%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC409-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:03:51 PM UTC 2026
% Result : Unsatisfiable 6.64s 1.78s
% Output : Refutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 28
% Syntax : Number of formulae : 116 ( 21 unt; 10 def)
% Number of atoms : 404 ( 56 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 522 ( 234 ~; 281 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f77,axiom,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause77) ).
fof(f78,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause78) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f107,axiom,
! [X0] :
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,nil),X1) ),
inference(reorient_equations,[],[f125]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause138) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause141) ).
fof(f173,axiom,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X2 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X0,X1),X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X2)
| memberP(X1,X2)
| X0 = X2 ),
inference(reorient_equations,[],[f173]) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
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,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(X1,cons(X0,nil)) = sk3
| app(cons(X0,nil),X1) != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| sk3 = app(X1,cons(X0,nil))
| app(cons(X0,nil),X1) != sk4 ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
memberP(sk2,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
~ memberP(sk1,sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f214,plain,
memberP(sk4,sk5),
inference(definition_unfolding,[],[f209,f204]) ).
fof(f215,plain,
~ memberP(sk3,sk5),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f225,plain,
! [X2,X1] :
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f240,definition,
! [X0] : sF0(X0) = cons(X0,nil),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f241,plain,
! [X0] : cons(X0,nil) = sF0(X0),
inference(reorient_equations,[],[f240]) ).
fof(f242,definition,
! [X0,X1] : sF1(X1,X0) = app(X1,sF0(X0)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f243,plain,
! [X0,X1] : app(X1,sF0(X0)) = sF1(X1,X0),
inference(reorient_equations,[],[f242]) ).
fof(f244,definition,
! [X0,X1] : sF2(X0,X1) = app(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f245,plain,
! [X0,X1] : app(sF0(X0),X1) = sF2(X0,X1),
inference(reorient_equations,[],[f244]) ).
fof(f246,plain,
! [X0,X1] :
( sk4 != sF2(X0,X1)
| ~ ssList(X1)
| sk3 = sF1(X1,X0)
| ~ ssItem(X0) ),
inference(definition_folding,[],[f207,f245,f241,f243,f241]) ).
fof(f249,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f254,definition,
( spl3_1
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f255,plain,
( nil = sk4
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( nil != sk4
| spl3_1 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl3_2
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f260,plain,
( nil = sk3
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f211,f258,f254]) ).
fof(f267,definition,
( spl3_4
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f268,plain,
( ssList(nil)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f303,plain,
spl3_4,
inference(avatar_split_clause,[],[f8,f267]) ).
fof(f308,plain,
! [X2,X0,X1] :
( memberP(sF1(X0,X1),X2)
| ~ ssList(sF0(X1))
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ memberP(X0,X2) ),
inference(superposition,[],[f151,f243]) ).
fof(f316,plain,
! [X2,X0,X1] :
( memberP(sF1(X0,X1),X2)
| ~ ssList(sF0(X1))
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ memberP(sF0(X1),X2) ),
inference(superposition,[],[f152,f243]) ).
fof(f396,plain,
! [X0] :
( ssList(sF0(X0))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[],[f86,f241]) ).
fof(f397,plain,
( ! [X0] :
( ssList(sF0(X0))
| ~ ssItem(X0) )
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f396,f268]) ).
fof(f408,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| nil = sk4 ),
inference(resolution,[],[f107,f203]) ).
fof(f420,plain,
( ~ memberP(nil,sk5)
| ~ spl3_2 ),
inference(superposition,[],[f215,f260]) ).
fof(f426,definition,
( spl3_17
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f427,plain,
( ssList(tl(sk4))
| ~ spl3_17 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
( ~ ssList(tl(sk4))
| spl3_17 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f433,plain,
( ~ ssList(sk4)
| nil = sk4
| spl3_17 ),
inference(resolution,[],[f428,f77]) ).
fof(f434,plain,
( nil = sk4
| spl3_17 ),
inference(forward_subsumption_resolution,[],[f433,f203]) ).
fof(f435,plain,
( $false
| spl3_1
| spl3_17 ),
inference(forward_subsumption_resolution,[],[f434,f256]) ).
fof(f436,plain,
( spl3_1
| spl3_17 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f438,plain,
( memberP(nil,sk5)
| ~ spl3_1 ),
inference(superposition,[],[f214,f255]) ).
fof(f442,plain,
( $false
| ~ spl3_1
| ~ spl3_2 ),
inference(forward_subsumption_resolution,[],[f438,f420]) ).
fof(f443,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f445,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| spl3_1 ),
inference(forward_subsumption_resolution,[],[f408,f256]) ).
fof(f457,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| ~ ssList(tl(sk4))
| ~ ssItem(hd(sk4))
| ~ ssItem(X0)
| memberP(tl(sk4),X0)
| hd(sk4) = X0 )
| spl3_1 ),
inference(superposition,[],[f174,f445]) ).
fof(f458,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| ~ ssItem(hd(sk4))
| ~ ssItem(X0)
| memberP(tl(sk4),X0)
| hd(sk4) = X0 )
| spl3_1
| ~ spl3_17 ),
inference(forward_subsumption_resolution,[],[f457,f427]) ).
fof(f460,definition,
( spl3_19
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition]) ).
fof(f461,plain,
( ssItem(hd(sk4))
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f462,plain,
( ~ ssItem(hd(sk4))
| spl3_19 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f464,definition,
( spl3_20
<=> ! [X0] :
( ~ memberP(sk4,X0)
| hd(sk4) = X0
| memberP(tl(sk4),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl3_20])],[avatar_definition]) ).
fof(f465,plain,
( ! [X0] :
( memberP(tl(sk4),X0)
| hd(sk4) = X0
| ~ memberP(sk4,X0)
| ~ ssItem(X0) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f466,plain,
( ~ spl3_19
| spl3_20
| spl3_1
| ~ spl3_17 ),
inference(avatar_split_clause,[],[f458,f426,f254,f464,f460]) ).
fof(f580,plain,
( ~ ssList(sk4)
| nil = sk4
| spl3_19 ),
inference(resolution,[],[f78,f462]) ).
fof(f585,plain,
( nil = sk4
| spl3_19 ),
inference(forward_subsumption_resolution,[],[f580,f203]) ).
fof(f587,plain,
( $false
| spl3_1
| spl3_19 ),
inference(forward_subsumption_resolution,[],[f585,f256]) ).
fof(f588,plain,
( spl3_1
| spl3_19 ),
inference(avatar_contradiction_clause,[],[f587]) ).
fof(f596,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(hd(sk4),X0) = app(cons(hd(sk4),nil),X0) )
| ~ spl3_19 ),
inference(resolution,[],[f461,f126]) ).
fof(f597,plain,
( ! [X0] :
( cons(hd(sk4),X0) = app(sF0(hd(sk4)),X0)
| ~ ssList(X0) )
| ~ spl3_19 ),
inference(forward_demodulation,[],[f596,f241]) ).
fof(f598,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(hd(sk4),X0) = sF2(hd(sk4),X0) )
| ~ spl3_19 ),
inference(forward_demodulation,[],[f597,f245]) ).
fof(f604,plain,
( cons(hd(sk4),tl(sk4)) = sF2(hd(sk4),tl(sk4))
| ~ spl3_17
| ~ spl3_19 ),
inference(resolution,[],[f598,f427]) ).
fof(f623,plain,
! [X0] :
( memberP(sF0(X0),X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f249,f241]) ).
fof(f629,plain,
( ! [X0] :
( memberP(sF0(X0),X0)
| ~ ssItem(X0) )
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f623,f268]) ).
fof(f655,plain,
( sk4 = sF2(hd(sk4),tl(sk4))
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(forward_demodulation,[],[f604,f445]) ).
fof(f663,plain,
( sk4 != sk4
| ~ ssList(tl(sk4))
| sk3 = sF1(tl(sk4),hd(sk4))
| ~ ssItem(hd(sk4))
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(superposition,[],[f246,f655]) ).
fof(f664,plain,
( ~ ssList(tl(sk4))
| sk3 = sF1(tl(sk4),hd(sk4))
| ~ ssItem(hd(sk4))
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(trivial_inequality_removal,[],[f663]) ).
fof(f665,plain,
( sk3 = sF1(tl(sk4),hd(sk4))
| ~ ssItem(hd(sk4))
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(forward_subsumption_resolution,[],[f664,f427]) ).
fof(f667,plain,
( sk3 = sF1(tl(sk4),hd(sk4))
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(forward_subsumption_resolution,[],[f665,f461]) ).
fof(f669,definition,
( spl3_29
<=> ssList(sF0(hd(sk4))) ),
introduced(definition,[new_symbols(definition,[spl3_29])],[avatar_definition]) ).
fof(f670,plain,
( ssList(sF0(hd(sk4)))
| ~ spl3_29 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f671,plain,
( ~ ssList(sF0(hd(sk4)))
| spl3_29 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f677,plain,
( ~ ssItem(hd(sk4))
| ~ spl3_4
| spl3_29 ),
inference(resolution,[],[f671,f397]) ).
fof(f678,plain,
( $false
| ~ spl3_4
| ~ spl3_19
| spl3_29 ),
inference(forward_subsumption_resolution,[],[f677,f461]) ).
fof(f679,plain,
( ~ spl3_4
| ~ spl3_19
| spl3_29 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f695,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssList(sF0(hd(sk4)))
| ~ ssList(tl(sk4))
| ~ ssItem(X0)
| ~ memberP(sF0(hd(sk4)),X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(superposition,[],[f316,f667]) ).
fof(f697,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssList(sF0(hd(sk4)))
| ~ ssList(tl(sk4))
| ~ ssItem(X0)
| ~ memberP(tl(sk4),X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19 ),
inference(superposition,[],[f308,f667]) ).
fof(f698,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssList(tl(sk4))
| ~ ssItem(X0)
| ~ memberP(tl(sk4),X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f697,f670]) ).
fof(f700,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssList(tl(sk4))
| ~ ssItem(X0)
| ~ memberP(sF0(hd(sk4)),X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f695,f670]) ).
fof(f701,plain,
( ! [X0] :
( ~ memberP(tl(sk4),X0)
| ~ ssItem(X0)
| memberP(sk3,X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f698,f427]) ).
fof(f703,plain,
( ! [X0] :
( ~ memberP(sF0(hd(sk4)),X0)
| ~ ssItem(X0)
| memberP(sk3,X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f700,f427]) ).
fof(f754,plain,
( ! [X0] :
( hd(sk4) = X0
| ~ memberP(sk4,X0)
| ~ ssItem(X0)
| ~ ssItem(X0)
| memberP(sk3,X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(resolution,[],[f465,f701]) ).
fof(f757,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| hd(sk4) = X0
| ~ ssItem(X0)
| memberP(sk3,X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(duplicate_literal_removal,[],[f754]) ).
fof(f759,plain,
( sk5 = hd(sk4)
| ~ ssItem(sk5)
| memberP(sk3,sk5)
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(resolution,[],[f757,f214]) ).
fof(f760,plain,
( sk5 = hd(sk4)
| memberP(sk3,sk5)
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f759,f208]) ).
fof(f761,plain,
( sk5 = hd(sk4)
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f760,f215]) ).
fof(f767,plain,
( ! [X0] :
( ~ memberP(sF0(sk5),X0)
| ~ ssItem(X0)
| memberP(sk3,X0) )
| spl3_1
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(superposition,[],[f703,f761]) ).
fof(f770,plain,
( ~ ssItem(sk5)
| memberP(sk3,sk5)
| ~ ssItem(sk5)
| spl3_1
| ~ spl3_4
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(resolution,[],[f767,f629]) ).
fof(f771,plain,
( ~ ssItem(sk5)
| memberP(sk3,sk5)
| spl3_1
| ~ spl3_4
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(duplicate_literal_removal,[],[f770]) ).
fof(f772,plain,
( memberP(sk3,sk5)
| spl3_1
| ~ spl3_4
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f771,f208]) ).
fof(f773,plain,
( $false
| spl3_1
| ~ spl3_4
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(forward_subsumption_resolution,[],[f772,f215]) ).
fof(f774,plain,
( spl3_1
| ~ spl3_4
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(avatar_contradiction_clause,[],[f773]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f261]) ).
cnf(s11,plain,
spl3_4,
inference(sat_conversion,[],[f303]) ).
cnf(s16,plain,
( spl3_1
| spl3_17 ),
inference(sat_conversion,[],[f436]) ).
cnf(s17,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f443]) ).
cnf(s19,plain,
( spl3_1
| ~ spl3_17
| ~ spl3_19
| spl3_20 ),
inference(sat_conversion,[],[f466]) ).
cnf(s26,plain,
( spl3_1
| spl3_19 ),
inference(sat_conversion,[],[f588]) ).
cnf(s32,plain,
( ~ spl3_4
| ~ spl3_19
| spl3_29 ),
inference(sat_conversion,[],[f679]) ).
cnf(s40,plain,
( spl3_1
| ~ spl3_4
| ~ spl3_17
| ~ spl3_19
| ~ spl3_20
| ~ spl3_29 ),
inference(sat_conversion,[],[f774]) ).
cnf(s51,plain,
spl3_1,
inference(rat,[],[s40,s19,s32,s16,s26,s11]) ).
cnf(s52,plain,
~ spl3_2,
inference(rat,[],[s17,s51]) ).
cnf(s53,plain,
$false,
inference(rat,[],[s1,s52,s51]) ).
fof(f775,plain,
$false,
inference(avatar_sat_refutation,[],[s53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC409-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.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 09:31:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 6.64/1.78 % (1659555)Input is clausal, will run a generic CNF schedule.
% 6.64/1.78 % (1659611)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3312430012:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.64/1.78 % (1659611)Instruction limit reached!
% 6.64/1.78 % (1659611)------------------------------
% 6.64/1.78 % (1659611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659611)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659611)Termination reason: Instruction limit
% 6.64/1.78 % (1659611)Termination phase: Saturation
% 6.64/1.78 % (1659611)Time elapsed: 0.033 s
% 6.64/1.78 % (1659611)Peak memory usage: 89 MB
% 6.64/1.78 % (1659611)Instructions burned: 115 (million)
% 6.64/1.78 % (1659610)lrs+10_1_sil=8000:sp=occurrence:random_seed=965474594:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.64/1.78 % (1659608)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=309728807:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.64/1.78 % (1659607)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=3188879205:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.64/1.78 % (1659609)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2549014342:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.64/1.78 % (1659612)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1029574624:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.64/1.78 % (1659613)dis-21_1_sil=8000:lcm=predicate:random_seed=259759574:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.64/1.78 % (1659613)Instruction limit reached!
% 6.64/1.78 % (1659613)------------------------------
% 6.64/1.78 % (1659613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659613)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659613)Termination reason: Instruction limit
% 6.64/1.78 % (1659613)Termination phase: Saturation
% 6.64/1.78 % (1659613)Time elapsed: 0.054 s
% 6.64/1.78 % (1659613)Peak memory usage: 89 MB
% 6.64/1.78 % (1659613)Instructions burned: 119 (million)
% 6.64/1.78 % (1659610)Instruction limit reached!
% 6.64/1.78 % (1659610)------------------------------
% 6.64/1.78 % (1659610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659610)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659610)Termination reason: Instruction limit
% 6.64/1.78 % (1659610)Termination phase: Saturation
% 6.64/1.78 % (1659610)Time elapsed: 0.062 s
% 6.64/1.78 % (1659610)Peak memory usage: 90 MB
% 6.64/1.78 % (1659610)Instructions burned: 107 (million)
% 6.64/1.78 % (1659615)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3901108989:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.64/1.78 % (1659615)Instruction limit reached!
% 6.64/1.78 % (1659615)------------------------------
% 6.64/1.78 % (1659615)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659615)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659615)Termination reason: Instruction limit
% 6.64/1.78 % (1659615)Termination phase: Saturation
% 6.64/1.78 % (1659615)Time elapsed: 0.043 s
% 6.64/1.78 % (1659615)Peak memory usage: 88 MB
% 6.64/1.78 % (1659615)Instructions burned: 146 (million)
% 6.64/1.78 % (1659612)Instruction limit reached!
% 6.64/1.78 % (1659612)------------------------------
% 6.64/1.78 % (1659612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659612)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659612)Termination reason: Instruction limit
% 6.64/1.78 % (1659612)Termination phase: Saturation
% 6.64/1.78 % (1659612)Time elapsed: 0.121 s
% 6.64/1.78 % (1659612)Peak memory usage: 90 MB
% 6.64/1.78 % (1659612)Instructions burned: 181 (million)
% 6.64/1.78 % (1659622)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2249425189:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 6.64/1.78 % (1659623)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4274179648:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.64/1.78 % (1659625)lrs+10_64_to=lpo:sil=8000:random_seed=1104728671:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 6.64/1.78 % (1659625)Instruction limit reached!
% 6.64/1.78 % (1659625)------------------------------
% 6.64/1.78 % (1659625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659625)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659625)Termination reason: Instruction limit
% 6.64/1.78 % (1659625)Termination phase: Saturation
% 6.64/1.78 % (1659625)Time elapsed: 0.036 s
% 6.64/1.78 % (1659625)Peak memory usage: 90 MB
% 6.64/1.78 % (1659625)Instructions burned: 127 (million)
% 6.64/1.78 % (1659626)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=537277928:avsq=on:i=194:fgj=on:bd=preordered_2997 on theBenchmark for (2997ds/194Mi)
% 6.64/1.78 % (1659622)Instruction limit reached!
% 6.64/1.78 % (1659622)------------------------------
% 6.64/1.78 % (1659622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659622)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659622)Termination reason: Instruction limit
% 6.64/1.78 % (1659622)Termination phase: Saturation
% 6.64/1.78 % (1659622)Time elapsed: 0.096 s
% 6.64/1.78 % (1659622)Peak memory usage: 91 MB
% 6.64/1.78 % (1659622)Instructions burned: 189 (million)
% 6.64/1.78 % (1659623)Instruction limit reached!
% 6.64/1.78 % (1659623)------------------------------
% 6.64/1.78 % (1659623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659623)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659623)Termination reason: Instruction limit
% 6.64/1.78 % (1659623)Termination phase: Saturation
% 6.64/1.78 % (1659623)Time elapsed: 0.118 s
% 6.64/1.78 % (1659623)Peak memory usage: 89 MB
% 6.64/1.78 % (1659623)Instructions burned: 220 (million)
% 6.64/1.78 % (1659626)Instruction limit reached!
% 6.64/1.78 % (1659626)------------------------------
% 6.64/1.78 % (1659626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659626)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659626)Termination reason: Instruction limit
% 6.64/1.78 % (1659626)Termination phase: Saturation
% 6.64/1.78 % (1659626)Time elapsed: 0.065 s
% 6.64/1.78 % (1659626)Peak memory usage: 90 MB
% 6.64/1.78 % (1659626)Instructions burned: 196 (million)
% 6.64/1.78 % (1659630)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=737239736:i=157:gtg=all_2996 on theBenchmark for (2996ds/157Mi)
% 6.64/1.78 % (1659634)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=29375870:i=107_2995 on theBenchmark for (2995ds/107Mi)
% 6.64/1.78 % (1659632)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=100938584:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 6.64/1.78 % (1659634)Instruction limit reached!
% 6.64/1.78 % (1659634)------------------------------
% 6.64/1.78 % (1659634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659634)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659634)Termination reason: Instruction limit
% 6.64/1.78 % (1659634)Termination phase: Saturation
% 6.64/1.78 % (1659634)Time elapsed: 0.036 s
% 6.64/1.78 % (1659634)Peak memory usage: 90 MB
% 6.64/1.78 % (1659634)Instructions burned: 109 (million)
% 6.64/1.78 % (1659633)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2945111247:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2995 on theBenchmark for (2995ds/106Mi)
% 6.64/1.78 % (1659630)Instruction limit reached!
% 6.64/1.78 % (1659630)------------------------------
% 6.64/1.78 % (1659630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659630)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659630)Termination reason: Instruction limit
% 6.64/1.78 % (1659630)Termination phase: Saturation
% 6.64/1.78 % (1659630)Time elapsed: 0.094 s
% 6.64/1.78 % (1659630)Peak memory usage: 91 MB
% 6.64/1.78 % (1659630)Instructions burned: 157 (million)
% 6.64/1.78 % (1659633)Instruction limit reached!
% 6.64/1.78 % (1659633)------------------------------
% 6.64/1.78 % (1659633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659633)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659633)Termination reason: Instruction limit
% 6.64/1.78 % (1659633)Termination phase: Saturation
% 6.64/1.78 % (1659633)Time elapsed: 0.057 s
% 6.64/1.78 % (1659633)Peak memory usage: 89 MB
% 6.64/1.78 % (1659633)Instructions burned: 108 (million)
% 6.64/1.78 % (1659638)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3717779841:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2994 on theBenchmark for (2994ds/242Mi)
% 6.64/1.78 % (1659640)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3978031486:cond=fast:i=5208:av=off_2993 on theBenchmark for (2993ds/5208Mi)
% 6.64/1.78 % (1659638)Instruction limit reached!
% 6.64/1.78 % (1659638)------------------------------
% 6.64/1.78 % (1659638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659638)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659638)Termination reason: Instruction limit
% 6.64/1.78 % (1659638)Termination phase: Saturation
% 6.64/1.78 % (1659638)Time elapsed: 0.079 s
% 6.64/1.78 % (1659638)Peak memory usage: 89 MB
% 6.64/1.78 % (1659638)Instructions burned: 242 (million)
% 6.64/1.78 % (1659641)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=2702496666:i=134:sd=2:doe=on:ss=axioms:sgt=14_2993 on theBenchmark for (2993ds/134Mi)
% 6.64/1.78 % (1659644)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=3236713979:i=499:bd=all_2992 on theBenchmark for (2992ds/499Mi)
% 6.64/1.78 % (1659607)First to succeed.
% 6.64/1.78 % (1659607)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1659555"
% 6.64/1.78 % (1659609)Also succeeded, but the first one will report.
% 6.64/1.78 % (1659641)Instruction limit reached!
% 6.64/1.78 % (1659641)------------------------------
% 6.64/1.78 % (1659641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659641)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659641)Termination reason: Instruction limit
% 6.64/1.78 % (1659641)Termination phase: Saturation
% 6.64/1.78 % (1659641)Time elapsed: 0.086 s
% 6.64/1.78 % (1659641)Peak memory usage: 90 MB
% 6.64/1.78 % (1659641)Instructions burned: 134 (million)
% 6.64/1.78 % (1659644)Instruction limit reached!
% 6.64/1.78 % (1659644)------------------------------
% 6.64/1.78 % (1659644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.64/1.78 % (1659644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.64/1.78 % (1659644)CaDiCaL version: 2.1.3
% 6.64/1.78 % (1659644)Termination reason: Instruction limit
% 6.64/1.78 % (1659644)Termination phase: Saturation
% 6.64/1.78 % (1659644)Time elapsed: 0.140 s
% 6.64/1.78 % (1659644)Peak memory usage: 97 MB
% 6.64/1.78 % (1659644)Instructions burned: 503 (million)
% 6.64/1.78 % (1659647)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=2256119947:i=191:fgj=on:bd=all_2991 on theBenchmark for (2991ds/191Mi)
% 6.64/1.78 % (1659648)lrs-11_32_anc=all:sil=8000:spb=goal_then_units:sac=on:random_seed=2483986999:i=264:kws=precedence:fsr=off_2990 on theBenchmark for (2990ds/264Mi)
% 6.64/1.78 % (1659607)Refutation found. Thanks to Tanya!
% 6.64/1.78 % SZS status Unsatisfiable for theBenchmark
% 6.64/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 8.61/1.98 % (1659607)------------------------------
% 8.61/1.98 % (1659607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.98 % (1659607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.98 % (1659607)CaDiCaL version: 2.1.3
% 8.61/1.98 % (1659607)Termination reason: Refutation
% 8.61/1.98 % (1659607)Time elapsed: 0.714 s
% 8.61/1.98 % (1659607)Peak memory usage: 131 MB
% 8.61/1.98 % (1659607)Instructions burned: 1059 (million)
% 8.61/1.98 % (1659607)------------------------------
% 8.61/1.98 % (1659607)------------------------------
% 8.61/1.98 % (1659555)Success in time 1.129 s
% 8.61/1.98 % Vampire exiting
%------------------------------------------------------------------------------