%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC062-1 : 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 : n001.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 01:02:16 PM UTC 2026
% Result : Unsatisfiable 7.45s 1.96s
% Output : Refutation 9.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 124 ( 12 unt; 8 def)
% Number of atoms : 396 ( 60 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 506 ( 234 ~; 264 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f73,axiom,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f75,axiom,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
fof(f76,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f100,axiom,
! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
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(f107,axiom,
! [X0] :
( ~ ssList(X0)
| cons(hd(X0),tl(X0)) = X0
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox/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(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) != sk4
| ~ ssList(X1)
| sk3 = app(X1,cons(X0,nil))
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f206]) ).
fof(f208,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f210,negated_conjecture,
! [X0] :
( nil = sk2
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f211,negated_conjecture,
( nil != sk1
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
! [X0] :
( nil != sk1
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f216,plain,
! [X0] :
( nil = sk4
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f210,f204,f204,f205]) ).
fof(f217,plain,
( nil != sk3
| neq(sk4,nil) ),
inference(definition_unfolding,[],[f211,f205,f204]) ).
fof(f218,plain,
! [X0] :
( nil != sk3
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f212,f205,f204,f205]) ).
fof(f237,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f241,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f244,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f259,definition,
( spl0_3
<=> ! [X0] :
( ~ ssList(X0)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f260,plain,
( ! [X0] :
( ~ neq(X0,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,definition,
( spl0_4
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f265,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f218,f262,f259]) ).
fof(f267,definition,
( spl0_5
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f269,plain,
( neq(sk4,nil)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f270,plain,
( spl0_5
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f217,f262,f267]) ).
fof(f272,definition,
( spl0_6
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f273,plain,
( nil != sk4
| spl0_6 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f274,plain,
( nil = sk4
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f216,f272,f259]) ).
fof(f277,plain,
( ~ spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f208,f262,f272]) ).
fof(f282,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) )
| ~ spl0_3 ),
inference(resolution,[],[f102,f260]) ).
fof(f283,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0) )
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f282]) ).
fof(f285,plain,
( ! [X0] :
( ~ segmentP(sk4,X0)
| nil = X0
| ~ segmentP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f283,f8]) ).
fof(f291,plain,
sk3 = app(sk3,nil),
inference(resolution,[],[f73,f202]) ).
fof(f294,plain,
! [X0,X1] :
( ~ ssList(X1)
| cons(hd(X1),X0) = app(cons(hd(X1),nil),X0)
| ~ ssList(X0)
| nil = X1 ),
inference(resolution,[],[f126,f76]) ).
fof(f295,plain,
! [X0] :
( cons(hd(sk4),X0) = app(cons(hd(sk4),nil),X0)
| ~ ssList(X0)
| nil = sk4 ),
inference(resolution,[],[f294,f203]) ).
fof(f317,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| nil = sk4 ),
inference(resolution,[],[f107,f203]) ).
fof(f372,definition,
( spl0_9
<=> ssList(tl(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f373,plain,
( ssList(tl(sk4))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f374,plain,
( ~ ssList(tl(sk4))
| spl0_9 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f376,definition,
( spl0_10
<=> ssItem(hd(sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f377,plain,
( ssItem(hd(sk4))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
( ~ ssItem(hd(sk4))
| spl0_10 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f385,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_9 ),
inference(resolution,[],[f374,f75]) ).
fof(f386,plain,
( nil = sk4
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f385,f203]) ).
fof(f387,plain,
( $false
| spl0_6
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f386,f273]) ).
fof(f388,plain,
( spl0_6
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f387]) ).
fof(f390,plain,
( neq(nil,nil)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f269,f274]) ).
fof(f399,plain,
( ~ ssList(nil)
| ~ spl0_5
| ~ spl0_6 ),
inference(resolution,[],[f390,f244]) ).
fof(f400,plain,
( $false
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f399,f8]) ).
fof(f401,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f404,plain,
( ! [X0] :
( ~ ssList(X0)
| cons(hd(sk4),X0) = app(cons(hd(sk4),nil),X0) )
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f295,f273]) ).
fof(f405,plain,
( sk4 = cons(hd(sk4),tl(sk4))
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f317,f273]) ).
fof(f436,plain,
( cons(hd(sk4),tl(sk4)) = app(cons(hd(sk4),nil),tl(sk4))
| spl0_6
| ~ spl0_9 ),
inference(resolution,[],[f404,f373]) ).
fof(f466,plain,
( ~ ssList(sk4)
| nil = sk4
| spl0_10 ),
inference(resolution,[],[f378,f76]) ).
fof(f467,plain,
( nil = sk4
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f466,f203]) ).
fof(f468,plain,
( $false
| spl0_6
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f467,f273]) ).
fof(f469,plain,
( spl0_6
| spl0_10 ),
inference(avatar_contradiction_clause,[],[f468]) ).
fof(f470,plain,
( sk4 = app(cons(hd(sk4),nil),tl(sk4))
| spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[],[f436,f405]) ).
fof(f471,plain,
( sk4 != sk4
| ~ ssList(tl(sk4))
| sk3 = app(tl(sk4),cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| spl0_6
| ~ spl0_9 ),
inference(superposition,[],[f207,f470]) ).
fof(f474,plain,
( ~ ssList(tl(sk4))
| sk3 = app(tl(sk4),cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f471]) ).
fof(f476,plain,
( sk3 = app(tl(sk4),cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| spl0_6
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f474,f373]) ).
fof(f478,definition,
( spl0_17
<=> ssList(cons(hd(sk4),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f479,plain,
( ssList(cons(hd(sk4),nil))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f480,plain,
( ~ ssList(cons(hd(sk4),nil))
| spl0_17 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f485,plain,
( sk3 = app(tl(sk4),cons(hd(sk4),nil))
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f476,f377]) ).
fof(f487,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| spl0_17 ),
inference(resolution,[],[f480,f86]) ).
fof(f488,plain,
( ~ ssItem(hd(sk4))
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f487,f8]) ).
fof(f489,plain,
( $false
| ~ spl0_10
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f488,f377]) ).
fof(f490,plain,
( ~ spl0_10
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f489]) ).
fof(f492,plain,
( cons(hd(sk4),nil) = app(nil,cons(hd(sk4),nil))
| ~ spl0_17 ),
inference(resolution,[],[f479,f74]) ).
fof(f500,definition,
( spl0_19
<=> nil = cons(hd(sk4),nil) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f501,plain,
( nil != cons(hd(sk4),nil)
| spl0_19 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f502,plain,
( nil = cons(hd(sk4),nil)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f518,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(cons(hd(sk4),nil),X0))
| ~ ssList(X0) )
| ~ spl0_17 ),
inference(superposition,[],[f237,f492]) ).
fof(f519,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(cons(hd(sk4),nil),X0))
| ~ ssList(X0) )
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f518,f8]) ).
fof(f520,plain,
( ! [X0] :
( segmentP(app(cons(hd(sk4),nil),X0),cons(hd(sk4),nil))
| ~ ssList(app(cons(hd(sk4),nil),X0))
| ~ ssList(X0) )
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f519,f479]) ).
fof(f534,plain,
( nil != nil
| ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ~ spl0_19 ),
inference(superposition,[],[f100,f502]) ).
fof(f536,plain,
( ~ ssItem(hd(sk4))
| ~ ssList(nil)
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f534]) ).
fof(f537,plain,
( ~ ssList(nil)
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f536,f377]) ).
fof(f539,plain,
( $false
| ~ spl0_10
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f537,f8]) ).
fof(f540,plain,
( ~ spl0_10
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f539]) ).
fof(f559,plain,
( ! [X0] :
( segmentP(app(sk3,X0),cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) )
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f237,f485]) ).
fof(f560,plain,
( ! [X0] :
( segmentP(app(sk3,X0),cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) )
| spl0_6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f559,f373]) ).
fof(f561,plain,
( ! [X0] :
( segmentP(app(sk3,X0),cons(hd(sk4),nil))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) )
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f560,f479]) ).
fof(f577,plain,
( segmentP(sk3,cons(hd(sk4),nil))
| ~ ssList(sk3)
| ~ ssList(nil)
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f561,f291]) ).
fof(f578,plain,
( segmentP(sk3,cons(hd(sk4),nil))
| ~ ssList(nil)
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f577,f202]) ).
fof(f579,plain,
( segmentP(sk3,cons(hd(sk4),nil))
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f578,f8]) ).
fof(f584,plain,
( segmentP(sk4,cons(hd(sk4),nil))
| ~ ssList(sk4)
| ~ ssList(tl(sk4))
| spl0_6
| ~ spl0_9
| ~ spl0_17 ),
inference(superposition,[],[f520,f470]) ).
fof(f585,plain,
( segmentP(sk4,cons(hd(sk4),nil))
| ~ ssList(tl(sk4))
| spl0_6
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f584,f203]) ).
fof(f586,plain,
( segmentP(sk4,cons(hd(sk4),nil))
| spl0_6
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f585,f373]) ).
fof(f587,plain,
( nil = cons(hd(sk4),nil)
| ~ segmentP(sk3,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[],[f586,f285]) ).
fof(f588,plain,
( ~ segmentP(sk3,cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_17
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f587,f501]) ).
fof(f589,plain,
( ~ ssList(cons(hd(sk4),nil))
| ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f588,f579]) ).
fof(f590,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f589,f479]) ).
fof(f591,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f590]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f265]) ).
cnf(s3,plain,
( ~ spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f270]) ).
cnf(s4,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f275]) ).
cnf(s6,plain,
( spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f277]) ).
cnf(s10,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f388]) ).
cnf(s11,plain,
( ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f401]) ).
cnf(s16,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f469]) ).
cnf(s18,plain,
( ~ spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f490]) ).
cnf(s22,plain,
( ~ spl0_10
| ~ spl0_19 ),
inference(sat_conversion,[],[f540]) ).
cnf(s25,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f591]) ).
cnf(s26,plain,
spl0_3,
inference(rat,[],[s6,s2,s4]) ).
cnf(s27,plain,
spl0_6,
inference(rat,[],[s25,s18,s22,s10,s16,s26]) ).
cnf(s28,plain,
~ spl0_5,
inference(rat,[],[s11,s27]) ).
cnf(s29,plain,
spl0_4,
inference(rat,[],[s6,s27]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s3,s28,s29]) ).
fof(f592,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC062-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:46:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 7.45/1.96 % (192378)Input is clausal, will run a generic CNF schedule.
% 7.45/1.96 % (192383)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=3578810523:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.45/1.96 % (192385)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1007943904:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.45/1.96 % (192386)lrs+10_1_sil=8000:sp=occurrence:random_seed=1831252537:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.45/1.96 % (192384)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3430827814:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.45/1.96 % (192387)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2784294439:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.45/1.96 % (192389)dis-21_1_sil=8000:lcm=predicate:random_seed=1016308090: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)
% 7.45/1.96 % (192388)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1698730563:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.45/1.96 % (192387)Instruction limit reached!
% 7.45/1.96 % (192387)------------------------------
% 7.45/1.96 % (192387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192387)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192387)Termination reason: Instruction limit
% 7.45/1.96 % (192387)Termination phase: Saturation
% 7.45/1.96 % (192387)Time elapsed: 0.055 s
% 7.45/1.96 % (192387)Peak memory usage: 88 MB
% 7.45/1.96 % (192387)Instructions burned: 116 (million)
% 7.45/1.96 % (192389)Instruction limit reached!
% 7.45/1.96 % (192389)------------------------------
% 7.45/1.96 % (192389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192389)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192389)Termination reason: Instruction limit
% 7.45/1.96 % (192389)Termination phase: Saturation
% 7.45/1.96 % (192389)Time elapsed: 0.061 s
% 7.45/1.96 % (192389)Peak memory usage: 89 MB
% 7.45/1.96 % (192389)Instructions burned: 118 (million)
% 7.45/1.96 % (192386)Instruction limit reached!
% 7.45/1.96 % (192386)------------------------------
% 7.45/1.96 % (192386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192386)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192386)Termination reason: Instruction limit
% 7.45/1.96 % (192386)Termination phase: Saturation
% 7.45/1.96 % (192386)Time elapsed: 0.064 s
% 7.45/1.96 % (192386)Peak memory usage: 89 MB
% 7.45/1.96 % (192386)Instructions burned: 108 (million)
% 7.45/1.96 % (192388)Instruction limit reached!
% 7.45/1.96 % (192388)------------------------------
% 7.45/1.96 % (192388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192388)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192388)Termination reason: Instruction limit
% 7.45/1.96 % (192388)Termination phase: Saturation
% 7.45/1.96 % (192388)Time elapsed: 0.085 s
% 7.45/1.96 % (192388)Peak memory usage: 90 MB
% 7.45/1.96 % (192388)Instructions burned: 182 (million)
% 7.45/1.96 % (192397)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=1408394117:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 7.45/1.96 % (192397)Refutation not found, incomplete strategy
% 7.45/1.96 % (192397)------------------------------
% 7.45/1.96 % (192397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192397)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192397)Termination reason: Refutation not found, incomplete strategy
% 7.45/1.96 % (192397)Time elapsed: 0.003 s
% 7.45/1.96 % (192397)Peak memory usage: 89 MB
% 7.45/1.96 % (192397)Instructions burned: 2 (million)
% 7.45/1.96 % (192398)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3239161952: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)
% 7.45/1.96 % (192400)lrs+10_64_to=lpo:sil=8000:random_seed=1118124481:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 7.45/1.96 % (192399)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3068858911:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 7.45/1.96 % (192400)Instruction limit reached!
% 7.45/1.96 % (192400)------------------------------
% 7.45/1.96 % (192400)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192400)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192400)Termination reason: Instruction limit
% 7.45/1.96 % (192400)Termination phase: Saturation
% 7.45/1.96 % (192400)Time elapsed: 0.037 s
% 7.45/1.96 % (192400)Peak memory usage: 90 MB
% 7.45/1.96 % (192400)Instructions burned: 126 (million)
% 7.45/1.96 % (192399)Instruction limit reached!
% 7.45/1.96 % (192399)------------------------------
% 7.45/1.96 % (192399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192399)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192399)Termination reason: Instruction limit
% 7.45/1.96 % (192399)Termination phase: Saturation
% 7.45/1.96 % (192399)Time elapsed: 0.091 s
% 7.45/1.96 % (192399)Peak memory usage: 88 MB
% 7.45/1.96 % (192399)Instructions burned: 221 (million)
% 7.45/1.96 % (192398)Instruction limit reached!
% 7.45/1.96 % (192398)------------------------------
% 7.45/1.96 % (192398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192398)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192398)Termination reason: Instruction limit
% 7.45/1.96 % (192398)Termination phase: Saturation
% 7.45/1.96 % (192398)Time elapsed: 0.108 s
% 7.45/1.96 % (192398)Peak memory usage: 90 MB
% 7.45/1.96 % (192398)Instructions burned: 190 (million)
% 7.45/1.96 % (192405)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=210837717:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 7.45/1.96 % (192405)Instruction limit reached!
% 7.45/1.96 % (192405)------------------------------
% 7.45/1.96 % (192405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192405)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192405)Termination reason: Instruction limit
% 7.45/1.96 % (192405)Termination phase: Saturation
% 7.45/1.96 % (192405)Time elapsed: 0.070 s
% 7.45/1.96 % (192405)Peak memory usage: 90 MB
% 7.45/1.96 % (192405)Instructions burned: 196 (million)
% 7.45/1.96 % (192397)------------------------------
% 7.45/1.96 % (192397)------------------------------
% 7.45/1.96 % (192407)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3727848004:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 7.45/1.96 % (192406)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2268396571:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 7.45/1.96 % (192409)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=1011242055:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 7.45/1.96 % (192406)Instruction limit reached!
% 7.45/1.96 % (192406)------------------------------
% 7.45/1.96 % (192406)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192409)Instruction limit reached!
% 7.45/1.96 % (192409)------------------------------
% 7.45/1.96 % (192409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192409)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192406)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192406)Termination reason: Instruction limit
% 7.45/1.96 % (192406)Termination phase: Saturation
% 7.45/1.96 % (192409)Termination reason: Instruction limit
% 7.45/1.96 % (192409)Termination phase: Saturation
% 7.45/1.96 % (192406)Time elapsed: 0.097 s
% 7.45/1.96 % (192409)Time elapsed: 0.031 s
% 7.45/1.96 % (192406)Peak memory usage: 91 MB
% 7.45/1.96 % (192409)Peak memory usage: 91 MB
% 7.45/1.96 % (192409)Instructions burned: 110 (million)
% 7.45/1.96 % (192406)Instructions burned: 158 (million)
% 7.45/1.96 % (192410)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3644430322:i=107_2994 on theBenchmark for (2994ds/107Mi)
% 7.45/1.96 % (192415)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=4051280379:cond=fast:i=5208:av=off_2993 on theBenchmark for (2993ds/5208Mi)
% 7.45/1.96 % (192410)Instruction limit reached!
% 7.45/1.96 % (192410)------------------------------
% 7.45/1.96 % (192410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192410)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192410)Termination reason: Instruction limit
% 7.45/1.96 % (192410)Termination phase: Saturation
% 7.45/1.96 % (192410)Time elapsed: 0.068 s
% 7.45/1.96 % (192410)Peak memory usage: 90 MB
% 7.45/1.96 % (192410)Instructions burned: 108 (million)
% 7.45/1.96 % (192414)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=4001591004:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 7.45/1.96 % (192418)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1454074568:i=134:sd=2:doe=on:ss=axioms:sgt=14_2992 on theBenchmark for (2992ds/134Mi)
% 7.45/1.96 % (192414)Instruction limit reached!
% 7.45/1.96 % (192414)------------------------------
% 7.45/1.96 % (192414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192414)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192414)Termination reason: Instruction limit
% 7.45/1.96 % (192414)Termination phase: Saturation
% 7.45/1.96 % (192414)Time elapsed: 0.149 s
% 7.45/1.96 % (192414)Peak memory usage: 89 MB
% 7.45/1.96 % (192414)Instructions burned: 242 (million)
% 7.45/1.96 % (192418)Instruction limit reached!
% 7.45/1.96 % (192418)------------------------------
% 7.45/1.96 % (192418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192418)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192418)Termination reason: Instruction limit
% 7.45/1.96 % (192418)Termination phase: Saturation
% 7.45/1.96 % (192418)Time elapsed: 0.088 s
% 7.45/1.96 % (192418)Peak memory usage: 90 MB
% 7.45/1.96 % (192418)Instructions burned: 134 (million)
% 7.45/1.96 % (192421)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=1571869911:i=499:bd=all_2990 on theBenchmark for (2990ds/499Mi)
% 7.45/1.96 % (192422)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=1799729903:i=191:fgj=on:bd=all_2990 on theBenchmark for (2990ds/191Mi)
% 7.45/1.96 % (192407)First to succeed.
% 7.45/1.96 % (192407)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-192378"
% 7.45/1.96 % (192415)Also succeeded, but the first one will report.
% 7.45/1.96 % (192422)Instruction limit reached!
% 7.45/1.96 % (192422)------------------------------
% 7.45/1.96 % (192422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192422)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192422)Termination reason: Instruction limit
% 7.45/1.96 % (192422)Termination phase: Saturation
% 7.45/1.96 % (192422)Time elapsed: 0.121 s
% 7.45/1.96 % (192422)Peak memory usage: 90 MB
% 7.45/1.96 % (192422)Instructions burned: 191 (million)
% 7.45/1.96 % (192421)Instruction limit reached!
% 7.45/1.96 % (192421)------------------------------
% 7.45/1.96 % (192421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.45/1.96 % (192421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.45/1.96 % (192421)CaDiCaL version: 2.1.3
% 7.45/1.96 % (192421)Termination reason: Instruction limit
% 7.45/1.96 % (192421)Termination phase: Saturation
% 7.45/1.96 % (192421)Time elapsed: 0.263 s
% 7.45/1.96 % (192421)Peak memory usage: 98 MB
% 7.45/1.96 % (192421)Instructions burned: 499 (million)
% 7.45/1.96 % (192407)Refutation found. Thanks to Tanya!
% 7.45/1.96 % SZS status Unsatisfiable for theBenchmark
% 7.45/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 9.91/2.14 % (192407)------------------------------
% 9.91/2.14 % (192407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.91/2.14 % (192407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.91/2.14 % (192407)CaDiCaL version: 2.1.3
% 9.91/2.14 % (192407)Termination reason: Refutation
% 9.91/2.14 % (192407)Time elapsed: 0.609 s
% 9.91/2.14 % (192407)Peak memory usage: 130 MB
% 9.91/2.14 % (192407)Instructions burned: 1031 (million)
% 9.91/2.14 % (192407)------------------------------
% 9.91/2.14 % (192407)------------------------------
% 9.91/2.14 % (192378)Success in time 1.351 s
% 9.91/2.14 % Vampire exiting
%------------------------------------------------------------------------------