%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET108-7 : 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 12:43:09 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 12 unt; 0 def)
% Number of atoms : 18 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 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(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
fof(f174,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
fof(f175,negated_conjecture,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
fof(f180,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(f190,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f180]) ).
fof(f266,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f174,f180]) ).
fof(f267,plain,
~ member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f175,f180,f180,f180]) ).
fof(f285,plain,
! [X2,X0,X1] :
( member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(consistent_polarity_flipping,[],[f190]) ).
fof(f396,plain,
~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(consistent_polarity_flipping,[],[f266]) ).
fof(f397,plain,
member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),cross_product(universal_class,universal_class)),
inference(consistent_polarity_flipping,[],[f267]) ).
fof(f1261,plain,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))),unordered_pair(first(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),unordered_pair(second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),second(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))))))),
inference(resolution,[],[f285,f396]) ).
fof(f2182,plain,
member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
inference(superposition,[],[f397,f1261]) ).
fof(f2277,plain,
$false,
inference(forward_subsumption_resolution,[],[f2182,f396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 00:45:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.17/0.48 % (3926970)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3926976)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3926976)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=544666631:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3926975)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=653756588_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3926977)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1859297137:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3926978)dis+10_1_sil=32000:sp=arity:random_seed=3270547918:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3926979)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3915778775:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3926981)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4283874689:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (3926980)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1468497709:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3926976) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3926970-3926976"...
% 0.17/0.48 % (3926976)...printing done.
% 0.17/0.48 % (3926976)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3926976)------------------------------
% 0.17/0.48 % (3926976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3926976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3926976)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3926976)Termination reason: Refutation
% 0.17/0.48 % (3926976)Time elapsed: 0.037 s
% 0.17/0.48 % (3926976)Peak memory usage: 13 MB
% 0.17/0.48 % (3926976)Instructions burned: 100 (million)
% 0.17/0.48 % (3926970)Success in time 0.064 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------