%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 12:17:54 PM UTC 2026
% Result : Unsatisfiable 1.44s 0.70s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 33
% Syntax : Number of formulae : 142 ( 35 unt; 10 def)
% Number of atoms : 335 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 364 ( 171 ~; 183 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 104 ( 0 sgn 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',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/Axioms/SET004-0.ax',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/Axioms/SET004-0.ax',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/Axioms/SET004-0.ax',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/Axioms/SET004-0.ax',cartesian_product3) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',restriction2) ).
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/Axioms/SET004-0.ax',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(f63,axiom,
! [X0] :
( ~ function(X0)
| subclass(X0,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',function1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f133,axiom,
! [X2,X0,X1] : segment(X0,X1,X2) = domain_of(restrict(X0,X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',segment) ).
fof(f163,axiom,
! [X0,X1] :
( ~ member(X0,recursion_equation_functions(X1))
| function(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax',recursion_equation_functions1) ).
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(f201,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
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,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),xr),
inference(resolution,[],[f21,f268]) ).
fof(f277,plain,
member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,universal_class)),
inference(resolution,[],[f22,f268]) ).
fof(f325,plain,
member(u,y),
inference(resolution,[],[f195,f277]) ).
fof(f326,plain,
member(z,universal_class),
inference(resolution,[],[f196,f277]) ).
fof(f327,plain,
( null_class = intersection(intersection(xr,cross_product(y,unordered_pair(z,z))),cross_product(unordered_pair(u,u),universal_class))
| ~ member(u,universal_class) ),
inference(resolution,[],[f203,f269]) ).
fof(f328,plain,
( null_class = intersection(cross_product(unordered_pair(u,u),universal_class),intersection(xr,cross_product(y,unordered_pair(z,z))))
| ~ member(u,universal_class) ),
inference(forward_demodulation,[],[f327,f201]) ).
fof(f330,definition,
( spl0_1
<=> member(u,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f332,plain,
( ~ member(u,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f334,definition,
( spl0_2
<=> null_class = intersection(cross_product(unordered_pair(u,u),universal_class),intersection(xr,cross_product(y,unordered_pair(z,z)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f336,plain,
( null_class = intersection(cross_product(unordered_pair(u,u),universal_class),intersection(xr,cross_product(y,unordered_pair(z,z))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f337,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f328,f334,f330]) ).
fof(f388,definition,
( spl0_11
<=> function(null_class) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f389,plain,
( ~ function(null_class)
| spl0_11 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f390,plain,
( function(null_class)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f451,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f68,f24]) ).
fof(f456,plain,
! [X0] :
( function(X0)
| null_class = recursion_equation_functions(X0) ),
inference(resolution,[],[f68,f163]) ).
fof(f747,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[],[f2,f24]) ).
fof(f883,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f2584,definition,
( spl0_142
<=> function(universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_142])],[avatar_definition]) ).
fof(f2585,plain,
( function(universal_class)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f2586,plain,
( ~ function(universal_class)
| spl0_142 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f3536,plain,
member(u,universal_class),
inference(resolution,[],[f883,f325]) ).
fof(f3538,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f3536,f332]) ).
fof(f3539,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f3538]) ).
fof(f3647,plain,
( ! [X0] :
( ~ member(X0,cross_product(unordered_pair(u,u),universal_class))
| ~ member(X0,intersection(xr,cross_product(y,unordered_pair(z,z))))
| member(X0,null_class) )
| ~ spl0_2 ),
inference(superposition,[],[f23,f336]) ).
fof(f3701,definition,
( spl0_187
<=> null_class = complement(cross_product(universal_class,universal_class)) ),
introduced(definition,[new_symbols(definition,[spl0_187])],[avatar_definition]) ).
fof(f3703,plain,
( null_class = complement(cross_product(universal_class,universal_class))
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f3701]) ).
fof(f3785,definition,
( spl0_196
<=> member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z))) ),
introduced(definition,[new_symbols(definition,[spl0_196])],[avatar_definition]) ).
fof(f3786,plain,
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f3785]) ).
fof(f3787,plain,
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| spl0_196 ),
inference(avatar_component_clause,[],[f3785]) ).
fof(f3789,definition,
( spl0_197
<=> member(u,unordered_pair(u,u)) ),
introduced(definition,[new_symbols(definition,[spl0_197])],[avatar_definition]) ).
fof(f3790,plain,
( member(u,unordered_pair(u,u))
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f3789]) ).
fof(f3791,plain,
( ~ member(u,unordered_pair(u,u))
| spl0_197 ),
inference(avatar_component_clause,[],[f3789]) ).
fof(f3793,plain,
( ~ member(z,unordered_pair(z,z))
| ~ member(u,y)
| spl0_196 ),
inference(resolution,[],[f3787,f197]) ).
fof(f3794,plain,
( ~ member(z,unordered_pair(z,z))
| spl0_196 ),
inference(forward_subsumption_resolution,[],[f3793,f325]) ).
fof(f3797,plain,
( ~ member(z,universal_class)
| spl0_196 ),
inference(resolution,[],[f3794,f9]) ).
fof(f3801,plain,
( $false
| spl0_196 ),
inference(forward_subsumption_resolution,[],[f3797,f326]) ).
fof(f3802,plain,
spl0_196,
inference(avatar_contradiction_clause,[],[f3801]) ).
fof(f3814,plain,
( ~ member(u,universal_class)
| spl0_197 ),
inference(resolution,[],[f3791,f9]) ).
fof(f3818,plain,
( $false
| spl0_197 ),
inference(forward_subsumption_resolution,[],[f3814,f3536]) ).
fof(f3819,plain,
spl0_197,
inference(avatar_contradiction_clause,[],[f3818]) ).
fof(f3954,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),intersection(xr,cross_product(y,unordered_pair(z,z))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(u,u)) )
| ~ spl0_2 ),
inference(resolution,[],[f3647,f197]) ).
fof(f3984,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),xr)
| ~ member(X1,universal_class)
| ~ member(X0,unordered_pair(u,u))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(y,unordered_pair(z,z)))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),null_class) )
| ~ spl0_2 ),
inference(resolution,[],[f3954,f23]) ).
fof(f4061,plain,
( ~ member(z,universal_class)
| ~ member(u,unordered_pair(u,u))
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2 ),
inference(resolution,[],[f3984,f276]) ).
fof(f4062,plain,
( ~ member(u,unordered_pair(u,u))
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f4061,f326]) ).
fof(f4063,plain,
( ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2
| ~ spl0_197 ),
inference(forward_subsumption_resolution,[],[f4062,f3790]) ).
fof(f4064,plain,
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2
| ~ spl0_196
| ~ spl0_197 ),
inference(forward_subsumption_resolution,[],[f4063,f3786]) ).
fof(f4465,plain,
( subclass(universal_class,cross_product(universal_class,universal_class))
| ~ spl0_142 ),
inference(resolution,[],[f2585,f63]) ).
fof(f4470,plain,
( ! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class) )
| ~ spl0_142 ),
inference(resolution,[],[f4465,f1]) ).
fof(f4544,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| member(X0,universal_class) )
| ~ spl0_142 ),
inference(resolution,[],[f4470,f195]) ).
fof(f4545,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),universal_class)
| null_class = complement(cross_product(universal_class,universal_class))
| ~ spl0_142 ),
inference(resolution,[],[f4470,f451]) ).
fof(f4547,definition,
( spl0_246
<=> member(regular(complement(cross_product(universal_class,universal_class))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_246])],[avatar_definition]) ).
fof(f4549,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),universal_class)
| spl0_246 ),
inference(avatar_component_clause,[],[f4547]) ).
fof(f4550,plain,
( spl0_187
| ~ spl0_246
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f4545,f2584,f4547,f3701]) ).
fof(f4551,plain,
( ! [X0] : member(X0,universal_class)
| ~ spl0_142 ),
inference(forward_subsumption_resolution,[],[f4544,f11]) ).
fof(f4569,plain,
( $false
| ~ spl0_142
| spl0_246 ),
inference(resolution,[],[f4551,f4549]) ).
fof(f4571,plain,
( ~ spl0_142
| spl0_246 ),
inference(avatar_contradiction_clause,[],[f4569]) ).
fof(f4605,plain,
( null_class = recursion_equation_functions(universal_class)
| spl0_142 ),
inference(resolution,[],[f2586,f456]) ).
fof(f4627,plain,
( ! [X0] :
( ~ member(X0,null_class)
| function(universal_class) )
| spl0_142 ),
inference(superposition,[],[f163,f4605]) ).
fof(f4636,plain,
( ! [X0] : ~ member(X0,null_class)
| spl0_142 ),
inference(forward_subsumption_resolution,[],[f4627,f2586]) ).
fof(f4643,plain,
( $false
| ~ spl0_2
| spl0_142
| ~ spl0_196
| ~ spl0_197 ),
inference(resolution,[],[f4636,f4064]) ).
fof(f4647,plain,
( ~ spl0_2
| spl0_142
| ~ spl0_196
| ~ spl0_197 ),
inference(avatar_contradiction_clause,[],[f4643]) ).
fof(f4648,plain,
( subclass(null_class,cross_product(universal_class,universal_class))
| ~ spl0_11 ),
inference(resolution,[],[f390,f63]) ).
fof(f4681,plain,
( ! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,null_class) )
| ~ spl0_11 ),
inference(resolution,[],[f4648,f1]) ).
fof(f4807,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),null_class)
| subclass(complement(cross_product(universal_class,universal_class)),X0) )
| ~ spl0_11 ),
inference(resolution,[],[f4681,f747]) ).
fof(f4811,plain,
( ! [X0] :
( ~ member(not_subclass_element(null_class,X0),null_class)
| subclass(complement(cross_product(universal_class,universal_class)),X0) )
| ~ spl0_11
| ~ spl0_187 ),
inference(forward_demodulation,[],[f4807,f3703]) ).
fof(f4812,plain,
( ! [X0] :
( subclass(null_class,X0)
| ~ member(not_subclass_element(null_class,X0),null_class) )
| ~ spl0_11
| ~ spl0_187 ),
inference(forward_demodulation,[],[f4811,f3703]) ).
fof(f4813,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_11
| ~ spl0_187 ),
inference(forward_subsumption_resolution,[],[f4812,f2]) ).
fof(f4820,plain,
( ! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1) )
| ~ spl0_11
| ~ spl0_187 ),
inference(resolution,[],[f4813,f1]) ).
fof(f4832,plain,
( ! [X0] : member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),X0)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_187
| ~ spl0_196
| ~ spl0_197 ),
inference(resolution,[],[f4820,f4064]) ).
fof(f4888,plain,
( ! [X0] : ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),X0)
| ~ spl0_2
| ~ spl0_11
| ~ spl0_187
| ~ spl0_196
| ~ spl0_197 ),
inference(resolution,[],[f4832,f24]) ).
fof(f4908,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_187
| ~ spl0_196
| ~ spl0_197 ),
inference(forward_subsumption_resolution,[],[f4888,f4832]) ).
fof(f4909,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_187
| ~ spl0_196
| ~ spl0_197 ),
inference(avatar_contradiction_clause,[],[f4908]) ).
fof(f4924,plain,
( null_class = recursion_equation_functions(null_class)
| spl0_11 ),
inference(resolution,[],[f389,f456]) ).
fof(f4927,plain,
( ~ member(z,universal_class)
| ~ member(u,unordered_pair(u,u))
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2 ),
inference(resolution,[],[f276,f3984]) ).
fof(f4931,definition,
( spl0_257
<=> member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class) ),
introduced(definition,[new_symbols(definition,[spl0_257])],[avatar_definition]) ).
fof(f4933,plain,
( member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f4931]) ).
fof(f4970,plain,
( ! [X0] :
( ~ member(X0,null_class)
| function(null_class) )
| spl0_11 ),
inference(superposition,[],[f163,f4924]) ).
fof(f4978,plain,
( ! [X0] : ~ member(X0,null_class)
| spl0_11 ),
inference(forward_subsumption_resolution,[],[f4970,f389]) ).
fof(f4985,plain,
( ~ member(z,universal_class)
| ~ member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),cross_product(y,unordered_pair(z,z)))
| member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2
| ~ spl0_197 ),
inference(forward_subsumption_resolution,[],[f4927,f3790]) ).
fof(f4987,plain,
( ~ member(z,universal_class)
| member(unordered_pair(unordered_pair(u,u),unordered_pair(u,unordered_pair(z,z))),null_class)
| ~ spl0_2
| ~ spl0_196
| ~ spl0_197 ),
inference(forward_subsumption_resolution,[],[f4985,f3786]) ).
fof(f4989,definition,
( spl0_258
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_258])],[avatar_definition]) ).
fof(f4991,plain,
( ~ member(z,universal_class)
| spl0_258 ),
inference(avatar_component_clause,[],[f4989]) ).
fof(f4992,plain,
( spl0_257
| ~ spl0_258
| ~ spl0_2
| ~ spl0_196
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f4987,f3789,f3785,f334,f4989,f4931]) ).
fof(f4996,plain,
( $false
| spl0_258 ),
inference(forward_subsumption_resolution,[],[f4991,f326]) ).
fof(f4997,plain,
spl0_258,
inference(avatar_contradiction_clause,[],[f4996]) ).
fof(f5043,plain,
( $false
| spl0_11
| ~ spl0_257 ),
inference(forward_subsumption_resolution,[],[f4933,f4978]) ).
fof(f5044,plain,
( spl0_11
| ~ spl0_257 ),
inference(avatar_contradiction_clause,[],[f5043]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f337]) ).
cnf(s153,plain,
spl0_1,
inference(sat_conversion,[],[f3539]) ).
cnf(s171,plain,
spl0_196,
inference(sat_conversion,[],[f3802]) ).
cnf(s174,plain,
spl0_197,
inference(sat_conversion,[],[f3819]) ).
cnf(s207,plain,
( ~ spl0_142
| spl0_187
| ~ spl0_246 ),
inference(sat_conversion,[],[f4550]) ).
cnf(s208,plain,
( ~ spl0_142
| spl0_246 ),
inference(sat_conversion,[],[f4571]) ).
cnf(s222,plain,
( ~ spl0_2
| spl0_142
| ~ spl0_196
| ~ spl0_197 ),
inference(sat_conversion,[],[f4647]) ).
cnf(s235,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_187
| ~ spl0_196
| ~ spl0_197 ),
inference(sat_conversion,[],[f4909]) ).
cnf(s240,plain,
( ~ spl0_2
| ~ spl0_196
| ~ spl0_197
| spl0_257
| ~ spl0_258 ),
inference(sat_conversion,[],[f4992]) ).
cnf(s241,plain,
spl0_258,
inference(sat_conversion,[],[f4997]) ).
cnf(s246,plain,
( spl0_11
| ~ spl0_257 ),
inference(sat_conversion,[],[f5044]) ).
cnf(s247,plain,
( ~ spl0_2
| ~ spl0_196
| ~ spl0_197
| spl0_257 ),
inference(rat,[],[s240,s241]) ).
cnf(s255,plain,
spl0_2,
inference(rat,[],[s1,s153]) ).
cnf(s256,plain,
spl0_257,
inference(rat,[],[s247,s171,s174,s255]) ).
cnf(s257,plain,
spl0_142,
inference(rat,[],[s222,s174,s171,s255]) ).
cnf(s260,plain,
spl0_11,
inference(rat,[],[s246,s256]) ).
cnf(s263,plain,
spl0_246,
inference(rat,[],[s208,s257]) ).
cnf(s264,plain,
spl0_187,
inference(rat,[],[s207,s263,s257]) ).
cnf(s265,plain,
$false,
inference(rat,[],[s235,s174,s171,s255,s264,s260]) ).
fof(f5045,plain,
$false,
inference(avatar_sat_refutation,[],[s265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM060-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 18:46:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.44/0.70 % (1099028)Will run a generic schedule for satisfiability detection.
% 1.44/0.70 % (1099038)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=622795773:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.44/0.70 % (1099033)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1624695519_2999 on theBenchmark for (2999ds/0Mi)
% 1.44/0.70 % (1099035)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3655745375:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.44/0.70 % (1099036)dis+10_1_sil=32000:sp=arity:random_seed=3959859823:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.44/0.70 % (1099037)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2816389085:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.44/0.70 % (1099039)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2429368953:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.44/0.70 % (1099034)% WARNING: option uhcvi not known.
% 1.44/0.70 % (1099034)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2589079235:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.44/0.70 % (1099037)Instruction limit reached!
% 1.44/0.70 % (1099037)------------------------------
% 1.44/0.70 % (1099037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.70 % (1099037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.70 % (1099037)CaDiCaL version: 2.1.3
% 1.44/0.70 % (1099037)Termination reason: Instruction limit
% 1.44/0.70 % (1099037)Termination phase: Saturation
% 1.44/0.70 % (1099037)Time elapsed: 0.069 s
% 1.44/0.70 % (1099037)Peak memory usage: 13 MB
% 1.44/0.70 % (1099037)Instructions burned: 116 (million)
% 1.44/0.70 % (1099036)Instruction limit reached!
% 1.44/0.70 % (1099036)------------------------------
% 1.44/0.70 % (1099036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.70 % (1099036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.70 % (1099036)CaDiCaL version: 2.1.3
% 1.44/0.70 % (1099036)Termination reason: Instruction limit
% 1.44/0.70 % (1099036)Termination phase: Saturation
% 1.44/0.70 % (1099036)Time elapsed: 0.070 s
% 1.44/0.70 % (1099036)Peak memory usage: 13 MB
% 1.44/0.70 % (1099036)Instructions burned: 104 (million)
% 1.44/0.70 % (1099038)Instruction limit reached!
% 1.44/0.70 % (1099038)------------------------------
% 1.44/0.70 % (1099038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.70 % (1099038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.70 % (1099038)CaDiCaL version: 2.1.3
% 1.44/0.70 % (1099038)Termination reason: Instruction limit
% 1.44/0.70 % (1099038)Termination phase: Saturation
% 1.44/0.70 % (1099038)Time elapsed: 0.082 s
% 1.44/0.70 % (1099038)Peak memory usage: 13 MB
% 1.44/0.70 % (1099038)Instructions burned: 131 (million)
% 1.44/0.70 % (1099047)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2640123232:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.44/0.70 % (1099048)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1379366749:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.44/0.70 % (1099049)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2088245972:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.44/0.70 % (1099039)Instruction limit reached!
% 1.44/0.70 % (1099039)------------------------------
% 1.44/0.70 % (1099039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.70 % (1099039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.70 % (1099039)CaDiCaL version: 2.1.3
% 1.44/0.70 % (1099039)Termination reason: Instruction limit
% 1.44/0.70 % (1099039)Termination phase: Saturation
% 1.44/0.70 % (1099039)Time elapsed: 0.112 s
% 1.44/0.70 % (1099039)Peak memory usage: 14 MB
% 1.44/0.70 % (1099039)Instructions burned: 159 (million)
% 1.44/0.70 % (1099053)ott-21_1_sil=16000:fs=off:random_seed=3647145839:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.44/0.70 % (1099048)Instruction limit reached!
% 1.44/0.70 % (1099048)------------------------------
% 1.44/0.70 % (1099048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.70 % (1099048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.70 % (1099048)CaDiCaL version: 2.1.3
% 1.44/0.70 % (1099048)Termination reason: Instruction limit
% 1.44/0.70 % (1099048)Termination phase: Saturation
% 1.44/0.70 % (1099048)Time elapsed: 0.085 s
% 1.44/0.70 % (1099048)Peak memory usage: 13 MB
% 1.44/0.70 % (1099048)Instructions burned: 131 (million)
% 1.44/0.70 % (1099055)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=223188851:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.44/0.70 % TRYING [1]
% 1.44/0.70 % TRYING [2]
% 1.44/0.70 % (1099053)Instruction limit reached!
% 1.44/0.70 % (1099053)------------------------------
% 1.44/0.70 % (1099053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.44/0.70 % (1099053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.44/0.70 % (1099053)CaDiCaL version: 2.1.3
% 1.44/0.70 % (1099053)Termination reason: Instruction limit
% 1.44/0.70 % (1099053)Termination phase: Saturation
% 1.44/0.70 % (1099053)Time elapsed: 0.099 s
% 1.44/0.70 % (1099053)Peak memory usage: 13 MB
% 1.44/0.70 % (1099053)Instructions burned: 181 (million)
% 1.44/0.70 % TRYING [3]
% 1.44/0.70 % (1099049) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1099028-1099049"...
% 1.44/0.70 % (1099049)...printing done.
% 1.44/0.70 % (1099049)Refutation found. Thanks to Tanya!
% 1.44/0.70 % SZS status Unsatisfiable for theBenchmark
% 1.44/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.70 % (1099049)------------------------------
% 0.15/0.70 % (1099049)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.70 % (1099049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.70 % (1099049)CaDiCaL version: 2.1.3
% 0.15/0.70 % (1099049)Termination reason: Refutation
% 0.15/0.70 % (1099049)Time elapsed: 0.148 s
% 0.15/0.70 % (1099049)Peak memory usage: 14 MB
% 0.15/0.70 % (1099049)Instructions burned: 213 (million)
% 0.15/0.70 % (1099028)Success in time 0.289 s
% 0.15/0.70 % Vampire exiting
%------------------------------------------------------------------------------