%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU167+3 : 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 : n003.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 08:45:17 AM UTC 2026
% Result : Theorem 0.09s 0.57s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 31 ( 13 ~; 6 |; 8 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t118_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
& subset(cartesian_product2(A,C),cartesian_product2(B,C)) ) ),
file('theBenchmark.p',t118_zfmisc_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t119_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t119_zfmisc_1) ).
fof(t119_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(assume_negation,[status(cth)],[t119_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B,C,D] :
( ~ subset(cartesian_product2(A,C),cartesian_product2(B,D))
& subset(C,D)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t119_zfmisc_1_neg]) ).
fof(sk_t119_zfmisc_1_neg,plain,
( ~ subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3))
& subset(sK1,sK3)
& subset(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1,sK3]),skolemize(A,sK0),skolemize(B,sK2),skolemize(C,sK1),skolemize(D,sK3)],[nnf_6]) ).
cnf(c_9,negated_conjecture,
~ subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t119_zfmisc_1_neg]) ).
cnf(c_10,negated_conjecture,
subset(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t119_zfmisc_1_neg]) ).
cnf(c_11,negated_conjecture,
subset(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_t119_zfmisc_1_neg]) ).
cnf(c_12,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
cnf(c_13,plain,
( subset(cartesian_product2(C,A),cartesian_product2(C,B))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t118_zfmisc_1]) ).
cnf(c_14,plain,
( subset(cartesian_product2(A,C),cartesian_product2(B,C))
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t118_zfmisc_1]) ).
cnf(c_16,plain,
( ~ subset(A,cartesian_product2(sK2,sK3))
| ~ subset(cartesian_product2(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_18,negated_conjecture,
subset(cartesian_product2(A,sK1),cartesian_product2(A,sK3)),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_21,plain,
( ~ subset(sK0,A)
| ~ subset(cartesian_product2(A,sK1),cartesian_product2(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_29,plain,
~ subset(cartesian_product2(sK2,sK1),cartesian_product2(sK2,sK3)),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_30,plain,
$false,
inference(resolve,[status(thm)],[c_29,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n003.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sat Sep 26 08:45:24 UTC 2026
% 0.09/0.55 % CPUTime :
% 0.09/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.55 % Process 2478419 was started by sandbox on n003,
% 0.09/0.55 % Sat Sep 26 08:45:24 2026
% 0.09/0.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.56
% 0.09/0.56 % From the command line: assign(max_seconds, 300).
% 0.09/0.57
% 0.09/0.57 % SZS status Theorem for theBenchmark
% 0.09/0.57
% 0.09/0.57 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.57 % Length of proof is 14.
% 0.09/0.57 % Level of proof is 5.
% 0.09/0.57 % Maximum clause weight is 10.000.
% 0.09/0.57 % Given clauses 9.
% 0.09/0.57
% 0.09/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------