%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET167-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:40:22 PM UTC 2026
% Result : Unsatisfiable 2.75s 1.37s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 11 unt; 2 def)
% Number of atoms : 47 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 17 |; 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 : 16 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
member(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_members_of_union2_1) ).
fof(f123,negated_conjecture,
~ member(x,union(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_members_of_union2_2) ).
fof(f135,plain,
~ member(x,complement(intersection(complement(y),complement(z)))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f197,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f204,plain,
( ~ member(x,universal_class)
| member(x,intersection(complement(y),complement(z))) ),
inference(resolution,[],[f25,f135]) ).
fof(f207,definition,
( spl1_1
<=> member(x,intersection(complement(y),complement(z))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f208,plain,
( member(x,intersection(complement(y),complement(z)))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f210,definition,
( spl1_2
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f211,plain,
( ~ member(x,universal_class)
| spl1_2 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f212,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f204,f210,f207]) ).
fof(f213,plain,
( ! [X0] : ~ member(x,X0)
| spl1_2 ),
inference(resolution,[],[f211,f197]) ).
fof(f214,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f213,f122]) ).
fof(f221,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f214]) ).
fof(f223,plain,
( member(x,complement(y))
| ~ spl1_1 ),
inference(resolution,[],[f208,f21]) ).
fof(f225,plain,
( ~ member(x,y)
| ~ spl1_1 ),
inference(resolution,[],[f223,f24]) ).
fof(f226,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f225,f122]) ).
fof(f227,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f226]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f212]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f221]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f227]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f228,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET167-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 01:04:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.37 % (4122747)Input is clausal, will run a generic CNF schedule.
% 2.75/1.37 % (4122758)dis-21_1_sil=8000:lcm=predicate:random_seed=805583878: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)
% 2.75/1.37 % (4122758)First to succeed.
% 2.75/1.37 % (4122758)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4122747"
% 2.75/1.37 % (4122752)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=1262996915:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.75/1.37 % (4122756)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2192688668:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.75/1.37 % (4122754)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=82369636:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.75/1.37 % (4122755)lrs+10_1_sil=8000:sp=occurrence:random_seed=1273290494:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.75/1.37 % (4122757)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2968342090:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/1.37 % (4122753)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2869777874:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.75/1.37 % (4122755)Refutation not found, incomplete strategy
% 2.75/1.37 % (4122755)------------------------------
% 2.75/1.37 % (4122755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.37 % (4122755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.37 % (4122755)CaDiCaL version: 2.1.3
% 2.75/1.37 % (4122755)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.37 % (4122755)Time elapsed: 0.004 s
% 2.75/1.37 % (4122755)Peak memory usage: 88 MB
% 2.75/1.37 % (4122755)Instructions burned: 4 (million)
% 2.75/1.37 % (4122756)Also succeeded, but the first one will report.
% 2.75/1.37 % (4122757)Also succeeded, but the first one will report.
% 2.75/1.37 % (4122758)Refutation found. Thanks to Tanya!
% 2.75/1.37 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.37 % (4122758)------------------------------
% 2.75/1.37 % (4122758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.37 % (4122758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.37 % (4122758)CaDiCaL version: 2.1.3
% 2.75/1.37 % (4122758)Termination reason: Refutation
% 2.75/1.37 % (4122758)Time elapsed: 0.003 s
% 2.75/1.37 % (4122758)Peak memory usage: 89 MB
% 2.75/1.37 % (4122758)Instructions burned: 7 (million)
% 2.75/1.37 % (4122758)------------------------------
% 2.75/1.37 % (4122758)------------------------------
% 2.75/1.37 % (4122747)Success in time 0.308 s
% 2.75/1.37 % Vampire exiting
%------------------------------------------------------------------------------