%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:43:07 PM UTC 2026
% Result : Unsatisfiable 0.37s 0.47s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 17 unt; 1 def)
% Number of atoms : 85 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 27 ~; 37 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f113,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f117,axiom,
! [X0] :
( X0 = null_class
| member(not_subclass_element(X0,null_class),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f118,plain,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f117]) ).
fof(f156,axiom,
! [X0] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0))
| singleton(not_subclass_element(X0,null_class)) = X0
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_of_elements_in_class) ).
fof(f157,plain,
! [X0] :
( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0))
| singleton(not_subclass_element(X0,null_class)) = X0
| null_class = X0 ),
inference(reorient_equations,[],[f156]) ).
fof(f158,negated_conjecture,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
fof(f159,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(reorient_equations,[],[f158]) ).
fof(f160,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_2) ).
fof(f161,plain,
x != singleton(not_subclass_element(x,null_class)),
inference(reorient_equations,[],[f160]) ).
fof(f162,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
fof(f163,plain,
null_class != x,
inference(reorient_equations,[],[f162]) ).
fof(f242,plain,
! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0))
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| null_class = X0 ),
inference(definition_unfolding,[],[f157,f12,f12,f12]) ).
fof(f243,plain,
not_subclass_element(x,null_class) = not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),
inference(definition_unfolding,[],[f159,f12]) ).
fof(f244,plain,
x != unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)),
inference(definition_unfolding,[],[f161,f12]) ).
fof(f284,definition,
( spl0_2
<=> member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f285,plain,
( ~ member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| spl0_2 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f286,plain,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f328,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| ~ spl0_2 ),
inference(resolution,[],[f21,f286]) ).
fof(f341,plain,
( ~ member(not_subclass_element(x,null_class),unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))
| ~ spl0_2 ),
inference(resolution,[],[f328,f24]) ).
fof(f343,plain,
( member(not_subclass_element(x,null_class),x)
| ~ spl0_2 ),
inference(resolution,[],[f22,f286]) ).
fof(f361,plain,
( member(not_subclass_element(x,null_class),intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x))
| null_class = intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x) ),
inference(superposition,[],[f118,f243]) ).
fof(f491,plain,
( ! [X0] :
( ~ subclass(x,X0)
| member(not_subclass_element(x,null_class),X0) )
| ~ spl0_2 ),
inference(resolution,[],[f1,f343]) ).
fof(f493,plain,
( member(not_subclass_element(x,null_class),universal_class)
| ~ spl0_2 ),
inference(resolution,[],[f491,f4]) ).
fof(f540,plain,
( ! [X0] : member(not_subclass_element(x,null_class),unordered_pair(X0,not_subclass_element(x,null_class)))
| ~ spl0_2 ),
inference(resolution,[],[f493,f10]) ).
fof(f641,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f540,f341]) ).
fof(f649,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f641]) ).
fof(f650,plain,
( null_class = intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f361,f285]) ).
fof(f673,plain,
( not_subclass_element(x,null_class) = not_subclass_element(null_class,null_class)
| spl0_2 ),
inference(superposition,[],[f243,f650]) ).
fof(f679,plain,
( x != unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))
| spl0_2 ),
inference(superposition,[],[f244,f673]) ).
fof(f681,plain,
( null_class = intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x)
| spl0_2 ),
inference(superposition,[],[f650,f673]) ).
fof(f2107,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
| x = unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))
| null_class = x
| spl0_2 ),
inference(superposition,[],[f242,f673]) ).
fof(f2112,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
| null_class = x
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2107,f679]) ).
fof(f2125,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x),null_class),intersection(complement(unordered_pair(not_subclass_element(null_class,null_class),not_subclass_element(null_class,null_class))),x))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2112,f163]) ).
fof(f2138,plain,
( member(not_subclass_element(null_class,null_class),null_class)
| spl0_2 ),
inference(forward_demodulation,[],[f2125,f681]) ).
fof(f2149,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f2138,f113]) ).
fof(f2150,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2149]) ).
cnf(s8,plain,
~ spl0_2,
inference(sat_conversion,[],[f649]) ).
cnf(s72,plain,
spl0_2,
inference(sat_conversion,[],[f2150]) ).
cnf(s75,plain,
$false,
inference(rat,[],[s8,s72]) ).
fof(f2155,plain,
$false,
inference(avatar_sat_refutation,[],[s75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:44:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.47 % (4052956)Will run a generic schedule for satisfiability detection.
% 0.37/0.47 % (4052966)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2898662574:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.47 % (4052961)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1987691323_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.47 % (4052963)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1485186630:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.47 % (4052964)dis+10_1_sil=32000:sp=arity:random_seed=2386318944:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.47 % (4052965)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3332729566:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.37/0.47 % (4052967)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2476950278:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.47 % (4052962)% WARNING: option uhcvi not known.
% 0.37/0.47 % (4052962)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1277357050:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.47 % (4052966) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4052956-4052966"...
% 0.37/0.47 % (4052966)...printing done.
% 0.37/0.47 % (4052966)Refutation found. Thanks to Tanya!
% 0.37/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.37/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.47 % (4052966)------------------------------
% 0.37/0.47 % (4052966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.47 % (4052966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.47 % (4052966)CaDiCaL version: 2.1.3
% 0.37/0.47 % (4052966)Termination reason: Refutation
% 0.37/0.47 % (4052966)Time elapsed: 0.034 s
% 0.37/0.47 % (4052966)Peak memory usage: 13 MB
% 0.37/0.47 % (4052966)Instructions burned: 93 (million)
% 0.37/0.47 % (4052956)Success in time 0.063 s
% 0.37/0.47 % Vampire exiting
%------------------------------------------------------------------------------