%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU090+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 : n012.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 2.16s 16.13s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 71 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 30 ~; 19 |; 21 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 44 ( 36 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2,X3] : cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
fof(f53,axiom,
! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f55,axiom,
! [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(f56,conjecture,
! [X0,X1,X2,X3] :
( ( finite(X0)
& finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product4(X0,X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
fof(f57,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( finite(X0)
& finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product4(X0,X1,X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f70,plain,
? [X0,X1,X2,X3] :
( ~ finite(cartesian_product4(X0,X1,X2,X3))
& finite(X0)
& finite(X1)
& finite(X2)
& finite(X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f71,plain,
? [X0,X1,X2,X3] :
( ~ finite(cartesian_product4(X0,X1,X2,X3))
& finite(X0)
& finite(X1)
& finite(X2)
& finite(X3) ),
inference(flattening,[],[f70]) ).
fof(f79,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f80,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(flattening,[],[f79]) ).
fof(f85,plain,
! [X0,X1,X2] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X0)
| ~ finite(X1)
| ~ finite(X2) ),
inference(ennf_transformation,[],[f55]) ).
fof(f86,plain,
! [X0,X1,X2] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X0)
| ~ finite(X1)
| ~ finite(X2) ),
inference(flattening,[],[f85]) ).
fof(f92,plain,
( ~ finite(cartesian_product4(sK0,sK1,sK2,sK3))
& finite(sK0)
& finite(sK1)
& finite(sK2)
& finite(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f71]) ).
fof(f102,plain,
finite(sK3),
inference(cnf_transformation,[],[f92]) ).
fof(f103,plain,
finite(sK2),
inference(cnf_transformation,[],[f92]) ).
fof(f104,plain,
finite(sK1),
inference(cnf_transformation,[],[f92]) ).
fof(f105,plain,
finite(sK0),
inference(cnf_transformation,[],[f92]) ).
fof(f106,plain,
~ finite(cartesian_product4(sK0,sK1,sK2,sK3)),
inference(cnf_transformation,[],[f92]) ).
fof(f108,plain,
! [X2,X3,X0,X1] : cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3),
inference(cnf_transformation,[],[f14]) ).
fof(f120,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X2,X0,X1] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X0)
| ~ finite(X1)
| ~ finite(X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f136,plain,
~ finite(cartesian_product2(cartesian_product3(sK0,sK1,sK2),sK3)),
inference(definition_unfolding,[],[f106,f108]) ).
fof(f145,plain,
( ~ finite(cartesian_product3(sK0,sK1,sK2))
| ~ finite(sK3) ),
inference(resolution,[],[f120,f136]) ).
fof(f146,plain,
~ finite(cartesian_product3(sK0,sK1,sK2)),
inference(forward_subsumption_resolution,[],[f145,f102]) ).
fof(f148,plain,
( ~ finite(sK0)
| ~ finite(sK1)
| ~ finite(sK2) ),
inference(resolution,[],[f123,f146]) ).
fof(f149,plain,
( ~ finite(sK1)
| ~ finite(sK2) ),
inference(forward_subsumption_resolution,[],[f148,f105]) ).
fof(f150,plain,
~ finite(sK2),
inference(forward_subsumption_resolution,[],[f149,f104]) ).
fof(f151,plain,
$false,
inference(forward_subsumption_resolution,[],[f150,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/15.54 % Computer : n012.cluster.edu
% 0.06/15.54 % Model : x86_64 x86_64
% 0.06/15.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/15.54 % Memory : 8046.5625MB
% 0.06/15.54 % OS : Linux 6.8.0-71-generic
% 0.06/15.54 % CPULimit : 300
% 0.06/15.54 % WCLimit : 300
% 0.06/15.54 % DateTime : Mon Sep 28 03:32:39 UTC 2026
% 0.06/15.54 % CPUTime :
% 0.06/15.54 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/15.56 Running first-order theorem proving
% 0.06/15.56 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
% 2.16/16.13 % (2991709)Detected formulas, will run a generic FOF schedule.
% 2.16/16.13 % (2991714)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=3509194138:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.16/16.13 % (2991718)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4253811233:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.16/16.13 % (2991715)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=352189882:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.16/16.13 % (2991719)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4249433839:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.16/16.13 % (2991720)dis-21_1_sil=8000:lcm=predicate:random_seed=1361102957: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)
% 2.16/16.13 % (2991717)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2158991768:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.16/16.13 % (2991716)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=1979778469:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.16/16.13 % (2991717)Refutation not found, incomplete strategy
% 2.16/16.13 % (2991717)------------------------------
% 2.16/16.13 % (2991717)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.16/16.13 % (2991717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/16.13 % (2991717)CaDiCaL version: 2.1.3
% 2.16/16.13 % (2991717)Termination reason: Refutation not found, incomplete strategy
% 2.16/16.13 % (2991717)Time elapsed: 0.001 s
% 2.16/16.13 % (2991717)Peak memory usage: 88 MB
% 2.16/16.13 % (2991717)Instructions burned: 1 (million)
% 2.16/16.13 % (2991718)First to succeed.
% 2.16/16.13 % (2991720)Also succeeded, but the first one will report.
% 2.16/16.13 % (2991718)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2991709"
% 2.16/16.13 % (2991719)Also succeeded, but the first one will report.
% 2.16/16.13 % (2991717)------------------------------
% 2.16/16.13 % (2991717)------------------------------
% 2.16/16.13 % (2991718)Refutation found. Thanks to Tanya!
% 2.16/16.13 % SZS status Theorem for theBenchmark
% 2.16/16.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.16/16.13 % (2991718)------------------------------
% 2.16/16.13 % (2991718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.16/16.13 % (2991718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.16/16.13 % (2991718)CaDiCaL version: 2.1.3
% 2.16/16.13 % (2991718)Termination reason: Refutation
% 2.16/16.13 % (2991718)Time elapsed: 0.002 s
% 2.16/16.13 % (2991718)Peak memory usage: 88 MB
% 2.16/16.13 % (2991718)Instructions burned: 3 (million)
% 2.16/16.13 % (2991718)------------------------------
% 2.16/16.13 % (2991718)------------------------------
% 2.16/16.13 % (2991709)Success in time 0.27 s
% 2.16/16.13 % Vampire exiting
%------------------------------------------------------------------------------