%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM155-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:11:50 PM UTC 2026
% Result : Unsatisfiable 8.71s 7.11s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 38
% Syntax : Number of formulae : 146 ( 43 unt; 15 def)
% Number of atoms : 302 ( 69 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 286 ( 130 ~; 146 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 11 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f44,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f176,negated_conjecture,
member(x,ordinal_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_ordinal_between_1) ).
fof(f177,negated_conjecture,
member(y,ordinal_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_ordinal_between_2) ).
fof(f178,negated_conjecture,
member(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_ordinal_between_3) ).
fof(f179,negated_conjecture,
member(y,successor(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_ordinal_between_4) ).
fof(f185,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f44,f26,f12]) ).
fof(f204,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(f270,plain,
member(y,complement(intersection(complement(x),complement(unordered_pair(x,x))))),
inference(definition_unfolding,[],[f179,f185]) ).
fof(f277,definition,
sF0 = complement(x),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f278,plain,
complement(x) = sF0,
inference(reorient_equations,[],[f277]) ).
fof(f279,definition,
sF1 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f280,plain,
unordered_pair(x,x) = sF1,
inference(reorient_equations,[],[f279]) ).
fof(f281,definition,
sF2 = complement(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f282,plain,
complement(sF1) = sF2,
inference(reorient_equations,[],[f281]) ).
fof(f283,definition,
sF3 = intersection(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f284,plain,
intersection(sF0,sF2) = sF3,
inference(reorient_equations,[],[f283]) ).
fof(f285,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f286,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f285]) ).
fof(f287,plain,
member(y,sF4),
inference(definition_folding,[],[f270,f286,f284,f282,f280,f278]) ).
fof(f289,plain,
! [X0] :
( ~ member(X0,sF4)
| ~ member(X0,sF3) ),
inference(superposition,[],[f24,f286]) ).
fof(f292,plain,
~ member(y,sF3),
inference(resolution,[],[f287,f289]) ).
fof(f296,plain,
! [X0] :
( ~ member(X0,sF2)
| member(X0,sF3)
| ~ member(X0,sF0) ),
inference(superposition,[],[f23,f284]) ).
fof(f299,definition,
( spl5_1
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f300,plain,
( member(x,universal_class)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f301,plain,
( ~ member(x,universal_class)
| spl5_1 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f308,plain,
! [X0] :
( ~ member(X0,sF1)
| x = X0
| x = X0 ),
inference(superposition,[],[f8,f280]) ).
fof(f309,plain,
! [X0] :
( ~ member(X0,sF1)
| x = X0 ),
inference(duplicate_literal_removal,[],[f308]) ).
fof(f315,plain,
! [X0] :
( ~ subclass(ordinal_numbers,X0)
| member(y,X0) ),
inference(resolution,[],[f1,f177]) ).
fof(f316,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X0,X1),X2)
| member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0) ),
inference(resolution,[],[f1,f23]) ).
fof(f321,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,sF0)
| member(X0,x) ),
inference(superposition,[],[f25,f278]) ).
fof(f323,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(X0,sF2)
| member(X0,sF1) ),
inference(superposition,[],[f25,f282]) ).
fof(f324,plain,
! [X0,X1] :
( ~ member(X0,regular(X1))
| member(X0,null_class)
| ~ member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f23,f70]) ).
fof(f327,plain,
member(y,universal_class),
inference(resolution,[],[f315,f4]) ).
fof(f329,plain,
( member(y,sF2)
| member(y,sF1) ),
inference(resolution,[],[f327,f323]) ).
fof(f330,plain,
( member(y,sF0)
| member(y,x) ),
inference(resolution,[],[f327,f321]) ).
fof(f333,definition,
( spl5_3
<=> member(y,x) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f335,plain,
( member(y,x)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f337,definition,
( spl5_4
<=> member(y,sF0) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f340,plain,
( spl5_3
| spl5_4 ),
inference(avatar_split_clause,[],[f330,f337,f333]) ).
fof(f342,definition,
( spl5_5
<=> member(y,sF1) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f344,plain,
( member(y,sF1)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f346,definition,
( spl5_6
<=> member(y,sF2) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f348,plain,
( member(y,sF2)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f349,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f329,f346,f342]) ).
fof(f351,plain,
( x = y
| ~ spl5_5 ),
inference(resolution,[],[f344,f309]) ).
fof(f363,plain,
( member(y,sF3)
| ~ member(y,sF0)
| ~ spl5_6 ),
inference(resolution,[],[f348,f296]) ).
fof(f366,plain,
( ~ member(y,sF0)
| ~ spl5_6 ),
inference(forward_subsumption_resolution,[],[f363,f292]) ).
fof(f367,plain,
( ~ spl5_4
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f366,f346,f337]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f316,f4]) ).
fof(f373,plain,
! [X0] :
( ~ member(x,X0)
| member(x,universal_class) ),
inference(resolution,[],[f369,f176]) ).
fof(f383,plain,
( ! [X0] : ~ member(x,X0)
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f373,f301]) ).
fof(f385,plain,
( $false
| spl5_1 ),
inference(resolution,[],[f383,f178]) ).
fof(f392,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f385]) ).
fof(f402,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(f407,plain,
( null_class = sF1
| x = regular(sF1) ),
inference(resolution,[],[f68,f309]) ).
fof(f455,definition,
( spl5_16
<=> x = regular(sF1) ),
introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition]) ).
fof(f457,plain,
( x = regular(sF1)
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f459,definition,
( spl5_17
<=> null_class = sF1 ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
fof(f461,plain,
( null_class = sF1
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f462,plain,
( spl5_16
| spl5_17 ),
inference(avatar_split_clause,[],[f407,f459,f455]) ).
fof(f723,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f2,f21]) ).
fof(f749,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f723,f3]) ).
fof(f774,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f749]) ).
fof(f793,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f774,f70]) ).
fof(f798,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f793,f7]) ).
fof(f799,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f798]) ).
fof(f871,plain,
! [X2,X0,X1] :
( ~ member(X1,X0)
| member(X1,null_class)
| ~ member(X1,unordered_pair(X2,X0))
| null_class = unordered_pair(X2,X0)
| regular(unordered_pair(X2,X0)) = X2
| null_class = unordered_pair(X2,X0) ),
inference(superposition,[],[f324,f402]) ).
fof(f874,plain,
! [X2,X0,X1] :
( ~ member(X1,unordered_pair(X2,X0))
| member(X1,null_class)
| ~ member(X1,X0)
| null_class = unordered_pair(X2,X0)
| regular(unordered_pair(X2,X0)) = X2 ),
inference(duplicate_literal_removal,[],[f871]) ).
fof(f876,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X0,X1)
| unordered_pair(X0,X1) = null_class
| regular(unordered_pair(X0,X1)) = X0
| member(X0,null_class) ),
inference(resolution,[],[f874,f9]) ).
fof(f921,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f799,f774]) ).
fof(f944,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f204,f921]) ).
fof(f945,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f944]) ).
fof(f949,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f945,f68]) ).
fof(f955,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f945,f949]) ).
fof(f1202,plain,
! [X0] :
( ~ member(y,X0)
| null_class = unordered_pair(y,X0)
| y = regular(unordered_pair(y,X0))
| member(y,null_class) ),
inference(resolution,[],[f876,f327]) ).
fof(f1203,plain,
! [X0] :
( ~ member(y,X0)
| null_class = unordered_pair(y,X0)
| y = regular(unordered_pair(y,X0)) ),
inference(forward_subsumption_resolution,[],[f1202,f955]) ).
fof(f1419,plain,
( null_class = unordered_pair(y,x)
| y = regular(unordered_pair(y,x))
| ~ spl5_3 ),
inference(resolution,[],[f1203,f335]) ).
fof(f1462,definition,
( spl5_56
<=> y = regular(unordered_pair(y,x)) ),
introduced(definition,[new_symbols(definition,[spl5_56])],[avatar_definition]) ).
fof(f1463,plain,
( y != regular(unordered_pair(y,x))
| spl5_56 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f1464,plain,
( y = regular(unordered_pair(y,x))
| ~ spl5_56 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f1466,definition,
( spl5_57
<=> null_class = unordered_pair(y,x) ),
introduced(definition,[new_symbols(definition,[spl5_57])],[avatar_definition]) ).
fof(f1468,plain,
( null_class = unordered_pair(y,x)
| ~ spl5_57 ),
inference(avatar_component_clause,[],[f1466]) ).
fof(f1469,plain,
( spl5_56
| spl5_57
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f1419,f333,f1466,f1462]) ).
fof(f1488,plain,
( member(y,null_class)
| ~ spl5_5
| ~ spl5_17 ),
inference(forward_demodulation,[],[f344,f461]) ).
fof(f1495,plain,
( $false
| ~ spl5_5
| ~ spl5_17 ),
inference(forward_subsumption_resolution,[],[f1488,f955]) ).
fof(f1496,plain,
( ~ spl5_5
| ~ spl5_17 ),
inference(avatar_contradiction_clause,[],[f1495]) ).
fof(f1631,plain,
( ! [X0] :
( ~ member(X0,y)
| member(X0,null_class)
| ~ member(X0,unordered_pair(y,x))
| null_class = unordered_pair(y,x) )
| ~ spl5_56 ),
inference(superposition,[],[f324,f1464]) ).
fof(f1644,plain,
( ! [X0] :
( ~ member(X0,y)
| ~ member(X0,unordered_pair(y,x))
| null_class = unordered_pair(y,x) )
| ~ spl5_56 ),
inference(forward_subsumption_resolution,[],[f1631,f955]) ).
fof(f1646,definition,
( spl5_71
<=> ! [X0] :
( ~ member(X0,y)
| ~ member(X0,unordered_pair(y,x)) ) ),
introduced(definition,[new_symbols(definition,[spl5_71])],[avatar_definition]) ).
fof(f1647,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(y,x))
| ~ member(X0,y) )
| ~ spl5_71 ),
inference(avatar_component_clause,[],[f1646]) ).
fof(f1648,plain,
( spl5_57
| spl5_71
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f1644,f1462,f1646,f1466]) ).
fof(f1650,plain,
( ~ member(x,y)
| ~ member(x,universal_class)
| ~ spl5_71 ),
inference(resolution,[],[f1647,f10]) ).
fof(f1660,plain,
( ~ member(x,universal_class)
| ~ spl5_71 ),
inference(forward_subsumption_resolution,[],[f1650,f178]) ).
fof(f1661,plain,
( $false
| ~ spl5_1
| ~ spl5_71 ),
inference(forward_subsumption_resolution,[],[f1660,f300]) ).
fof(f1662,plain,
( ~ spl5_1
| ~ spl5_71 ),
inference(avatar_contradiction_clause,[],[f1661]) ).
fof(f1665,plain,
( member(y,null_class)
| ~ member(y,universal_class)
| ~ spl5_57 ),
inference(superposition,[],[f9,f1468]) ).
fof(f1669,plain,
( ~ member(y,universal_class)
| ~ spl5_57 ),
inference(forward_subsumption_resolution,[],[f1665,f955]) ).
fof(f1670,plain,
( $false
| ~ spl5_57 ),
inference(forward_subsumption_resolution,[],[f1669,f327]) ).
fof(f1671,plain,
~ spl5_57,
inference(avatar_contradiction_clause,[],[f1670]) ).
fof(f1674,plain,
( x != regular(unordered_pair(x,x))
| ~ spl5_5
| spl5_56 ),
inference(forward_demodulation,[],[f1463,f351]) ).
fof(f1697,plain,
( x != regular(sF1)
| ~ spl5_5
| spl5_56 ),
inference(forward_demodulation,[],[f1674,f280]) ).
fof(f1700,plain,
( $false
| ~ spl5_5
| ~ spl5_16
| spl5_56 ),
inference(forward_subsumption_resolution,[],[f1697,f457]) ).
fof(f1701,plain,
( ~ spl5_5
| ~ spl5_16
| spl5_56 ),
inference(avatar_contradiction_clause,[],[f1700]) ).
cnf(s2,plain,
( spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f340]) ).
cnf(s3,plain,
( spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f349]) ).
cnf(s6,plain,
( ~ spl5_4
| ~ spl5_6 ),
inference(sat_conversion,[],[f367]) ).
cnf(s8,plain,
spl5_1,
inference(sat_conversion,[],[f392]) ).
cnf(s14,plain,
( spl5_16
| spl5_17 ),
inference(sat_conversion,[],[f462]) ).
cnf(s40,plain,
( ~ spl5_3
| spl5_56
| spl5_57 ),
inference(sat_conversion,[],[f1469]) ).
cnf(s43,plain,
( ~ spl5_5
| ~ spl5_17 ),
inference(sat_conversion,[],[f1496]) ).
cnf(s54,plain,
( ~ spl5_56
| spl5_57
| spl5_71 ),
inference(sat_conversion,[],[f1648]) ).
cnf(s55,plain,
( ~ spl5_1
| ~ spl5_71 ),
inference(sat_conversion,[],[f1662]) ).
cnf(s56,plain,
~ spl5_57,
inference(sat_conversion,[],[f1671]) ).
cnf(s59,plain,
( ~ spl5_5
| ~ spl5_16
| spl5_56 ),
inference(sat_conversion,[],[f1701]) ).
cnf(s60,plain,
( ~ spl5_56
| spl5_71 ),
inference(rat,[],[s54,s56]) ).
cnf(s64,plain,
( ~ spl5_3
| spl5_56 ),
inference(rat,[],[s40,s56]) ).
cnf(s67,plain,
~ spl5_71,
inference(rat,[],[s55,s8]) ).
cnf(s68,plain,
~ spl5_56,
inference(rat,[],[s60,s67]) ).
cnf(s69,plain,
~ spl5_3,
inference(rat,[],[s64,s68]) ).
cnf(s70,plain,
spl5_4,
inference(rat,[],[s2,s69]) ).
cnf(s71,plain,
~ spl5_6,
inference(rat,[],[s6,s70]) ).
cnf(s72,plain,
spl5_5,
inference(rat,[],[s3,s71]) ).
cnf(s73,plain,
~ spl5_16,
inference(rat,[],[s59,s68,s72]) ).
cnf(s74,plain,
~ spl5_17,
inference(rat,[],[s43,s72]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s14,s74,s73]) ).
fof(f1702,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM155-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n017.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 27 18:57:12 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.71/7.09 % (2880799)Input is clausal, will run a generic CNF schedule.
% 8.71/7.09 % (2880807)lrs+10_1_sil=8000:sp=occurrence:random_seed=1391038924:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.71/7.09 % (2880805)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2224605782:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.71/7.09 % (2880806)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3637339838:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.71/7.09 % (2880804)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=2031559434:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.71/7.09 % (2880810)dis-21_1_sil=8000:lcm=predicate:random_seed=2941894200: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)
% 8.71/7.09 % (2880808)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1676282460:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.71/7.09 % (2880807)Instruction limit reached!
% 8.71/7.09 % (2880807)------------------------------
% 8.71/7.09 % (2880807)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.09 % (2880807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.09 % (2880807)CaDiCaL version: 2.1.3
% 8.71/7.09 % (2880807)Termination reason: Instruction limit
% 8.71/7.09 % (2880807)Termination phase: Saturation
% 8.71/7.09 % (2880807)Time elapsed: 0.043 s
% 8.71/7.09 % (2880807)Peak memory usage: 90 MB
% 8.71/7.09 % (2880807)Instructions burned: 112 (million)
% 8.71/7.09 % (2880809)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2869783095:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.71/7.09 % (2880810)Instruction limit reached!
% 8.71/7.09 % (2880810)------------------------------
% 8.71/7.09 % (2880810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.09 % (2880810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.09 % (2880810)CaDiCaL version: 2.1.3
% 8.71/7.09 % (2880810)Termination reason: Instruction limit
% 8.71/7.09 % (2880810)Termination phase: Saturation
% 8.71/7.09 % (2880810)Time elapsed: 0.071 s
% 8.71/7.09 % (2880810)Peak memory usage: 89 MB
% 8.71/7.09 % (2880810)Instructions burned: 119 (million)
% 8.71/7.09 % (2880808)Instruction limit reached!
% 8.71/7.09 % (2880808)------------------------------
% 8.71/7.09 % (2880808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.09 % (2880808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.09 % (2880808)CaDiCaL version: 2.1.3
% 8.71/7.09 % (2880808)Termination reason: Instruction limit
% 8.71/7.09 % (2880808)Termination phase: Saturation
% 8.71/7.09 % (2880808)Time elapsed: 0.073 s
% 8.71/7.09 % (2880808)Peak memory usage: 89 MB
% 8.71/7.09 % (2880808)Instructions burned: 114 (million)
% 8.71/7.09 % (2880809)Instruction limit reached!
% 8.71/7.09 % (2880809)------------------------------
% 8.71/7.09 % (2880809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.09 % (2880809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.09 % (2880809)CaDiCaL version: 2.1.3
% 8.71/7.09 % (2880809)Termination reason: Instruction limit
% 8.71/7.09 % (2880809)Termination phase: Saturation
% 8.71/7.09 % (2880809)Time elapsed: 0.070 s
% 8.71/7.09 % (2880809)Peak memory usage: 91 MB
% 8.71/7.09 % (2880809)Instructions burned: 180 (million)
% 8.71/7.09 % (2880817)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=4231171850:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 8.71/7.09 % (2880817)Refutation not found, incomplete strategy
% 8.71/7.09 % (2880817)------------------------------
% 8.71/7.09 % (2880817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.09 % (2880817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.09 % (2880817)CaDiCaL version: 2.1.3
% 8.71/7.09 % (2880817)Termination reason: Refutation not found, incomplete strategy
% 8.71/7.09 % (2880817)Time elapsed: 0.005 s
% 8.71/7.09 % (2880817)Peak memory usage: 88 MB
% 8.71/7.09 % (2880817)Instructions burned: 5 (million)
% 8.71/7.09 % (2880821)lrs+10_64_to=lpo:sil=8000:random_seed=375542454:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 8.71/7.11 % (2880820)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1626445911:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.71/7.11 % (2880819)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3909298140: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)
% 8.71/7.11 % (2880821)Instruction limit reached!
% 8.71/7.11 % (2880821)------------------------------
% 8.71/7.11 % (2880821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880821)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880821)Termination reason: Instruction limit
% 8.71/7.11 % (2880821)Termination phase: Saturation
% 8.71/7.11 % (2880821)Time elapsed: 0.044 s
% 8.71/7.11 % (2880821)Peak memory usage: 89 MB
% 8.71/7.11 % (2880821)Instructions burned: 126 (million)
% 8.71/7.11 % (2880819)Instruction limit reached!
% 8.71/7.11 % (2880819)------------------------------
% 8.71/7.11 % (2880819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880819)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880819)Termination reason: Instruction limit
% 8.71/7.11 % (2880819)Termination phase: Saturation
% 8.71/7.11 % (2880819)Time elapsed: 0.093 s
% 8.71/7.11 % (2880819)Peak memory usage: 90 MB
% 8.71/7.11 % (2880819)Instructions burned: 190 (million)
% 8.71/7.11 % (2880826)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1769891706:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 8.71/7.11 % (2880820)Instruction limit reached!
% 8.71/7.11 % (2880820)------------------------------
% 8.71/7.11 % (2880820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880820)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880820)Termination reason: Instruction limit
% 8.71/7.11 % (2880820)Termination phase: Saturation
% 8.71/7.11 % (2880820)Time elapsed: 0.139 s
% 8.71/7.11 % (2880820)Peak memory usage: 90 MB
% 8.71/7.11 % (2880820)Instructions burned: 219 (million)
% 8.71/7.11 % (2880826)Instruction limit reached!
% 8.71/7.11 % (2880826)------------------------------
% 8.71/7.11 % (2880826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880826)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880826)Termination reason: Instruction limit
% 8.71/7.11 % (2880826)Termination phase: Saturation
% 8.71/7.11 % (2880826)Time elapsed: 0.049 s
% 8.71/7.11 % (2880826)Peak memory usage: 90 MB
% 8.71/7.11 % (2880826)Instructions burned: 196 (million)
% 8.71/7.11 % (2880817)------------------------------
% 8.71/7.11 % (2880817)------------------------------
% 8.71/7.11 % (2880827)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=485083766:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 8.71/7.11 % (2880830)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=1908213146:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 8.71/7.11 % (2880829)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2016963884:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 8.71/7.11 % (2880830)Instruction limit reached!
% 8.71/7.11 % (2880830)------------------------------
% 8.71/7.11 % (2880830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880830)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880830)Termination reason: Instruction limit
% 8.71/7.11 % (2880830)Termination phase: Saturation
% 8.71/7.11 % (2880830)Time elapsed: 0.034 s
% 8.71/7.11 % (2880830)Peak memory usage: 90 MB
% 8.71/7.11 % (2880830)Instructions burned: 107 (million)
% 8.71/7.11 % (2880831)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=4292024381:i=107_2994 on theBenchmark for (2994ds/107Mi)
% 8.71/7.11 % (2880827)Instruction limit reached!
% 8.71/7.11 % (2880827)------------------------------
% 8.71/7.11 % (2880827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880827)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880827)Termination reason: Instruction limit
% 8.71/7.11 % (2880827)Termination phase: Saturation
% 8.71/7.11 % (2880827)Time elapsed: 0.112 s
% 8.71/7.11 % (2880827)Peak memory usage: 91 MB
% 8.71/7.11 % (2880827)Instructions burned: 157 (million)
% 8.71/7.11 % (2880835)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3169907725:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2993 on theBenchmark for (2993ds/242Mi)
% 8.71/7.11 % (2880831)Instruction limit reached!
% 8.71/7.11 % (2880831)------------------------------
% 8.71/7.11 % (2880831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880831)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880831)Termination reason: Instruction limit
% 8.71/7.11 % (2880831)Termination phase: Saturation
% 8.71/7.11 % (2880831)Time elapsed: 0.076 s
% 8.71/7.11 % (2880831)Peak memory usage: 90 MB
% 8.71/7.11 % (2880831)Instructions burned: 108 (million)
% 8.71/7.11 % (2880835)Instruction limit reached!
% 8.71/7.11 % (2880835)------------------------------
% 8.71/7.11 % (2880835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880835)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880835)Termination reason: Instruction limit
% 8.71/7.11 % (2880835)Termination phase: Saturation
% 8.71/7.11 % (2880835)Time elapsed: 0.088 s
% 8.71/7.11 % (2880835)Peak memory usage: 90 MB
% 8.71/7.11 % (2880835)Instructions burned: 244 (million)
% 8.71/7.11 % (2880837)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=1444640081:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 8.71/7.11 % (2880839)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=2544361995:i=134:sd=2:doe=on:ss=axioms:sgt=14_2992 on theBenchmark for (2992ds/134Mi)
% 8.71/7.11 % (2880841)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=4215609961:i=499:bd=all_2991 on theBenchmark for (2991ds/499Mi)
% 8.71/7.11 % (2880804)First to succeed.
% 8.71/7.11 % (2880839)Instruction limit reached!
% 8.71/7.11 % (2880839)------------------------------
% 8.71/7.11 % (2880839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880839)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880839)Termination reason: Instruction limit
% 8.71/7.11 % (2880839)Termination phase: Saturation
% 8.71/7.11 % (2880839)Time elapsed: 0.083 s
% 8.71/7.11 % (2880839)Peak memory usage: 89 MB
% 8.71/7.11 % (2880839)Instructions burned: 135 (million)
% 8.71/7.11 % (2880804)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2880799"
% 8.71/7.11 % (2880841)Instruction limit reached!
% 8.71/7.11 % (2880841)------------------------------
% 8.71/7.11 % (2880841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880841)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880841)Termination reason: Instruction limit
% 8.71/7.11 % (2880841)Termination phase: Saturation
% 8.71/7.11 % (2880841)Time elapsed: 0.152 s
% 8.71/7.11 % (2880841)Peak memory usage: 96 MB
% 8.71/7.11 % (2880841)Instructions burned: 503 (million)
% 8.71/7.11 % (2880844)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=1261138187:i=191:fgj=on:bd=all_2990 on theBenchmark for (2990ds/191Mi)
% 8.71/7.11 % (2880845)lrs-11_32_anc=all:sil=8000:spb=goal_then_units:sac=on:random_seed=66830728:i=264:kws=precedence:fsr=off_2989 on theBenchmark for (2989ds/264Mi)
% 8.71/7.11 % (2880844)Instruction limit reached!
% 8.71/7.11 % (2880844)------------------------------
% 8.71/7.11 % (2880844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.71/7.11 % (2880844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.71/7.11 % (2880844)CaDiCaL version: 2.1.3
% 8.71/7.11 % (2880844)Termination reason: Instruction limit
% 8.71/7.11 % (2880844)Termination phase: Saturation
% 8.71/7.11 % (2880844)Time elapsed: 0.114 s
% 8.71/7.11 % (2880844)Peak memory usage: 90 MB
% 8.71/7.11 % (2880844)Instructions burned: 192 (million)
% 8.71/7.11 % (2880804)Refutation found. Thanks to Tanya!
% 8.71/7.11 % SZS status Unsatisfiable for theBenchmark
% 8.71/7.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/7.31 % (2880804)------------------------------
% 0.17/7.31 % (2880804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/7.31 % (2880804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/7.31 % (2880804)CaDiCaL version: 2.1.3
% 0.17/7.31 % (2880804)Termination reason: Refutation
% 0.17/7.31 % (2880804)Time elapsed: 0.836 s
% 0.17/7.31 % (2880804)Peak memory usage: 133 MB
% 0.17/7.31 % (2880804)Instructions burned: 1264 (million)
% 0.17/7.31 % (2880804)------------------------------
% 0.17/7.31 % (2880804)------------------------------
% 0.17/7.31 % (2880799)Success in time 1.256 s
% 0.17/7.31 % Vampire exiting
%------------------------------------------------------------------------------