%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:42:40 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 19 unt; 2 def)
% Number of atoms : 81 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 26 ~; 21 |; 16 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f9,axiom,
! [X0,X1] :
( ( member(X0,universal_class)
& member(X1,universal_class) )
=> ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',first_second) ).
fof(f44,conjecture,
! [X0,X1,X2] :
( ( member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) )
=> ( first(X2) = X0
& second(X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1,X2] :
( ( member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) )
=> ( first(X2) = X0
& second(X2) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 )
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1] :
( ( first(ordered_pair(X0,X1)) = X0
& second(ordered_pair(X0,X1)) = X1 )
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ),
inference(flattening,[],[f48]) ).
fof(f60,plain,
? [X0,X1,X2] :
( ( first(X2) != X0
| second(X2) != X1 )
& member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1,X2] :
( ( first(X2) != X0
| second(X2) != X1 )
& member(X0,universal_class)
& member(X1,universal_class)
& X2 = ordered_pair(X0,X1) ),
inference(flattening,[],[f60]) ).
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(f79,plain,
! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| second(ordered_pair(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f80,plain,
! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| first(ordered_pair(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f149,plain,
( sK7 != second(sK8)
| sK6 != first(sK8) ),
inference(cnf_transformation,[],[f61]) ).
fof(f150,plain,
sK8 = ordered_pair(sK6,sK7),
inference(cnf_transformation,[],[f61]) ).
fof(f151,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f61]) ).
fof(f152,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f61]) ).
fof(f153,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(f161,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0 ),
inference(definition_unfolding,[],[f80,f153]) ).
fof(f162,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1 ),
inference(definition_unfolding,[],[f79,f153]) ).
fof(f190,plain,
sK8 = unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))),
inference(definition_unfolding,[],[f150,f153]) ).
fof(f222,definition,
( spl9_1
<=> sK6 = first(sK8) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f226,definition,
( spl9_2
<=> sK7 = second(sK8) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f228,plain,
( sK7 != second(sK8)
| spl9_2 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f149,f226,f222]) ).
fof(f478,plain,
! [X0] :
( ~ member(X0,universal_class)
| sK6 = first(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(X0,X0)))) ),
inference(resolution,[],[f161,f152]) ).
fof(f530,plain,
! [X0] :
( ~ member(X0,universal_class)
| second(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(X0,X0)))) = X0 ),
inference(resolution,[],[f162,f152]) ).
fof(f843,plain,
sK6 = first(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(resolution,[],[f478,f151]) ).
fof(f863,plain,
sK6 = first(sK8),
inference(forward_demodulation,[],[f843,f190]) ).
fof(f866,plain,
spl9_1,
inference(avatar_split_clause,[],[f863,f222]) ).
fof(f903,plain,
sK7 = second(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))),
inference(resolution,[],[f530,f151]) ).
fof(f923,plain,
sK7 = second(sK8),
inference(forward_demodulation,[],[f903,f190]) ).
fof(f924,plain,
( $false
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f923,f228]) ).
fof(f925,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f924]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f229]) ).
cnf(s54,plain,
spl9_1,
inference(sat_conversion,[],[f866]) ).
cnf(s61,plain,
spl9_2,
inference(sat_conversion,[],[f925]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s1,s61,s54]) ).
fof(f926,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 00:14:48 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.18/0.51 % (3143098)Will run a generic schedule for satisfiability detection.
% 0.18/0.51 % (3143108)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4178066314:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.51 % (3143104)% WARNING: option uhcvi not known.
% 0.18/0.51 % (3143106)dis+10_1_sil=32000:sp=arity:random_seed=649917050:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.51 % (3143103)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=49088047_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.51 % (3143104)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3004955134:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.51 % (3143109)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=443604233:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.51 % (3143105)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3796092585:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.51 % (3143107)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2528590164:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.51 % (3143104) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3143098-3143104"...
% 0.18/0.51 % (3143106) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3143098-3143106"...
% 0.18/0.51 % (3143104)...printing done.
% 0.18/0.51 % (3143104)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51 % (3143104)------------------------------
% 0.18/0.51 % (3143104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.51 % (3143104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.51 % (3143104)CaDiCaL version: 2.1.3
% 0.18/0.51 % (3143104)Termination reason: Refutation
% 0.18/0.51 % (3143104)Time elapsed: 0.024 s
% 0.18/0.51 % (3143104)Peak memory usage: 13 MB
% 0.18/0.51 % (3143104)Instructions burned: 32 (million)
% 0.18/0.51 % (3143098)Success in time 0.064 s
% 0.18/0.51 % Vampire exiting
%------------------------------------------------------------------------------