%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM060-1 : 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 : n009.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 12:11:40 PM UTC 2026
% Result : Unsatisfiable 14.66s 3.14s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 36
% Syntax : Number of formulae : 140 ( 49 unt; 14 def)
% Number of atoms : 282 ( 47 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 274 ( 132 ~; 137 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 15 con; 0-3 aty)
% Number of variables : 128 ( 0 sgn 128 !; 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(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
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(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(f31,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| restrict(X1,singleton(X0),universal_class) = null_class
| member(X0,domain_of(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f32,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| null_class = restrict(X1,singleton(X0),universal_class)
| member(X0,domain_of(X1)) ),
inference(reorient_equations,[],[f31]) ).
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(f133,axiom,
! [X2,X0,X1] : segment(X0,X1,X2) = domain_of(restrict(X0,X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment) ).
fof(f176,negated_conjecture,
member(ordered_pair(u,z),intersection(xr,cross_product(y,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_segments_property4_1) ).
fof(f177,negated_conjecture,
~ member(u,segment(xr,y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_segments_property4_2) ).
fof(f178,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(f192,plain,
! [X2,X0,X1] : segment(X0,X1,X2) = domain_of(intersection(X0,cross_product(X1,unordered_pair(X2,X2)))),
inference(definition_unfolding,[],[f133,f28,f12]) ).
fof(f195,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,f178]) ).
fof(f196,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,f178]) ).
fof(f197,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,f178]) ).
fof(f202,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(f203,plain,
! [X0,X1] :
( member(X0,domain_of(X1))
| null_class = intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f32,f28,f12]) ).
fof(f268,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),intersection(xr,cross_product(y,universal_class))),
inference(definition_unfolding,[],[f176,f178]) ).
fof(f269,plain,
~ member(u,domain_of(intersection(xr,cross_product(y,unordered_pair(z,z))))),
inference(definition_unfolding,[],[f177,f192]) ).
fof(f276,definition,
sF0 = unordered_pair(u,u),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f277,plain,
unordered_pair(u,u) = sF0,
inference(reorient_equations,[],[f276]) ).
fof(f278,definition,
sF1 = unordered_pair(z,z),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f279,plain,
unordered_pair(z,z) = sF1,
inference(reorient_equations,[],[f278]) ).
fof(f280,definition,
sF2 = unordered_pair(u,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f281,plain,
unordered_pair(u,sF1) = sF2,
inference(reorient_equations,[],[f280]) ).
fof(f282,definition,
sF3 = unordered_pair(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f283,plain,
unordered_pair(sF0,sF2) = sF3,
inference(reorient_equations,[],[f282]) ).
fof(f284,definition,
sF4 = cross_product(y,universal_class),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f285,plain,
cross_product(y,universal_class) = sF4,
inference(reorient_equations,[],[f284]) ).
fof(f286,definition,
sF5 = intersection(xr,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f287,plain,
intersection(xr,sF4) = sF5,
inference(reorient_equations,[],[f286]) ).
fof(f288,plain,
member(sF3,sF5),
inference(definition_folding,[],[f268,f287,f285,f283,f281,f279,f277]) ).
fof(f289,definition,
sF6 = cross_product(y,sF1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f290,plain,
cross_product(y,sF1) = sF6,
inference(reorient_equations,[],[f289]) ).
fof(f291,definition,
sF7 = intersection(xr,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f292,plain,
intersection(xr,sF6) = sF7,
inference(reorient_equations,[],[f291]) ).
fof(f293,definition,
sF8 = domain_of(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f294,plain,
domain_of(sF7) = sF8,
inference(reorient_equations,[],[f293]) ).
fof(f295,plain,
~ member(u,sF8),
inference(definition_folding,[],[f269,f294,f292,f290,f279]) ).
fof(f296,plain,
! [X0] :
( ~ member(X0,sF5)
| member(X0,xr) ),
inference(superposition,[],[f21,f287]) ).
fof(f297,plain,
! [X0] :
( ~ member(X0,sF5)
| member(X0,sF4) ),
inference(superposition,[],[f22,f287]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sF1)),cross_product(X1,X2))
| member(X0,X1) ),
inference(superposition,[],[f195,f279]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sF1)),cross_product(X1,X2))
| member(z,X2) ),
inference(superposition,[],[f196,f279]) ).
fof(f312,plain,
member(sF3,sF4),
inference(resolution,[],[f288,f297]) ).
fof(f313,plain,
member(sF3,xr),
inference(resolution,[],[f288,f296]) ).
fof(f315,plain,
( member(u,sF0)
| ~ member(u,universal_class) ),
inference(superposition,[],[f9,f277]) ).
fof(f317,plain,
( member(z,sF1)
| ~ member(z,universal_class) ),
inference(superposition,[],[f9,f279]) ).
fof(f319,definition,
( spl9_1
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f320,plain,
( member(z,universal_class)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f321,plain,
( ~ member(z,universal_class)
| spl9_1 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f323,definition,
( spl9_2
<=> member(z,sF1) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f325,plain,
( member(z,sF1)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f326,plain,
( ~ spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f317,f323,f319]) ).
fof(f337,definition,
( spl9_5
<=> member(u,universal_class) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f338,plain,
( member(u,universal_class)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f339,plain,
( ~ member(u,universal_class)
| spl9_5 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f341,definition,
( spl9_6
<=> member(u,sF0) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
fof(f343,plain,
( member(u,sF0)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f344,plain,
( ~ spl9_5
| spl9_6 ),
inference(avatar_split_clause,[],[f315,f341,f337]) ).
fof(f377,plain,
! [X0] :
( ~ member(X0,sF6)
| member(X0,sF7)
| ~ member(X0,xr) ),
inference(superposition,[],[f23,f292]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( ~ subclass(intersection(X0,X1),X2)
| member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0) ),
inference(resolution,[],[f1,f23]) ).
fof(f397,definition,
( spl9_14
<=> member(u,y) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
fof(f398,plain,
( ~ member(u,y)
| spl9_14 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f399,plain,
( member(u,y)
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f430,plain,
! [X0] :
( ~ member(X0,universal_class)
| null_class = intersection(sF7,cross_product(unordered_pair(X0,X0),universal_class))
| member(X0,sF8) ),
inference(superposition,[],[f203,f294]) ).
fof(f433,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(u,u),sF2),cross_product(X0,X1))
| member(u,X0) ),
inference(superposition,[],[f303,f281]) ).
fof(f436,plain,
! [X0,X1] :
( ~ member(unordered_pair(sF0,sF2),cross_product(X0,X1))
| member(u,X0) ),
inference(forward_demodulation,[],[f433,f277]) ).
fof(f438,plain,
! [X0,X1] :
( ~ member(sF3,cross_product(X0,X1))
| member(u,X0) ),
inference(forward_demodulation,[],[f436,f283]) ).
fof(f441,plain,
( ~ member(sF3,sF4)
| member(u,y) ),
inference(superposition,[],[f438,f285]) ).
fof(f476,plain,
! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sF1)),cross_product(X1,X2))
| ~ member(z,X2)
| ~ member(X0,X1) ),
inference(superposition,[],[f197,f279]) ).
fof(f549,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(u,u),sF2),cross_product(X0,X1))
| member(z,X1) ),
inference(superposition,[],[f308,f281]) ).
fof(f552,plain,
! [X0,X1] :
( ~ member(unordered_pair(sF0,sF2),cross_product(X0,X1))
| member(z,X1) ),
inference(forward_demodulation,[],[f549,f277]) ).
fof(f554,plain,
! [X0,X1] :
( ~ member(sF3,cross_product(X0,X1))
| member(z,X1) ),
inference(forward_demodulation,[],[f552,f283]) ).
fof(f557,plain,
( ~ member(sF3,sF4)
| member(z,universal_class) ),
inference(superposition,[],[f554,f285]) ).
fof(f558,plain,
member(z,universal_class),
inference(forward_subsumption_resolution,[],[f557,f312]) ).
fof(f559,plain,
( $false
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f558,f321]) ).
fof(f560,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f563,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f383,f4]) ).
fof(f577,plain,
( ! [X0] :
( ~ member(u,X0)
| member(u,universal_class) )
| ~ spl9_14 ),
inference(resolution,[],[f563,f399]) ).
fof(f593,plain,
( ! [X0] : ~ member(u,X0)
| spl9_5
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f577,f339]) ).
fof(f594,plain,
( $false
| spl9_5
| ~ spl9_14 ),
inference(resolution,[],[f593,f399]) ).
fof(f599,plain,
( spl9_5
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f601,plain,
member(u,y),
inference(forward_subsumption_resolution,[],[f441,f312]) ).
fof(f603,plain,
( $false
| spl9_14 ),
inference(forward_subsumption_resolution,[],[f601,f398]) ).
fof(f604,plain,
spl9_14,
inference(avatar_contradiction_clause,[],[f603]) ).
fof(f652,plain,
( null_class = intersection(sF7,cross_product(unordered_pair(u,u),universal_class))
| member(u,sF8)
| ~ spl9_5 ),
inference(resolution,[],[f338,f430]) ).
fof(f655,plain,
( null_class = intersection(sF7,cross_product(unordered_pair(u,u),universal_class))
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f652,f295]) ).
fof(f656,plain,
( null_class = intersection(sF7,cross_product(sF0,universal_class))
| ~ spl9_5 ),
inference(forward_demodulation,[],[f655,f277]) ).
fof(f659,plain,
( ! [X0] :
( ~ member(X0,cross_product(sF0,universal_class))
| member(X0,null_class)
| ~ member(X0,sF7) )
| ~ spl9_5 ),
inference(superposition,[],[f23,f656]) ).
fof(f1163,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(u,u),sF2),cross_product(X0,X1))
| ~ member(z,X1)
| ~ member(u,X0) ),
inference(superposition,[],[f476,f281]) ).
fof(f1166,plain,
! [X0,X1] :
( member(unordered_pair(sF0,sF2),cross_product(X0,X1))
| ~ member(z,X1)
| ~ member(u,X0) ),
inference(forward_demodulation,[],[f1163,f277]) ).
fof(f1171,plain,
! [X0,X1] :
( member(sF3,cross_product(X0,X1))
| ~ member(z,X1)
| ~ member(u,X0) ),
inference(forward_demodulation,[],[f1166,f283]) ).
fof(f1196,plain,
( ~ member(z,universal_class)
| ~ member(u,sF0)
| member(sF3,null_class)
| ~ member(sF3,sF7)
| ~ spl9_5 ),
inference(resolution,[],[f1171,f659]) ).
fof(f1199,plain,
( member(sF3,sF6)
| ~ member(z,sF1)
| ~ member(u,y) ),
inference(superposition,[],[f1171,f290]) ).
fof(f1201,plain,
( member(sF3,sF6)
| ~ member(u,y)
| ~ spl9_2 ),
inference(forward_subsumption_resolution,[],[f1199,f325]) ).
fof(f1202,plain,
( ~ member(u,sF0)
| member(sF3,null_class)
| ~ member(sF3,sF7)
| ~ spl9_1
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f1196,f320]) ).
fof(f1211,plain,
( member(sF3,sF6)
| ~ spl9_2
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1201,f399]) ).
fof(f1212,plain,
( member(sF3,null_class)
| ~ member(sF3,sF7)
| ~ spl9_1
| ~ spl9_5
| ~ spl9_6 ),
inference(forward_subsumption_resolution,[],[f1202,f343]) ).
fof(f1214,plain,
( member(sF3,sF7)
| ~ member(sF3,xr)
| ~ spl9_2
| ~ spl9_14 ),
inference(resolution,[],[f1211,f377]) ).
fof(f1217,plain,
( member(sF3,sF7)
| ~ spl9_2
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f1214,f313]) ).
fof(f1226,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f2,f21]) ).
fof(f1380,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f3,f1226]) ).
fof(f1386,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f1380]) ).
fof(f1391,plain,
! [X0] :
( subclass(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f1386,f70]) ).
fof(f1429,plain,
! [X0] :
( null_class = X0
| ~ subclass(X0,null_class)
| null_class = X0 ),
inference(resolution,[],[f1391,f7]) ).
fof(f1430,plain,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
inference(duplicate_literal_removal,[],[f1429]) ).
fof(f1468,plain,
! [X0] : null_class = intersection(null_class,X0),
inference(resolution,[],[f1430,f1386]) ).
fof(f1487,plain,
! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) ),
inference(superposition,[],[f202,f1468]) ).
fof(f1492,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(trivial_inequality_removal,[],[f1487]) ).
fof(f1514,plain,
null_class = domain_of(null_class),
inference(resolution,[],[f1492,f68]) ).
fof(f1520,plain,
! [X0] : ~ member(X0,null_class),
inference(superposition,[],[f1492,f1514]) ).
fof(f2407,plain,
( ~ member(sF3,sF7)
| ~ spl9_1
| ~ spl9_5
| ~ spl9_6 ),
inference(forward_subsumption_resolution,[],[f1212,f1520]) ).
fof(f2487,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| ~ spl9_5
| ~ spl9_6
| ~ spl9_14 ),
inference(forward_subsumption_resolution,[],[f2407,f1217]) ).
fof(f2488,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_5
| ~ spl9_6
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f2487]) ).
cnf(s1,plain,
( ~ spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f326]) ).
cnf(s3,plain,
( ~ spl9_5
| spl9_6 ),
inference(sat_conversion,[],[f344]) ).
cnf(s12,plain,
spl9_1,
inference(sat_conversion,[],[f560]) ).
cnf(s16,plain,
( spl9_5
| ~ spl9_14 ),
inference(sat_conversion,[],[f599]) ).
cnf(s17,plain,
spl9_14,
inference(sat_conversion,[],[f604]) ).
cnf(s115,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_5
| ~ spl9_6
| ~ spl9_14 ),
inference(sat_conversion,[],[f2488]) ).
cnf(s117,plain,
spl9_5,
inference(rat,[],[s16,s17]) ).
cnf(s125,plain,
spl9_6,
inference(rat,[],[s3,s117]) ).
cnf(s126,plain,
~ spl9_2,
inference(rat,[],[s115,s17,s12,s117,s125]) ).
cnf(s128,plain,
$false,
inference(rat,[],[s1,s126,s12]) ).
fof(f2489,plain,
$false,
inference(avatar_sat_refutation,[],[s128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM060-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n009.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 18:46:44 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 14.66/3.14 % (2328385)Input is clausal, will run a generic CNF schedule.
% 14.66/3.14 % (2328394)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1529931527:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 14.66/3.14 % (2328398)dis-21_1_sil=8000:lcm=predicate:random_seed=3478742177: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)
% 14.66/3.14 % (2328398)Instruction limit reached!
% 14.66/3.14 % (2328398)------------------------------
% 14.66/3.14 % (2328398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328398)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328398)Termination reason: Instruction limit
% 14.66/3.14 % (2328398)Termination phase: Saturation
% 14.66/3.14 % (2328398)Time elapsed: 0.076 s
% 14.66/3.14 % (2328398)Peak memory usage: 89 MB
% 14.66/3.14 % (2328398)Instructions burned: 118 (million)
% 14.66/3.14 % (2328393)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2229506780:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 14.66/3.14 % (2328392)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=1198904674:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 14.66/3.14 % (2328395)lrs+10_1_sil=8000:sp=occurrence:random_seed=3099685408:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 14.66/3.14 % (2328396)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=634712770:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 14.66/3.14 % (2328397)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2748178544:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 14.66/3.14 % (2328395)Instruction limit reached!
% 14.66/3.14 % (2328395)------------------------------
% 14.66/3.14 % (2328395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328395)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328395)Termination reason: Instruction limit
% 14.66/3.14 % (2328395)Termination phase: Saturation
% 14.66/3.14 % (2328395)Time elapsed: 0.111 s
% 14.66/3.14 % (2328395)Peak memory usage: 90 MB
% 14.66/3.14 % (2328395)Instructions burned: 107 (million)
% 14.66/3.14 % (2328396)Instruction limit reached!
% 14.66/3.14 % (2328396)------------------------------
% 14.66/3.14 % (2328396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328396)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328396)Termination reason: Instruction limit
% 14.66/3.14 % (2328396)Termination phase: Saturation
% 14.66/3.14 % (2328396)Time elapsed: 0.117 s
% 14.66/3.14 % (2328396)Peak memory usage: 89 MB
% 14.66/3.14 % (2328396)Instructions burned: 114 (million)
% 14.66/3.14 % (2328403)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=2021396344:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 14.66/3.14 % (2328397)Instruction limit reached!
% 14.66/3.14 % (2328397)------------------------------
% 14.66/3.14 % (2328397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328397)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328397)Termination reason: Instruction limit
% 14.66/3.14 % (2328397)Termination phase: Saturation
% 14.66/3.14 % (2328397)Time elapsed: 0.194 s
% 14.66/3.14 % (2328397)Peak memory usage: 91 MB
% 14.66/3.14 % (2328397)Instructions burned: 180 (million)
% 14.66/3.14 % (2328403)Instruction limit reached!
% 14.66/3.14 % (2328403)------------------------------
% 14.66/3.14 % (2328403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328403)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328403)Termination reason: Instruction limit
% 14.66/3.14 % (2328403)Termination phase: Saturation
% 14.66/3.14 % (2328403)Time elapsed: 0.158 s
% 14.66/3.14 % (2328403)Peak memory usage: 89 MB
% 14.66/3.14 % (2328403)Instructions burned: 143 (million)
% 14.66/3.14 % (2328408)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1465084472:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 14.66/3.14 % (2328407)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1666667645:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 14.66/3.14 % (2328410)lrs+10_64_to=lpo:sil=8000:random_seed=1381009502:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 14.66/3.14 % (2328411)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3173569922:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 14.66/3.14 % (2328410)Instruction limit reached!
% 14.66/3.14 % (2328410)------------------------------
% 14.66/3.14 % (2328410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328410)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328410)Termination reason: Instruction limit
% 14.66/3.14 % (2328410)Termination phase: Saturation
% 14.66/3.14 % (2328410)Time elapsed: 0.125 s
% 14.66/3.14 % (2328410)Peak memory usage: 90 MB
% 14.66/3.14 % (2328410)Instructions burned: 126 (million)
% 14.66/3.14 % (2328407)Instruction limit reached!
% 14.66/3.14 % (2328407)------------------------------
% 14.66/3.14 % (2328407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328407)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328407)Termination reason: Instruction limit
% 14.66/3.14 % (2328407)Termination phase: Saturation
% 14.66/3.14 % (2328407)Time elapsed: 0.182 s
% 14.66/3.14 % (2328407)Peak memory usage: 90 MB
% 14.66/3.14 % (2328407)Instructions burned: 189 (million)
% 14.66/3.14 % (2328408)Instruction limit reached!
% 14.66/3.14 % (2328408)------------------------------
% 14.66/3.14 % (2328408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328408)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328408)Termination reason: Instruction limit
% 14.66/3.14 % (2328408)Termination phase: Saturation
% 14.66/3.14 % (2328408)Time elapsed: 0.218 s
% 14.66/3.14 % (2328408)Peak memory usage: 90 MB
% 14.66/3.14 % (2328408)Instructions burned: 219 (million)
% 14.66/3.14 % (2328411)Instruction limit reached!
% 14.66/3.14 % (2328411)------------------------------
% 14.66/3.14 % (2328411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328411)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328411)Termination reason: Instruction limit
% 14.66/3.14 % (2328411)Termination phase: Saturation
% 14.66/3.14 % (2328411)Time elapsed: 0.103 s
% 14.66/3.14 % (2328411)Peak memory usage: 90 MB
% 14.66/3.14 % (2328411)Instructions burned: 196 (million)
% 14.66/3.14 % (2328416)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=92649284:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 14.66/3.14 % (2328417)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3387396522:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 14.66/3.14 % (2328416)Instruction limit reached!
% 14.66/3.14 % (2328416)------------------------------
% 14.66/3.14 % (2328416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328419)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1080714272:i=107_2991 on theBenchmark for (2991ds/107Mi)
% 14.66/3.14 % (2328418)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=1689552672:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2991 on theBenchmark for (2991ds/106Mi)
% 14.66/3.14 % (2328416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328416)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328416)Termination reason: Instruction limit
% 14.66/3.14 % (2328416)Termination phase: Saturation
% 14.66/3.14 % (2328416)Time elapsed: 0.097 s
% 14.66/3.14 % (2328416)Peak memory usage: 91 MB
% 14.66/3.14 % (2328416)Instructions burned: 158 (million)
% 14.66/3.14 % (2328418)Instruction limit reached!
% 14.66/3.14 % (2328418)------------------------------
% 14.66/3.14 % (2328418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328418)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328418)Termination reason: Instruction limit
% 14.66/3.14 % (2328418)Termination phase: Saturation
% 14.66/3.14 % (2328418)Time elapsed: 0.101 s
% 14.66/3.14 % (2328418)Peak memory usage: 89 MB
% 14.66/3.14 % (2328418)Instructions burned: 106 (million)
% 14.66/3.14 % (2328419)Instruction limit reached!
% 14.66/3.14 % (2328419)------------------------------
% 14.66/3.14 % (2328419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328419)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328419)Termination reason: Instruction limit
% 14.66/3.14 % (2328419)Termination phase: Saturation
% 14.66/3.14 % (2328419)Time elapsed: 0.115 s
% 14.66/3.14 % (2328419)Peak memory usage: 90 MB
% 14.66/3.14 % (2328419)Instructions burned: 107 (million)
% 14.66/3.14 % (2328424)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1424540229:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2988 on theBenchmark for (2988ds/242Mi)
% 14.66/3.14 % (2328425)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=1393536111:cond=fast:i=5208:av=off_2987 on theBenchmark for (2987ds/5208Mi)
% 14.66/3.14 % (2328426)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1836467504:i=134:sd=2:doe=on:ss=axioms:sgt=14_2987 on theBenchmark for (2987ds/134Mi)
% 14.66/3.14 % (2328426)Refutation not found, incomplete strategy
% 14.66/3.14 % (2328426)------------------------------
% 14.66/3.14 % (2328426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328426)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328426)Termination reason: Refutation not found, incomplete strategy
% 14.66/3.14 % (2328426)Time elapsed: 0.009 s
% 14.66/3.14 % (2328426)Peak memory usage: 89 MB
% 14.66/3.14 % (2328426)Instructions burned: 6 (million)
% 14.66/3.14 % (2328424)Instruction limit reached!
% 14.66/3.14 % (2328424)------------------------------
% 14.66/3.14 % (2328424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.66/3.14 % (2328424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.66/3.14 % (2328424)CaDiCaL version: 2.1.3
% 14.66/3.14 % (2328424)Termination reason: Instruction limit
% 14.66/3.14 % (2328424)Termination phase: Saturation
% 14.66/3.14 % (2328424)Time elapsed: 0.249 s
% 14.66/3.14 % (2328424)Peak memory usage: 91 MB
% 14.66/3.14 % (2328424)Instructions burned: 242 (million)
% 14.66/3.14 % (2328392)First to succeed.
% 14.66/3.14 % (2328392)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2328385"
% 14.66/3.14 % (2328430)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=3776178935:i=499:bd=all_2984 on theBenchmark for (2984ds/499Mi)
% 14.66/3.14 % (2328394)Also succeeded, but the first one will report.
% 14.66/3.14 % (2328426)------------------------------
% 14.66/3.14 % (2328426)------------------------------
% 14.66/3.14 % (2328392)Refutation found. Thanks to Tanya!
% 14.66/3.14 % SZS status Unsatisfiable for theBenchmark
% 14.66/3.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/3.41 % (2328392)------------------------------
% 0.24/3.41 % (2328392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/3.41 % (2328392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/3.41 % (2328392)CaDiCaL version: 2.1.3
% 0.24/3.41 % (2328392)Termination reason: Refutation
% 0.24/3.41 % (2328392)Time elapsed: 1.379 s
% 0.24/3.41 % (2328392)Peak memory usage: 133 MB
% 0.24/3.41 % (2328392)Instructions burned: 1309 (million)
% 0.24/3.41 % (2328392)------------------------------
% 0.24/3.41 % (2328392)------------------------------
% 0.24/3.41 % (2328385)Success in time 2.088 s
% 0.24/3.41 % Vampire exiting
%------------------------------------------------------------------------------