%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET510-6 : 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 : n004.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 12:41:04 PM UTC 2026
% Result : Unsatisfiable 3.37s 1.70s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 41
% Syntax : Number of formulae : 151 ( 43 unt; 19 def)
% Number of atoms : 358 ( 69 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 367 ( 160 ~; 190 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 21 ( 19 usr; 18 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 50 !; 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(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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f54,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f55,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f66,axiom,
! [X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(image(X0,X1),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
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(f71,axiom,
! [X0,X1] : sum_class(image(X0,singleton(X1))) = apply(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
fof(f72,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f73,axiom,
! [X0] :
( ~ member(X0,universal_class)
| X0 = null_class
| member(apply(choice,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
fof(f74,plain,
! [X0] :
( ~ member(X0,universal_class)
| null_class = X0
| member(apply(choice,X0),X0) ),
inference(reorient_equations,[],[f73]) ).
fof(f122,negated_conjecture,
singleton(universal_class) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_singleton_is_null_class_1) ).
fof(f123,plain,
null_class != singleton(universal_class),
inference(reorient_equations,[],[f122]) ).
fof(f124,plain,
! [X0] : sum_class(X0) = domain_of(intersection(element_relation,cross_product(universal_class,X0))),
inference(definition_unfolding,[],[f54,f28]) ).
fof(f125,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f126,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f125,f28]) ).
fof(f127,plain,
! [X0,X1] : apply(X0,X1) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f71,f124,f126,f12]) ).
fof(f154,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f55,f124]) ).
fof(f162,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),universal_class)
| ~ member(X1,universal_class)
| ~ function(X0) ),
inference(definition_unfolding,[],[f66,f126]) ).
fof(f163,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X0)
| null_class = X0
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f74,f127]) ).
fof(f186,plain,
null_class != unordered_pair(universal_class,universal_class),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f191,definition,
sF0 = complement(identity_relation),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f192,plain,
complement(identity_relation) = sF0,
inference(reorient_equations,[],[f191]) ).
fof(f200,definition,
sF4 = unordered_pair(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f201,plain,
unordered_pair(universal_class,universal_class) = sF4,
inference(reorient_equations,[],[f200]) ).
fof(f202,plain,
null_class != sF4,
inference(definition_folding,[],[f186,f201]) ).
fof(f204,definition,
( spl5_1
<=> null_class = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f206,plain,
( null_class != sF4
| spl5_1 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f202,f204]) ).
fof(f239,definition,
( spl5_8
<=> function(choice) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f241,plain,
( function(choice)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f242,plain,
spl5_8,
inference(avatar_split_clause,[],[f72,f239]) ).
fof(f264,definition,
( spl5_13
<=> complement(identity_relation) = sF0 ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
fof(f266,plain,
( complement(identity_relation) = sF0
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
spl5_13,
inference(avatar_split_clause,[],[f192,f264]) ).
fof(f284,definition,
( spl5_17
<=> unordered_pair(universal_class,universal_class) = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
fof(f286,plain,
( unordered_pair(universal_class,universal_class) = sF4
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f287,plain,
spl5_17,
inference(avatar_split_clause,[],[f201,f284]) ).
fof(f288,plain,
( member(sF4,universal_class)
| ~ spl5_17 ),
inference(superposition,[],[f11,f286]) ).
fof(f290,definition,
( spl5_18
<=> member(sF4,universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition]) ).
fof(f292,plain,
( member(sF4,universal_class)
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,plain,
( spl5_18
| ~ spl5_17 ),
inference(avatar_split_clause,[],[f288,f284,f290]) ).
fof(f295,plain,
( ! [X0] :
( ~ member(X0,sF0)
| ~ member(X0,identity_relation) )
| ~ spl5_13 ),
inference(superposition,[],[f24,f266]) ).
fof(f335,definition,
( spl5_25
<=> null_class = sF0 ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
fof(f347,definition,
( spl5_27
<=> member(universal_class,universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_27])],[avatar_definition]) ).
fof(f348,plain,
( member(universal_class,universal_class)
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f349,plain,
( ~ member(universal_class,universal_class)
| spl5_27 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f506,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f523,plain,
( ! [X0] :
( ~ member(X0,sF4)
| universal_class = X0
| universal_class = X0 )
| ~ spl5_17 ),
inference(superposition,[],[f8,f286]) ).
fof(f524,plain,
( ! [X0] :
( ~ member(X0,sF4)
| universal_class = X0 )
| ~ spl5_17 ),
inference(duplicate_literal_removal,[],[f523]) ).
fof(f529,definition,
( spl5_50
<=> null_class = identity_relation ),
introduced(definition,[new_symbols(definition,[spl5_50])],[avatar_definition]) ).
fof(f530,plain,
( null_class != identity_relation
| spl5_50 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f580,plain,
( universal_class = regular(sF4)
| null_class = sF4
| ~ spl5_17 ),
inference(resolution,[],[f524,f68]) ).
fof(f582,plain,
( universal_class = regular(sF4)
| spl5_1
| ~ spl5_17 ),
inference(forward_subsumption_resolution,[],[f580,f206]) ).
fof(f593,definition,
( spl5_58
<=> universal_class = regular(sF4) ),
introduced(definition,[new_symbols(definition,[spl5_58])],[avatar_definition]) ).
fof(f595,plain,
( universal_class = regular(sF4)
| ~ spl5_58 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f596,plain,
( spl5_58
| spl5_1
| ~ spl5_17 ),
inference(avatar_split_clause,[],[f582,f284,f204,f593]) ).
fof(f599,plain,
( null_class = intersection(sF4,universal_class)
| null_class = sF4
| ~ spl5_58 ),
inference(superposition,[],[f70,f595]) ).
fof(f602,plain,
( null_class = intersection(sF4,universal_class)
| spl5_1
| ~ spl5_58 ),
inference(forward_subsumption_resolution,[],[f599,f206]) ).
fof(f605,definition,
( spl5_59
<=> null_class = intersection(sF4,universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_59])],[avatar_definition]) ).
fof(f607,plain,
( null_class = intersection(sF4,universal_class)
| ~ spl5_59 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f608,plain,
( spl5_59
| spl5_1
| ~ spl5_58 ),
inference(avatar_split_clause,[],[f602,f593,f204,f605]) ).
fof(f609,plain,
( ! [X0] :
( ~ member(X0,sF4)
| ~ member(X0,universal_class)
| member(X0,null_class) )
| ~ spl5_59 ),
inference(superposition,[],[f23,f607]) ).
fof(f655,plain,
( ~ member(regular(sF4),universal_class)
| member(regular(sF4),null_class)
| null_class = sF4
| ~ spl5_59 ),
inference(resolution,[],[f609,f68]) ).
fof(f657,plain,
( ~ member(regular(sF4),universal_class)
| member(regular(sF4),null_class)
| spl5_1
| ~ spl5_59 ),
inference(forward_subsumption_resolution,[],[f655,f206]) ).
fof(f658,plain,
( ~ member(universal_class,universal_class)
| member(regular(sF4),null_class)
| spl5_1
| ~ spl5_58
| ~ spl5_59 ),
inference(forward_demodulation,[],[f657,f595]) ).
fof(f920,plain,
( null_class = sF4
| ~ member(sF4,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),null_class)
| ~ spl5_59 ),
inference(resolution,[],[f163,f609]) ).
fof(f921,plain,
( null_class = sF4
| ~ member(sF4,universal_class)
| universal_class = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| ~ spl5_17 ),
inference(resolution,[],[f163,f524]) ).
fof(f923,plain,
( ~ member(sF4,universal_class)
| universal_class = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| spl5_1
| ~ spl5_17 ),
inference(forward_subsumption_resolution,[],[f921,f206]) ).
fof(f924,plain,
( ~ member(sF4,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),null_class)
| spl5_1
| ~ spl5_59 ),
inference(forward_subsumption_resolution,[],[f920,f206]) ).
fof(f944,plain,
( universal_class = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| spl5_1
| ~ spl5_17
| ~ spl5_18 ),
inference(forward_subsumption_resolution,[],[f923,f292]) ).
fof(f945,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),null_class)
| spl5_1
| ~ spl5_18
| ~ spl5_59 ),
inference(forward_subsumption_resolution,[],[f924,f292]) ).
fof(f947,definition,
( spl5_97
<=> universal_class = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))) ),
introduced(definition,[new_symbols(definition,[spl5_97])],[avatar_definition]) ).
fof(f949,plain,
( universal_class = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| ~ spl5_97 ),
inference(avatar_component_clause,[],[f947]) ).
fof(f950,plain,
( spl5_97
| spl5_1
| ~ spl5_17
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f944,f290,f284,f204,f947]) ).
fof(f952,definition,
( spl5_98
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),null_class) ),
introduced(definition,[new_symbols(definition,[spl5_98])],[avatar_definition]) ).
fof(f956,definition,
( spl5_99
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_99])],[avatar_definition]) ).
fof(f959,plain,
( spl5_98
| ~ spl5_99
| spl5_1
| ~ spl5_18
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f945,f605,f290,f204,f956,f952]) ).
fof(f1115,plain,
( member(universal_class,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))),universal_class)
| ~ spl5_97 ),
inference(superposition,[],[f154,f949]) ).
fof(f1146,plain,
( ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))),universal_class)
| spl5_27
| ~ spl5_97 ),
inference(forward_subsumption_resolution,[],[f1115,f349]) ).
fof(f1157,definition,
( spl5_117
<=> member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_117])],[avatar_definition]) ).
fof(f1159,plain,
( ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))),universal_class)
| spl5_117 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f1160,plain,
( ~ spl5_117
| spl5_27
| ~ spl5_97 ),
inference(avatar_split_clause,[],[f1146,f947,f347,f1157]) ).
fof(f1165,plain,
( ~ member(unordered_pair(sF4,sF4),universal_class)
| ~ function(choice)
| spl5_117 ),
inference(resolution,[],[f1159,f162]) ).
fof(f1166,plain,
( ~ function(choice)
| spl5_117 ),
inference(forward_subsumption_resolution,[],[f1165,f11]) ).
fof(f1167,plain,
( $false
| ~ spl5_8
| spl5_117 ),
inference(forward_subsumption_resolution,[],[f1166,f241]) ).
fof(f1168,plain,
( ~ spl5_8
| spl5_117 ),
inference(avatar_contradiction_clause,[],[f1167]) ).
fof(f1169,plain,
( universal_class != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| ~ member(universal_class,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),universal_class) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
fof(f1172,plain,
( member(regular(sF4),null_class)
| spl5_1
| ~ spl5_27
| ~ spl5_58
| ~ spl5_59 ),
inference(forward_subsumption_resolution,[],[f658,f348]) ).
fof(f1176,definition,
( spl5_118
<=> member(universal_class,null_class) ),
introduced(definition,[new_symbols(definition,[spl5_118])],[avatar_definition]) ).
fof(f1178,plain,
( member(universal_class,null_class)
| ~ spl5_118 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f1180,plain,
( member(universal_class,null_class)
| spl5_1
| ~ spl5_27
| ~ spl5_58
| ~ spl5_59 ),
inference(forward_demodulation,[],[f1172,f595]) ).
fof(f1191,plain,
( spl5_118
| spl5_1
| ~ spl5_27
| ~ spl5_58
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f1180,f605,f593,f347,f204,f1176]) ).
fof(f1730,plain,
( ! [X0] :
( member(universal_class,X0)
| null_class = X0 )
| ~ spl5_118 ),
inference(resolution,[],[f506,f1178]) ).
fof(f1750,plain,
( null_class = sF0
| ~ member(universal_class,identity_relation)
| ~ spl5_13
| ~ spl5_118 ),
inference(resolution,[],[f1730,f295]) ).
fof(f1762,definition,
( spl5_200
<=> member(universal_class,identity_relation) ),
introduced(definition,[new_symbols(definition,[spl5_200])],[avatar_definition]) ).
fof(f1763,plain,
( member(universal_class,identity_relation)
| ~ spl5_200 ),
inference(avatar_component_clause,[],[f1762]) ).
fof(f1764,plain,
( ~ member(universal_class,identity_relation)
| spl5_200 ),
inference(avatar_component_clause,[],[f1762]) ).
fof(f1765,plain,
( ~ spl5_200
| spl5_25
| ~ spl5_13
| ~ spl5_118 ),
inference(avatar_split_clause,[],[f1750,f1176,f264,f335,f1762]) ).
fof(f1838,definition,
( spl5_209
<=> member(universal_class,sF0) ),
introduced(definition,[new_symbols(definition,[spl5_209])],[avatar_definition]) ).
fof(f1840,plain,
( member(universal_class,sF0)
| ~ spl5_209 ),
inference(avatar_component_clause,[],[f1838]) ).
fof(f2512,plain,
( null_class != identity_relation
| universal_class != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),null_class)
| member(universal_class,identity_relation) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
fof(f2544,plain,
( ~ member(universal_class,identity_relation)
| ~ spl5_13
| ~ spl5_209 ),
inference(resolution,[],[f1840,f295]) ).
fof(f2546,plain,
( null_class = identity_relation
| ~ spl5_118
| spl5_200 ),
inference(resolution,[],[f1764,f1730]) ).
fof(f2547,plain,
( $false
| spl5_50
| ~ spl5_118
| spl5_200 ),
inference(forward_subsumption_resolution,[],[f2546,f530]) ).
fof(f2548,plain,
( spl5_50
| ~ spl5_118
| spl5_200 ),
inference(avatar_contradiction_clause,[],[f2547]) ).
fof(f2552,plain,
( $false
| ~ spl5_13
| ~ spl5_200
| ~ spl5_209 ),
inference(forward_subsumption_resolution,[],[f2544,f1763]) ).
fof(f2553,plain,
( ~ spl5_13
| ~ spl5_200
| ~ spl5_209 ),
inference(avatar_contradiction_clause,[],[f2552]) ).
fof(f2554,plain,
( null_class != sF0
| universal_class != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class)))))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(sF4,sF4),universal_class)),universal_class))))))),null_class)
| member(universal_class,sF0) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
cnf(s1,plain,
~ spl5_1,
inference(sat_conversion,[],[f207]) ).
cnf(s8,plain,
spl5_8,
inference(sat_conversion,[],[f242]) ).
cnf(s13,plain,
spl5_13,
inference(sat_conversion,[],[f267]) ).
cnf(s17,plain,
spl5_17,
inference(sat_conversion,[],[f287]) ).
cnf(s18,plain,
( ~ spl5_17
| spl5_18 ),
inference(sat_conversion,[],[f293]) ).
cnf(s41,plain,
( spl5_1
| ~ spl5_17
| spl5_58 ),
inference(sat_conversion,[],[f596]) ).
cnf(s43,plain,
( spl5_1
| ~ spl5_58
| spl5_59 ),
inference(sat_conversion,[],[f608]) ).
cnf(s67,plain,
( spl5_1
| ~ spl5_17
| ~ spl5_18
| spl5_97 ),
inference(sat_conversion,[],[f950]) ).
cnf(s68,plain,
( spl5_1
| ~ spl5_18
| ~ spl5_59
| spl5_98
| ~ spl5_99 ),
inference(sat_conversion,[],[f959]) ).
cnf(s78,plain,
( spl5_27
| ~ spl5_97
| ~ spl5_117 ),
inference(sat_conversion,[],[f1160]) ).
cnf(s79,plain,
( ~ spl5_8
| spl5_117 ),
inference(sat_conversion,[],[f1168]) ).
cnf(s80,plain,
( ~ spl5_27
| ~ spl5_97
| spl5_99 ),
inference(sat_conversion,[],[f1169]) ).
cnf(s84,plain,
( spl5_1
| ~ spl5_27
| ~ spl5_58
| ~ spl5_59
| spl5_118 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s159,plain,
( ~ spl5_13
| spl5_25
| ~ spl5_118
| ~ spl5_200 ),
inference(sat_conversion,[],[f1765]) ).
cnf(s258,plain,
( ~ spl5_50
| ~ spl5_97
| ~ spl5_98
| spl5_200 ),
inference(sat_conversion,[],[f2512]) ).
cnf(s269,plain,
( spl5_50
| ~ spl5_118
| spl5_200 ),
inference(sat_conversion,[],[f2548]) ).
cnf(s271,plain,
( ~ spl5_13
| ~ spl5_200
| ~ spl5_209 ),
inference(sat_conversion,[],[f2553]) ).
cnf(s272,plain,
( ~ spl5_25
| ~ spl5_97
| ~ spl5_98
| spl5_209 ),
inference(sat_conversion,[],[f2554]) ).
cnf(s273,plain,
spl5_18,
inference(rat,[],[s18,s17]) ).
cnf(s276,plain,
spl5_117,
inference(rat,[],[s79,s8]) ).
cnf(s277,plain,
spl5_97,
inference(rat,[],[s67,s273,s17,s1]) ).
cnf(s278,plain,
spl5_58,
inference(rat,[],[s41,s17,s1]) ).
cnf(s279,plain,
spl5_27,
inference(rat,[],[s78,s276,s277]) ).
cnf(s280,plain,
spl5_59,
inference(rat,[],[s43,s1,s278]) ).
cnf(s282,plain,
spl5_118,
inference(rat,[],[s84,s278,s280,s1,s279]) ).
cnf(s284,plain,
spl5_99,
inference(rat,[],[s80,s277,s279]) ).
cnf(s286,plain,
spl5_98,
inference(rat,[],[s68,s284,s1,s273,s280]) ).
cnf(s301,plain,
spl5_200,
inference(rat,[],[s258,s269,s277,s286,s282]) ).
cnf(s302,plain,
~ spl5_209,
inference(rat,[],[s271,s13,s301]) ).
cnf(s303,plain,
spl5_25,
inference(rat,[],[s159,s282,s13,s301]) ).
cnf(s304,plain,
$false,
inference(rat,[],[s272,s286,s277,s302,s303]) ).
fof(f2555,plain,
$false,
inference(avatar_sat_refutation,[],[s304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET510-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:01:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.37/1.70 % (4073481)Input is clausal, will run a generic CNF schedule.
% 3.37/1.70 % (4073489)lrs+10_1_sil=8000:sp=occurrence:random_seed=1449222558:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.37/1.70 % (4073489)Refutation not found, incomplete strategy
% 3.37/1.70 % (4073489)------------------------------
% 3.37/1.70 % (4073489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073489)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073489)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.70 % (4073489)Time elapsed: 0.001 s
% 3.37/1.70 % (4073489)Peak memory usage: 87 MB
% 3.37/1.70 % (4073490)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=258840586:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.37/1.70 % (4073488)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3656820753:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.37/1.70 % (4073492)dis-21_1_sil=8000:lcm=predicate:random_seed=1686644141: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)
% 3.37/1.70 % (4073486)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=3385276257:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.37/1.70 % (4073487)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3116618619:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.37/1.70 % (4073491)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2133550536:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.37/1.70 % (4073490)Instruction limit reached!
% 3.37/1.70 % (4073490)------------------------------
% 3.37/1.70 % (4073490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073490)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073490)Termination reason: Instruction limit
% 3.37/1.70 % (4073490)Termination phase: Saturation
% 3.37/1.70 % (4073490)Time elapsed: 0.067 s
% 3.37/1.70 % (4073490)Peak memory usage: 88 MB
% 3.37/1.70 % (4073490)Instructions burned: 114 (million)
% 3.37/1.70 % (4073492)Instruction limit reached!
% 3.37/1.70 % (4073492)------------------------------
% 3.37/1.70 % (4073492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073492)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073492)Termination reason: Instruction limit
% 3.37/1.70 % (4073492)Termination phase: Saturation
% 3.37/1.70 % (4073492)Time elapsed: 0.070 s
% 3.37/1.70 % (4073492)Peak memory usage: 89 MB
% 3.37/1.70 % (4073492)Instructions burned: 119 (million)
% 3.37/1.70 % (4073489)------------------------------
% 3.37/1.70 % (4073489)------------------------------
% 3.37/1.70 % (4073491)Instruction limit reached!
% 3.37/1.70 % (4073491)------------------------------
% 3.37/1.70 % (4073491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073491)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073491)Termination reason: Instruction limit
% 3.37/1.70 % (4073491)Termination phase: Saturation
% 3.37/1.70 % (4073491)Time elapsed: 0.133 s
% 3.37/1.70 % (4073491)Peak memory usage: 90 MB
% 3.37/1.70 % (4073491)Instructions burned: 181 (million)
% 3.37/1.70 % (4073502)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=881276521:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.37/1.70 % (4073502)Refutation not found, incomplete strategy
% 3.37/1.70 % (4073502)------------------------------
% 3.37/1.70 % (4073502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073502)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073502)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.70 % (4073502)Time elapsed: 0.002 s
% 3.37/1.70 % (4073502)Peak memory usage: 88 MB
% 3.37/1.70 % (4073502)Instructions burned: 3 (million)
% 3.37/1.70 % (4073500)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=2805007638:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.37/1.70 % (4073501)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=451120620: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)
% 3.37/1.70 % (4073500)Refutation not found, incomplete strategy
% 3.37/1.70 % (4073500)------------------------------
% 3.37/1.70 % (4073500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073500)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073500)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.70 % (4073500)Time elapsed: 0.003 s
% 3.37/1.70 % (4073500)Peak memory usage: 88 MB
% 3.37/1.70 % (4073500)Instructions burned: 3 (million)
% 3.37/1.70 % (4073503)lrs+10_64_to=lpo:sil=8000:random_seed=2664903677:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 3.37/1.70 % (4073501)Instruction limit reached!
% 3.37/1.70 % (4073501)------------------------------
% 3.37/1.70 % (4073501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073501)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073501)Termination reason: Instruction limit
% 3.37/1.70 % (4073501)Termination phase: Saturation
% 3.37/1.70 % (4073501)Time elapsed: 0.097 s
% 3.37/1.70 % (4073501)Peak memory usage: 90 MB
% 3.37/1.70 % (4073501)Instructions burned: 190 (million)
% 3.37/1.70 % (4073502)------------------------------
% 3.37/1.70 % (4073502)------------------------------
% 3.37/1.70 % (4073503)Instruction limit reached!
% 3.37/1.70 % (4073503)------------------------------
% 3.37/1.70 % (4073503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073503)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073503)Termination reason: Instruction limit
% 3.37/1.70 % (4073503)Termination phase: Saturation
% 3.37/1.70 % (4073503)Time elapsed: 0.080 s
% 3.37/1.70 % (4073503)Peak memory usage: 89 MB
% 3.37/1.70 % (4073503)Instructions burned: 126 (million)
% 3.37/1.70 % (4073500)------------------------------
% 3.37/1.70 % (4073500)------------------------------
% 3.37/1.70 % (4073508)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2677285328:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 3.37/1.70 % (4073509)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4102777321:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 3.37/1.70 % (4073509)First to succeed.
% 3.37/1.70 % (4073509)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4073481"
% 3.37/1.70 % (4073510)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=279610176:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 3.37/1.70 % (4073508)Instruction limit reached!
% 3.37/1.70 % (4073508)------------------------------
% 3.37/1.70 % (4073508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.70 % (4073508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.70 % (4073508)CaDiCaL version: 2.1.3
% 3.37/1.70 % (4073508)Termination reason: Instruction limit
% 3.37/1.70 % (4073508)Termination phase: Saturation
% 3.37/1.70 % (4073508)Time elapsed: 0.122 s
% 3.37/1.70 % (4073508)Peak memory usage: 89 MB
% 3.37/1.70 % (4073508)Instructions burned: 194 (million)
% 3.37/1.70 % (4073512)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=965684444:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 3.37/1.70 % (4073488)Also succeeded, but the first one will report.
% 3.37/1.70 % (4073486)Also succeeded, but the first one will report.
% 3.37/1.70 % (4073509)Refutation found. Thanks to Tanya!
% 3.37/1.70 % SZS status Unsatisfiable for theBenchmark
% 3.37/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.80 % (4073509)------------------------------
% 3.37/1.80 % (4073509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.80 % (4073509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.80 % (4073509)CaDiCaL version: 2.1.3
% 3.37/1.80 % (4073509)Termination reason: Refutation
% 3.37/1.80 % (4073509)Time elapsed: 0.036 s
% 3.37/1.80 % (4073509)Peak memory usage: 91 MB
% 3.37/1.80 % (4073509)Instructions burned: 94 (million)
% 3.37/1.80 % (4073509)------------------------------
% 3.37/1.80 % (4073509)------------------------------
% 3.37/1.80 % (4073481)Success in time 0.855 s
% 3.37/1.80 % Vampire exiting
%------------------------------------------------------------------------------