%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET070-6 : 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 : n003.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 12:39:56 PM UTC 2026
% Result : Unsatisfiable 6.77s 2.00s
% Output : Refutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 153 ( 19 unt; 15 def)
% Number of atoms : 367 ( 87 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 356 ( 142 ~; 201 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 59 !; 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(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
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(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(f101,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unordered_pair_equals_singleton2_1) ).
fof(f102,negated_conjecture,
unordered_pair(x,y) != singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unordered_pair_equals_singleton2_2) ).
fof(f151,plain,
unordered_pair(x,y) != unordered_pair(y,y),
inference(definition_unfolding,[],[f102,f12]) ).
fof(f155,definition,
sF0 = unordered_pair(x,y),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f156,plain,
unordered_pair(x,y) = sF0,
inference(reorient_equations,[],[f155]) ).
fof(f157,definition,
sF1 = unordered_pair(y,y),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f158,plain,
unordered_pair(y,y) = sF1,
inference(reorient_equations,[],[f157]) ).
fof(f159,plain,
sF0 != sF1,
inference(definition_folding,[],[f151,f158,f156]) ).
fof(f162,plain,
! [X0] :
( ~ member(X0,sF0)
| x = X0
| y = X0 ),
inference(superposition,[],[f8,f156]) ).
fof(f163,plain,
! [X0] :
( ~ member(X0,sF1)
| y = X0
| y = X0 ),
inference(superposition,[],[f8,f158]) ).
fof(f164,plain,
! [X0] :
( ~ member(X0,sF1)
| y = X0 ),
inference(duplicate_literal_removal,[],[f163]) ).
fof(f170,definition,
( spl2_1
<=> member(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f171,plain,
( member(y,universal_class)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( ~ member(y,universal_class)
| spl2_1 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl2_2
<=> member(y,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f176,plain,
( member(y,sF1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f179,plain,
( member(y,sF0)
| ~ member(y,universal_class) ),
inference(superposition,[],[f10,f156]) ).
fof(f180,plain,
( member(y,sF1)
| ~ member(y,universal_class) ),
inference(superposition,[],[f10,f158]) ).
fof(f188,plain,
! [X0] :
( subclass(sF0,X0)
| x = not_subclass_element(sF0,X0)
| y = not_subclass_element(sF0,X0) ),
inference(resolution,[],[f2,f162]) ).
fof(f189,plain,
! [X0] :
( subclass(sF1,X0)
| y = not_subclass_element(sF1,X0) ),
inference(resolution,[],[f2,f164]) ).
fof(f190,plain,
! [X0] :
( ~ subclass(X0,sF1)
| y = not_subclass_element(sF1,X0)
| sF1 = X0 ),
inference(resolution,[],[f189,f7]) ).
fof(f191,plain,
! [X0] :
( ~ subclass(X0,sF0)
| y = not_subclass_element(sF0,X0)
| x = not_subclass_element(sF0,X0)
| sF0 = X0 ),
inference(resolution,[],[f188,f7]) ).
fof(f192,plain,
( y = not_subclass_element(sF0,sF1)
| x = not_subclass_element(sF0,sF1)
| sF0 = sF1
| y = not_subclass_element(sF1,sF0) ),
inference(resolution,[],[f191,f189]) ).
fof(f195,plain,
( y = not_subclass_element(sF0,sF1)
| x = not_subclass_element(sF0,sF1)
| y = not_subclass_element(sF1,sF0) ),
inference(forward_subsumption_resolution,[],[f192,f159]) ).
fof(f197,definition,
( spl2_3
<=> y = not_subclass_element(sF1,sF0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f198,plain,
( y != not_subclass_element(sF1,sF0)
| spl2_3 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f199,plain,
( y = not_subclass_element(sF1,sF0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl2_4
<=> x = not_subclass_element(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f202,plain,
( x != not_subclass_element(sF0,sF1)
| spl2_4 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( x = not_subclass_element(sF0,sF1)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f205,definition,
( spl2_5
<=> y = not_subclass_element(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f206,plain,
( y != not_subclass_element(sF0,sF1)
| spl2_5 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f207,plain,
( y = not_subclass_element(sF0,sF1)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f208,plain,
( spl2_3
| spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f195,f205,f201,f197]) ).
fof(f211,definition,
( spl2_6
<=> subclass(sF1,sF0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f212,plain,
( ~ subclass(sF1,sF0)
| spl2_6 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f213,plain,
( subclass(sF1,sF0)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f221,plain,
! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f68,f8]) ).
fof(f222,plain,
( null_class = sF0
| x = regular(sF0)
| y = regular(sF0) ),
inference(resolution,[],[f68,f162]) ).
fof(f229,definition,
( spl2_8
<=> null_class = sF1 ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f231,plain,
( null_class = sF1
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f234,definition,
( spl2_9
<=> y = regular(sF0) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f236,plain,
( y = regular(sF0)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f238,definition,
( spl2_10
<=> x = regular(sF0) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f240,plain,
( x = regular(sF0)
| ~ spl2_10 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f242,definition,
( spl2_11
<=> null_class = sF0 ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f243,plain,
( null_class != sF0
| spl2_11 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,plain,
( spl2_9
| spl2_10
| spl2_11 ),
inference(avatar_split_clause,[],[f222,f242,f238,f234]) ).
fof(f252,plain,
! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ),
inference(equality_factoring,[],[f221]) ).
fof(f258,plain,
! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = null_class ),
inference(equality_resolution,[],[f252]) ).
fof(f261,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class
| unordered_pair(X0,X0) = null_class ),
inference(superposition,[],[f68,f258]) ).
fof(f262,plain,
! [X0] :
( member(X0,unordered_pair(X0,X0))
| unordered_pair(X0,X0) = null_class ),
inference(duplicate_literal_removal,[],[f261]) ).
fof(f280,plain,
( null_class != sF0
| ~ spl2_8 ),
inference(superposition,[],[f159,f231]) ).
fof(f288,plain,
( ~ spl2_11
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f280,f229,f242]) ).
fof(f312,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) ),
inference(resolution,[],[f23,f1]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f312,f4]) ).
fof(f317,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(resolution,[],[f314,f262]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X1),X2)
| member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(resolution,[],[f314,f2]) ).
fof(f335,plain,
( member(y,sF0)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f179,f171]) ).
fof(f350,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class
| unordered_pair(X0,X0) = null_class ),
inference(resolution,[],[f317,f262]) ).
fof(f363,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(duplicate_literal_removal,[],[f350]) ).
fof(f403,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1)
| subclass(X0,X1) ),
inference(resolution,[],[f320,f2]) ).
fof(f413,plain,
! [X0,X1] :
( member(not_subclass_element(X0,X1),universal_class)
| subclass(X0,X1) ),
inference(duplicate_literal_removal,[],[f403]) ).
fof(f452,plain,
( ~ member(y,sF0)
| subclass(sF1,sF0)
| ~ spl2_3 ),
inference(superposition,[],[f3,f199]) ).
fof(f459,plain,
( subclass(sF1,sF0)
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f452,f335]) ).
fof(f478,definition,
( spl2_18
<=> member(y,sF0) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f480,plain,
( member(y,sF0)
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f489,definition,
( spl2_19
<=> ! [X0] : ~ member(y,X0) ),
introduced(definition,[new_symbols(definition,[spl2_19])],[avatar_definition]) ).
fof(f490,plain,
( ! [X0] : ~ member(y,X0)
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f495,plain,
( null_class = unordered_pair(y,y)
| spl2_1 ),
inference(resolution,[],[f172,f363]) ).
fof(f496,plain,
( null_class = sF1
| spl2_1 ),
inference(forward_demodulation,[],[f495,f158]) ).
fof(f543,plain,
( member(y,sF0)
| null_class = sF0
| ~ spl2_9 ),
inference(superposition,[],[f68,f236]) ).
fof(f544,plain,
( member(y,sF0)
| ~ spl2_9
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f543,f243]) ).
fof(f546,plain,
( spl2_18
| ~ spl2_9
| spl2_11 ),
inference(avatar_split_clause,[],[f544,f242,f234,f478]) ).
fof(f548,plain,
( member(x,sF0)
| null_class = sF0
| ~ spl2_10 ),
inference(superposition,[],[f68,f240]) ).
fof(f549,plain,
( member(x,sF0)
| ~ spl2_10
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f548,f243]) ).
fof(f553,plain,
( ! [X0] :
( ~ member(x,X0)
| member(x,universal_class) )
| ~ spl2_10
| spl2_11 ),
inference(resolution,[],[f549,f314]) ).
fof(f555,plain,
( ! [X0] : ~ member(x,X0)
| ~ spl2_10
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f553,f101]) ).
fof(f556,plain,
( $false
| ~ spl2_10
| spl2_11 ),
inference(resolution,[],[f555,f549]) ).
fof(f562,plain,
( ~ spl2_10
| spl2_11 ),
inference(avatar_contradiction_clause,[],[f556]) ).
fof(f566,plain,
( ! [X0] :
( ~ member(y,X0)
| member(y,universal_class) )
| ~ spl2_18 ),
inference(resolution,[],[f480,f314]) ).
fof(f568,plain,
( ! [X0] : ~ member(y,X0)
| spl2_1
| ~ spl2_18 ),
inference(forward_subsumption_resolution,[],[f566,f172]) ).
fof(f569,plain,
( spl2_19
| spl2_1
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f568,f478,f170,f489]) ).
fof(f570,plain,
( $false
| ~ spl2_18
| ~ spl2_19 ),
inference(resolution,[],[f490,f480]) ).
fof(f576,plain,
( ~ spl2_18
| ~ spl2_19 ),
inference(avatar_contradiction_clause,[],[f570]) ).
fof(f582,plain,
( member(y,sF1)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f180,f171]) ).
fof(f598,plain,
( spl2_8
| spl2_1 ),
inference(avatar_split_clause,[],[f496,f170,f229]) ).
fof(f618,plain,
( spl2_2
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f582,f170,f174]) ).
fof(f630,plain,
( ~ member(y,sF1)
| subclass(sF0,sF1)
| ~ spl2_5 ),
inference(superposition,[],[f3,f207]) ).
fof(f634,plain,
( subclass(sF0,sF1)
| ~ spl2_2
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f630,f176]) ).
fof(f635,plain,
( y = not_subclass_element(sF1,sF0)
| sF0 = sF1
| ~ spl2_2
| ~ spl2_5 ),
inference(resolution,[],[f634,f190]) ).
fof(f637,plain,
( sF0 = sF1
| ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f635,f198]) ).
fof(f638,plain,
( $false
| ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(forward_subsumption_resolution,[],[f637,f159]) ).
fof(f639,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(avatar_contradiction_clause,[],[f638]) ).
fof(f643,plain,
( member(x,universal_class)
| subclass(sF0,sF1)
| ~ spl2_4 ),
inference(superposition,[],[f413,f203]) ).
fof(f647,definition,
( spl2_20
<=> subclass(sF0,sF1) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f648,plain,
( ~ subclass(sF0,sF1)
| spl2_20 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f649,plain,
( subclass(sF0,sF1)
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f656,plain,
( subclass(sF0,sF1)
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f643,f101]) ).
fof(f670,plain,
( spl2_20
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f656,f201,f647]) ).
fof(f671,plain,
( y = not_subclass_element(sF1,sF0)
| sF0 = sF1
| ~ spl2_20 ),
inference(resolution,[],[f649,f190]) ).
fof(f672,plain,
( ~ subclass(sF1,sF0)
| sF0 = sF1
| ~ spl2_20 ),
inference(resolution,[],[f649,f7]) ).
fof(f673,plain,
( sF0 = sF1
| spl2_3
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f671,f198]) ).
fof(f674,plain,
( $false
| spl2_3
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f673,f159]) ).
fof(f675,plain,
( spl2_3
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f674]) ).
fof(f676,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f459,f212]) ).
fof(f677,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_6 ),
inference(avatar_contradiction_clause,[],[f676]) ).
fof(f678,plain,
( sF0 = sF1
| ~ spl2_6
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f672,f213]) ).
fof(f679,plain,
( $false
| ~ spl2_6
| ~ spl2_20 ),
inference(forward_subsumption_resolution,[],[f678,f159]) ).
fof(f680,plain,
( ~ spl2_6
| ~ spl2_20 ),
inference(avatar_contradiction_clause,[],[f679]) ).
fof(f686,plain,
( y = not_subclass_element(sF0,sF1)
| x = not_subclass_element(sF0,sF1)
| sF0 = sF1
| ~ spl2_6 ),
inference(resolution,[],[f213,f191]) ).
fof(f688,plain,
( x = not_subclass_element(sF0,sF1)
| sF0 = sF1
| spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f686,f206]) ).
fof(f689,plain,
( sF0 = sF1
| spl2_4
| spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f688,f202]) ).
fof(f690,plain,
( $false
| spl2_4
| spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f689,f159]) ).
fof(f691,plain,
( spl2_4
| spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f692,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| spl2_20 ),
inference(forward_subsumption_resolution,[],[f634,f648]) ).
fof(f693,plain,
( ~ spl2_2
| ~ spl2_5
| spl2_20 ),
inference(avatar_contradiction_clause,[],[f692]) ).
cnf(s2,plain,
( spl2_3
| spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f208]) ).
cnf(s5,plain,
( spl2_9
| spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f245]) ).
cnf(s7,plain,
( ~ spl2_8
| ~ spl2_11 ),
inference(sat_conversion,[],[f288]) ).
cnf(s19,plain,
( ~ spl2_9
| spl2_11
| spl2_18 ),
inference(sat_conversion,[],[f546]) ).
cnf(s20,plain,
( ~ spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f562]) ).
cnf(s22,plain,
( spl2_1
| ~ spl2_18
| spl2_19 ),
inference(sat_conversion,[],[f569]) ).
cnf(s23,plain,
( ~ spl2_18
| ~ spl2_19 ),
inference(sat_conversion,[],[f576]) ).
cnf(s28,plain,
( spl2_1
| spl2_8 ),
inference(sat_conversion,[],[f598]) ).
cnf(s31,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f618]) ).
cnf(s36,plain,
( ~ spl2_2
| spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f639]) ).
cnf(s41,plain,
( ~ spl2_4
| spl2_20 ),
inference(sat_conversion,[],[f670]) ).
cnf(s42,plain,
( spl2_3
| ~ spl2_20 ),
inference(sat_conversion,[],[f675]) ).
cnf(s43,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_6 ),
inference(sat_conversion,[],[f677]) ).
cnf(s44,plain,
( ~ spl2_6
| ~ spl2_20 ),
inference(sat_conversion,[],[f680]) ).
cnf(s45,plain,
( spl2_4
| spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f691]) ).
cnf(s46,plain,
( ~ spl2_2
| ~ spl2_5
| spl2_20 ),
inference(sat_conversion,[],[f693]) ).
cnf(s49,plain,
spl2_1,
inference(rat,[],[s22,s23,s19,s5,s20,s7,s28]) ).
cnf(s51,plain,
spl2_2,
inference(rat,[],[s31,s49]) ).
cnf(s60,plain,
spl2_3,
inference(rat,[],[s41,s2,s36,s42,s51]) ).
cnf(s61,plain,
spl2_6,
inference(rat,[],[s43,s49,s60]) ).
cnf(s62,plain,
~ spl2_20,
inference(rat,[],[s44,s61]) ).
cnf(s63,plain,
~ spl2_4,
inference(rat,[],[s41,s62]) ).
cnf(s64,plain,
~ spl2_5,
inference(rat,[],[s46,s51,s62]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s45,s61,s64,s63]) ).
fof(f694,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET070-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n003.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 00:31:12 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 6.77/2.00 % (1079518)Input is clausal, will run a generic CNF schedule.
% 6.77/2.00 % (1079524)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2145609383:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.77/2.00 % (1079526)lrs+10_1_sil=8000:sp=occurrence:random_seed=226415401:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.77/2.00 % (1079528)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1388488819:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.77/2.00 % (1079527)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2472507308:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.77/2.00 % (1079529)dis-21_1_sil=8000:lcm=predicate:random_seed=1873268399: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)
% 6.77/2.00 % (1079523)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=3620441012:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.77/2.00 % (1079525)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1707978455:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.77/2.00 % (1079526)Refutation not found, incomplete strategy
% 6.77/2.00 % (1079526)------------------------------
% 6.77/2.00 % (1079526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079526)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079526)Termination reason: Refutation not found, incomplete strategy
% 6.77/2.00 % (1079526)Time elapsed: 0.002 s
% 6.77/2.00 % (1079526)Peak memory usage: 87 MB
% 6.77/2.00 % (1079526)Instructions burned: 1 (million)
% 6.77/2.00 % (1079529)Instruction limit reached!
% 6.77/2.00 % (1079529)------------------------------
% 6.77/2.00 % (1079529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079529)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079529)Termination reason: Instruction limit
% 6.77/2.00 % (1079529)Termination phase: Saturation
% 6.77/2.00 % (1079529)Time elapsed: 0.063 s
% 6.77/2.00 % (1079529)Peak memory usage: 88 MB
% 6.77/2.00 % (1079529)Instructions burned: 117 (million)
% 6.77/2.00 % (1079527)Instruction limit reached!
% 6.77/2.00 % (1079527)------------------------------
% 6.77/2.00 % (1079527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079527)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079527)Termination reason: Instruction limit
% 6.77/2.00 % (1079527)Termination phase: Saturation
% 6.77/2.00 % (1079527)Time elapsed: 0.066 s
% 6.77/2.00 % (1079527)Peak memory usage: 89 MB
% 6.77/2.00 % (1079527)Instructions burned: 115 (million)
% 6.77/2.00 % (1079528)Instruction limit reached!
% 6.77/2.00 % (1079528)------------------------------
% 6.77/2.00 % (1079528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079528)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079528)Termination reason: Instruction limit
% 6.77/2.00 % (1079528)Termination phase: Saturation
% 6.77/2.00 % (1079528)Time elapsed: 0.132 s
% 6.77/2.00 % (1079528)Peak memory usage: 90 MB
% 6.77/2.00 % (1079528)Instructions burned: 181 (million)
% 6.77/2.00 % (1079537)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=3352770271:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 6.77/2.00 % (1079538)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1701736339: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)
% 6.77/2.00 % (1079537)Refutation not found, incomplete strategy
% 6.77/2.00 % (1079537)------------------------------
% 6.77/2.00 % (1079537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079537)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079537)Termination reason: Refutation not found, incomplete strategy
% 6.77/2.00 % (1079537)Time elapsed: 0.003 s
% 6.77/2.00 % (1079537)Peak memory usage: 88 MB
% 6.77/2.00 % (1079537)Instructions burned: 3 (million)
% 6.77/2.00 % (1079526)------------------------------
% 6.77/2.00 % (1079526)------------------------------
% 6.77/2.00 % (1079539)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4228146289:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 6.77/2.00 % (1079538)Instruction limit reached!
% 6.77/2.00 % (1079538)------------------------------
% 6.77/2.00 % (1079538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079538)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079538)Termination reason: Instruction limit
% 6.77/2.00 % (1079538)Termination phase: Saturation
% 6.77/2.00 % (1079538)Time elapsed: 0.107 s
% 6.77/2.00 % (1079538)Peak memory usage: 91 MB
% 6.77/2.00 % (1079538)Instructions burned: 191 (million)
% 6.77/2.00 % (1079542)lrs+10_64_to=lpo:sil=8000:random_seed=3893882507:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 6.77/2.00 % (1079539)Instruction limit reached!
% 6.77/2.00 % (1079539)------------------------------
% 6.77/2.00 % (1079539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079539)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079539)Termination reason: Instruction limit
% 6.77/2.00 % (1079539)Termination phase: Saturation
% 6.77/2.00 % (1079539)Time elapsed: 0.128 s
% 6.77/2.00 % (1079539)Peak memory usage: 89 MB
% 6.77/2.00 % (1079539)Instructions burned: 220 (million)
% 6.77/2.00 % (1079537)------------------------------
% 6.77/2.00 % (1079537)------------------------------
% 6.77/2.00 % (1079544)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1178651038:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 6.77/2.00 % (1079542)Instruction limit reached!
% 6.77/2.00 % (1079542)------------------------------
% 6.77/2.00 % (1079542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079542)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079542)Termination reason: Instruction limit
% 6.77/2.00 % (1079542)Termination phase: Saturation
% 6.77/2.00 % (1079542)Time elapsed: 0.082 s
% 6.77/2.00 % (1079542)Peak memory usage: 89 MB
% 6.77/2.00 % (1079542)Instructions burned: 127 (million)
% 6.77/2.00 % (1079546)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2326772660:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 6.77/2.00 % (1079544)Instruction limit reached!
% 6.77/2.00 % (1079544)------------------------------
% 6.77/2.00 % (1079544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079544)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079544)Termination reason: Instruction limit
% 6.77/2.00 % (1079544)Termination phase: Saturation
% 6.77/2.00 % (1079544)Time elapsed: 0.120 s
% 6.77/2.00 % (1079544)Peak memory usage: 89 MB
% 6.77/2.00 % (1079544)Instructions burned: 195 (million)
% 6.77/2.00 % (1079547)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3690345872:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.77/2.00 % (1079549)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=4096820089:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 6.77/2.00 % (1079546)Instruction limit reached!
% 6.77/2.00 % (1079546)------------------------------
% 6.77/2.00 % (1079546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079546)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079546)Termination reason: Instruction limit
% 6.77/2.00 % (1079546)Termination phase: Saturation
% 6.77/2.00 % (1079546)Time elapsed: 0.103 s
% 6.77/2.00 % (1079546)Peak memory usage: 91 MB
% 6.77/2.00 % (1079546)Instructions burned: 157 (million)
% 6.77/2.00 % (1079523)First to succeed.
% 6.77/2.00 % (1079523)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1079518"
% 6.77/2.00 % (1079549)Instruction limit reached!
% 6.77/2.00 % (1079549)------------------------------
% 6.77/2.00 % (1079549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079549)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079549)Termination reason: Instruction limit
% 6.77/2.00 % (1079549)Termination phase: Saturation
% 6.77/2.00 % (1079549)Time elapsed: 0.063 s
% 6.77/2.00 % (1079549)Peak memory usage: 90 MB
% 6.77/2.00 % (1079549)Instructions burned: 107 (million)
% 6.77/2.00 % (1079525)Also succeeded, but the first one will report.
% 6.77/2.00 % (1079551)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3743477844:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 6.77/2.00 % (1079551)Refutation not found, incomplete strategy
% 6.77/2.00 % (1079551)------------------------------
% 6.77/2.00 % (1079551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.77/2.00 % (1079551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/2.00 % (1079551)CaDiCaL version: 2.1.3
% 6.77/2.00 % (1079551)Termination reason: Refutation not found, incomplete strategy
% 6.77/2.00 % (1079551)Time elapsed: 0.005 s
% 6.77/2.00 % (1079551)Peak memory usage: 88 MB
% 6.77/2.00 % (1079551)Instructions burned: 7 (million)
% 6.77/2.00 % (1079554)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=4246806320:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 6.77/2.00 % (1079555)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3428461826:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 6.77/2.00 % (1079523)Refutation found. Thanks to Tanya!
% 6.77/2.00 % SZS status Unsatisfiable for theBenchmark
% 6.77/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 8.41/2.10 % (1079523)------------------------------
% 8.41/2.10 % (1079523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.41/2.10 % (1079523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.41/2.10 % (1079523)CaDiCaL version: 2.1.3
% 8.41/2.10 % (1079523)Termination reason: Refutation
% 8.41/2.10 % (1079523)Time elapsed: 0.690 s
% 8.41/2.10 % (1079523)Peak memory usage: 129 MB
% 8.41/2.10 % (1079523)Instructions burned: 1039 (million)
% 8.41/2.10 % (1079523)------------------------------
% 8.41/2.10 % (1079523)------------------------------
% 8.41/2.10 % (1079518)Success in time 1.126 s
% 8.41/2.10 % Vampire exiting
%------------------------------------------------------------------------------