%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:45:06 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 14 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 7 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] : cartesian_product2(set_union2(X0,X1),set_union2(X2,X3)) = set_union2(set_union2(set_union2(cartesian_product2(X0,X2),cartesian_product2(X0,X3)),cartesian_product2(X1,X2)),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] : cartesian_product2(set_union2(X0,X1),set_union2(X2,X3)) = set_union2(set_union2(set_union2(cartesian_product2(X0,X2),cartesian_product2(X0,X3)),cartesian_product2(X1,X2)),cartesian_product2(X1,X3)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1,X2] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).
fof(f14,plain,
? [X0,X1,X2,X3] : cartesian_product2(set_union2(X0,X1),set_union2(X2,X3)) != set_union2(set_union2(set_union2(cartesian_product2(X0,X2),cartesian_product2(X0,X3)),cartesian_product2(X1,X2)),cartesian_product2(X1,X3)),
inference(ennf_transformation,[],[f9]) ).
fof(f21,plain,
! [X2,X0,X1] : cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f22,plain,
! [X2,X0,X1] : cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f23,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(set_union2(set_union2(cartesian_product2(sK2,sK4),cartesian_product2(sK2,sK5)),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK5)),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X2,X0,X1] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(set_union2(cartesian_product2(sK2,sK4),cartesian_product2(sK2,sK5)),set_union2(cartesian_product2(sK3,sK4),cartesian_product2(sK3,sK5))),
inference(forward_demodulation,[],[f23,f24]) ).
fof(f26,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(cartesian_product2(sK2,sK4),set_union2(cartesian_product2(sK2,sK5),set_union2(cartesian_product2(sK3,sK4),cartesian_product2(sK3,sK5)))),
inference(forward_demodulation,[],[f25,f24]) ).
fof(f27,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(cartesian_product2(sK2,sK4),set_union2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,set_union2(sK4,sK5)))),
inference(forward_demodulation,[],[f26,f21]) ).
fof(f63,plain,
! [X2,X3,X0,X1] : set_union2(cartesian_product2(X0,X1),set_union2(cartesian_product2(X0,X2),X3)) = set_union2(cartesian_product2(X0,set_union2(X1,X2)),X3),
inference(superposition,[],[f24,f21]) ).
fof(f969,plain,
cartesian_product2(set_union2(sK2,sK3),set_union2(sK4,sK5)) != set_union2(cartesian_product2(sK2,set_union2(sK4,sK5)),cartesian_product2(sK3,set_union2(sK4,sK5))),
inference(superposition,[],[f27,f63]) ).
fof(f1034,plain,
$false,
inference(forward_subsumption_resolution,[],[f969,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:17:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 0.17/0.47 % (2632252)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (2632261)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3708790758:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (2632258)% WARNING: option uhcvi not known.
% 0.17/0.47 % (2632257)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3373226132_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (2632258)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1897531361:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (2632259)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1277801637:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (2632260)dis+10_1_sil=32000:sp=arity:random_seed=355334726:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (2632262)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3349951091:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (2632263)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4127578207:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % (2632261) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2632252-2632261"...
% 0.17/0.47 % (2632258) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2632252-2632258"...
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (2632261)...printing done.
% 0.17/0.47 % (2632261)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (2632261)------------------------------
% 0.17/0.47 % (2632261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (2632261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (2632261)CaDiCaL version: 2.1.3
% 0.17/0.47 % (2632261)Termination reason: Refutation
% 0.17/0.47 % (2632261)Time elapsed: 0.011 s
% 0.17/0.47 % (2632261)Peak memory usage: 12 MB
% 0.17/0.47 % (2632261)Instructions burned: 32 (million)
% 0.17/0.47 % (2632252)Success in time 0.051 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------