%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC343-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 01:05:38 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 41
% Syntax : Number of formulae : 210 ( 32 unt; 20 def)
% Number of atoms : 701 ( 184 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 877 ( 386 ~; 471 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 21 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
app(sk3,sk5) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
sk4 = app(sk3,sk5),
inference(reorient_equations,[],[f207]) ).
fof(f209,negated_conjecture,
strictorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk5
| ~ ssItem(X2)
| ~ ssList(X3)
| app(X3,cons(X2,nil)) != sk3
| ~ lt(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) != sk5
| ~ ssItem(X2)
| ~ ssList(X3)
| sk3 != app(X3,cons(X2,nil))
| ~ lt(X2,X0) ),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
( nil = sk4
| nil != sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f214,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f216,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f215]) ).
fof(f217,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f218,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f217]) ).
fof(f219,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f220,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f222,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f221]) ).
fof(f223,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f224,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f223]) ).
fof(f225,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(sk9(X0),cons(sk8(X0),nil)) = sk1
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f226,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| sk1 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f225]) ).
fof(f227,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f228,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil = sk1 ),
inference(reorient_equations,[],[f227]) ).
fof(f229,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
fof(f230,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f229]) ).
fof(f231,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
fof(f232,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f231]) ).
fof(f233,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f233]) ).
fof(f235,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_23) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f235]) ).
fof(f237,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| app(sk9(X0),cons(sk8(X0),nil)) = sk1
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_24) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| sk1 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f237]) ).
fof(f239,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| app(sk1,X0) != sk2
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_25) ).
fof(f240,plain,
! [X0] :
( ~ ssList(X0)
| sk2 != app(sk1,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk1)
| nil != sk2 ),
inference(reorient_equations,[],[f239]) ).
fof(f243,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f214,f204,f205,f205,f205]) ).
fof(f244,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f216,f204,f205,f205,f204]) ).
fof(f245,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f218,f204,f205,f205,f205]) ).
fof(f246,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f220,f204,f205,f205,f205]) ).
fof(f247,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f222,f204,f205,f205,f205]) ).
fof(f248,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f224,f204,f205,f205,f205]) ).
fof(f249,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f226,f204,f205,f205,f205,f205]) ).
fof(f250,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(definition_unfolding,[],[f228,f204,f205,f205,f205]) ).
fof(f251,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk7(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f230,f204,f205,f205,f204]) ).
fof(f252,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f232,f204,f205,f205,f204]) ).
fof(f253,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f234,f204,f205,f205,f204]) ).
fof(f254,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| ssList(sk9(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f236,f204,f205,f205,f204]) ).
fof(f255,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f238,f204,f205,f205,f205,f204]) ).
fof(f256,plain,
! [X0] :
( ~ ssList(X0)
| sk4 != app(sk3,X0)
| lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(definition_unfolding,[],[f240,f204,f205,f205,f204]) ).
fof(f436,plain,
~ ssList(sk5),
inference(consistent_polarity_flipping,[],[f206]) ).
fof(f437,plain,
! [X2,X3,X0,X1] :
( sk3 != app(X3,cons(X2,nil))
| ssList(X1)
| app(cons(X0,nil),X1) != sk5
| ~ ssItem(X2)
| ssList(X3)
| ~ ssItem(X0)
| lt(X2,X0) ),
inference(consistent_polarity_flipping,[],[f211]) ).
fof(f438,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f243]) ).
fof(f439,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk6(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f244]) ).
fof(f440,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ~ ssList(sk7(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f245]) ).
fof(f441,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f246]) ).
fof(f442,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f247]) ).
fof(f443,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ~ ssList(sk9(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f248]) ).
fof(f444,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f249]) ).
fof(f445,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ~ lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| nil = sk3 ),
inference(consistent_polarity_flipping,[],[f250]) ).
fof(f446,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ~ ssList(sk7(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f251]) ).
fof(f447,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f252]) ).
fof(f448,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ssItem(sk8(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f253]) ).
fof(f449,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ~ ssList(sk9(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f254]) ).
fof(f450,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f255]) ).
fof(f451,plain,
! [X0] :
( ssList(X0)
| sk4 != app(sk3,X0)
| ~ lt(sk8(X0),sk6(X0))
| ~ strictorderedP(sk3)
| nil != sk4 ),
inference(consistent_polarity_flipping,[],[f256]) ).
fof(f459,definition,
( spl0_1
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f463,definition,
( spl0_2
<=> strictorderedP(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f467,definition,
( spl0_3
<=> ! [X0] :
( ssList(X0)
| ~ lt(sk8(X0),sk6(X0))
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f468,plain,
( ! [X0] :
( ~ lt(sk8(X0),sk6(X0))
| ssList(X0)
| sk4 != app(sk3,X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f469,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f451,f467,f463,f459]) ).
fof(f471,definition,
( spl0_4
<=> ! [X0] :
( ssList(X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f472,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| sk3 = app(sk9(X0),cons(sk8(X0),nil))
| ssList(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f473,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f450,f471,f463,f459]) ).
fof(f475,definition,
( spl0_5
<=> ! [X0] :
( ssList(X0)
| ~ ssList(sk9(X0))
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f476,plain,
( ! [X0] :
( ~ ssList(sk9(X0))
| ssList(X0)
| sk4 != app(sk3,X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f477,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f449,f475,f463,f459]) ).
fof(f479,definition,
( spl0_6
<=> ! [X0] :
( ssList(X0)
| ssItem(sk8(X0))
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f480,plain,
( ! [X0] :
( ssItem(sk8(X0))
| ssList(X0)
| sk4 != app(sk3,X0) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f481,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f448,f479,f463,f459]) ).
fof(f483,definition,
( spl0_7
<=> ! [X0] :
( ssList(X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f484,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| app(cons(sk6(X0),nil),sk7(X0)) = X0
| ssList(X0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f485,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f447,f483,f463,f459]) ).
fof(f487,definition,
( spl0_8
<=> ! [X0] :
( ssList(X0)
| ~ ssList(sk7(X0))
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f488,plain,
( ! [X0] :
( ~ ssList(sk7(X0))
| ssList(X0)
| sk4 != app(sk3,X0) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f489,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f446,f487,f463,f459]) ).
fof(f491,definition,
( spl0_9
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f494,plain,
( spl0_9
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f445,f467,f463,f491]) ).
fof(f495,plain,
( spl0_9
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f444,f471,f463,f491]) ).
fof(f496,plain,
( spl0_9
| ~ spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f443,f475,f463,f491]) ).
fof(f497,plain,
( spl0_9
| ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f442,f479,f463,f491]) ).
fof(f498,plain,
( spl0_9
| ~ spl0_2
| spl0_7 ),
inference(avatar_split_clause,[],[f441,f483,f463,f491]) ).
fof(f499,plain,
( spl0_9
| ~ spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f440,f487,f463,f491]) ).
fof(f501,definition,
( spl0_10
<=> ! [X0] :
( ssList(X0)
| ssItem(sk6(X0))
| sk4 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f502,plain,
( ! [X0] :
( ssItem(sk6(X0))
| ssList(X0)
| sk4 != app(sk3,X0) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f503,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f439,f501,f463,f459]) ).
fof(f504,plain,
( spl0_9
| ~ spl0_2
| spl0_10 ),
inference(avatar_split_clause,[],[f438,f501,f463,f491]) ).
fof(f505,plain,
( ~ spl0_9
| spl0_1 ),
inference(avatar_split_clause,[],[f212,f459,f491]) ).
fof(f506,plain,
spl0_2,
inference(avatar_split_clause,[],[f209,f463]) ).
fof(f549,plain,
( sk4 != sk4
| sk3 = app(sk9(sk5),cons(sk8(sk5),nil))
| ssList(sk5)
| ~ spl0_4 ),
inference(superposition,[],[f472,f208]) ).
fof(f550,plain,
( sk3 = app(sk9(sk5),cons(sk8(sk5),nil))
| ssList(sk5)
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f549]) ).
fof(f552,definition,
( spl0_20
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f554,plain,
( ssList(sk5)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f556,definition,
( spl0_21
<=> sk3 = app(sk9(sk5),cons(sk8(sk5),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f558,plain,
( sk3 = app(sk9(sk5),cons(sk8(sk5),nil))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( spl0_20
| spl0_21
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f550,f471,f556,f552]) ).
fof(f560,plain,
( sk4 != sk4
| sk5 = app(cons(sk6(sk5),nil),sk7(sk5))
| ssList(sk5)
| ~ spl0_7 ),
inference(superposition,[],[f484,f208]) ).
fof(f561,plain,
( sk5 = app(cons(sk6(sk5),nil),sk7(sk5))
| ssList(sk5)
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f560]) ).
fof(f563,definition,
( spl0_22
<=> sk5 = app(cons(sk6(sk5),nil),sk7(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f565,plain,
( sk5 = app(cons(sk6(sk5),nil),sk7(sk5))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f566,plain,
( spl0_20
| spl0_22
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f561,f483,f563,f552]) ).
fof(f567,plain,
( ! [X0,X1] :
( sk3 != sk3
| ssList(X0)
| sk5 != app(cons(X1,nil),X0)
| ~ ssItem(sk8(sk5))
| ssList(sk9(sk5))
| ~ ssItem(X1)
| lt(sk8(sk5),X1) )
| ~ spl0_21 ),
inference(superposition,[],[f437,f558]) ).
fof(f568,plain,
( ! [X0,X1] :
( ssList(X0)
| sk5 != app(cons(X1,nil),X0)
| ~ ssItem(sk8(sk5))
| ssList(sk9(sk5))
| ~ ssItem(X1)
| lt(sk8(sk5),X1) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f567]) ).
fof(f570,definition,
( spl0_23
<=> ssList(sk9(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f572,plain,
( ssList(sk9(sk5))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f574,definition,
( spl0_24
<=> ssItem(sk8(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f576,plain,
( ~ ssItem(sk8(sk5))
| spl0_24 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f578,definition,
( spl0_25
<=> ! [X0,X1] :
( ssList(X0)
| lt(sk8(sk5),X1)
| ~ ssItem(X1)
| sk5 != app(cons(X1,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f579,plain,
( ! [X0,X1] :
( sk5 != app(cons(X1,nil),X0)
| lt(sk8(sk5),X1)
| ~ ssItem(X1)
| ssList(X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f580,plain,
( spl0_23
| ~ spl0_24
| spl0_25
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f568,f556,f578,f574,f570]) ).
fof(f583,plain,
( ssList(sk5)
| sk4 != app(sk3,sk5)
| ~ spl0_6
| spl0_24 ),
inference(resolution,[],[f480,f576]) ).
fof(f585,definition,
( spl0_26
<=> sk4 = app(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f587,plain,
( sk4 != app(sk3,sk5)
| spl0_26 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f588,plain,
( ~ spl0_26
| spl0_20
| ~ spl0_6
| spl0_24 ),
inference(avatar_split_clause,[],[f583,f574,f479,f552,f585]) ).
fof(f589,plain,
( sk4 != sk4
| spl0_26 ),
inference(superposition,[],[f587,f208]) ).
fof(f590,plain,
( $false
| spl0_26 ),
inference(trivial_inequality_removal,[],[f589]) ).
fof(f591,plain,
spl0_26,
inference(avatar_contradiction_clause,[],[f590]) ).
fof(f592,plain,
( $false
| ~ spl0_20 ),
inference(resolution,[],[f554,f436]) ).
fof(f593,plain,
~ spl0_20,
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f594,plain,
( sk5 != sk5
| lt(sk8(sk5),sk6(sk5))
| ~ ssItem(sk6(sk5))
| ssList(sk7(sk5))
| ~ spl0_22
| ~ spl0_25 ),
inference(superposition,[],[f579,f565]) ).
fof(f595,plain,
( lt(sk8(sk5),sk6(sk5))
| ~ ssItem(sk6(sk5))
| ssList(sk7(sk5))
| ~ spl0_22
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f594]) ).
fof(f597,definition,
( spl0_27
<=> ssList(sk7(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f599,plain,
( ssList(sk7(sk5))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f601,definition,
( spl0_28
<=> ssItem(sk6(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f603,plain,
( ~ ssItem(sk6(sk5))
| spl0_28 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f605,definition,
( spl0_29
<=> lt(sk8(sk5),sk6(sk5)) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f607,plain,
( lt(sk8(sk5),sk6(sk5))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f609,plain,
( ssList(sk5)
| sk4 != app(sk3,sk5)
| ~ spl0_10
| spl0_28 ),
inference(resolution,[],[f603,f502]) ).
fof(f610,plain,
( ~ spl0_26
| spl0_20
| ~ spl0_10
| spl0_28 ),
inference(avatar_split_clause,[],[f609,f601,f501,f552,f585]) ).
fof(f611,plain,
( ssList(sk5)
| sk4 != app(sk3,sk5)
| ~ spl0_3
| ~ spl0_29 ),
inference(resolution,[],[f607,f468]) ).
fof(f612,plain,
( ~ spl0_26
| spl0_20
| ~ spl0_3
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f611,f605,f467,f552,f585]) ).
fof(f613,plain,
( ssList(sk5)
| sk4 != app(sk3,sk5)
| ~ spl0_5
| ~ spl0_23 ),
inference(resolution,[],[f572,f476]) ).
fof(f614,plain,
( ~ spl0_26
| spl0_20
| ~ spl0_5
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f613,f570,f475,f552,f585]) ).
fof(f617,plain,
( spl0_27
| ~ spl0_28
| spl0_29
| ~ spl0_22
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f595,f578,f563,f605,f601,f597]) ).
fof(f618,plain,
( ssList(sk5)
| sk4 != app(sk3,sk5)
| ~ spl0_8
| ~ spl0_27 ),
inference(resolution,[],[f599,f488]) ).
fof(f619,plain,
( ~ spl0_26
| spl0_20
| ~ spl0_8
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f618,f597,f487,f552,f585]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f469]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f473]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f477]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f481]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_7 ),
inference(sat_conversion,[],[f485]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f489]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f494]) ).
cnf(s8,plain,
( ~ spl0_2
| spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f495]) ).
cnf(s9,plain,
( ~ spl0_2
| spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f496]) ).
cnf(s10,plain,
( ~ spl0_2
| spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f497]) ).
cnf(s11,plain,
( ~ spl0_2
| spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f498]) ).
cnf(s12,plain,
( ~ spl0_2
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f499]) ).
cnf(s13,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_10 ),
inference(sat_conversion,[],[f503]) ).
cnf(s14,plain,
( ~ spl0_2
| spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f504]) ).
cnf(s15,plain,
( spl0_1
| ~ spl0_9 ),
inference(sat_conversion,[],[f505]) ).
cnf(s16,plain,
spl0_2,
inference(sat_conversion,[],[f506]) ).
cnf(s27,plain,
( ~ spl0_4
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f559]) ).
cnf(s28,plain,
( ~ spl0_7
| spl0_20
| spl0_22 ),
inference(sat_conversion,[],[f566]) ).
cnf(s29,plain,
( ~ spl0_21
| spl0_23
| ~ spl0_24
| spl0_25 ),
inference(sat_conversion,[],[f580]) ).
cnf(s31,plain,
( ~ spl0_6
| spl0_20
| spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f588]) ).
cnf(s32,plain,
spl0_26,
inference(sat_conversion,[],[f591]) ).
cnf(s33,plain,
~ spl0_20,
inference(sat_conversion,[],[f593]) ).
cnf(s35,plain,
( ~ spl0_10
| spl0_20
| ~ spl0_26
| spl0_28 ),
inference(sat_conversion,[],[f610]) ).
cnf(s36,plain,
( ~ spl0_3
| spl0_20
| ~ spl0_26
| ~ spl0_29 ),
inference(sat_conversion,[],[f612]) ).
cnf(s37,plain,
( ~ spl0_5
| spl0_20
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f614]) ).
cnf(s39,plain,
( ~ spl0_22
| ~ spl0_25
| spl0_27
| ~ spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f617]) ).
cnf(s40,plain,
( ~ spl0_8
| spl0_20
| ~ spl0_26
| ~ spl0_27 ),
inference(sat_conversion,[],[f619]) ).
cnf(s41,plain,
( ~ spl0_6
| spl0_24 ),
inference(rat,[],[s31,s32,s33]) ).
cnf(s42,plain,
( ~ spl0_7
| spl0_22 ),
inference(rat,[],[s28,s33]) ).
cnf(s43,plain,
( ~ spl0_4
| spl0_21 ),
inference(rat,[],[s27,s33]) ).
cnf(s48,plain,
( spl0_9
| spl0_10 ),
inference(rat,[],[s14,s16]) ).
cnf(s49,plain,
( ~ spl0_1
| spl0_10 ),
inference(rat,[],[s13,s16]) ).
cnf(s50,plain,
( spl0_8
| spl0_9 ),
inference(rat,[],[s12,s16]) ).
cnf(s51,plain,
( spl0_7
| spl0_9 ),
inference(rat,[],[s11,s16]) ).
cnf(s52,plain,
( spl0_6
| spl0_9 ),
inference(rat,[],[s10,s16]) ).
cnf(s53,plain,
( spl0_5
| spl0_9 ),
inference(rat,[],[s9,s16]) ).
cnf(s54,plain,
( spl0_4
| spl0_9 ),
inference(rat,[],[s8,s16]) ).
cnf(s55,plain,
( spl0_3
| spl0_9 ),
inference(rat,[],[s7,s16]) ).
cnf(s56,plain,
( ~ spl0_1
| spl0_8 ),
inference(rat,[],[s6,s16]) ).
cnf(s57,plain,
( ~ spl0_1
| spl0_7 ),
inference(rat,[],[s5,s16]) ).
cnf(s58,plain,
( ~ spl0_1
| spl0_6 ),
inference(rat,[],[s4,s16]) ).
cnf(s59,plain,
( ~ spl0_1
| spl0_5 ),
inference(rat,[],[s3,s16]) ).
cnf(s60,plain,
( ~ spl0_1
| spl0_4 ),
inference(rat,[],[s2,s16]) ).
cnf(s61,plain,
( ~ spl0_1
| spl0_3 ),
inference(rat,[],[s1,s16]) ).
cnf(s62,plain,
spl0_9,
inference(rat,[],[s29,s39,s36,s43,s37,s41,s42,s40,s35,s55,s54,s53,s52,s51,s50,s48,s33,s32]) ).
cnf(s63,plain,
spl0_1,
inference(rat,[],[s15,s62]) ).
cnf(s64,plain,
spl0_10,
inference(rat,[],[s49,s63]) ).
cnf(s65,plain,
spl0_8,
inference(rat,[],[s56,s63]) ).
cnf(s66,plain,
spl0_7,
inference(rat,[],[s57,s63]) ).
cnf(s67,plain,
spl0_6,
inference(rat,[],[s58,s63]) ).
cnf(s68,plain,
spl0_5,
inference(rat,[],[s59,s63]) ).
cnf(s69,plain,
spl0_4,
inference(rat,[],[s60,s63]) ).
cnf(s70,plain,
spl0_3,
inference(rat,[],[s61,s63]) ).
cnf(s71,plain,
spl0_28,
inference(rat,[],[s35,s32,s33,s64]) ).
cnf(s72,plain,
~ spl0_27,
inference(rat,[],[s40,s32,s33,s65]) ).
cnf(s73,plain,
spl0_22,
inference(rat,[],[s42,s66]) ).
cnf(s74,plain,
spl0_24,
inference(rat,[],[s41,s67]) ).
cnf(s75,plain,
~ spl0_23,
inference(rat,[],[s37,s32,s33,s68]) ).
cnf(s76,plain,
spl0_21,
inference(rat,[],[s43,s69]) ).
cnf(s77,plain,
~ spl0_29,
inference(rat,[],[s36,s32,s33,s70]) ).
cnf(s78,plain,
~ spl0_25,
inference(rat,[],[s39,s77,s71,s72,s73]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s29,s78,s74,s75,s76]) ).
fof(f620,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC343-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 09:11:30 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.26 % (2904445)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (2904456)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3904597314:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.26 % (2904451)% WARNING: option uhcvi not known.
% 0.20/0.26 % (2904456) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2904445-2904456"...
% 0.20/0.26 % (2904456)...printing done.
% 0.20/0.26 % (2904452)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4201807736:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.26 % (2904450)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2773121268_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.26 % (2904451)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2765719991:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.26 % (2904453)dis+10_1_sil=32000:sp=arity:random_seed=3453809952:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.26 % (2904456)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2904456)------------------------------
% 0.20/0.27 % (2904456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2904456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2904456)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2904456)Termination reason: Refutation
% 0.20/0.27 % (2904456)Time elapsed: 0.006 s
% 0.20/0.27 % (2904456)Peak memory usage: 13 MB
% 0.20/0.27 % (2904456)Instructions burned: 16 (million)
% 0.20/0.27 % (2904445)Success in time 0.031 s
% 0.20/0.27 % Vampire exiting
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