102_27
| ~ spl102_28
| ~ spl102_34 ),
inference(forward_subsumption_resolution,[],[f2029,f1154]) ).
fof(f2036,plain,
( sK97 = cons(sK19(sK97,sK95,sK96),sK92(sK94,sK96,sK95))
| ~ spl102_1
| ~ spl102_3
| ~ spl102_6
| ~ spl102_26
| spl102_27
| ~ spl102_28
| ~ spl102_34 ),
inference(superposition,[],[f1547,f2031]) ).
fof(f2094,plain,
( sK96 != sK96
| sK19(sK97,sK95,sK96) = sK91(sK94,sK96,sK95)
| ~ spl102_6
| ~ spl102_28 ),
inference(superposition,[],[f1594,f1211]) ).
fof(f2096,plain,
( sK19(sK97,sK95,sK96) = sK91(sK94,sK96,sK95)
| ~ spl102_6
| ~ spl102_28 ),
inference(trivial_inequality_removal,[],[f2094]) ).
fof(f2098,plain,
( sK94 = cons(sK19(sK97,sK95,sK96),sK92(sK94,sK96,sK95))
| ~ spl102_6
| ~ spl102_28
| ~ spl102_29 ),
inference(superposition,[],[f1561,f2096]) ).
fof(f2106,plain,
( sK94 = sK97
| ~ spl102_1
| ~ spl102_3
| ~ spl102_6
| ~ spl102_26
| spl102_27
| ~ spl102_28
| ~ spl102_29
| ~ spl102_34 ),
inference(forward_demodulation,[],[f2098,f2036]) ).
fof(f2109,plain,
( $false
| ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_6
| ~ spl102_26
| spl102_27
| ~ spl102_28
| ~ spl102_29
| ~ spl102_34 ),
inference(forward_subsumption_resolution,[],[f2106,f1172]) ).
fof(f2110,plain,
( ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_6
| ~ spl102_26
| spl102_27
| ~ spl102_28
| ~ spl102_29
| ~ spl102_34 ),
inference(avatar_contradiction_clause,[],[f2109]) ).
cnf(s1,plain,
( spl102_1
| spl102_2 ),
inference(sat_conversion,[],[f1158]) ).
cnf(s2,plain,
( spl102_2
| spl102_3 ),
inference(sat_conversion,[],[f1163]) ).
cnf(s3,plain,
( spl102_2
| spl102_4 ),
inference(sat_conversion,[],[f1168]) ).
cnf(s4,plain,
( spl102_2
| ~ spl102_5 ),
inference(sat_conversion,[],[f1173]) ).
cnf(s5,plain,
~ spl102_2,
inference(sat_conversion,[],[f1183]) ).
cnf(s6,plain,
( ~ spl102_3
| spl102_6
| spl102_7 ),
inference(sat_conversion,[],[f1216]) ).
cnf(s13,plain,
( ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_7
| ~ spl102_16
| spl102_17 ),
inference(sat_conversion,[],[f1365]) ).
cnf(s23,plain,
( ~ spl102_1
| ~ spl102_3
| ~ spl102_4
| spl102_5
| ~ spl102_7
| spl102_16 ),
inference(sat_conversion,[],[f1542]) ).
cnf(s24,plain,
( ~ spl102_3
| spl102_26
| spl102_27 ),
inference(sat_conversion,[],[f1552]) ).
cnf(s25,plain,
( ~ spl102_1
| spl102_27
| spl102_28 ),
inference(sat_conversion,[],[f1557]) ).
cnf(s26,plain,
( ~ spl102_1
| spl102_27
| spl102_29 ),
inference(sat_conversion,[],[f1562]) ).
cnf(s29,plain,
( ~ spl102_3
| spl102_7
| spl102_26 ),
inference(sat_conversion,[],[f1569]) ).
cnf(s33,plain,
( ~ spl102_4
| ~ spl102_28
| spl102_34 ),
inference(sat_conversion,[],[f1606]) ).
cnf(s35,plain,
( ~ spl102_3
| ~ spl102_4
| spl102_7
| ~ spl102_27 ),
inference(sat_conversion,[],[f1638]) ).
cnf(s36,plain,
( spl102_5
| ~ spl102_7
| ~ spl102_30 ),
inference(sat_conversion,[],[f1643]) ).
cnf(s37,plain,
( ~ spl102_7
| ~ spl102_26 ),
inference(sat_conversion,[],[f1722]) ).
cnf(s48,plain,
( ~ spl102_1
| ~ spl102_17
| ~ spl102_27
| spl102_30 ),
inference(sat_conversion,[],[f1923]) ).
cnf(s62,plain,
( ~ spl102_1
| ~ spl102_3
| spl102_5
| ~ spl102_6
| ~ spl102_26
| spl102_27
| ~ spl102_28
| ~ spl102_29
| ~ spl102_34 ),
inference(sat_conversion,[],[f2110]) ).
cnf(s63,plain,
~ spl102_5,
inference(rat,[],[s4,s5]) ).
cnf(s64,plain,
spl102_4,
inference(rat,[],[s3,s5]) ).
cnf(s65,plain,
spl102_3,
inference(rat,[],[s2,s5]) ).
cnf(s66,plain,
spl102_1,
inference(rat,[],[s1,s5]) ).
cnf(s67,plain,
~ spl102_7,
inference(rat,[],[s13,s48,s24,s23,s36,s37,s63,s65,s66,s64]) ).
cnf(s68,plain,
spl102_26,
inference(rat,[],[s29,s65,s67]) ).
cnf(s69,plain,
~ spl102_27,
inference(rat,[],[s35,s65,s64,s67]) ).
cnf(s70,plain,
spl102_6,
inference(rat,[],[s6,s65,s67]) ).
cnf(s71,plain,
spl102_29,
inference(rat,[],[s26,s66,s69]) ).
cnf(s72,plain,
spl102_28,
inference(rat,[],[s25,s66,s69]) ).
cnf(s75,plain,
spl102_34,
inference(rat,[],[s33,s64,s72]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s62,s69,s71,s68,s70,s66,s65,s63,s75,s72]) ).
fof(f2111,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX025+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 14:55:17 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 7.00/1.83 % (2691662)Detected formulas, will run a generic FOF schedule.
% 7.00/1.83 % (2691670)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3811191190:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.00/1.83 % (2691670)Refutation not found, incomplete strategy
% 7.00/1.83 % (2691670)------------------------------
% 7.00/1.83 % (2691670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691670)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691670)Termination reason: Refutation not found, incomplete strategy
% 7.00/1.83 % (2691670)Time elapsed: 0.003 s
% 7.00/1.83 % (2691670)Peak memory usage: 89 MB
% 7.00/1.83 % (2691670)Instructions burned: 6 (million)
% 7.00/1.83 % (2691669)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=1058929710:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.00/1.83 % (2691667)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=4167198073:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.00/1.83 % (2691668)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=1764442821:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.00/1.83 % (2691673)dis-21_1_sil=8000:lcm=predicate:random_seed=2065778084: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)
% 7.00/1.83 % (2691672)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1922155394:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.00/1.83 % (2691671)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=7752856:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.00/1.83 % (2691671)Instruction limit reached!
% 7.00/1.83 % (2691671)------------------------------
% 7.00/1.83 % (2691671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691671)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691671)Termination reason: Instruction limit
% 7.00/1.83 % (2691671)Termination phase: Saturation
% 7.00/1.83 % (2691671)Time elapsed: 0.075 s
% 7.00/1.83 % (2691671)Peak memory usage: 88 MB
% 7.00/1.83 % (2691671)Instructions burned: 119 (million)
% 7.00/1.83 % (2691673)Instruction limit reached!
% 7.00/1.83 % (2691673)------------------------------
% 7.00/1.83 % (2691673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691673)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691673)Termination reason: Instruction limit
% 7.00/1.83 % (2691673)Termination phase: Saturation
% 7.00/1.83 % (2691673)Time elapsed: 0.079 s
% 7.00/1.83 % (2691673)Peak memory usage: 90 MB
% 7.00/1.83 % (2691673)Instructions burned: 130 (million)
% 7.00/1.83 % (2691672)Instruction limit reached!
% 7.00/1.83 % (2691672)------------------------------
% 7.00/1.83 % (2691672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691672)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691672)Termination reason: Instruction limit
% 7.00/1.83 % (2691672)Termination phase: Saturation
% 7.00/1.83 % (2691672)Time elapsed: 0.102 s
% 7.00/1.83 % (2691672)Peak memory usage: 90 MB
% 7.00/1.83 % (2691672)Instructions burned: 140 (million)
% 7.00/1.83 % (2691670)------------------------------
% 7.00/1.83 % (2691670)------------------------------
% 7.00/1.83 % (2691682)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1781593109:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.00/1.83 % (2691681)lrs+10_1_sil=8000:sp=occurrence:random_seed=2052605335:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 7.00/1.83 % (2691683)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3793827821:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.00/1.83 % (2691682)Instruction limit reached!
% 7.00/1.83 % (2691682)------------------------------
% 7.00/1.83 % (2691682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691682)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691682)Termination reason: Instruction limit
% 7.00/1.83 % (2691682)Termination phase: Saturation
% 7.00/1.83 % (2691682)Time elapsed: 0.048 s
% 7.00/1.83 % (2691682)Peak memory usage: 91 MB
% 7.00/1.83 % (2691682)Instructions burned: 158 (million)
% 7.00/1.83 % (2691684)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=1752431641:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.00/1.83 % (2691689)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=285229795:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.00/1.83 % (2691681)Instruction limit reached!
% 7.00/1.83 % (2691681)------------------------------
% 7.00/1.83 % (2691681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691681)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691681)Termination reason: Instruction limit
% 7.00/1.83 % (2691681)Termination phase: Saturation
% 7.00/1.83 % (2691681)Time elapsed: 0.177 s
% 7.00/1.83 % (2691681)Peak memory usage: 92 MB
% 7.00/1.83 % (2691681)Instructions burned: 286 (million)
% 7.00/1.83 % (2691684)Instruction limit reached!
% 7.00/1.83 % (2691684)------------------------------
% 7.00/1.83 % (2691684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691684)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691684)Termination reason: Instruction limit
% 7.00/1.83 % (2691684)Termination phase: Saturation
% 7.00/1.83 % (2691684)Time elapsed: 0.147 s
% 7.00/1.83 % (2691684)Peak memory usage: 92 MB
% 7.00/1.83 % (2691684)Instructions burned: 249 (million)
% 7.00/1.83 % (2691683)Instruction limit reached!
% 7.00/1.83 % (2691683)------------------------------
% 7.00/1.83 % (2691683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691683)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691683)Termination reason: Instruction limit
% 7.00/1.83 % (2691683)Termination phase: Saturation
% 7.00/1.83 % (2691683)Time elapsed: 0.215 s
% 7.00/1.83 % (2691683)Peak memory usage: 92 MB
% 7.00/1.83 % (2691683)Instructions burned: 326 (million)
% 7.00/1.83 % (2691689)Instruction limit reached!
% 7.00/1.83 % (2691689)------------------------------
% 7.00/1.83 % (2691689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691689)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691689)Termination reason: Instruction limit
% 7.00/1.83 % (2691689)Termination phase: Saturation
% 7.00/1.83 % (2691689)Time elapsed: 0.095 s
% 7.00/1.83 % (2691689)Peak memory usage: 90 MB
% 7.00/1.83 % (2691689)Instructions burned: 297 (million)
% 7.00/1.83 % (2691691)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1743584968:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 7.00/1.83 % (2691692)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2749367377:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.00/1.83 % (2691694)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1498923027:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 7.00/1.83 % (2691693)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=82503633:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 7.00/1.83 % (2691694)Instruction limit reached!
% 7.00/1.83 % (2691694)------------------------------
% 7.00/1.83 % (2691694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691694)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691694)Termination reason: Instruction limit
% 7.00/1.83 % (2691694)Termination phase: Saturation
% 7.00/1.83 % (2691694)Time elapsed: 0.031 s
% 7.00/1.83 % (2691694)Peak memory usage: 89 MB
% 7.00/1.83 % (2691694)Instructions burned: 116 (million)
% 7.00/1.83 % (2691692)Instruction limit reached!
% 7.00/1.83 % (2691692)------------------------------
% 7.00/1.83 % (2691692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691692)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691692)Termination reason: Instruction limit
% 7.00/1.83 % (2691692)Termination phase: Saturation
% 7.00/1.83 % (2691692)Time elapsed: 0.078 s
% 7.00/1.83 % (2691692)Peak memory usage: 91 MB
% 7.00/1.83 % (2691692)Instructions burned: 114 (million)
% 7.00/1.83 % (2691693)Instruction limit reached!
% 7.00/1.83 % (2691693)------------------------------
% 7.00/1.83 % (2691693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.00/1.83 % (2691693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.00/1.83 % (2691693)CaDiCaL version: 2.1.3
% 7.00/1.83 % (2691693)Termination reason: Instruction limit
% 7.00/1.83 % (2691693)Termination phase: Saturation
% 7.00/1.83 % (2691693)Time elapsed: 0.066 s
% 7.00/1.83 % (2691693)Peak memory usage: 89 MB
% 7.00/1.83 % (2691693)Instructions burned: 128 (million)
% 7.00/1.83 % (2691699)lrs+10_1_sil=8000:sp=occurrence:random_seed=427896087:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 7.00/1.84 % (2691667)First to succeed.
% 7.00/1.84 % (2691667)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2691662"
% 7.00/1.84 % (2691700)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3614908577:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 7.00/1.84 % (2691701)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2003397092:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 7.00/1.84 % (2691667)Refutation found. Thanks to Tanya!
% 7.00/1.84 % SZS status Theorem for theBenchmark
% 7.00/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 8.91/2.02 % (2691667)------------------------------
% 8.91/2.02 % (2691667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.91/2.02 % (2691667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.91/2.02 % (2691667)CaDiCaL version: 2.1.3
% 8.91/2.02 % (2691667)Termination reason: Refutation
% 8.91/2.02 % (2691667)Time elapsed: 0.753 s
% 8.91/2.02 % (2691667)Peak memory usage: 131 MB
% 8.91/2.02 % (2691667)Instructions burned: 1147 (million)
% 8.91/2.02 % (2691667)------------------------------
% 8.91/2.02 % (2691667)------------------------------
% 8.91/2.02 % (2691662)Success in time 1.187 s
% 8.91/2.02 % Vampire exiting
%------------------------------------------------------------------------------