%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET104-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:43:08 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 14 unt; 0 def)
% Number of atoms : 26 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 7 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f123,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X1,X0) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f138,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f166,negated_conjecture,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_2_of_ordered_pair_2) ).
fof(f167,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_2_of_ordered_pair_3) ).
fof(f172,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f223,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X1,X0) = unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f234,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f253,plain,
unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f166,f12,f12,f172]) ).
fof(f345,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X1,X0) = unordered_pair(X1,X1) ),
inference(consistent_polarity_flipping,[],[f223]) ).
fof(f360,plain,
! [X0] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(consistent_polarity_flipping,[],[f234]) ).
fof(f378,plain,
member(x,universal_class),
inference(consistent_polarity_flipping,[],[f167]) ).
fof(f501,plain,
null_class = unordered_pair(x,x),
inference(resolution,[],[f360,f378]) ).
fof(f502,plain,
unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))),
inference(superposition,[],[f253,f501]) ).
fof(f1297,plain,
! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x),
inference(resolution,[],[f345,f378]) ).
fof(f1314,plain,
! [X0] : unordered_pair(X0,X0) = unordered_pair(x,X0),
inference(superposition,[],[f120,f1297]) ).
fof(f1361,plain,
unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(y,y))),
inference(superposition,[],[f502,f1314]) ).
fof(f1374,plain,
$false,
inference(trivial_inequality_removal,[],[f1361]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET104-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:45:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.44 % (3925557)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (3925568)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1248997456:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.44 % (3925563)% WARNING: option uhcvi not known.
% 0.09/0.44 % (3925562)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=562547044_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.44 % (3925564)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=353950996:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.44 % (3925565)dis+10_1_sil=32000:sp=arity:random_seed=40396214:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.44 % (3925566)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2158511721:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.44 % (3925567)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1950903671:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.44 % (3925563)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3408990612:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.44 % (3925568) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3925557-3925568"...
% 0.09/0.44 % (3925568)...printing done.
% 0.09/0.44 % (3925568)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (3925568)------------------------------
% 0.09/0.44 % (3925568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (3925568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (3925568)CaDiCaL version: 2.1.3
% 0.09/0.44 % (3925568)Termination reason: Refutation
% 0.09/0.44 % (3925568)Time elapsed: 0.013 s
% 0.09/0.44 % (3925568)Peak memory usage: 12 MB
% 0.09/0.44 % (3925568)Instructions burned: 32 (million)
% 0.09/0.45 % (3925557)Success in time 0.045 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------