%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC284-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 01:03:17 PM UTC 2026
% Result : Unsatisfiable 0.83s 0.97s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 45
% Syntax : Number of formulae : 194 ( 33 unt; 19 def)
% Number of atoms : 605 ( 54 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 799 ( 388 ~; 392 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f62,axiom,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause62) ).
fof(f71,axiom,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f121,axiom,
! [X0,X1] :
( app(X0,X1) != nil
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X0 ),
inference(reorient_equations,[],[f121]) ).
fof(f149,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| memberP(cons(X1,X2),X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clause141) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
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/sandbox/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(f189,axiom,
! [X2,X3,X0,X1] :
( app(X0,cons(X1,X2)) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(X3)
| memberP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause175) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( memberP(sk6,sk8)
| memberP(sk7,sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f214,negated_conjecture,
( ~ leq(sk8,sk5)
| memberP(sk7,sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f215,negated_conjecture,
( ~ leq(sk8,sk5)
| ~ leq(sk5,sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f216,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f217,negated_conjecture,
( ssItem(sk9)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
fof(f218,negated_conjecture,
( cons(sk9,nil) = sk3
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
fof(f219,plain,
( sk3 = cons(sk9,nil)
| ~ neq(sk4,nil) ),
inference(reorient_equations,[],[f218]) ).
fof(f223,plain,
sk3 = app(app(sk6,cons(sk5,nil)),sk7),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f226,plain,
! [X2,X0,X1] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2)))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f189]) ).
fof(f227,plain,
! [X2,X1] :
( ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1)
| memberP(cons(X1,X2),X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f234,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(duplicate_literal_removal,[],[f227]) ).
fof(f244,definition,
( spl0_3
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f245,plain,
( ~ neq(sk4,nil)
| spl0_3 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f251,definition,
( spl0_5
<=> sk3 = cons(sk9,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f252,plain,
( sk3 = cons(sk9,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_split_clause,[],[f219,f251,f244]) ).
fof(f255,definition,
( spl0_6
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f256,plain,
( ssItem(sk9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f217,f255,f244]) ).
fof(f259,definition,
( spl0_7
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f262,definition,
( spl0_8
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f263,plain,
( nil = sk3
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f216,f262,f259]) ).
fof(f266,definition,
( spl0_9
<=> leq(sk5,sk8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f267,plain,
( ~ leq(sk5,sk8)
| spl0_9 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,definition,
( spl0_10
<=> leq(sk8,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f270,plain,
( ~ leq(sk8,sk5)
| spl0_10 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f271,plain,
( ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f215,f269,f266]) ).
fof(f273,definition,
( spl0_11
<=> memberP(sk7,sk8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f274,plain,
( memberP(sk7,sk8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( spl0_11
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f214,f269,f273]) ).
fof(f277,definition,
( spl0_12
<=> memberP(sk6,sk8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f278,plain,
( memberP(sk6,sk8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f280,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f212,f277,f273]) ).
fof(f290,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(resolution,[],[f102,f245]) ).
fof(f295,plain,
( ~ ssList(nil)
| nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f290,f203]) ).
fof(f296,plain,
( nil = sk4
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f295,f8]) ).
fof(f313,plain,
( spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f296,f244,f259]) ).
fof(f322,plain,
( nil != sk3
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil)))
| nil = app(sk6,cons(sk5,nil)) ),
inference(superposition,[],[f122,f223]) ).
fof(f325,plain,
( ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil)))
| nil = app(sk6,cons(sk5,nil))
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f322,f263]) ).
fof(f326,plain,
( ~ ssList(app(sk6,cons(sk5,nil)))
| nil = app(sk6,cons(sk5,nil))
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f325,f208]) ).
fof(f328,definition,
( spl0_15
<=> nil = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f329,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f331,definition,
( spl0_16
<=> ssList(app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f332,plain,
( ~ ssList(app(sk6,cons(sk5,nil)))
| spl0_16 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( spl0_15
| ~ spl0_16
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f326,f262,f331,f328]) ).
fof(f334,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| spl0_16 ),
inference(resolution,[],[f332,f85]) ).
fof(f335,plain,
( ~ ssList(cons(sk5,nil))
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f334,f207]) ).
fof(f339,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_16 ),
inference(resolution,[],[f335,f86]) ).
fof(f340,plain,
( ~ ssItem(sk5)
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f339,f8]) ).
fof(f341,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f340,f206]) ).
fof(f342,plain,
spl0_16,
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f387,definition,
( spl0_19
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f388,plain,
( ~ ssList(cons(sk5,nil))
| spl0_19 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f398,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| spl0_19 ),
inference(resolution,[],[f388,f86]) ).
fof(f399,plain,
( ~ ssItem(sk5)
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f398,f8]) ).
fof(f400,plain,
( $false
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f399,f206]) ).
fof(f401,plain,
spl0_19,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f412,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(superposition,[],[f151,f223]) ).
fof(f419,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(forward_subsumption_resolution,[],[f412,f208]) ).
fof(f422,definition,
( spl0_21
<=> ! [X0] :
( memberP(sk3,X0)
| ~ memberP(app(sk6,cons(sk5,nil)),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f423,plain,
( ! [X0] :
( ~ memberP(app(sk6,cons(sk5,nil)),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f424,plain,
( ~ spl0_16
| spl0_21 ),
inference(avatar_split_clause,[],[f419,f422,f331]) ).
fof(f456,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(superposition,[],[f152,f223]) ).
fof(f457,plain,
( ! [X0] :
( memberP(nil,X0)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(cons(sk5,nil),X0) )
| ~ spl0_15 ),
inference(superposition,[],[f152,f329]) ).
fof(f462,plain,
( ! [X0] :
( memberP(nil,X0)
| ~ ssList(cons(sk5,nil))
| ~ ssItem(X0)
| ~ memberP(cons(sk5,nil),X0) )
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f457,f207]) ).
fof(f463,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[],[f456,f208]) ).
fof(f464,plain,
( ! [X0] :
( ~ ssList(cons(sk5,nil))
| ~ ssItem(X0)
| ~ memberP(cons(sk5,nil),X0) )
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f462,f71]) ).
fof(f466,definition,
( spl0_23
<=> ! [X0] :
( memberP(sk3,X0)
| ~ memberP(sk7,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f467,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ memberP(sk7,X0)
| ~ ssItem(X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f468,plain,
( ~ spl0_16
| spl0_23 ),
inference(avatar_split_clause,[],[f463,f466,f331]) ).
fof(f470,definition,
( spl0_24
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(cons(sk5,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f471,plain,
( ! [X0] :
( ~ memberP(cons(sk5,nil),X0)
| ~ ssItem(X0) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f472,plain,
( spl0_24
| ~ spl0_19
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f464,f328,f387,f470]) ).
fof(f629,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(superposition,[],[f161,f223]) ).
fof(f668,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(forward_subsumption_resolution,[],[f629,f207]) ).
fof(f682,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[],[f668,f208]) ).
fof(f692,definition,
( spl0_30
<=> sk3 = app(sk6,app(cons(sk5,nil),sk7)) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f693,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f695,plain,
( ~ spl0_19
| spl0_30 ),
inference(avatar_split_clause,[],[f682,f692,f387]) ).
fof(f791,plain,
( ~ ssItem(sk5)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_24 ),
inference(resolution,[],[f471,f234]) ).
fof(f794,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ spl0_24 ),
inference(duplicate_literal_removal,[],[f791]) ).
fof(f795,plain,
( ~ ssList(nil)
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f794,f206]) ).
fof(f796,plain,
( $false
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f795,f8]) ).
fof(f797,plain,
~ spl0_24,
inference(avatar_contradiction_clause,[],[f796]) ).
fof(f802,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssList(nil)
| ~ ssItem(sk9)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk9 = X0 )
| ~ spl0_5 ),
inference(superposition,[],[f174,f252]) ).
fof(f807,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(sk9)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk9 = X0 )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f802,f8]) ).
fof(f809,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| memberP(nil,X0)
| sk9 = X0 )
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f807,f256]) ).
fof(f810,plain,
( ! [X0] :
( ~ memberP(sk3,X0)
| ~ ssItem(X0)
| sk9 = X0 )
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f809,f71]) ).
fof(f873,plain,
( ! [X0] :
( ~ ssItem(X0)
| sk9 = X0
| ~ memberP(sk7,X0)
| ~ ssItem(X0) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_23 ),
inference(resolution,[],[f810,f467]) ).
fof(f874,plain,
( ! [X0] :
( ~ memberP(sk7,X0)
| sk9 = X0
| ~ ssItem(X0) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f873]) ).
fof(f934,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) )
| ~ spl0_30 ),
inference(superposition,[],[f151,f693]) ).
fof(f953,definition,
( spl0_34
<=> ssList(app(cons(sk5,nil),sk7)) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f954,plain,
( ~ ssList(app(cons(sk5,nil),sk7))
| spl0_34 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f981,plain,
( ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| spl0_34 ),
inference(resolution,[],[f954,f85]) ).
fof(f982,plain,
( ~ ssList(cons(sk5,nil))
| spl0_34 ),
inference(forward_subsumption_resolution,[],[f981,f208]) ).
fof(f983,plain,
( ~ spl0_19
| spl0_34 ),
inference(avatar_split_clause,[],[f982,f953,f387]) ).
fof(f997,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(nil)
| ~ spl0_21 ),
inference(resolution,[],[f423,f226]) ).
fof(f999,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(nil)
| ~ spl0_21 ),
inference(duplicate_literal_removal,[],[f997]) ).
fof(f1002,plain,
( memberP(sk3,sk5)
| ~ ssList(sk6)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(nil)
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f999,f206]) ).
fof(f1004,plain,
( memberP(sk3,sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(nil)
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1002,f207]) ).
fof(f1009,plain,
( memberP(sk3,sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1004,f8]) ).
fof(f1011,definition,
( spl0_42
<=> memberP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f1012,plain,
( memberP(sk3,sk5)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1013,plain,
( ~ spl0_16
| spl0_42
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1009,f422,f1011,f331]) ).
fof(f1014,plain,
( ~ ssItem(sk5)
| sk5 = sk9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_42 ),
inference(resolution,[],[f1012,f810]) ).
fof(f1015,plain,
( sk5 = sk9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f1014,f206]) ).
fof(f1320,plain,
( sk8 = sk9
| ~ ssItem(sk8)
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_23 ),
inference(resolution,[],[f874,f274]) ).
fof(f1321,plain,
( sk8 = sk9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1320,f211]) ).
fof(f1355,plain,
( sk5 = sk8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(superposition,[],[f1321,f1015]) ).
fof(f1390,plain,
( ~ leq(sk8,sk8)
| ~ spl0_5
| ~ spl0_6
| spl0_9
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(superposition,[],[f267,f1355]) ).
fof(f1391,plain,
( ~ leq(sk8,sk8)
| ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(superposition,[],[f270,f1355]) ).
fof(f1513,plain,
( ~ ssItem(sk8)
| ~ spl0_5
| ~ spl0_6
| spl0_9
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(resolution,[],[f1390,f62]) ).
fof(f1517,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| spl0_9
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f1513,f211]) ).
fof(f1518,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_9
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f1517]) ).
fof(f1539,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssItem(X0)
| ~ memberP(sk6,X0) )
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f934,f207]) ).
fof(f1547,definition,
( spl0_69
<=> ! [X0] :
( memberP(sk3,X0)
| ~ memberP(sk6,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_69])],[avatar_definition]) ).
fof(f1548,plain,
( ! [X0] :
( memberP(sk3,X0)
| ~ memberP(sk6,X0)
| ~ ssItem(X0) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1547]) ).
fof(f1549,plain,
( ~ spl0_34
| spl0_69
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f1539,f692,f1547,f953]) ).
fof(f1553,plain,
( ~ ssItem(sk8)
| ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(resolution,[],[f1391,f62]) ).
fof(f1557,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f1553,f211]) ).
fof(f1558,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f1557]) ).
fof(f1684,plain,
( ! [X0] :
( ~ memberP(sk6,X0)
| ~ ssItem(X0)
| ~ ssItem(X0)
| sk9 = X0 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_69 ),
inference(resolution,[],[f1548,f810]) ).
fof(f1686,plain,
( ! [X0] :
( ~ memberP(sk6,X0)
| ~ ssItem(X0)
| sk9 = X0 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_69 ),
inference(duplicate_literal_removal,[],[f1684]) ).
fof(f1695,plain,
( ~ ssItem(sk8)
| sk8 = sk9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_69 ),
inference(resolution,[],[f1686,f278]) ).
fof(f1696,plain,
( sk8 = sk9
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_69 ),
inference(forward_subsumption_resolution,[],[f1695,f211]) ).
fof(f1707,plain,
( sk5 = sk8
| ~ spl0_5
| ~ spl0_6
| ~ spl0_12
| ~ spl0_42
| ~ spl0_69 ),
inference(superposition,[],[f1696,f1015]) ).
fof(f1748,plain,
( ~ leq(sk8,sk8)
| ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_12
| ~ spl0_42
| ~ spl0_69 ),
inference(superposition,[],[f270,f1707]) ).
fof(f1886,plain,
( ~ ssItem(sk8)
| ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_12
| ~ spl0_42
| ~ spl0_69 ),
inference(resolution,[],[f1748,f62]) ).
fof(f1890,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_12
| ~ spl0_42
| ~ spl0_69 ),
inference(forward_subsumption_resolution,[],[f1886,f211]) ).
fof(f1891,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_12
| ~ spl0_42
| ~ spl0_69 ),
inference(avatar_contradiction_clause,[],[f1890]) ).
cnf(s3,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f257]) ).
cnf(s5,plain,
( ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f264]) ).
cnf(s6,plain,
( ~ spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f271]) ).
cnf(s7,plain,
( ~ spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f280]) ).
cnf(s13,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f313]) ).
cnf(s14,plain,
( ~ spl0_8
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f333]) ).
cnf(s15,plain,
spl0_16,
inference(sat_conversion,[],[f342]) ).
cnf(s20,plain,
spl0_19,
inference(sat_conversion,[],[f401]) ).
cnf(s21,plain,
( ~ spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f424]) ).
cnf(s27,plain,
( ~ spl0_16
| spl0_23 ),
inference(sat_conversion,[],[f468]) ).
cnf(s28,plain,
( ~ spl0_15
| ~ spl0_19
| spl0_24 ),
inference(sat_conversion,[],[f472]) ).
cnf(s40,plain,
( ~ spl0_19
| spl0_30 ),
inference(sat_conversion,[],[f695]) ).
cnf(s47,plain,
~ spl0_24,
inference(sat_conversion,[],[f797]) ).
cnf(s56,plain,
( ~ spl0_19
| spl0_34 ),
inference(sat_conversion,[],[f983]) ).
cnf(s58,plain,
( ~ spl0_16
| ~ spl0_21
| spl0_42 ),
inference(sat_conversion,[],[f1013]) ).
cnf(s85,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_9
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(sat_conversion,[],[f1518]) ).
cnf(s91,plain,
( ~ spl0_30
| ~ spl0_34
| spl0_69 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s93,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_11
| ~ spl0_23
| ~ spl0_42 ),
inference(sat_conversion,[],[f1558]) ).
cnf(s102,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_10
| ~ spl0_12
| ~ spl0_42
| ~ spl0_69 ),
inference(sat_conversion,[],[f1891]) ).
cnf(s103,plain,
( ~ spl0_15
| ~ spl0_19 ),
inference(rat,[],[s28,s47]) ).
cnf(s104,plain,
spl0_34,
inference(rat,[],[s56,s20]) ).
cnf(s105,plain,
spl0_30,
inference(rat,[],[s40,s20]) ).
cnf(s106,plain,
~ spl0_15,
inference(rat,[],[s103,s20]) ).
cnf(s108,plain,
spl0_69,
inference(rat,[],[s91,s104,s105]) ).
cnf(s124,plain,
spl0_23,
inference(rat,[],[s27,s15]) ).
cnf(s125,plain,
spl0_21,
inference(rat,[],[s21,s15]) ).
cnf(s143,plain,
spl0_42,
inference(rat,[],[s58,s15,s125]) ).
cnf(s145,plain,
~ spl0_8,
inference(rat,[],[s14,s15,s106]) ).
cnf(s146,plain,
~ spl0_7,
inference(rat,[],[s5,s145]) ).
cnf(s147,plain,
spl0_3,
inference(rat,[],[s13,s146]) ).
cnf(s148,plain,
spl0_6,
inference(rat,[],[s4,s147]) ).
cnf(s149,plain,
spl0_5,
inference(rat,[],[s3,s147]) ).
cnf(s152,plain,
spl0_11,
inference(rat,[],[s102,s7,s9,s148,s149,s143,s108]) ).
cnf(s154,plain,
spl0_10,
inference(rat,[],[s93,s143,s124,s149,s148,s152]) ).
cnf(s155,plain,
spl0_9,
inference(rat,[],[s85,s143,s124,s149,s148,s152]) ).
cnf(s161,plain,
$false,
inference(rat,[],[s6,s154,s155]) ).
fof(f1892,plain,
$false,
inference(avatar_sat_refutation,[],[s161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC284-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n002.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 08:55:21 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.83/0.97 % (218617)Input is clausal, will run a generic CNF schedule.
% 0.83/0.97 % (218626)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3039827991:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.83/0.97 % (218626)First to succeed.
% 0.83/0.97 % (218626)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-218617"
% 0.83/0.97 % (218624)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1835078612:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.83/0.97 % (218623)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4040087171:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.83/0.97 % (218622)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=730677091:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.83/0.97 % (218625)lrs+10_1_sil=8000:sp=occurrence:random_seed=1411925552:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.83/0.97 % (218628)dis-21_1_sil=8000:lcm=predicate:random_seed=2074609215: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)
% 0.83/0.97 % (218627)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1019952000:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.83/0.97 % (218625)Also succeeded, but the first one will report.
% 0.83/0.97 % (218628)Instruction limit reached!
% 0.83/0.97 % (218628)------------------------------
% 0.83/0.97 % (218628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/0.97 % (218628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.97 % (218628)CaDiCaL version: 2.1.3
% 0.83/0.97 % (218628)Termination reason: Instruction limit
% 0.83/0.97 % (218628)Termination phase: Saturation
% 0.83/0.97 % (218628)Time elapsed: 0.063 s
% 0.83/0.97 % (218628)Peak memory usage: 89 MB
% 0.83/0.97 % (218628)Instructions burned: 117 (million)
% 0.83/0.97 % (218627)Instruction limit reached!
% 0.83/0.97 % (218627)------------------------------
% 0.83/0.97 % (218627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/0.97 % (218627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.97 % (218627)CaDiCaL version: 2.1.3
% 0.83/0.97 % (218627)Termination reason: Instruction limit
% 0.83/0.97 % (218627)Termination phase: Saturation
% 0.83/0.97 % (218627)Time elapsed: 0.124 s
% 0.83/0.97 % (218627)Peak memory usage: 90 MB
% 0.83/0.97 % (218627)Instructions burned: 181 (million)
% 0.83/0.97 % (218626)Refutation found. Thanks to Tanya!
% 0.83/0.97 % SZS status Unsatisfiable for theBenchmark
% 0.83/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.17 % (218626)------------------------------
% 2.86/1.17 % (218626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.17 % (218626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.17 % (218626)CaDiCaL version: 2.1.3
% 2.86/1.17 % (218626)Termination reason: Refutation
% 2.86/1.17 % (218626)Time elapsed: 0.029 s
% 2.86/1.17 % (218626)Peak memory usage: 90 MB
% 2.86/1.17 % (218626)Instructions burned: 79 (million)
% 2.86/1.17 % (218626)------------------------------
% 2.86/1.17 % (218626)------------------------------
% 2.86/1.17 % (218617)Success in time 0.315 s
% 2.86/1.17 % Vampire exiting
%------------------------------------------------------------------------------