%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET968+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:42:26 PM UTC 2026
% Result : Theorem 5.23s 1.87s
% Output : Refutation 5.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 18 unt; 1 def)
% Number of atoms : 20 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 9 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 23 !; 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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t4_xboole_1) ).
fof(f12,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(f13,plain,
cartesian_product2(set_union2(sK0,sK1),set_union2(sK2,sK3)) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f12]) ).
fof(f14,plain,
cartesian_product2(set_union2(sK0,sK1),set_union2(sK2,sK3)) != set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3)),
inference(cnf_transformation,[],[f13]) ).
fof(f15,plain,
! [X2,X0,X1] : set_union2(set_union2(X0,X1),X2) = set_union2(X0,set_union2(X1,X2)),
inference(cnf_transformation,[],[f10]) ).
fof(f18,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(f19,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(f20,definition,
~ sP4(cartesian_product2(set_union2(sK0,sK1),set_union2(sK2,sK3))),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f21,plain,
sP4(set_union2(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),cartesian_product2(sK1,sK2)),cartesian_product2(sK1,sK3))),
inference(inequality_splitting,[],[f14,f20]) ).
fof(f22,plain,
~ sP4(set_union2(cartesian_product2(sK0,set_union2(sK2,sK3)),cartesian_product2(sK1,set_union2(sK2,sK3)))),
inference(forward_demodulation,[],[f20,f19]) ).
fof(f23,plain,
sP4(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),set_union2(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3)))),
inference(forward_demodulation,[],[f21,f15]) ).
fof(f24,plain,
~ sP4(set_union2(cartesian_product2(sK0,set_union2(sK2,sK3)),set_union2(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3)))),
inference(forward_demodulation,[],[f22,f18]) ).
fof(f25,plain,
sP4(set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK0,sK3),set_union2(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3))))),
inference(forward_demodulation,[],[f23,f15]) ).
fof(f26,plain,
~ sP4(set_union2(set_union2(cartesian_product2(sK0,sK2),cartesian_product2(sK0,sK3)),set_union2(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3)))),
inference(forward_demodulation,[],[f24,f18]) ).
fof(f27,plain,
~ sP4(set_union2(cartesian_product2(sK0,sK2),set_union2(cartesian_product2(sK0,sK3),set_union2(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3))))),
inference(forward_demodulation,[],[f26,f15]) ).
fof(f28,plain,
$false,
inference(forward_subsumption_resolution,[],[f27,f25]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n016.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 28 03:21:48 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.47 Running first-order theorem proving
% 0.23/0.47 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.23/1.87 % (3225629)Detected formulas, will run a generic FOF schedule.
% 5.23/1.87 % (3225644)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3148275110:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.23/1.87 % (3225647)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=129531811:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.23/1.87 % (3225645)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4018924376:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.23/1.87 % (3225642)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2257887775:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.23/1.87 % (3225643)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3929315605:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.23/1.87 % (3225645)First to succeed.
% 5.23/1.87 % (3225645)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3225629"
% 5.23/1.87 % (3225647)Also succeeded, but the first one will report.
% 5.23/1.87 % (3225646)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=202997861:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.23/1.87 % (3225648)dis-21_1_sil=8000:lcm=predicate:random_seed=372582143:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.23/1.87 % (3225648)Refutation not found, incomplete strategy
% 5.23/1.87 % (3225648)------------------------------
% 5.23/1.87 % (3225648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.87 % (3225648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.87 % (3225648)CaDiCaL version: 2.1.3
% 5.23/1.87 % (3225648)Termination reason: Refutation not found, incomplete strategy
% 5.23/1.87 % (3225648)Time elapsed: 0.002 s
% 5.23/1.87 % (3225648)Peak memory usage: 88 MB
% 5.23/1.87 % (3225646)Also succeeded, but the first one will report.
% 5.23/1.87 % (3225645)Refutation found. Thanks to Tanya!
% 5.23/1.87 % SZS status Theorem for theBenchmark
% 5.23/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 5.23/1.87 % (3225645)------------------------------
% 5.23/1.87 % (3225645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.23/1.87 % (3225645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.23/1.87 % (3225645)CaDiCaL version: 2.1.3
% 5.23/1.87 % (3225645)Termination reason: Refutation
% 5.23/1.87 % (3225645)Time elapsed: 0.003 s
% 5.23/1.87 % (3225645)Peak memory usage: 88 MB
% 5.23/1.87 % (3225645)Instructions burned: 1 (million)
% 5.23/1.87 % (3225645)------------------------------
% 5.23/1.87 % (3225645)------------------------------
% 5.23/1.87 % (3225629)Success in time 0.64 s
% 5.23/1.87 % Vampire exiting
%------------------------------------------------------------------------------