%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET113-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:43:10 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 16 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f175,axiom,
! [X0] :
( member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class))
| first(X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f181,negated_conjecture,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets1_1) ).
fof(f182,negated_conjecture,
first(x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
fof(f183,plain,
x != first(x),
inference(reorient_equations,[],[f182]) ).
fof(f188,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(f275,plain,
! [X0] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| first(X0) = X0 ),
inference(definition_unfolding,[],[f175,f188]) ).
fof(f281,plain,
~ member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f181,f188]) ).
fof(f408,plain,
! [X0] :
( ~ member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| first(X0) = X0 ),
inference(consistent_polarity_flipping,[],[f275]) ).
fof(f412,plain,
member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)),
inference(consistent_polarity_flipping,[],[f281]) ).
fof(f1178,plain,
x = first(x),
inference(resolution,[],[f408,f412]) ).
fof(f1189,plain,
$false,
inference(forward_subsumption_resolution,[],[f1178,f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET113-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 % Computer : n020.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Mon Sep 28 00:48:05 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 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
% 0.16/0.51 % (3928705)Will run a generic schedule for satisfiability detection.
% 0.16/0.51 % (3928710)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=777856007_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.51 % (3928711)% WARNING: option uhcvi not known.
% 0.16/0.51 % (3928712)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2224794547:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.51 % (3928711)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=635617438:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.51 % (3928713)dis+10_1_sil=32000:sp=arity:random_seed=3922360311:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.51 % (3928714)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1230749087:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.51 % (3928715)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2539309805:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.51 % (3928716)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=483513811:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.51 % (3928711) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3928705-3928711"...
% 0.16/0.51 % (3928711)...printing done.
% 0.16/0.51 % (3928711)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51 % (3928711)------------------------------
% 0.16/0.51 % (3928711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.51 % (3928711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.51 % (3928711)CaDiCaL version: 2.1.3
% 0.16/0.51 % (3928711)Termination reason: Refutation
% 0.16/0.51 % (3928711)Time elapsed: 0.030 s
% 0.16/0.51 % (3928711)Peak memory usage: 12 MB
% 0.16/0.51 % (3928711)Instructions burned: 43 (million)
% 0.16/0.51 % (3928705)Success in time 0.069 s
% 0.16/0.51 % Vampire exiting
%------------------------------------------------------------------------------