%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET090-7 : 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 12:43:03 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 12 unt; 2 def)
% Number of atoms : 50 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f137,axiom,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f143,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(member_of(singleton(X0)),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists1) ).
fof(f144,axiom,
! [X0] :
( ~ member(X0,universal_class)
| singleton(member_of(singleton(X0))) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists2) ).
fof(f145,plain,
! [X0] :
( ~ member(X0,universal_class)
| singleton(X0) = singleton(member_of(singleton(X0))) ),
inference(reorient_equations,[],[f144]) ).
fof(f148,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_1) ).
fof(f149,negated_conjecture,
member_of(singleton(u)) != u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_member_of_singleton_is_unique_2) ).
fof(f150,plain,
u != member_of(singleton(u)),
inference(reorient_equations,[],[f149]) ).
fof(f215,plain,
! [X0,X1] :
( ~ member(X0,unordered_pair(X1,X1))
| X0 = X1 ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f220,plain,
! [X0] :
( member(member_of(unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f143,f12]) ).
fof(f221,plain,
! [X0] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X0) = unordered_pair(member_of(unordered_pair(X0,X0)),member_of(unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f145,f12,f12,f12]) ).
fof(f223,plain,
u != member_of(unordered_pair(u,u)),
inference(definition_unfolding,[],[f150,f12]) ).
fof(f807,plain,
unordered_pair(u,u) = unordered_pair(member_of(unordered_pair(u,u)),member_of(unordered_pair(u,u))),
inference(resolution,[],[f221,f148]) ).
fof(f871,plain,
( member(member_of(unordered_pair(u,u)),unordered_pair(u,u))
| ~ member(member_of(unordered_pair(u,u)),universal_class) ),
inference(superposition,[],[f9,f807]) ).
fof(f885,definition,
( spl0_38
<=> member(member_of(unordered_pair(u,u)),universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f887,plain,
( ~ member(member_of(unordered_pair(u,u)),universal_class)
| spl0_38 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f895,definition,
( spl0_40
<=> member(member_of(unordered_pair(u,u)),unordered_pair(u,u)) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f897,plain,
( member(member_of(unordered_pair(u,u)),unordered_pair(u,u))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f895]) ).
fof(f899,plain,
( ~ spl0_38
| spl0_40 ),
inference(avatar_split_clause,[],[f871,f895,f885]) ).
fof(f974,plain,
( u = member_of(unordered_pair(u,u))
| ~ spl0_40 ),
inference(resolution,[],[f897,f215]) ).
fof(f980,plain,
( $false
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f974,f223]) ).
fof(f981,plain,
~ spl0_40,
inference(avatar_contradiction_clause,[],[f980]) ).
fof(f991,plain,
( ~ member(u,universal_class)
| spl0_38 ),
inference(resolution,[],[f887,f220]) ).
fof(f999,plain,
( $false
| spl0_38 ),
inference(forward_subsumption_resolution,[],[f991,f148]) ).
fof(f1000,plain,
spl0_38,
inference(avatar_contradiction_clause,[],[f999]) ).
cnf(s33,plain,
( ~ spl0_38
| spl0_40 ),
inference(sat_conversion,[],[f899]) ).
cnf(s45,plain,
~ spl0_40,
inference(sat_conversion,[],[f981]) ).
cnf(s46,plain,
spl0_38,
inference(sat_conversion,[],[f1000]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s33,s45,s46]) ).
fof(f1001,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n004.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:38:39 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.16/0.50 % (4036324)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (4036331)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=966263620:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (4036330)% WARNING: option uhcvi not known.
% 0.16/0.50 % (4036329)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4130816799_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (4036333)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=64574681:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (4036330)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2888446928:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (4036332)dis+10_1_sil=32000:sp=arity:random_seed=2802220183:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (4036334)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2675857174:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (4036335)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3506663517:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (4036332) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4036324-4036332"...
% 0.16/0.50 % (4036332)...printing done.
% 0.16/0.50 % (4036332)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 % (4036332)------------------------------
% 0.16/0.50 % (4036332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (4036332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (4036332)CaDiCaL version: 2.1.3
% 0.16/0.50 % (4036332)Termination reason: Refutation
% 0.16/0.50 % (4036332)Time elapsed: 0.022 s
% 0.16/0.50 % (4036332)Peak memory usage: 12 MB
% 0.16/0.50 % (4036332)Instructions burned: 31 (million)
% 0.16/0.50 % (4036324)Success in time 0.064 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------