%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:41:05 PM UTC 2026
% Result : Unsatisfiable 5.76s 1.83s
% Output : Refutation 7.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 43
% Syntax : Number of formulae : 177 ( 42 unt; 27 def)
% Number of atoms : 412 ( 81 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 427 ( 192 ~; 212 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 25 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f122,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_singleton_of_set_1) ).
fof(f123,plain,
x = singleton(member_of(x)),
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
member_of(x) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_singleton_of_set_2) ).
fof(f125,plain,
x = member_of(x),
inference(reorient_equations,[],[f124]) ).
fof(f188,plain,
x = unordered_pair(member_of(x),member_of(x)),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f193,definition,
sF0 = complement(identity_relation),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f194,plain,
complement(identity_relation) = sF0,
inference(reorient_equations,[],[f193]) ).
fof(f197,definition,
sF2 = complement(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f198,plain,
complement(sF1) = sF2,
inference(reorient_equations,[],[f197]) ).
fof(f202,definition,
sF4 = member_of(x),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f203,plain,
member_of(x) = sF4,
inference(reorient_equations,[],[f202]) ).
fof(f204,definition,
sF5 = unordered_pair(sF4,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f205,plain,
unordered_pair(sF4,sF4) = sF5,
inference(reorient_equations,[],[f204]) ).
fof(f206,plain,
x = sF5,
inference(definition_folding,[],[f188,f205,f203,f203]) ).
fof(f207,plain,
x = sF4,
inference(definition_folding,[],[f125,f203]) ).
fof(f209,definition,
( spl6_1
<=> x = sF4 ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f211,plain,
( x = sF4
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f212,plain,
spl6_1,
inference(avatar_split_clause,[],[f207,f209]) ).
fof(f214,definition,
( spl6_2
<=> x = sF5 ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f216,plain,
( x = sF5
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
spl6_2,
inference(avatar_split_clause,[],[f206,f214]) ).
fof(f274,definition,
( spl6_14
<=> complement(identity_relation) = sF0 ),
introduced(definition,[new_symbols(definition,[spl6_14])],[avatar_definition]) ).
fof(f276,plain,
( complement(identity_relation) = sF0
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f277,plain,
spl6_14,
inference(avatar_split_clause,[],[f194,f274]) ).
fof(f284,definition,
( spl6_16
<=> complement(sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl6_16])],[avatar_definition]) ).
fof(f286,plain,
( complement(sF1) = sF2
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f287,plain,
spl6_16,
inference(avatar_split_clause,[],[f198,f284]) ).
fof(f299,definition,
( spl6_19
<=> unordered_pair(sF4,sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl6_19])],[avatar_definition]) ).
fof(f301,plain,
( unordered_pair(sF4,sF4) = sF5
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f302,plain,
spl6_19,
inference(avatar_split_clause,[],[f205,f299]) ).
fof(f303,plain,
( sF4 = sF5
| ~ spl6_1
| ~ spl6_2 ),
inference(forward_demodulation,[],[f216,f211]) ).
fof(f306,definition,
( spl6_20
<=> sF4 = sF5 ),
introduced(definition,[new_symbols(definition,[spl6_20])],[avatar_definition]) ).
fof(f308,plain,
( sF4 = sF5
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f309,plain,
( spl6_20
| ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f303,f214,f209,f306]) ).
fof(f315,plain,
( member(sF5,universal_class)
| ~ spl6_19 ),
inference(superposition,[],[f11,f301]) ).
fof(f316,plain,
( member(sF4,universal_class)
| ~ spl6_19
| ~ spl6_20 ),
inference(forward_demodulation,[],[f315,f308]) ).
fof(f318,definition,
( spl6_22
<=> member(sF4,universal_class) ),
introduced(definition,[new_symbols(definition,[spl6_22])],[avatar_definition]) ).
fof(f320,plain,
( member(sF4,universal_class)
| ~ spl6_22 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f321,plain,
( spl6_22
| ~ spl6_19
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f316,f306,f299,f318]) ).
fof(f323,plain,
( ! [X0] :
( ~ member(X0,sF0)
| ~ member(X0,identity_relation) )
| ~ spl6_14 ),
inference(superposition,[],[f24,f276]) ).
fof(f324,plain,
( ! [X0] :
( ~ member(X0,sF2)
| ~ member(X0,sF1) )
| ~ spl6_16 ),
inference(superposition,[],[f24,f286]) ).
fof(f334,definition,
( spl6_24
<=> member(null_class,sF1) ),
introduced(definition,[new_symbols(definition,[spl6_24])],[avatar_definition]) ).
fof(f335,plain,
( member(null_class,sF1)
| ~ spl6_24 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f336,plain,
( ~ member(null_class,sF1)
| spl6_24 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f363,definition,
( spl6_29
<=> null_class = sF0 ),
introduced(definition,[new_symbols(definition,[spl6_29])],[avatar_definition]) ).
fof(f364,plain,
( null_class != sF0
| spl6_29 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f373,plain,
( member(sF4,sF5)
| ~ member(sF4,universal_class)
| ~ spl6_19 ),
inference(superposition,[],[f9,f301]) ).
fof(f374,plain,
( member(sF4,sF5)
| ~ spl6_19
| ~ spl6_22 ),
inference(forward_subsumption_resolution,[],[f373,f320]) ).
fof(f375,plain,
( member(sF4,sF4)
| ~ spl6_19
| ~ spl6_20
| ~ spl6_22 ),
inference(forward_demodulation,[],[f374,f308]) ).
fof(f377,definition,
( spl6_31
<=> member(sF4,sF4) ),
introduced(definition,[new_symbols(definition,[spl6_31])],[avatar_definition]) ).
fof(f379,plain,
( member(sF4,sF4)
| ~ spl6_31 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f380,plain,
( spl6_31
| ~ spl6_19
| ~ spl6_20
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f375,f318,f306,f299,f377]) ).
fof(f388,definition,
( spl6_32
<=> null_class = sF2 ),
introduced(definition,[new_symbols(definition,[spl6_32])],[avatar_definition]) ).
fof(f535,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f557,plain,
( ! [X0] :
( ~ member(X0,sF5)
| sF4 = X0
| sF4 = X0 )
| ~ spl6_19 ),
inference(superposition,[],[f8,f301]) ).
fof(f558,plain,
( ! [X0] :
( ~ member(X0,sF5)
| sF4 = X0 )
| ~ spl6_19 ),
inference(duplicate_literal_removal,[],[f557]) ).
fof(f559,plain,
( ! [X0] :
( ~ member(X0,sF4)
| sF4 = X0 )
| ~ spl6_19
| ~ spl6_20 ),
inference(forward_demodulation,[],[f558,f308]) ).
fof(f562,plain,
( sF4 = regular(sF4)
| null_class = sF4
| ~ spl6_19
| ~ spl6_20 ),
inference(resolution,[],[f559,f68]) ).
fof(f565,definition,
( spl6_54
<=> null_class = sF4 ),
introduced(definition,[new_symbols(definition,[spl6_54])],[avatar_definition]) ).
fof(f566,plain,
( null_class != sF4
| spl6_54 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f567,plain,
( null_class = sF4
| ~ spl6_54 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f569,definition,
( spl6_55
<=> sF4 = regular(sF4) ),
introduced(definition,[new_symbols(definition,[spl6_55])],[avatar_definition]) ).
fof(f571,plain,
( sF4 = regular(sF4)
| ~ spl6_55 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f572,plain,
( spl6_54
| spl6_55
| ~ spl6_19
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f562,f306,f299,f569,f565]) ).
fof(f589,plain,
( member(null_class,null_class)
| ~ spl6_31
| ~ spl6_54 ),
inference(superposition,[],[f379,f567]) ).
fof(f599,definition,
( spl6_58
<=> member(null_class,null_class) ),
introduced(definition,[new_symbols(definition,[spl6_58])],[avatar_definition]) ).
fof(f601,plain,
( member(null_class,null_class)
| ~ spl6_58 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f602,plain,
( spl6_58
| ~ spl6_31
| ~ spl6_54 ),
inference(avatar_split_clause,[],[f589,f565,f377,f599]) ).
fof(f628,plain,
( null_class = intersection(sF4,sF4)
| null_class = sF4
| ~ spl6_55 ),
inference(superposition,[],[f70,f571]) ).
fof(f630,plain,
( null_class = intersection(sF4,sF4)
| spl6_54
| ~ spl6_55 ),
inference(forward_subsumption_resolution,[],[f628,f566]) ).
fof(f632,definition,
( spl6_62
<=> null_class = intersection(sF4,sF4) ),
introduced(definition,[new_symbols(definition,[spl6_62])],[avatar_definition]) ).
fof(f634,plain,
( null_class = intersection(sF4,sF4)
| ~ spl6_62 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f635,plain,
( spl6_62
| spl6_54
| ~ spl6_55 ),
inference(avatar_split_clause,[],[f630,f569,f565,f632]) ).
fof(f1053,definition,
( spl6_99
<=> member(null_class,complement(null_class)) ),
introduced(definition,[new_symbols(definition,[spl6_99])],[avatar_definition]) ).
fof(f1054,plain,
( member(null_class,complement(null_class))
| ~ spl6_99 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1055,plain,
( ~ member(null_class,complement(null_class))
| spl6_99 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1606,definition,
( spl6_123
<=> null_class = identity_relation ),
introduced(definition,[new_symbols(definition,[spl6_123])],[avatar_definition]) ).
fof(f1607,plain,
( null_class != identity_relation
| spl6_123 ),
inference(avatar_component_clause,[],[f1606]) ).
fof(f1977,plain,
( ! [X0] :
( member(null_class,X0)
| null_class = X0 )
| ~ spl6_58 ),
inference(resolution,[],[f535,f601]) ).
fof(f1990,definition,
( spl6_181
<=> ! [X0] :
( member(null_class,X0)
| null_class = X0 ) ),
introduced(definition,[new_symbols(definition,[spl6_181])],[avatar_definition]) ).
fof(f1991,plain,
( ! [X0] :
( member(null_class,X0)
| null_class = X0 )
| ~ spl6_181 ),
inference(avatar_component_clause,[],[f1990]) ).
fof(f1997,plain,
( spl6_181
| ~ spl6_58 ),
inference(avatar_split_clause,[],[f1977,f599,f1990]) ).
fof(f2002,plain,
( null_class = complement(null_class)
| spl6_99
| ~ spl6_181 ),
inference(resolution,[],[f1991,f1055]) ).
fof(f2005,plain,
( null_class = sF1
| spl6_24
| ~ spl6_181 ),
inference(resolution,[],[f1991,f336]) ).
fof(f2018,plain,
( null_class = sF2
| ~ member(null_class,sF1)
| ~ spl6_16
| ~ spl6_181 ),
inference(resolution,[],[f1991,f324]) ).
fof(f2030,definition,
( spl6_183
<=> null_class = sF1 ),
introduced(definition,[new_symbols(definition,[spl6_183])],[avatar_definition]) ).
fof(f2033,plain,
( spl6_183
| spl6_24
| ~ spl6_181 ),
inference(avatar_split_clause,[],[f2005,f1990,f334,f2030]) ).
fof(f2041,definition,
( spl6_185
<=> null_class = complement(null_class) ),
introduced(definition,[new_symbols(definition,[spl6_185])],[avatar_definition]) ).
fof(f2044,plain,
( spl6_185
| spl6_99
| ~ spl6_181 ),
inference(avatar_split_clause,[],[f2002,f1990,f1053,f2041]) ).
fof(f2081,plain,
( null_class = sF2
| ~ spl6_16
| ~ spl6_24
| ~ spl6_181 ),
inference(forward_subsumption_resolution,[],[f2018,f335]) ).
fof(f2100,plain,
( spl6_32
| ~ spl6_16
| ~ spl6_24
| ~ spl6_181 ),
inference(avatar_split_clause,[],[f2081,f1990,f334,f284,f388]) ).
fof(f2327,plain,
( ~ member(null_class,null_class)
| ~ spl6_99 ),
inference(resolution,[],[f1054,f24]) ).
fof(f2330,plain,
( $false
| ~ spl6_58
| ~ spl6_99 ),
inference(forward_subsumption_resolution,[],[f2327,f601]) ).
fof(f2331,plain,
( ~ spl6_58
| ~ spl6_99 ),
inference(avatar_contradiction_clause,[],[f2330]) ).
fof(f2334,plain,
( null_class != sF1
| complement(sF1) != sF2
| null_class != complement(null_class)
| null_class = sF2 ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
fof(f2337,plain,
( null_class != sF2
| null_class != sF4
| ~ member(sF4,sF4)
| member(null_class,sF2) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
fof(f2338,plain,
( null_class != sF2
| null_class != complement(null_class)
| ~ member(null_class,sF2)
| member(null_class,complement(null_class)) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
fof(f2431,definition,
( spl6_217
<=> member(sF4,null_class) ),
introduced(definition,[new_symbols(definition,[spl6_217])],[avatar_definition]) ).
fof(f2433,plain,
( member(sF4,null_class)
| ~ spl6_217 ),
inference(avatar_component_clause,[],[f2431]) ).
fof(f2449,definition,
( spl6_220
<=> member(sF4,identity_relation) ),
introduced(definition,[new_symbols(definition,[spl6_220])],[avatar_definition]) ).
fof(f2450,plain,
( ~ member(sF4,identity_relation)
| spl6_220 ),
inference(avatar_component_clause,[],[f2449]) ).
fof(f2451,plain,
( member(sF4,identity_relation)
| ~ spl6_220 ),
inference(avatar_component_clause,[],[f2449]) ).
fof(f2453,definition,
( spl6_221
<=> member(sF4,sF0) ),
introduced(definition,[new_symbols(definition,[spl6_221])],[avatar_definition]) ).
fof(f2455,plain,
( member(sF4,sF0)
| ~ spl6_221 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f3036,plain,
( ! [X0] :
( member(X0,null_class)
| ~ member(X0,sF4)
| ~ member(X0,sF4) )
| ~ spl6_62 ),
inference(superposition,[],[f23,f634]) ).
fof(f3039,plain,
( ! [X0] :
( ~ member(X0,sF4)
| member(X0,null_class) )
| ~ spl6_62 ),
inference(duplicate_literal_removal,[],[f3036]) ).
fof(f3208,plain,
( member(sF4,null_class)
| ~ spl6_31
| ~ spl6_62 ),
inference(resolution,[],[f3039,f379]) ).
fof(f3219,plain,
( spl6_217
| ~ spl6_31
| ~ spl6_62 ),
inference(avatar_split_clause,[],[f3208,f632,f377,f2431]) ).
fof(f3265,plain,
( ! [X0] :
( member(sF4,X0)
| null_class = X0 )
| ~ spl6_217 ),
inference(resolution,[],[f2433,f535]) ).
fof(f3324,plain,
( null_class = sF0
| ~ member(sF4,identity_relation)
| ~ spl6_14
| ~ spl6_217 ),
inference(resolution,[],[f3265,f323]) ).
fof(f3332,plain,
( ~ member(sF4,identity_relation)
| ~ spl6_14
| spl6_29
| ~ spl6_217 ),
inference(forward_subsumption_resolution,[],[f3324,f364]) ).
fof(f3346,plain,
( $false
| ~ spl6_14
| spl6_29
| ~ spl6_217
| ~ spl6_220 ),
inference(forward_subsumption_resolution,[],[f3332,f2451]) ).
fof(f3347,plain,
( ~ spl6_14
| spl6_29
| ~ spl6_217
| ~ spl6_220 ),
inference(avatar_contradiction_clause,[],[f3346]) ).
fof(f3390,plain,
( null_class = identity_relation
| ~ spl6_217
| spl6_220 ),
inference(resolution,[],[f2450,f3265]) ).
fof(f3391,plain,
( $false
| spl6_123
| ~ spl6_217
| spl6_220 ),
inference(forward_subsumption_resolution,[],[f3390,f1607]) ).
fof(f3392,plain,
( spl6_123
| ~ spl6_217
| spl6_220 ),
inference(avatar_contradiction_clause,[],[f3391]) ).
fof(f3394,plain,
( null_class != identity_relation
| ~ member(sF4,null_class)
| member(sF4,identity_relation) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
fof(f3456,plain,
( ~ member(sF4,identity_relation)
| ~ spl6_14
| ~ spl6_221 ),
inference(resolution,[],[f2455,f323]) ).
fof(f3459,plain,
( $false
| ~ spl6_14
| ~ spl6_220
| ~ spl6_221 ),
inference(forward_subsumption_resolution,[],[f3456,f2451]) ).
fof(f3460,plain,
( ~ spl6_14
| ~ spl6_220
| ~ spl6_221 ),
inference(avatar_contradiction_clause,[],[f3459]) ).
fof(f3461,plain,
( null_class != sF0
| ~ member(sF4,null_class)
| member(sF4,sF0) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
cnf(s1,plain,
spl6_1,
inference(sat_conversion,[],[f212]) ).
cnf(s2,plain,
spl6_2,
inference(sat_conversion,[],[f217]) ).
cnf(s14,plain,
spl6_14,
inference(sat_conversion,[],[f277]) ).
cnf(s16,plain,
spl6_16,
inference(sat_conversion,[],[f287]) ).
cnf(s19,plain,
spl6_19,
inference(sat_conversion,[],[f302]) ).
cnf(s20,plain,
( ~ spl6_1
| ~ spl6_2
| spl6_20 ),
inference(sat_conversion,[],[f309]) ).
cnf(s22,plain,
( ~ spl6_19
| ~ spl6_20
| spl6_22 ),
inference(sat_conversion,[],[f321]) ).
cnf(s28,plain,
( ~ spl6_19
| ~ spl6_20
| ~ spl6_22
| spl6_31 ),
inference(sat_conversion,[],[f380]) ).
cnf(s41,plain,
( ~ spl6_19
| ~ spl6_20
| spl6_54
| spl6_55 ),
inference(sat_conversion,[],[f572]) ).
cnf(s44,plain,
( ~ spl6_31
| ~ spl6_54
| spl6_58 ),
inference(sat_conversion,[],[f602]) ).
cnf(s48,plain,
( spl6_54
| ~ spl6_55
| spl6_62 ),
inference(sat_conversion,[],[f635]) ).
cnf(s142,plain,
( ~ spl6_58
| spl6_181 ),
inference(sat_conversion,[],[f1997]) ).
cnf(s144,plain,
( spl6_24
| ~ spl6_181
| spl6_183 ),
inference(sat_conversion,[],[f2033]) ).
cnf(s147,plain,
( spl6_99
| ~ spl6_181
| spl6_185 ),
inference(sat_conversion,[],[f2044]) ).
cnf(s167,plain,
( ~ spl6_16
| ~ spl6_24
| spl6_32
| ~ spl6_181 ),
inference(sat_conversion,[],[f2100]) ).
cnf(s184,plain,
( ~ spl6_58
| ~ spl6_99 ),
inference(sat_conversion,[],[f2331]) ).
cnf(s186,plain,
( ~ spl6_16
| spl6_32
| ~ spl6_183
| ~ spl6_185 ),
inference(sat_conversion,[],[f2334]) ).
cnf(s189,plain,
( ~ spl6_31
| ~ spl6_32
| spl6_37
| ~ spl6_54 ),
inference(sat_conversion,[],[f2337]) ).
cnf(s190,plain,
( ~ spl6_32
| ~ spl6_37
| spl6_99
| ~ spl6_185 ),
inference(sat_conversion,[],[f2338]) ).
cnf(s248,plain,
( ~ spl6_31
| ~ spl6_62
| spl6_217 ),
inference(sat_conversion,[],[f3219]) ).
cnf(s254,plain,
( ~ spl6_14
| spl6_29
| ~ spl6_217
| ~ spl6_220 ),
inference(sat_conversion,[],[f3347]) ).
cnf(s260,plain,
( spl6_123
| ~ spl6_217
| spl6_220 ),
inference(sat_conversion,[],[f3392]) ).
cnf(s262,plain,
( ~ spl6_123
| ~ spl6_217
| spl6_220 ),
inference(sat_conversion,[],[f3394]) ).
cnf(s274,plain,
( ~ spl6_14
| ~ spl6_220
| ~ spl6_221 ),
inference(sat_conversion,[],[f3460]) ).
cnf(s275,plain,
( ~ spl6_29
| ~ spl6_217
| spl6_221 ),
inference(sat_conversion,[],[f3461]) ).
cnf(s279,plain,
spl6_20,
inference(rat,[],[s20,s2,s1]) ).
cnf(s280,plain,
spl6_22,
inference(rat,[],[s22,s19,s279]) ).
cnf(s282,plain,
spl6_31,
inference(rat,[],[s28,s279,s19,s280]) ).
cnf(s283,plain,
( ~ spl6_217
| spl6_220 ),
inference(rat,[],[s260,s262]) ).
cnf(s284,plain,
( spl6_54
| spl6_62 ),
inference(rat,[],[s48,s41,s19,s279]) ).
cnf(s285,plain,
( ~ spl6_58
| spl6_32
| spl6_24 ),
inference(rat,[],[s186,s144,s147,s142,s184,s16]) ).
cnf(s286,plain,
( ~ spl6_217
| spl6_29 ),
inference(rat,[],[s254,s283,s14]) ).
cnf(s287,plain,
( ~ spl6_54
| spl6_24 ),
inference(rat,[],[s190,s189,s147,s285,s142,s184,s44,s282]) ).
cnf(s288,plain,
~ spl6_217,
inference(rat,[],[s275,s274,s286,s283,s14]) ).
cnf(s289,plain,
~ spl6_62,
inference(rat,[],[s248,s282,s288]) ).
cnf(s290,plain,
spl6_54,
inference(rat,[],[s284,s289]) ).
cnf(s293,plain,
spl6_58,
inference(rat,[],[s44,s282,s290]) ).
cnf(s298,plain,
spl6_24,
inference(rat,[],[s287,s290]) ).
cnf(s301,plain,
~ spl6_99,
inference(rat,[],[s184,s293]) ).
cnf(s302,plain,
spl6_181,
inference(rat,[],[s142,s293]) ).
cnf(s306,plain,
spl6_32,
inference(rat,[],[s167,s302,s16,s298]) ).
cnf(s308,plain,
spl6_185,
inference(rat,[],[s147,s301,s302]) ).
cnf(s310,plain,
spl6_37,
inference(rat,[],[s189,s290,s282,s306]) ).
cnf(s312,plain,
$false,
inference(rat,[],[s190,s301,s308,s306,s310]) ).
fof(f3462,plain,
$false,
inference(avatar_sat_refutation,[],[s312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:02:33 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 5.76/1.83 % (1493493)Input is clausal, will run a generic CNF schedule.
% 5.76/1.83 % (1493503)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3174187603:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.76/1.83 % (1493504)dis-21_1_sil=8000:lcm=predicate:random_seed=4047451664: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)
% 5.76/1.83 % (1493499)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2766950451:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.76/1.83 % (1493498)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=1069817080:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.76/1.83 % (1493502)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=427714507:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.76/1.83 % (1493500)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=584386687:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.76/1.83 % (1493501)lrs+10_1_sil=8000:sp=occurrence:random_seed=2849661863:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.76/1.83 % (1493501)Refutation not found, incomplete strategy
% 5.76/1.83 % (1493501)------------------------------
% 5.76/1.83 % (1493501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493501)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493501)Termination reason: Refutation not found, incomplete strategy
% 5.76/1.83 % (1493501)Time elapsed: 0.001 s
% 5.76/1.83 % (1493501)Peak memory usage: 88 MB
% 5.76/1.83 % (1493503)Instruction limit reached!
% 5.76/1.83 % (1493503)------------------------------
% 5.76/1.83 % (1493503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493503)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493503)Termination reason: Instruction limit
% 5.76/1.83 % (1493503)Termination phase: Saturation
% 5.76/1.83 % (1493503)Time elapsed: 0.072 s
% 5.76/1.83 % (1493503)Peak memory usage: 90 MB
% 5.76/1.83 % (1493503)Instructions burned: 181 (million)
% 5.76/1.83 % (1493502)Instruction limit reached!
% 5.76/1.83 % (1493502)------------------------------
% 5.76/1.83 % (1493502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493502)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493502)Termination reason: Instruction limit
% 5.76/1.83 % (1493502)Termination phase: Saturation
% 5.76/1.83 % (1493502)Time elapsed: 0.067 s
% 5.76/1.83 % (1493502)Peak memory usage: 89 MB
% 5.76/1.83 % (1493502)Instructions burned: 114 (million)
% 5.76/1.83 % (1493504)Instruction limit reached!
% 5.76/1.83 % (1493504)------------------------------
% 5.76/1.83 % (1493504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493504)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493504)Termination reason: Instruction limit
% 5.76/1.83 % (1493504)Termination phase: Saturation
% 5.76/1.83 % (1493504)Time elapsed: 0.071 s
% 5.76/1.83 % (1493504)Peak memory usage: 89 MB
% 5.76/1.83 % (1493504)Instructions burned: 117 (million)
% 5.76/1.83 % (1493512)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=809783231:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.76/1.83 % (1493512)Instruction limit reached!
% 5.76/1.83 % (1493512)------------------------------
% 5.76/1.83 % (1493512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493512)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493512)Termination reason: Instruction limit
% 5.76/1.83 % (1493512)Termination phase: Saturation
% 5.76/1.83 % (1493512)Time elapsed: 0.055 s
% 5.76/1.83 % (1493512)Peak memory usage: 89 MB
% 5.76/1.83 % (1493512)Instructions burned: 146 (million)
% 5.76/1.83 % (1493514)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1242325461:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.76/1.83 % (1493513)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=72297210: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)
% 5.76/1.83 % (1493501)------------------------------
% 5.76/1.83 % (1493501)------------------------------
% 5.76/1.83 % (1493516)lrs+10_64_to=lpo:sil=8000:random_seed=1761104006:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.76/1.83 % (1493513)Instruction limit reached!
% 5.76/1.83 % (1493513)------------------------------
% 5.76/1.83 % (1493513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493513)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493513)Termination reason: Instruction limit
% 5.76/1.83 % (1493513)Termination phase: Saturation
% 5.76/1.83 % (1493513)Time elapsed: 0.105 s
% 5.76/1.83 % (1493513)Peak memory usage: 90 MB
% 5.76/1.83 % (1493513)Instructions burned: 190 (million)
% 5.76/1.83 % (1493516)Instruction limit reached!
% 5.76/1.83 % (1493516)------------------------------
% 5.76/1.83 % (1493516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493516)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493516)Termination reason: Instruction limit
% 5.76/1.83 % (1493516)Termination phase: Saturation
% 5.76/1.83 % (1493516)Time elapsed: 0.045 s
% 5.76/1.83 % (1493516)Peak memory usage: 89 MB
% 5.76/1.83 % (1493516)Instructions burned: 129 (million)
% 5.76/1.83 % (1493514)Instruction limit reached!
% 5.76/1.83 % (1493514)------------------------------
% 5.76/1.83 % (1493514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493514)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493514)Termination reason: Instruction limit
% 5.76/1.83 % (1493514)Termination phase: Saturation
% 5.76/1.83 % (1493514)Time elapsed: 0.140 s
% 5.76/1.83 % (1493514)Peak memory usage: 89 MB
% 5.76/1.83 % (1493514)Instructions burned: 220 (million)
% 5.76/1.83 % (1493519)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1255803640:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.76/1.83 % (1493522)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=653501515:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.76/1.83 % (1493521)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1222451108:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.76/1.83 % (1493523)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=1939296938:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 5.76/1.83 % (1493519)Instruction limit reached!
% 5.76/1.83 % (1493519)------------------------------
% 5.76/1.83 % (1493519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493519)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493519)Termination reason: Instruction limit
% 5.76/1.83 % (1493519)Termination phase: Saturation
% 5.76/1.83 % (1493519)Time elapsed: 0.122 s
% 5.76/1.83 % (1493519)Peak memory usage: 89 MB
% 5.76/1.83 % (1493519)Instructions burned: 195 (million)
% 5.76/1.83 % (1493523)Instruction limit reached!
% 5.76/1.83 % (1493523)------------------------------
% 5.76/1.83 % (1493523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493523)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493523)Termination reason: Instruction limit
% 5.76/1.83 % (1493523)Termination phase: Saturation
% 5.76/1.83 % (1493523)Time elapsed: 0.052 s
% 5.76/1.83 % (1493523)Peak memory usage: 97 MB
% 5.76/1.83 % (1493523)Instructions burned: 107 (million)
% 5.76/1.83 % (1493521)First to succeed.
% 5.76/1.83 % (1493521)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1493493"
% 5.76/1.83 % (1493528)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=792863895:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 5.76/1.83 % (1493529)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=2166075006:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 5.76/1.83 % (1493498)Also succeeded, but the first one will report.
% 5.76/1.83 % (1493528)Instruction limit reached!
% 5.76/1.83 % (1493528)------------------------------
% 5.76/1.83 % (1493528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.76/1.83 % (1493528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.76/1.83 % (1493528)CaDiCaL version: 2.1.3
% 5.76/1.83 % (1493528)Termination reason: Instruction limit
% 5.76/1.83 % (1493528)Termination phase: Saturation
% 5.76/1.83 % (1493528)Time elapsed: 0.071 s
% 5.76/1.83 % (1493528)Peak memory usage: 89 MB
% 5.76/1.83 % (1493528)Instructions burned: 107 (million)
% 5.76/1.83 % (1493500)Also succeeded, but the first one will report.
% 5.76/1.83 % (1493522)Also succeeded, but the first one will report.
% 5.76/1.83 % (1493521)Refutation found. Thanks to Tanya!
% 5.76/1.83 % SZS status Unsatisfiable for theBenchmark
% 5.76/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 7.27/2.02 % (1493521)------------------------------
% 7.27/2.02 % (1493521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.27/2.02 % (1493521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.27/2.02 % (1493521)CaDiCaL version: 2.1.3
% 7.27/2.02 % (1493521)Termination reason: Refutation
% 7.27/2.02 % (1493521)Time elapsed: 0.099 s
% 7.27/2.02 % (1493521)Peak memory usage: 92 MB
% 7.27/2.02 % (1493521)Instructions burned: 148 (million)
% 7.27/2.02 % (1493521)------------------------------
% 7.27/2.02 % (1493521)------------------------------
% 7.27/2.02 % (1493493)Success in time 0.963 s
% 7.27/2.02 % Vampire exiting
%------------------------------------------------------------------------------