%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC015-1 : 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 : n008.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 01:02:03 PM UTC 2026
% Result : Unsatisfiable 3.10s 1.32s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 37
% Syntax : Number of formulae : 178 ( 26 unt; 15 def)
% Number of atoms : 569 ( 105 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 735 ( 344 ~; 376 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause51) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause74) ).
fof(f75,axiom,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause75) ).
fof(f76,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause76) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause85) ).
fof(f100,axiom,
! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f107,axiom,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause104) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f129,axiom,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| ~ ssList(X1)
| nil = X1
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause123) ).
fof(f143,axiom,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X1,skaf45(X0,X1)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause132) ).
fof(f144,axiom,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| ~ ssList(X1)
| nil = X1
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause133) ).
fof(f155,axiom,
! [X2,X0,X1] :
( app(X0,X1) != X2
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| frontsegP(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause144) ).
fof(f163,axiom,
! [X2,X0,X1] :
( app(X0,X1) != app(X2,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause151) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
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,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f210,negated_conjecture,
! [X0,X1] :
( ~ ssList(X0)
| sk4 = X0
| ~ ssList(X1)
| tl(sk4) != X1
| app(sk3,X1) != X0
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,nil) != sk1
| app(cons(X0,nil),X1) != sk2
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f218,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f223,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| frontsegP(app(X0,X1),X0) ),
inference(equality_resolution,[],[f155]) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| sk4 = X0
| ~ ssList(tl(sk4))
| app(sk3,tl(sk4)) != X0
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f210]) ).
fof(f239,plain,
( ~ ssList(app(sk3,tl(sk4)))
| sk4 = app(sk3,tl(sk4))
| ~ ssList(tl(sk4))
| ~ neq(nil,sk4)
| ~ neq(sk4,nil) ),
inference(equality_resolution,[],[f238]) ).
fof(f240,plain,
neq(sk2,nil),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f245,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f248,definition,
( spl0_1
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f249,plain,
( neq(sk4,nil)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f252,definition,
( spl0_2
<=> ! [X0,X1] :
( ~ ssItem(X0)
| app(cons(X0,nil),X1) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f253,plain,
( ! [X0,X1] :
( ~ ssItem(X0)
| app(cons(X0,nil),X1) != sk2
| cons(X0,nil) != sk1
| ~ ssList(X1) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f211,f252,f248]) ).
fof(f256,definition,
( spl0_3
<=> neq(nil,sk4) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f257,plain,
( neq(nil,sk4)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( ~ neq(nil,sk4)
| spl0_3 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f260,definition,
( spl0_4
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f261,plain,
( ssList(tl(sk4))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f262,plain,
( ~ ssList(tl(sk4))
| spl0_4 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f264,definition,
( spl0_5
<=> sk4 = app(sk3,tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f266,plain,
( sk4 = app(sk3,tl(sk4))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f268,definition,
( spl0_6
<=> ssList(app(sk3,tl(sk4))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f270,plain,
( ~ ssList(app(sk3,tl(sk4)))
| spl0_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f271,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f239,f268,f264,f260,f256,f248]) ).
fof(f273,definition,
( spl0_7
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f275,plain,
( neq(sk2,nil)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f279,plain,
spl0_7,
inference(avatar_split_clause,[],[f240,f273]) ).
fof(f285,definition,
( spl0_9
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f286,plain,
( ssList(nil)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f321,plain,
spl0_9,
inference(avatar_split_clause,[],[f8,f285]) ).
fof(f324,plain,
( neq(sk4,nil)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f275,f204]) ).
fof(f327,plain,
( ! [X0,X1] :
( app(cons(X0,nil),X1) != sk4
| ~ ssItem(X0)
| cons(X0,nil) != sk1
| ~ ssList(X1) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f253,f204]) ).
fof(f328,plain,
( spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f324,f273,f248]) ).
fof(f329,plain,
( ! [X0,X1] :
( cons(X0,nil) != sk3
| app(cons(X0,nil),X1) != sk4
| ~ ssItem(X0)
| ~ ssList(X1) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f327,f205]) ).
fof(f361,plain,
( ~ ssList(nil)
| ~ ssList(sk4)
| nil = sk4
| spl0_3 ),
inference(resolution,[],[f102,f258]) ).
fof(f364,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f361,f286]) ).
fof(f365,plain,
( nil = sk4
| spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f364,f203]) ).
fof(f366,plain,
( ~ neq(nil,nil)
| spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f258,f365]) ).
fof(f367,plain,
( neq(nil,nil)
| ~ spl0_1
| spl0_3
| ~ spl0_9 ),
inference(superposition,[],[f249,f365]) ).
fof(f373,plain,
( $false
| ~ spl0_1
| spl0_3
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f367,f366]) ).
fof(f374,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f375,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_4 ),
inference(resolution,[],[f262,f75]) ).
fof(f376,plain,
( nil = sk4
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f375,f203]) ).
fof(f380,plain,
( neq(nil,nil)
| ~ spl0_3
| spl0_4 ),
inference(superposition,[],[f257,f376]) ).
fof(f384,plain,
( ~ ssList(nil)
| ~ spl0_3
| spl0_4 ),
inference(resolution,[],[f380,f245]) ).
fof(f385,plain,
( $false
| ~ spl0_3
| spl0_4
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f384,f286]) ).
fof(f386,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f387,plain,
( ~ ssList(sk3)
| ~ ssList(tl(sk4))
| spl0_6 ),
inference(resolution,[],[f270,f85]) ).
fof(f388,plain,
( ~ ssList(tl(sk4))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f387,f202]) ).
fof(f389,plain,
( $false
| ~ spl0_4
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f388,f261]) ).
fof(f390,plain,
( ~ spl0_4
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f455,definition,
( spl0_17
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f456,plain,
( nil != sk3
| spl0_17 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f457,plain,
( nil = sk3
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f459,definition,
( spl0_18
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f460,plain,
( nil = sk4
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f461,plain,
( nil != sk4
| spl0_18 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f492,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f223,f85]) ).
fof(f499,plain,
( frontsegP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(tl(sk4))
| ~ spl0_5 ),
inference(superposition,[],[f492,f266]) ).
fof(f504,plain,
( frontsegP(sk4,sk3)
| ~ ssList(tl(sk4))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f499,f202]) ).
fof(f505,plain,
( frontsegP(sk4,sk3)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f504,f261]) ).
fof(f507,plain,
( hd(sk3) = hd(sk4)
| ~ ssList(sk3)
| nil = sk3
| ~ ssList(tl(sk4))
| ~ spl0_5 ),
inference(superposition,[],[f129,f266]) ).
fof(f512,plain,
( hd(sk3) = hd(sk4)
| nil = sk3
| ~ ssList(tl(sk4))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f507,f202]) ).
fof(f514,plain,
( hd(sk3) = hd(sk4)
| nil = sk3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f512,f261]) ).
fof(f516,definition,
( spl0_19
<=> hd(sk3) = hd(sk4) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f518,plain,
( hd(sk3) = hd(sk4)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f519,plain,
( spl0_17
| spl0_19
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f514,f264,f260,f516,f455]) ).
fof(f521,plain,
( sk4 = app(nil,tl(sk4))
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f266,f457]) ).
fof(f543,plain,
( ~ ssList(sk3)
| ~ ssList(sk4)
| sk4 = app(sk3,skaf45(sk4,sk3))
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f143,f505]) ).
fof(f548,plain,
( ~ ssList(sk4)
| sk4 = app(sk3,skaf45(sk4,sk3))
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f543,f202]) ).
fof(f553,plain,
( sk4 = app(sk3,skaf45(sk4,sk3))
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f548,f203]) ).
fof(f572,plain,
( sk4 = tl(sk4)
| ~ ssList(tl(sk4))
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f74,f521]) ).
fof(f577,plain,
( sk4 = tl(sk4)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f572,f261]) ).
fof(f602,plain,
( sk4 = cons(hd(sk4),sk4)
| ~ ssList(sk4)
| nil = sk4
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[],[f107,f577]) ).
fof(f604,plain,
( sk4 = cons(hd(sk4),sk4)
| nil = sk4
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f602,f203]) ).
fof(f607,plain,
( sk4 = cons(hd(sk4),sk4)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f604,f461]) ).
fof(f642,plain,
( tl(sk4) = app(tl(sk3),tl(sk4))
| ~ ssList(sk3)
| nil = sk3
| ~ ssList(tl(sk4))
| ~ spl0_5 ),
inference(superposition,[],[f144,f266]) ).
fof(f700,plain,
( sk4 != sk4
| ~ ssItem(hd(sk4))
| ~ ssList(sk4)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_18 ),
inference(superposition,[],[f100,f607]) ).
fof(f703,plain,
( ~ ssItem(hd(sk4))
| ~ ssList(sk4)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_18 ),
inference(trivial_inequality_removal,[],[f700]) ).
fof(f704,plain,
( ~ ssItem(hd(sk4))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f703,f203]) ).
fof(f707,definition,
( spl0_20
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f708,plain,
( ssItem(hd(sk4))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f709,plain,
( ~ ssItem(hd(sk4))
| spl0_20 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f722,plain,
! [X0,X1] :
( app(X1,X0) != X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X1
| ~ ssList(X0) ),
inference(superposition,[],[f163,f74]) ).
fof(f734,plain,
! [X0,X1] :
( app(X1,X0) != X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X1 ),
inference(duplicate_literal_removal,[],[f722]) ).
fof(f743,plain,
( ! [X0,X1] :
( app(X1,X0) != X0
| ~ ssList(X1)
| ~ ssList(X0)
| nil = X1 )
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f734,f286]) ).
fof(f761,plain,
( ~ spl0_20
| ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f704,f459,f455,f264,f260,f707]) ).
fof(f780,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_20 ),
inference(resolution,[],[f709,f76]) ).
fof(f781,plain,
( nil = sk4
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f780,f203]) ).
fof(f791,plain,
( spl0_18
| spl0_20 ),
inference(avatar_split_clause,[],[f781,f707,f459]) ).
fof(f797,plain,
( neq(nil,nil)
| ~ spl0_1
| ~ spl0_18 ),
inference(superposition,[],[f249,f460]) ).
fof(f884,plain,
( ~ ssList(nil)
| ~ spl0_1
| ~ spl0_18 ),
inference(resolution,[],[f797,f245]) ).
fof(f885,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f884,f286]) ).
fof(f886,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f885]) ).
fof(f887,plain,
( tl(sk4) = app(tl(sk3),tl(sk4))
| nil = sk3
| ~ ssList(tl(sk4))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f642,f202]) ).
fof(f893,plain,
( tl(sk4) = app(tl(sk3),tl(sk4))
| nil = sk3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f887,f261]) ).
fof(f895,definition,
( spl0_24
<=> tl(sk4) = app(tl(sk3),tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f897,plain,
( tl(sk4) = app(tl(sk3),tl(sk4))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f898,plain,
( spl0_17
| spl0_24
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f893,f264,f260,f895,f455]) ).
fof(f942,plain,
( sk3 = cons(hd(sk4),tl(sk3))
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_19 ),
inference(superposition,[],[f107,f518]) ).
fof(f944,plain,
( sk3 = cons(hd(sk4),tl(sk3))
| nil = sk3
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f942,f202]) ).
fof(f947,plain,
( sk3 = cons(hd(sk4),tl(sk3))
| spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f944,f456]) ).
fof(f1068,definition,
( spl0_25
<=> ssList(tl(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f1069,plain,
( ssList(tl(sk3))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1070,plain,
( ~ ssList(tl(sk3))
| spl0_25 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1091,definition,
( spl0_30
<=> nil = tl(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f1092,plain,
( nil != tl(sk3)
| spl0_30 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1093,plain,
( nil = tl(sk3)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1133,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_25 ),
inference(resolution,[],[f1070,f75]) ).
fof(f1134,plain,
( nil = sk3
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f1133,f202]) ).
fof(f1135,plain,
( $false
| spl0_17
| spl0_25 ),
inference(forward_subsumption_resolution,[],[f1134,f456]) ).
fof(f1136,plain,
( spl0_17
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f1135]) ).
fof(f1239,plain,
( sk3 = cons(hd(sk4),nil)
| spl0_17
| ~ spl0_19
| ~ spl0_30 ),
inference(superposition,[],[f947,f1093]) ).
fof(f1260,plain,
( ! [X0] :
( sk3 != sk3
| sk4 != app(sk3,X0)
| ~ ssItem(hd(sk4))
| ~ ssList(X0) )
| ~ spl0_2
| spl0_17
| ~ spl0_19
| ~ spl0_30 ),
inference(superposition,[],[f329,f1239]) ).
fof(f1275,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| ~ ssItem(hd(sk4))
| ~ ssList(X0) )
| ~ spl0_2
| spl0_17
| ~ spl0_19
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f1260]) ).
fof(f1284,plain,
( ! [X0] :
( sk4 != app(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_2
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1275,f708]) ).
fof(f1735,plain,
( sk4 != sk4
| ~ ssList(skaf45(sk4,sk3))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(superposition,[],[f1284,f553]) ).
fof(f1739,plain,
( ~ ssList(skaf45(sk4,sk3))
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f1735]) ).
fof(f1742,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f1739,f51]) ).
fof(f1743,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f1742]) ).
fof(f2851,plain,
( tl(sk4) != tl(sk4)
| ~ ssList(tl(sk3))
| ~ ssList(tl(sk4))
| nil = tl(sk3)
| ~ spl0_9
| ~ spl0_24 ),
inference(superposition,[],[f743,f897]) ).
fof(f2852,plain,
( ~ ssList(tl(sk3))
| ~ ssList(tl(sk4))
| nil = tl(sk3)
| ~ spl0_9
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f2851]) ).
fof(f2857,plain,
( ~ ssList(tl(sk4))
| nil = tl(sk3)
| ~ spl0_9
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f2852,f1069]) ).
fof(f2864,plain,
( nil = tl(sk3)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_24
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f2857,f261]) ).
fof(f2870,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_24
| ~ spl0_25
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f2864,f1092]) ).
fof(f2871,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_24
| ~ spl0_25
| spl0_30 ),
inference(avatar_contradiction_clause,[],[f2870]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f254]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f271]) ).
cnf(s6,plain,
spl0_7,
inference(sat_conversion,[],[f279]) ).
cnf(s16,plain,
spl0_9,
inference(sat_conversion,[],[f321]) ).
cnf(s18,plain,
( spl0_1
| ~ spl0_7 ),
inference(sat_conversion,[],[f328]) ).
cnf(s20,plain,
( ~ spl0_1
| spl0_3
| ~ spl0_9 ),
inference(sat_conversion,[],[f374]) ).
cnf(s21,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_9 ),
inference(sat_conversion,[],[f386]) ).
cnf(s22,plain,
( ~ spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f390]) ).
cnf(s24,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f519]) ).
cnf(s26,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_17
| spl0_18
| ~ spl0_20 ),
inference(sat_conversion,[],[f761]) ).
cnf(s29,plain,
( spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f791]) ).
cnf(s30,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_18 ),
inference(sat_conversion,[],[f886]) ).
cnf(s32,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_17
| spl0_24 ),
inference(sat_conversion,[],[f898]) ).
cnf(s42,plain,
( spl0_17
| spl0_25 ),
inference(sat_conversion,[],[f1136]) ).
cnf(s90,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| spl0_17
| ~ spl0_19
| ~ spl0_20
| ~ spl0_30 ),
inference(sat_conversion,[],[f1743]) ).
cnf(s142,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_24
| ~ spl0_25
| spl0_30 ),
inference(sat_conversion,[],[f2871]) ).
cnf(s150,plain,
spl0_1,
inference(rat,[],[s18,s6]) ).
cnf(s151,plain,
~ spl0_18,
inference(rat,[],[s30,s16,s150]) ).
cnf(s152,plain,
spl0_3,
inference(rat,[],[s20,s16,s150]) ).
cnf(s154,plain,
spl0_20,
inference(rat,[],[s29,s151]) ).
cnf(s155,plain,
spl0_4,
inference(rat,[],[s21,s16,s152]) ).
cnf(s157,plain,
spl0_6,
inference(rat,[],[s22,s155]) ).
cnf(s158,plain,
spl0_5,
inference(rat,[],[s2,s157,s155,s152,s150]) ).
cnf(s159,plain,
~ spl0_17,
inference(rat,[],[s26,s154,s151,s155,s158]) ).
cnf(s160,plain,
spl0_25,
inference(rat,[],[s42,s159]) ).
cnf(s161,plain,
spl0_24,
inference(rat,[],[s32,s158,s155,s159]) ).
cnf(s162,plain,
spl0_19,
inference(rat,[],[s24,s158,s155,s159]) ).
cnf(s163,plain,
spl0_30,
inference(rat,[],[s142,s160,s155,s16,s161]) ).
cnf(s172,plain,
~ spl0_2,
inference(rat,[],[s90,s163,s154,s158,s159,s155,s162]) ).
cnf(s177,plain,
$false,
inference(rat,[],[s1,s172,s150]) ).
fof(f2874,plain,
$false,
inference(avatar_sat_refutation,[],[s177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC015-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 07:26:55 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.10/1.32 % (2077480)Input is clausal, will run a generic CNF schedule.
% 3.10/1.32 % (2077485)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=3899407649:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.10/1.32 % (2077488)lrs+10_1_sil=8000:sp=occurrence:random_seed=4085931679:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.10/1.32 % (2077489)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2941641118:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.10/1.32 % (2077486)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3918577633:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.10/1.32 % (2077491)dis-21_1_sil=8000:lcm=predicate:random_seed=1821309992: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)
% 3.10/1.32 % (2077487)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3831735766:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.10/1.32 % (2077490)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=919840544:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.10/1.32 % (2077491)Instruction limit reached!
% 3.10/1.32 % (2077491)------------------------------
% 3.10/1.32 % (2077491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.32 % (2077491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.32 % (2077491)CaDiCaL version: 2.1.3
% 3.10/1.32 % (2077491)Termination reason: Instruction limit
% 3.10/1.32 % (2077491)Termination phase: Saturation
% 3.10/1.32 % (2077491)Time elapsed: 0.060 s
% 3.10/1.32 % (2077491)Peak memory usage: 89 MB
% 3.10/1.32 % (2077491)Instructions burned: 118 (million)
% 3.10/1.32 % (2077490)First to succeed.
% 3.10/1.32 % (2077490)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2077480"
% 3.10/1.32 % (2077488)Instruction limit reached!
% 3.10/1.32 % (2077488)------------------------------
% 3.10/1.32 % (2077488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.32 % (2077488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.32 % (2077488)CaDiCaL version: 2.1.3
% 3.10/1.32 % (2077488)Termination reason: Instruction limit
% 3.10/1.32 % (2077488)Termination phase: Saturation
% 3.10/1.32 % (2077488)Time elapsed: 0.066 s
% 3.10/1.32 % (2077488)Peak memory usage: 89 MB
% 3.10/1.32 % (2077488)Instructions burned: 109 (million)
% 3.10/1.32 % (2077489)Instruction limit reached!
% 3.10/1.32 % (2077489)------------------------------
% 3.10/1.32 % (2077489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.32 % (2077489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.32 % (2077489)CaDiCaL version: 2.1.3
% 3.10/1.32 % (2077489)Termination reason: Instruction limit
% 3.10/1.32 % (2077489)Termination phase: Saturation
% 3.10/1.32 % (2077489)Time elapsed: 0.069 s
% 3.10/1.32 % (2077489)Peak memory usage: 89 MB
% 3.10/1.32 % (2077489)Instructions burned: 115 (million)
% 3.10/1.32 % (2077500)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=793121497: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)
% 3.10/1.32 % (2077499)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=1538845905:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.10/1.32 % (2077501)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1032419298:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.10/1.32 % (2077501)Also succeeded, but the first one will report.
% 3.10/1.32 % (2077499)Also succeeded, but the first one will report.
% 3.10/1.32 % (2077500)Instruction limit reached!
% 3.10/1.32 % (2077500)------------------------------
% 3.10/1.32 % (2077500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.32 % (2077500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.32 % (2077500)CaDiCaL version: 2.1.3
% 3.10/1.32 % (2077500)Termination reason: Instruction limit
% 3.10/1.32 % (2077500)Termination phase: Saturation
% 3.10/1.32 % (2077500)Time elapsed: 0.097 s
% 3.10/1.32 % (2077500)Peak memory usage: 90 MB
% 3.10/1.32 % (2077500)Instructions burned: 190 (million)
% 3.10/1.32 % (2077490)Refutation found. Thanks to Tanya!
% 3.10/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.10/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.41 % (2077490)------------------------------
% 3.81/1.41 % (2077490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.41 % (2077490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.41 % (2077490)CaDiCaL version: 2.1.3
% 3.81/1.41 % (2077490)Termination reason: Refutation
% 3.81/1.41 % (2077490)Time elapsed: 0.064 s
% 3.81/1.41 % (2077490)Peak memory usage: 91 MB
% 3.81/1.41 % (2077490)Instructions burned: 91 (million)
% 3.81/1.41 % (2077490)------------------------------
% 3.81/1.41 % (2077490)------------------------------
% 3.81/1.41 % (2077480)Success in time 0.466 s
% 3.81/1.41 % Vampire exiting
%------------------------------------------------------------------------------