%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET137-6 : 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 : n005.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 12:43:14 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 39 ( 19 unt; 1 def)
% Number of atoms : 65 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 25 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| 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,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
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(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(u,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple_kludge1_1) ).
fof(f105,negated_conjecture,
set_builder(u,set_builder(v,set_builder(w,null_class))) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_member_of_triple_kludge1_4) ).
fof(f106,plain,
null_class = set_builder(u,set_builder(v,set_builder(w,null_class))),
inference(reorient_equations,[],[f105]) ).
fof(f112,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f156,plain,
null_class = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),
inference(definition_unfolding,[],[f106,f112,f112,f112]) ).
fof(f177,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f205,plain,
member(u,universal_class),
inference(resolution,[],[f177,f102]) ).
fof(f209,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f214,plain,
! [X0] :
( member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
| ~ member(X0,universal_class)
| member(X0,null_class) ),
inference(superposition,[],[f25,f156]) ).
fof(f220,plain,
! [X0] :
( member(X0,complement(unordered_pair(u,u)))
| member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f214,f21]) ).
fof(f228,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,universal_class)
| ~ member(X0,unordered_pair(u,u)) ),
inference(resolution,[],[f220,f24]) ).
fof(f230,plain,
! [X0] :
( ~ member(X0,unordered_pair(u,u))
| member(X0,null_class) ),
inference(forward_subsumption_resolution,[],[f228,f177]) ).
fof(f238,plain,
( member(u,null_class)
| ~ member(u,universal_class) ),
inference(resolution,[],[f230,f10]) ).
fof(f249,plain,
member(u,null_class),
inference(forward_subsumption_resolution,[],[f238,f205]) ).
fof(f753,plain,
! [X0] :
( member(u,X0)
| null_class = X0 ),
inference(resolution,[],[f209,f249]) ).
fof(f832,definition,
( spl0_44
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f833,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f870,plain,
! [X0] :
( ~ member(u,X0)
| complement(X0) = null_class ),
inference(resolution,[],[f753,f24]) ).
fof(f982,plain,
null_class = complement(null_class),
inference(resolution,[],[f870,f249]) ).
fof(f1292,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,null_class) ),
inference(superposition,[],[f24,f982]) ).
fof(f1293,plain,
! [X0] : ~ member(X0,null_class),
inference(duplicate_literal_removal,[],[f1292]) ).
fof(f1295,plain,
spl0_44,
inference(avatar_split_clause,[],[f1293,f832]) ).
fof(f1373,plain,
( $false
| ~ spl0_44 ),
inference(resolution,[],[f833,f249]) ).
fof(f1389,plain,
~ spl0_44,
inference(avatar_contradiction_clause,[],[f1373]) ).
cnf(s51,plain,
spl0_44,
inference(sat_conversion,[],[f1295]) ).
cnf(s60,plain,
~ spl0_44,
inference(sat_conversion,[],[f1389]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s51,s60]) ).
fof(f1390,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET137-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:52:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.50 % (332554)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (332563)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2699668875:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (332560)% WARNING: option uhcvi not known.
% 0.16/0.50 % (332560)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1378374233:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (332561)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1587027812:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (332559)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=314346080_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (332562)dis+10_1_sil=32000:sp=arity:random_seed=2061711336:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (332564)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3117710126:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (332565)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=523078662:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (332563) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-332554-332563"...
% 0.16/0.50 % (332563)...printing done.
% 0.16/0.50 % (332563)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (332563)------------------------------
% 0.16/0.50 % (332563)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (332563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (332563)CaDiCaL version: 2.1.3
% 0.16/0.50 % (332563)Termination reason: Refutation
% 0.16/0.50 % (332563)Time elapsed: 0.029 s
% 0.16/0.50 % (332563)Peak memory usage: 13 MB
% 0.16/0.50 % (332563)Instructions burned: 81 (million)
% 0.16/0.50 % (332554)Success in time 0.077 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------