%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU089+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 : n007.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 12:47:13 PM UTC 2026
% Result : Theorem 2.50s 1.57s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 18 ~; 8 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 26 ( 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
fof(f51,axiom,
! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f53,conjecture,
! [X0,X1,X2] :
( ( finite(X0)
& finite(X1)
& finite(X2) )
=> finite(cartesian_product3(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
fof(f54,negated_conjecture,
~ ! [X0,X1,X2] :
( ( finite(X0)
& finite(X1)
& finite(X2) )
=> finite(cartesian_product3(X0,X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f67,plain,
? [X0,X1,X2] :
( ~ finite(cartesian_product3(X0,X1,X2))
& finite(X0)
& finite(X1)
& finite(X2) ),
inference(ennf_transformation,[],[f54]) ).
fof(f68,plain,
? [X0,X1,X2] :
( ~ finite(cartesian_product3(X0,X1,X2))
& finite(X0)
& finite(X1)
& finite(X2) ),
inference(flattening,[],[f67]) ).
fof(f76,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f77,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(flattening,[],[f76]) ).
fof(f83,plain,
( ~ finite(cartesian_product3(sK0,sK1,sK2))
& finite(sK0)
& finite(sK1)
& finite(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f68]) ).
fof(f93,plain,
finite(sK2),
inference(cnf_transformation,[],[f83]) ).
fof(f94,plain,
finite(sK1),
inference(cnf_transformation,[],[f83]) ).
fof(f95,plain,
finite(sK0),
inference(cnf_transformation,[],[f83]) ).
fof(f96,plain,
~ finite(cartesian_product3(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f83]) ).
fof(f98,plain,
! [X2,X0,X1] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
inference(cnf_transformation,[],[f14]) ).
fof(f110,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f123,plain,
~ finite(cartesian_product2(cartesian_product2(sK0,sK1),sK2)),
inference(definition_unfolding,[],[f96,f98]) ).
fof(f132,plain,
( ~ finite(cartesian_product2(sK0,sK1))
| ~ finite(sK2) ),
inference(resolution,[],[f110,f123]) ).
fof(f133,plain,
~ finite(cartesian_product2(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f132,f93]) ).
fof(f134,plain,
( ~ finite(sK0)
| ~ finite(sK1) ),
inference(resolution,[],[f133,f110]) ).
fof(f136,plain,
~ finite(sK1),
inference(forward_subsumption_resolution,[],[f134,f95]) ).
fof(f137,plain,
$false,
inference(forward_subsumption_resolution,[],[f136,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.62 % Computer : n007.cluster.edu
% 0.12/0.62 % Model : x86_64 x86_64
% 0.12/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.62 % Memory : 8046.5625MB
% 0.12/0.62 % OS : Linux 6.8.0-71-generic
% 0.12/0.62 % CPULimit : 300
% 0.12/0.62 % WCLimit : 300
% 0.12/0.62 % DateTime : Mon Sep 28 03:30:41 UTC 2026
% 0.12/0.62 % CPUTime :
% 0.12/0.62 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.66 Running first-order theorem proving
% 0.15/0.66 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
% 2.50/1.57 % (1999338)Detected formulas, will run a generic FOF schedule.
% 2.50/1.57 % (1999347)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=151297282:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.57 % (1999347)First to succeed.
% 2.50/1.57 % (1999347)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1999338"
% 2.50/1.57 % (1999349)dis-21_1_sil=8000:lcm=predicate:random_seed=1382167628: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)
% 2.50/1.57 % (1999343)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=4101117022:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.57 % (1999348)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1229539294:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.57 % (1999346)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4165361336:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.57 % (1999345)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=2920066084:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.57 % (1999344)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=1899320299:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.57 % (1999346)Refutation not found, incomplete strategy
% 2.50/1.57 % (1999346)------------------------------
% 2.50/1.57 % (1999346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.57 % (1999346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.57 % (1999346)CaDiCaL version: 2.1.3
% 2.50/1.57 % (1999346)Termination reason: Refutation not found, incomplete strategy
% 2.50/1.57 % (1999346)Time elapsed: 0.001 s
% 2.50/1.57 % (1999346)Peak memory usage: 88 MB
% 2.50/1.57 % (1999349)Also succeeded, but the first one will report.
% 2.50/1.57 % (1999348)Also succeeded, but the first one will report.
% 2.50/1.57 % (1999347)Refutation found. Thanks to Tanya!
% 2.50/1.57 % SZS status Theorem for theBenchmark
% 2.50/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.57 % (1999347)------------------------------
% 2.50/1.57 % (1999347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.57 % (1999347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.57 % (1999347)CaDiCaL version: 2.1.3
% 2.50/1.57 % (1999347)Termination reason: Refutation
% 2.50/1.57 % (1999347)Time elapsed: 0.002 s
% 2.50/1.57 % (1999347)Peak memory usage: 88 MB
% 2.50/1.57 % (1999347)Instructions burned: 2 (million)
% 2.50/1.57 % (1999347)------------------------------
% 2.50/1.57 % (1999347)------------------------------
% 2.50/1.57 % (1999338)Success in time 0.274 s
% 2.50/1.57 % Vampire exiting
%------------------------------------------------------------------------------