%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:45:00 AM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 28 ( 10 ~; 4 |; 11 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 21 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_zfmisc_1,axiom,
! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
file('theBenchmark.p',d3_zfmisc_1) ).
fof(t19_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(cartesian_product2(A,B)) ),
file('theBenchmark.p',t19_finset_1) ).
fof(t20_finset_1,conjecture,
! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
file('theBenchmark.p',t20_finset_1) ).
fof(t20_finset_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
inference(assume_negation,[status(cth)],[t20_finset_1]) ).
fof(nnf_58,plain,
? [A,B,C] :
( ~ finite(cartesian_product3(A,B,C))
& finite(C)
& finite(B)
& finite(A) ),
inference(fof_nnf,[status(thm)],[t20_finset_1_neg]) ).
fof(sk_t20_finset_1_neg,plain,
( ~ finite(cartesian_product3(sK0,sK1,sK2))
& finite(sK2)
& finite(sK1)
& finite(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_58]) ).
cnf(c_125,negated_conjecture,
~ finite(cartesian_product3(sK0,sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t20_finset_1_neg]) ).
cnf(c_126,negated_conjecture,
finite(sK2),
inference(split_conjunct,[status(thm)],[sk_t20_finset_1_neg]) ).
cnf(c_127,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_finset_1_neg]) ).
cnf(c_128,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_finset_1_neg]) ).
cnf(c_136,plain,
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(clausify,[status(thm)],[t19_finset_1]) ).
cnf(c_176,plain,
cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C),
inference(clausify,[status(thm)],[d3_zfmisc_1]) ).
cnf(c_188,negated_conjecture,
~ finite(cartesian_product2(cartesian_product2(sK0,sK1),sK2)),
inference(paramod,[status(thm)],[c_176,c_125]) ).
cnf(c_911,negated_conjecture,
( finite(cartesian_product2(sK0,A))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_136,c_128]) ).
cnf(c_199,negated_conjecture,
finite(cartesian_product2(sK0,sK1)),
inference(resolve,[status(thm)],[c_911,c_127]) ).
cnf(c_912,negated_conjecture,
( finite(cartesian_product2(A,sK2))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_136,c_126]) ).
cnf(c_913,negated_conjecture,
~ finite(cartesian_product2(sK0,sK1)),
inference(resolve,[status(thm)],[c_912,c_188]) ).
cnf(c_910,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_199,c_913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:38:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1274103 was started by sandbox on n002,
% 0.08/0.36 % Sat Sep 26 08:38:06 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.43
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43
% 0.14/0.43 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.14/0.43 % Length of proof is 12.
% 0.14/0.43 % Level of proof is 3.
% 0.14/0.43 % Maximum clause weight is 30.000.
% 0.14/0.43 % Given clauses 60.
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------