%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET167-6 : 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 : n004.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 12:43:20 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 14 unt; 2 def)
% Number of atoms : 63 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 36 ~; 26 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 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(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
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(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,complement(X1))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f122,negated_conjecture,
member(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_union2_1) ).
fof(f123,negated_conjecture,
~ member(x,union(y,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_union2_2) ).
fof(f186,plain,
~ member(x,complement(intersection(complement(y),complement(z)))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f191,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ subclass(X0,X1)
| ~ member(X2,X1) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f204,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f207,plain,
! [X0,X1] :
( member(X0,complement(X1))
| member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f208,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f250,plain,
~ member(x,y),
inference(consistent_polarity_flipping,[],[f122]) ).
fof(f251,plain,
member(x,complement(intersection(complement(y),complement(z)))),
inference(consistent_polarity_flipping,[],[f186]) ).
fof(f371,plain,
! [X0] :
( ~ member(x,X0)
| ~ subclass(y,X0) ),
inference(resolution,[],[f191,f250]) ).
fof(f403,definition,
( spl0_17
<=> subclass(y,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f405,plain,
( ~ subclass(y,universal_class)
| spl0_17 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f413,plain,
( $false
| spl0_17 ),
inference(resolution,[],[f405,f4]) ).
fof(f414,plain,
spl0_17,
inference(avatar_contradiction_clause,[],[f413]) ).
fof(f449,plain,
! [X0] :
( ~ member(x,complement(X0))
| ~ member(x,X0)
| ~ subclass(y,universal_class) ),
inference(resolution,[],[f208,f371]) ).
fof(f451,definition,
( spl0_19
<=> ! [X0] :
( ~ member(x,complement(X0))
| ~ member(x,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f452,plain,
( ! [X0] :
( ~ member(x,complement(X0))
| ~ member(x,X0) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f453,plain,
( ~ spl0_17
| spl0_19 ),
inference(avatar_split_clause,[],[f449,f451,f403]) ).
fof(f490,plain,
( ~ member(x,intersection(complement(y),complement(z)))
| ~ spl0_19 ),
inference(resolution,[],[f452,f251]) ).
fof(f495,plain,
( ~ member(x,complement(y))
| ~ spl0_19 ),
inference(resolution,[],[f490,f204]) ).
fof(f506,plain,
( member(x,y)
| ~ spl0_19 ),
inference(resolution,[],[f495,f207]) ).
fof(f509,plain,
( $false
| ~ spl0_19 ),
inference(resolution,[],[f506,f250]) ).
fof(f515,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f509]) ).
cnf(s12,plain,
spl0_17,
inference(sat_conversion,[],[f414]) ).
cnf(s13,plain,
( ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f453]) ).
cnf(s18,plain,
~ spl0_19,
inference(sat_conversion,[],[f515]) ).
cnf(s21,plain,
~ spl0_17,
inference(rat,[],[s13,s18]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s12,s21]) ).
fof(f516,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET167-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n004.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 00:58:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (4044249)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (4044260)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=444896650:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (4044255)% WARNING: option uhcvi not known.
% 0.11/0.45 % (4044260) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4044249-4044260"...
% 0.11/0.45 % (4044254)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1204213623_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (4044257)dis+10_1_sil=32000:sp=arity:random_seed=3312551436:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (4044256)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3709302859:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (4044255)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2474533063:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (4044258)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1404407847:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (4044260)...printing done.
% 0.11/0.45 % (4044259)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2560886020:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (4044260)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (4044260)------------------------------
% 0.11/0.45 % (4044260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (4044260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (4044260)CaDiCaL version: 2.1.3
% 0.11/0.45 % (4044260)Termination reason: Refutation
% 0.11/0.45 % (4044260)Time elapsed: 0.006 s
% 0.11/0.45 % (4044260)Peak memory usage: 13 MB
% 0.11/0.45 % (4044260)Instructions burned: 14 (million)
% 0.11/0.45 % (4044249)Success in time 0.034 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------