%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET016+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 : n002.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 12:42:36 PM UTC 2026
% Result : Theorem 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 18 unt; 2 def)
% Number of atoms : 84 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 30 ~; 28 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 33 !; 8 ?)
% 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(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0,X1,X2,X3] :
( ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) )
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) )
=> X0 = X2 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1,X2,X3] :
( X0 != X2
& ordered_pair(X0,X1) = ordered_pair(X2,X3)
& member(X0,universal_class) ),
inference(flattening,[],[f60]) ).
fof(f70,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ 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(f73,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f74,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f75,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f149,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f61]) ).
fof(f150,plain,
ordered_pair(sK6,sK7) = ordered_pair(sK8,sK9),
inference(cnf_transformation,[],[f61]) ).
fof(f151,plain,
sK6 != sK8,
inference(cnf_transformation,[],[f61]) ).
fof(f152,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f75,f74,f74]) ).
fof(f189,plain,
unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) = unordered_pair(unordered_pair(sK8,sK8),unordered_pair(sK8,unordered_pair(sK9,sK9))),
inference(definition_unfolding,[],[f150,f152,f152]) ).
fof(f192,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f70]) ).
fof(f210,plain,
( member(unordered_pair(sK8,sK8),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))))
| ~ member(unordered_pair(sK8,sK8),universal_class) ),
inference(superposition,[],[f192,f189]) ).
fof(f211,plain,
member(unordered_pair(sK8,sK8),unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(forward_subsumption_resolution,[],[f210,f73]) ).
fof(f383,plain,
( unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8)
| unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8) ),
inference(resolution,[],[f71,f211]) ).
fof(f398,definition,
( spl10_13
<=> unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
fof(f400,plain,
( unordered_pair(sK6,unordered_pair(sK7,sK7)) = unordered_pair(sK8,sK8)
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f402,definition,
( spl10_14
<=> unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
fof(f404,plain,
( unordered_pair(sK6,sK6) = unordered_pair(sK8,sK8)
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,plain,
( spl10_13
| spl10_14 ),
inference(avatar_split_clause,[],[f383,f402,f398]) ).
fof(f423,plain,
( member(sK6,unordered_pair(sK8,sK8))
| ~ member(sK6,universal_class)
| ~ spl10_13 ),
inference(superposition,[],[f192,f400]) ).
fof(f426,plain,
( member(sK6,unordered_pair(sK8,sK8))
| ~ spl10_13 ),
inference(forward_subsumption_resolution,[],[f423,f149]) ).
fof(f434,plain,
( sK6 = sK8
| sK6 = sK8
| ~ spl10_13 ),
inference(resolution,[],[f426,f71]) ).
fof(f437,plain,
( sK6 = sK8
| ~ spl10_13 ),
inference(duplicate_literal_removal,[],[f434]) ).
fof(f438,plain,
( $false
| ~ spl10_13 ),
inference(forward_subsumption_resolution,[],[f437,f151]) ).
fof(f439,plain,
~ spl10_13,
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f445,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK6,sK6))
| sK8 = X0
| sK8 = X0 )
| ~ spl10_14 ),
inference(superposition,[],[f71,f404]) ).
fof(f450,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK6,sK6))
| sK8 = X0 )
| ~ spl10_14 ),
inference(duplicate_literal_removal,[],[f445]) ).
fof(f499,plain,
( sK6 = sK8
| ~ member(sK6,universal_class)
| ~ spl10_14 ),
inference(resolution,[],[f450,f192]) ).
fof(f513,plain,
( ~ member(sK6,universal_class)
| ~ spl10_14 ),
inference(forward_subsumption_resolution,[],[f499,f151]) ).
fof(f516,plain,
( $false
| ~ spl10_14 ),
inference(forward_subsumption_resolution,[],[f513,f149]) ).
fof(f517,plain,
~ spl10_14,
inference(avatar_contradiction_clause,[],[f516]) ).
cnf(s8,plain,
( spl10_13
| spl10_14 ),
inference(sat_conversion,[],[f405]) ).
cnf(s9,plain,
~ spl10_13,
inference(sat_conversion,[],[f439]) ).
cnf(s15,plain,
~ spl10_14,
inference(sat_conversion,[],[f517]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s8,s15,s9]) ).
fof(f518,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET016+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.35 % Computer : n002.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 28 00:08:52 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 Running first-order model finding
% 0.11/0.38 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
% 0.14/0.42 % (4034821)Will run a generic schedule for satisfiability detection.
% 0.14/0.42 % (4034830)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2859403394:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.42 % (4034827)% WARNING: option uhcvi not known.
% 0.14/0.42 % (4034826)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2421172401_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.42 % (4034827)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2591998133:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.42 % (4034828)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=443470782:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.42 % (4034830) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4034821-4034830"...
% 0.14/0.42 % (4034829)dis+10_1_sil=32000:sp=arity:random_seed=4084775716:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.42 % (4034831)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3800638185:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.42 % (4034832)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=661069604:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.42 % (4034830)...printing done.
% 0.14/0.42 % (4034830)Refutation found. Thanks to Tanya!
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.42 % (4034830)------------------------------
% 0.14/0.42 % (4034830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.42 % (4034830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.42 % (4034830)CaDiCaL version: 2.1.3
% 0.14/0.42 % (4034830)Termination reason: Refutation
% 0.14/0.42 % (4034830)Time elapsed: 0.008 s
% 0.14/0.42 % (4034830)Peak memory usage: 12 MB
% 0.14/0.42 % (4034830)Instructions burned: 19 (million)
% 0.14/0.42 % (4034821)Success in time 0.034 s
% 0.14/0.42 % Vampire exiting
%------------------------------------------------------------------------------