%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET084+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:43:02 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 39 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 32 ( 12 ~; 10 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f44,conjecture,
! [X0,X1] :
( ( singleton(X0) = singleton(X1)
& member(X1,universal_class) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ( singleton(X0) = singleton(X1)
& member(X1,universal_class) )
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1] :
( X0 != X1
& singleton(X0) = singleton(X1)
& member(X1,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1] :
( X0 != X1
& singleton(X0) = singleton(X1)
& member(X1,universal_class) ),
inference(flattening,[],[f60]) ).
fof(f69,plain,
! [X2,X0,X1] :
( X0 != X2
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f4]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f74,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f149,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f61]) ).
fof(f150,plain,
singleton(sK6) = singleton(sK7),
inference(cnf_transformation,[],[f61]) ).
fof(f151,plain,
sK6 != sK7,
inference(cnf_transformation,[],[f61]) ).
fof(f189,plain,
unordered_pair(sK6,sK6) = unordered_pair(sK7,sK7),
inference(definition_unfolding,[],[f150,f74,f74]) ).
fof(f193,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f69]) ).
fof(f365,plain,
! [X0] :
( ~ member(X0,unordered_pair(sK7,sK7))
| sK6 = X0
| sK6 = X0 ),
inference(superposition,[],[f71,f189]) ).
fof(f366,plain,
! [X0] :
( ~ member(X0,unordered_pair(sK7,sK7))
| sK6 = X0 ),
inference(duplicate_literal_removal,[],[f365]) ).
fof(f368,plain,
( sK6 = sK7
| ~ member(sK7,universal_class) ),
inference(resolution,[],[f366,f193]) ).
fof(f380,plain,
~ member(sK7,universal_class),
inference(forward_subsumption_resolution,[],[f368,f151]) ).
fof(f382,plain,
$false,
inference(forward_subsumption_resolution,[],[f380,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET084+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n004.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:35:07 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.10/0.44 % (4034416)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (4034425)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2955665836:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.44 % (4034422)% WARNING: option uhcvi not known.
% 0.10/0.44 % (4034425) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4034416-4034425"...
% 0.10/0.44 % (4034425)...printing done.
% 0.10/0.44 % (4034421)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4078280416_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % (4034423)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3891662778:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (4034424)dis+10_1_sil=32000:sp=arity:random_seed=1957423714:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (4034426)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=668735098:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (4034427)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3679320492:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % (4034425)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (4034425)------------------------------
% 0.10/0.44 % (4034425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (4034425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (4034425)CaDiCaL version: 2.1.3
% 0.10/0.44 % (4034425)Termination reason: Refutation
% 0.10/0.44 % (4034425)Time elapsed: 0.005 s
% 0.10/0.44 % (4034425)Peak memory usage: 12 MB
% 0.10/0.44 % (4034425)Instructions burned: 14 (million)
% 0.10/0.44 % (4034416)Success in time 0.034 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------