%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET258-6 : 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 : n013.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 12:40:38 PM UTC 2026
% Result : Unsatisfiable 5.70s 1.78s
% Output : Refutation 6.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 35
% Syntax : Number of formulae : 128 ( 42 unt; 14 def)
% Number of atoms : 236 ( 57 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 216 ( 108 ~; 104 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 14 con; 0-3 aty)
% Number of variables : 106 ( 0 sgn 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f30,axiom,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f42,axiom,
! [X2,X0,X1] : second(not_subclass_element(restrict(X0,singleton(X1),X2),null_class)) = range(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range) ).
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,
member(x,domain_of(xr)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_alternate_defn1_1) ).
fof(f123,negated_conjecture,
~ member(ordered_pair(x,range(xr,x,universal_class)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_alternate_defn1_2) ).
fof(f128,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f133,plain,
! [X2,X0,X1] : range(X0,X1,X2) = second(not_subclass_element(intersection(X0,cross_product(unordered_pair(X1,X1),X2)),null_class)),
inference(definition_unfolding,[],[f42,f28,f12]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) ),
inference(definition_unfolding,[],[f14,f128]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) ),
inference(definition_unfolding,[],[f15,f128]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(definition_unfolding,[],[f16,f128]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f128]) ).
fof(f144,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f186,plain,
~ member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(second(not_subclass_element(intersection(xr,cross_product(unordered_pair(x,x),universal_class)),null_class)),second(not_subclass_element(intersection(xr,cross_product(unordered_pair(x,x),universal_class)),null_class))))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f123,f128,f133]) ).
fof(f191,definition,
sF0 = domain_of(xr),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f192,plain,
domain_of(xr) = sF0,
inference(reorient_equations,[],[f191]) ).
fof(f193,plain,
member(x,sF0),
inference(definition_folding,[],[f122,f192]) ).
fof(f194,definition,
sF1 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f195,plain,
unordered_pair(x,x) = sF1,
inference(reorient_equations,[],[f194]) ).
fof(f196,definition,
sF2 = cross_product(sF1,universal_class),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f197,plain,
cross_product(sF1,universal_class) = sF2,
inference(reorient_equations,[],[f196]) ).
fof(f198,definition,
sF3 = intersection(xr,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f199,plain,
intersection(xr,sF2) = sF3,
inference(reorient_equations,[],[f198]) ).
fof(f200,definition,
sF4 = not_subclass_element(sF3,null_class),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f201,plain,
not_subclass_element(sF3,null_class) = sF4,
inference(reorient_equations,[],[f200]) ).
fof(f202,definition,
sF5 = second(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f203,plain,
second(sF4) = sF5,
inference(reorient_equations,[],[f202]) ).
fof(f204,definition,
sF6 = unordered_pair(sF5,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f205,plain,
unordered_pair(sF5,sF5) = sF6,
inference(reorient_equations,[],[f204]) ).
fof(f206,definition,
sF7 = unordered_pair(x,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f207,plain,
unordered_pair(x,sF6) = sF7,
inference(reorient_equations,[],[f206]) ).
fof(f208,definition,
sF8 = unordered_pair(sF1,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f209,plain,
unordered_pair(sF1,sF7) = sF8,
inference(reorient_equations,[],[f208]) ).
fof(f210,definition,
sF9 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f211,plain,
cross_product(universal_class,universal_class) = sF9,
inference(reorient_equations,[],[f210]) ).
fof(f212,plain,
~ member(sF8,sF9),
inference(definition_folding,[],[f186,f211,f209,f207,f205,f203,f201,f199,f197,f195,f203,f201,f199,f197,f195,f195]) ).
fof(f217,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF2)
| member(X0,sF1) ),
inference(superposition,[],[f137,f197]) ).
fof(f222,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF2)
| member(X1,universal_class) ),
inference(superposition,[],[f138,f197]) ).
fof(f227,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f230,plain,
! [X0] :
( ~ member(X0,sF3)
| member(X0,sF2) ),
inference(superposition,[],[f22,f199]) ).
fof(f231,plain,
( member(sF4,sF3)
| subclass(sF3,null_class) ),
inference(superposition,[],[f2,f201]) ).
fof(f234,definition,
( spl10_1
<=> subclass(sF3,null_class) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f236,plain,
( subclass(sF3,null_class)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f243,definition,
( spl10_3
<=> member(sF4,sF3) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f245,plain,
( member(sF4,sF3)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,plain,
( spl10_1
| spl10_3 ),
inference(avatar_split_clause,[],[f231,f243,f234]) ).
fof(f248,plain,
! [X0] :
( ~ member(X0,sF2)
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(superposition,[],[f140,f197]) ).
fof(f255,definition,
( spl10_4
<=> member(sF5,universal_class) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f256,plain,
( member(sF5,universal_class)
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ member(sF5,universal_class)
| spl10_4 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f264,definition,
( spl10_6
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
fof(f265,plain,
( member(x,universal_class)
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f266,plain,
( ~ member(x,universal_class)
| spl10_6 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f311,plain,
( member(sF4,sF2)
| ~ spl10_3 ),
inference(resolution,[],[f230,f245]) ).
fof(f318,plain,
! [X0] :
( null_class != intersection(X0,cross_product(sF1,universal_class))
| ~ member(x,domain_of(X0)) ),
inference(superposition,[],[f144,f195]) ).
fof(f320,plain,
! [X0] :
( null_class != intersection(X0,sF2)
| ~ member(x,domain_of(X0)) ),
inference(forward_demodulation,[],[f318,f197]) ).
fof(f321,plain,
( null_class != sF3
| ~ member(x,domain_of(xr)) ),
inference(superposition,[],[f320,f199]) ).
fof(f322,plain,
( ~ member(x,sF0)
| null_class != sF3 ),
inference(forward_demodulation,[],[f321,f192]) ).
fof(f323,plain,
null_class != sF3,
inference(forward_subsumption_resolution,[],[f322,f193]) ).
fof(f329,plain,
! [X0] :
( ~ member(X0,sF1)
| x = X0
| x = X0 ),
inference(superposition,[],[f8,f195]) ).
fof(f332,plain,
! [X0] :
( ~ member(X0,sF1)
| x = X0 ),
inference(duplicate_literal_removal,[],[f329]) ).
fof(f338,plain,
! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sF6)),sF2)
| member(X0,sF1) ),
inference(superposition,[],[f217,f205]) ).
fof(f371,plain,
! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sF6)),sF2)
| member(sF5,universal_class) ),
inference(superposition,[],[f222,f205]) ).
fof(f372,plain,
( ! [X0] : ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sF6)),sF2)
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f371,f257]) ).
fof(f421,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) ),
inference(resolution,[],[f23,f1]) ).
fof(f428,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f227,f3]) ).
fof(f442,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f428]) ).
fof(f493,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),sF9)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f139,f211]) ).
fof(f502,plain,
! [X0] :
( member(unordered_pair(sF1,unordered_pair(x,unordered_pair(X0,X0))),sF9)
| ~ member(X0,universal_class)
| ~ member(x,universal_class) ),
inference(superposition,[],[f493,f195]) ).
fof(f585,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f421,f4]) ).
fof(f599,plain,
! [X0] :
( ~ member(x,X0)
| member(x,universal_class) ),
inference(resolution,[],[f585,f193]) ).
fof(f619,plain,
( ! [X0] : ~ member(x,X0)
| spl10_6 ),
inference(forward_subsumption_resolution,[],[f599,f266]) ).
fof(f638,plain,
( $false
| spl10_6 ),
inference(resolution,[],[f619,f193]) ).
fof(f643,plain,
spl10_6,
inference(avatar_contradiction_clause,[],[f638]) ).
fof(f647,plain,
( ! [X0] :
( member(unordered_pair(sF1,unordered_pair(x,unordered_pair(X0,X0))),sF9)
| ~ member(X0,universal_class) )
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f502,f265]) ).
fof(f680,plain,
( member(unordered_pair(sF1,unordered_pair(x,sF6)),sF9)
| ~ member(sF5,universal_class)
| ~ spl10_6 ),
inference(superposition,[],[f647,f205]) ).
fof(f685,plain,
( ~ subclass(null_class,sF3)
| null_class = sF3
| ~ spl10_1 ),
inference(resolution,[],[f236,f7]) ).
fof(f691,plain,
( ~ subclass(null_class,sF3)
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f685,f323]) ).
fof(f722,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f442,f70]) ).
fof(f723,plain,
( null_class = sF3
| ~ spl10_1 ),
inference(resolution,[],[f722,f691]) ).
fof(f726,plain,
( $false
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f723,f323]) ).
fof(f727,plain,
~ spl10_1,
inference(avatar_contradiction_clause,[],[f726]) ).
fof(f733,plain,
( sF4 = unordered_pair(unordered_pair(first(sF4),first(sF4)),unordered_pair(first(sF4),unordered_pair(second(sF4),second(sF4))))
| ~ spl10_3 ),
inference(resolution,[],[f311,f248]) ).
fof(f737,plain,
( sF4 = unordered_pair(unordered_pair(first(sF4),first(sF4)),unordered_pair(first(sF4),unordered_pair(sF5,sF5)))
| ~ spl10_3 ),
inference(forward_demodulation,[],[f733,f203]) ).
fof(f738,plain,
( sF4 = unordered_pair(unordered_pair(first(sF4),first(sF4)),unordered_pair(first(sF4),sF6))
| ~ spl10_3 ),
inference(forward_demodulation,[],[f737,f205]) ).
fof(f764,plain,
( ~ member(sF4,sF2)
| member(first(sF4),sF1)
| ~ spl10_3 ),
inference(superposition,[],[f338,f738]) ).
fof(f773,plain,
( member(first(sF4),sF1)
| ~ spl10_3 ),
inference(forward_subsumption_resolution,[],[f764,f311]) ).
fof(f774,plain,
( x = first(sF4)
| ~ spl10_3 ),
inference(resolution,[],[f773,f332]) ).
fof(f787,plain,
( sF4 = unordered_pair(unordered_pair(x,x),unordered_pair(x,sF6))
| ~ spl10_3 ),
inference(superposition,[],[f738,f774]) ).
fof(f788,plain,
( sF4 = unordered_pair(unordered_pair(x,x),sF7)
| ~ spl10_3 ),
inference(forward_demodulation,[],[f787,f207]) ).
fof(f789,plain,
( sF4 = unordered_pair(sF1,sF7)
| ~ spl10_3 ),
inference(forward_demodulation,[],[f788,f195]) ).
fof(f790,plain,
( sF4 = sF8
| ~ spl10_3 ),
inference(forward_demodulation,[],[f789,f209]) ).
fof(f799,plain,
( ~ member(unordered_pair(sF1,unordered_pair(x,sF6)),sF2)
| spl10_4 ),
inference(superposition,[],[f372,f195]) ).
fof(f806,plain,
( ~ member(unordered_pair(sF1,sF7),sF2)
| spl10_4 ),
inference(forward_demodulation,[],[f799,f207]) ).
fof(f808,plain,
( ~ member(sF8,sF2)
| spl10_4 ),
inference(forward_demodulation,[],[f806,f209]) ).
fof(f810,plain,
( ~ member(sF4,sF2)
| ~ spl10_3
| spl10_4 ),
inference(forward_demodulation,[],[f808,f790]) ).
fof(f813,plain,
( $false
| ~ spl10_3
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f810,f311]) ).
fof(f814,plain,
( ~ spl10_3
| spl10_4 ),
inference(avatar_contradiction_clause,[],[f813]) ).
fof(f820,plain,
( member(unordered_pair(sF1,unordered_pair(x,sF6)),sF9)
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f680,f256]) ).
fof(f822,plain,
( member(unordered_pair(sF1,sF7),sF9)
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_demodulation,[],[f820,f207]) ).
fof(f823,plain,
( member(sF8,sF9)
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_demodulation,[],[f822,f209]) ).
fof(f824,plain,
( $false
| ~ spl10_4
| ~ spl10_6 ),
inference(forward_subsumption_resolution,[],[f823,f212]) ).
fof(f825,plain,
( ~ spl10_4
| ~ spl10_6 ),
inference(avatar_contradiction_clause,[],[f824]) ).
cnf(s2,plain,
( spl10_1
| spl10_3 ),
inference(sat_conversion,[],[f246]) ).
cnf(s18,plain,
spl10_6,
inference(sat_conversion,[],[f643]) ).
cnf(s20,plain,
~ spl10_1,
inference(sat_conversion,[],[f727]) ).
cnf(s24,plain,
( ~ spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f814]) ).
cnf(s25,plain,
( ~ spl10_4
| ~ spl10_6 ),
inference(sat_conversion,[],[f825]) ).
cnf(s26,plain,
~ spl10_4,
inference(rat,[],[s25,s18]) ).
cnf(s27,plain,
~ spl10_3,
inference(rat,[],[s24,s26]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s2,s27,s20]) ).
fof(f826,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET258-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 % Computer : n013.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8046.5625MB
% 0.12/0.41 % OS : Linux 6.8.0-71-generic
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Mon Sep 28 01:13:22 UTC 2026
% 0.12/0.41 % CPUTime :
% 0.12/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.45 Running first-order theorem proving
% 0.12/0.45 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
% 5.70/1.78 % (718484)Input is clausal, will run a generic CNF schedule.
% 5.70/1.78 % (718489)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=1945046016:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.70/1.78 % (718491)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2558801828:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.70/1.78 % (718492)lrs+10_1_sil=8000:sp=occurrence:random_seed=3433105981:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.70/1.78 % (718493)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1546188057:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.70/1.78 % (718494)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1799078818:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.70/1.78 % (718495)dis-21_1_sil=8000:lcm=predicate:random_seed=2534653336: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)
% 5.70/1.78 % (718490)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2161294658:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.70/1.78 % (718495)Instruction limit reached!
% 5.70/1.78 % (718495)------------------------------
% 5.70/1.78 % (718495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718495)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718495)Termination reason: Instruction limit
% 5.70/1.78 % (718495)Termination phase: Saturation
% 5.70/1.78 % (718495)Time elapsed: 0.070 s
% 5.70/1.78 % (718495)Peak memory usage: 89 MB
% 5.70/1.78 % (718495)Instructions burned: 119 (million)
% 5.70/1.78 % (718493)Instruction limit reached!
% 5.70/1.78 % (718493)------------------------------
% 5.70/1.78 % (718493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718493)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718493)Termination reason: Instruction limit
% 5.70/1.78 % (718493)Termination phase: Saturation
% 5.70/1.78 % (718493)Time elapsed: 0.070 s
% 5.70/1.78 % (718493)Peak memory usage: 89 MB
% 5.70/1.78 % (718493)Instructions burned: 114 (million)
% 5.70/1.78 % (718492)Instruction limit reached!
% 5.70/1.78 % (718492)------------------------------
% 5.70/1.78 % (718492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718492)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718492)Termination reason: Instruction limit
% 5.70/1.78 % (718492)Termination phase: Saturation
% 5.70/1.78 % (718492)Time elapsed: 0.075 s
% 5.70/1.78 % (718492)Peak memory usage: 90 MB
% 5.70/1.78 % (718492)Instructions burned: 109 (million)
% 5.70/1.78 % (718494)Instruction limit reached!
% 5.70/1.78 % (718494)------------------------------
% 5.70/1.78 % (718494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718494)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718494)Termination reason: Instruction limit
% 5.70/1.78 % (718494)Termination phase: Saturation
% 5.70/1.78 % (718494)Time elapsed: 0.132 s
% 5.70/1.78 % (718494)Peak memory usage: 90 MB
% 5.70/1.78 % (718494)Instructions burned: 181 (million)
% 5.70/1.78 % (718505)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=658839122:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.70/1.78 % (718503)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=570818317:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.70/1.78 % (718504)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3296762655: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)
% 5.70/1.78 % (718503)Refutation not found, incomplete strategy
% 5.70/1.78 % (718503)------------------------------
% 5.70/1.78 % (718503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718503)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718503)Termination reason: Refutation not found, incomplete strategy
% 5.70/1.78 % (718503)Time elapsed: 0.002 s
% 5.70/1.78 % (718503)Peak memory usage: 88 MB
% 5.70/1.78 % (718503)Instructions burned: 1 (million)
% 5.70/1.78 % (718506)lrs+10_64_to=lpo:sil=8000:random_seed=1184493721:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.70/1.78 % (718504)Instruction limit reached!
% 5.70/1.78 % (718504)------------------------------
% 5.70/1.78 % (718504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718504)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718504)Termination reason: Instruction limit
% 5.70/1.78 % (718504)Termination phase: Saturation
% 5.70/1.78 % (718504)Time elapsed: 0.100 s
% 5.70/1.78 % (718504)Peak memory usage: 90 MB
% 5.70/1.78 % (718504)Instructions burned: 190 (million)
% 5.70/1.78 % (718505)Instruction limit reached!
% 5.70/1.78 % (718505)------------------------------
% 5.70/1.78 % (718505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718505)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718505)Termination reason: Instruction limit
% 5.70/1.78 % (718505)Termination phase: Saturation
% 5.70/1.78 % (718505)Time elapsed: 0.130 s
% 5.70/1.78 % (718505)Peak memory usage: 89 MB
% 5.70/1.78 % (718505)Instructions burned: 220 (million)
% 5.70/1.78 % (718506)Instruction limit reached!
% 5.70/1.78 % (718506)------------------------------
% 5.70/1.78 % (718506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718506)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718506)Termination reason: Instruction limit
% 5.70/1.78 % (718506)Termination phase: Saturation
% 5.70/1.78 % (718506)Time elapsed: 0.080 s
% 5.70/1.78 % (718506)Peak memory usage: 89 MB
% 5.70/1.78 % (718506)Instructions burned: 127 (million)
% 5.70/1.78 % (718489)First to succeed.
% 5.70/1.78 % (718489)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-718484"
% 5.70/1.78 % (718503)------------------------------
% 5.70/1.78 % (718503)------------------------------
% 5.70/1.78 % (718511)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3810853822:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.70/1.78 % (718512)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=942623943:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.70/1.78 % (718513)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3933371813:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 5.70/1.78 % (718511)Instruction limit reached!
% 5.70/1.78 % (718511)------------------------------
% 5.70/1.78 % (718511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718511)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718511)Termination reason: Instruction limit
% 5.70/1.78 % (718511)Termination phase: Saturation
% 5.70/1.78 % (718511)Time elapsed: 0.123 s
% 5.70/1.78 % (718511)Peak memory usage: 90 MB
% 5.70/1.78 % (718511)Instructions burned: 195 (million)
% 5.70/1.78 % (718512)Instruction limit reached!
% 5.70/1.78 % (718512)------------------------------
% 5.70/1.78 % (718512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718512)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718512)Termination reason: Instruction limit
% 5.70/1.78 % (718512)Termination phase: Saturation
% 5.70/1.78 % (718512)Time elapsed: 0.108 s
% 5.70/1.78 % (718512)Peak memory usage: 91 MB
% 5.70/1.78 % (718512)Instructions burned: 157 (million)
% 5.70/1.78 % (718514)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=2506561199:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 5.70/1.78 % (718514)Instruction limit reached!
% 5.70/1.78 % (718514)------------------------------
% 5.70/1.78 % (718514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.70/1.78 % (718514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.70/1.78 % (718514)CaDiCaL version: 2.1.3
% 5.70/1.78 % (718514)Termination reason: Instruction limit
% 5.70/1.78 % (718514)Termination phase: Saturation
% 5.70/1.78 % (718514)Time elapsed: 0.058 s
% 5.70/1.78 % (718514)Peak memory usage: 90 MB
% 5.70/1.78 % (718514)Instructions burned: 108 (million)
% 5.70/1.78 % (718489)Refutation found. Thanks to Tanya!
% 5.70/1.78 % SZS status Unsatisfiable for theBenchmark
% 5.70/1.78 % SZS output start Proof for theBenchmark
% See solution above
% 6.82/1.99 % (718489)------------------------------
% 6.82/1.99 % (718489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.82/1.99 % (718489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.82/1.99 % (718489)CaDiCaL version: 2.1.3
% 6.82/1.99 % (718489)Termination reason: Refutation
% 6.82/1.99 % (718489)Time elapsed: 0.504 s
% 6.82/1.99 % (718489)Peak memory usage: 131 MB
% 6.82/1.99 % (718489)Instructions burned: 1104 (million)
% 6.82/1.99 % (718489)------------------------------
% 6.82/1.99 % (718489)------------------------------
% 6.82/1.99 % (718484)Success in time 0.885 s
% 6.82/1.99 % Vampire exiting
%------------------------------------------------------------------------------