%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU090+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 : 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 : Sun Sep 27 08:45:00 AM UTC 2026
% Result : Theorem 6.88s 1.38s
% Output : CNFRefutation 6.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 52 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 45 ( 15 ~; 9 |; 17 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 34 ( 0 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_zfmisc_1,axiom,
! [A,B,C,D] : cartesian_product4(A,B,C,D) = cartesian_product2(cartesian_product3(A,B,C),D),
file('theBenchmark.p',d4_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,axiom,
! [A,B,C] :
( ( finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product3(A,B,C)) ),
file('theBenchmark.p',t20_finset_1) ).
fof(t21_finset_1,conjecture,
! [A,B,C,D] :
( ( finite(D)
& finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product4(A,B,C,D)) ),
file('theBenchmark.p',t21_finset_1) ).
fof(t21_finset_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( finite(D)
& finite(C)
& finite(B)
& finite(A) )
=> finite(cartesian_product4(A,B,C,D)) ),
inference(assume_negation,[status(cth)],[t21_finset_1]) ).
fof(nnf_61,plain,
? [A,B,C,D] :
( ~ finite(cartesian_product4(A,B,C,D))
& finite(D)
& finite(C)
& finite(B)
& finite(A) ),
inference(fof_nnf,[status(thm)],[t21_finset_1_neg]) ).
fof(sk_t21_finset_1_neg,plain,
( ~ finite(cartesian_product4(sK0,sK1,sK2,sK3))
& finite(sK3)
& finite(sK2)
& finite(sK1)
& finite(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_61]) ).
cnf(c_128,negated_conjecture,
~ finite(cartesian_product4(sK0,sK1,sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t21_finset_1_neg]) ).
cnf(c_129,negated_conjecture,
finite(sK3),
inference(split_conjunct,[status(thm)],[sk_t21_finset_1_neg]) ).
cnf(c_130,negated_conjecture,
finite(sK2),
inference(split_conjunct,[status(thm)],[sk_t21_finset_1_neg]) ).
cnf(c_131,negated_conjecture,
finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t21_finset_1_neg]) ).
cnf(c_132,negated_conjecture,
finite(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_finset_1_neg]) ).
cnf(c_139,plain,
( finite(cartesian_product3(A,B,C))
| ~ finite(C)
| ~ finite(B)
| ~ finite(A) ),
inference(clausify,[status(thm)],[t20_finset_1]) ).
cnf(c_141,plain,
( finite(cartesian_product2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(clausify,[status(thm)],[t19_finset_1]) ).
cnf(c_182,plain,
cartesian_product4(A,B,C,D) = cartesian_product2(cartesian_product3(A,B,C),D),
inference(clausify,[status(thm)],[d4_zfmisc_1]) ).
cnf(c_203,negated_conjecture,
~ finite(cartesian_product2(cartesian_product3(sK0,sK1,sK2),sK3)),
inference(paramod,[status(thm)],[c_182,c_128]) ).
cnf(c_5879,negated_conjecture,
( finite(cartesian_product3(sK0,A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_139,c_132]) ).
cnf(c_5880,negated_conjecture,
( finite(cartesian_product3(sK0,sK1,A))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_5879,c_131]) ).
cnf(c_234,negated_conjecture,
finite(cartesian_product3(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_5880,c_130]) ).
cnf(c_5881,negated_conjecture,
( finite(cartesian_product2(A,sK3))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_141,c_129]) ).
cnf(c_5882,negated_conjecture,
~ finite(cartesian_product3(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_5881,c_203]) ).
cnf(c_5878,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_234,c_5882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 08:40:15 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 446411 was started by sandbox on n016,
% 0.11/0.38 % Sat Sep 26 08:40:15 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 6.88/1.38
% 6.88/1.38 % SZS status Theorem for theBenchmark
% 6.88/1.38
% 6.88/1.38 % Proof 1 at 0.59 (+ 0.29) seconds.
% 6.88/1.38 % Length of proof is 15.
% 6.88/1.38 % Level of proof is 3.
% 6.88/1.38 % Maximum clause weight is 27.000.
% 6.88/1.38 % Given clauses 72.
% 6.88/1.38
% 6.88/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------