%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU090+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 : n002.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 12:51:54 PM UTC 2026
% Result : Theorem 0.11s 15.69s
% Output : Refutation 0.11s
% 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/sandbox2/benchmark/theBenchmark.p',d4_zfmisc_1) ).
fof(f17,axiom,
! [X0,X1] :
( ( finite(X0)
& finite(X1) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( finite(X0)
& finite(X1)
& finite(X2) )
=> finite(cartesian_product3(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_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/sandbox2/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(f104,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f105,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X0)
| ~ finite(X1)
| ~ finite(X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f107,plain,
! [X0,X1,X2] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X0)
| ~ finite(X1)
| ~ finite(X2) ),
inference(flattening,[],[f106]) ).
fof(f121,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(f122,plain,
? [X0,X1,X2,X3] :
( ~ finite(cartesian_product4(X0,X1,X2,X3))
& finite(X0)
& finite(X1)
& finite(X2)
& finite(X3) ),
inference(flattening,[],[f121]) ).
fof(f158,plain,
( ~ finite(cartesian_product4(sK26,sK27,sK28,sK29))
& finite(sK26)
& finite(sK27)
& finite(sK28)
& finite(sK29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29]),skolemize(X0,sK26),skolemize(X1,sK27),skolemize(X2,sK28),skolemize(X3,sK29)],[f122]) ).
fof(f182,plain,
! [X2,X3,X0,X1] : cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3),
inference(cnf_transformation,[],[f14]) ).
fof(f186,plain,
! [X0,X1] :
( finite(cartesian_product2(X0,X1))
| ~ finite(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f187,plain,
! [X2,X0,X1] :
( finite(cartesian_product3(X0,X1,X2))
| ~ finite(X0)
| ~ finite(X1)
| ~ finite(X2) ),
inference(cnf_transformation,[],[f107]) ).
fof(f277,plain,
finite(sK29),
inference(cnf_transformation,[],[f158]) ).
fof(f278,plain,
finite(sK28),
inference(cnf_transformation,[],[f158]) ).
fof(f279,plain,
finite(sK27),
inference(cnf_transformation,[],[f158]) ).
fof(f280,plain,
finite(sK26),
inference(cnf_transformation,[],[f158]) ).
fof(f281,plain,
~ finite(cartesian_product4(sK26,sK27,sK28,sK29)),
inference(cnf_transformation,[],[f158]) ).
fof(f290,plain,
~ finite(cartesian_product2(cartesian_product3(sK26,sK27,sK28),sK29)),
inference(definition_unfolding,[],[f281,f182]) ).
fof(f430,plain,
( ~ finite(cartesian_product3(sK26,sK27,sK28))
| ~ finite(sK29) ),
inference(resolution,[],[f186,f290]) ).
fof(f431,plain,
~ finite(cartesian_product3(sK26,sK27,sK28)),
inference(forward_subsumption_resolution,[],[f430,f277]) ).
fof(f495,plain,
( ~ finite(sK26)
| ~ finite(sK27)
| ~ finite(sK28) ),
inference(resolution,[],[f187,f431]) ).
fof(f496,plain,
( ~ finite(sK27)
| ~ finite(sK28) ),
inference(forward_subsumption_resolution,[],[f495,f280]) ).
fof(f497,plain,
~ finite(sK28),
inference(forward_subsumption_resolution,[],[f496,f279]) ).
fof(f498,plain,
$false,
inference(forward_subsumption_resolution,[],[f497,f278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/15.61 % Computer : n002.cluster.edu
% 0.11/15.61 % Model : x86_64 x86_64
% 0.11/15.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.61 % Memory : 8046.5625MB
% 0.11/15.61 % OS : Linux 6.8.0-71-generic
% 0.11/15.61 % CPULimit : 300
% 0.11/15.61 % WCLimit : 300
% 0.11/15.61 % DateTime : Mon Sep 28 03:35:42 UTC 2026
% 0.11/15.62 % CPUTime :
% 0.11/15.62 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/15.65 Running first-order model finding
% 0.11/15.65 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
% 0.11/15.69 % (4123301)Will run a generic schedule for satisfiability detection.
% 0.11/15.69 % (4123309)dis+10_1_sil=32000:sp=arity:random_seed=515896893:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/15.69 % (4123309) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4123301-4123309"...
% 0.11/15.69 % (4123307)% WARNING: option uhcvi not known.
% 0.11/15.69 % (4123309)...printing done.
% 0.11/15.69 % (4123309)Refutation found. Thanks to Tanya!
% 0.11/15.69 % SZS status Theorem for theBenchmark
% 0.11/15.69 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/15.69 % (4123309)------------------------------
% 0.11/15.69 % (4123309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/15.69 % (4123309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/15.69 % (4123309)CaDiCaL version: 2.1.3
% 0.11/15.69 % (4123309)Termination reason: Refutation
% 0.11/15.69 % (4123309)Time elapsed: 0.004 s
% 0.11/15.69 % (4123309)Peak memory usage: 12 MB
% 0.11/15.69 % (4123309)Instructions burned: 8 (million)
% 0.11/15.69 % (4123301)Success in time 0.029 s
% 0.11/15.69 % Vampire exiting
%------------------------------------------------------------------------------