%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:37:24 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 22 unt; 0 def)
% Number of atoms : 86 ( 62 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 63 ( 20 ~; 31 |; 7 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 56 ( 6 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t113_zfmisc_1,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
file('theBenchmark.p',t113_zfmisc_1) ).
fof(t123_zfmisc_1,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('theBenchmark.p',t123_zfmisc_1) ).
fof(t134_zfmisc_1,axiom,
! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( ( B = D
& A = C )
| B = empty_set
| A = empty_set ) ),
file('theBenchmark.p',t134_zfmisc_1) ).
fof(t17_xboole_1,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t138_zfmisc_1,conjecture,
! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set ) ),
file('theBenchmark.p',t138_zfmisc_1) ).
fof(t138_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set ) ),
inference(assume_negation,[status(cth)],[t138_zfmisc_1]) ).
cnf(c_12,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_19,plain,
( empty_set != A
| cartesian_product2(A,B) = empty_set ),
inference(clausify,[status(thm)],[t113_zfmisc_1]) ).
cnf(c_20,plain,
( empty_set != B
| cartesian_product2(A,B) = empty_set ),
inference(clausify,[status(thm)],[t113_zfmisc_1]) ).
cnf(c_21,plain,
cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(clausify,[status(thm)],[t123_zfmisc_1]) ).
cnf(c_22,plain,
set_intersection2(cartesian_product2(A,B),cartesian_product2(C,D)) = cartesian_product2(set_intersection2(A,C),set_intersection2(B,D)),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_23,plain,
( A = C
| empty_set = D
| empty_set = C
| cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(clausify,[status(thm)],[t134_zfmisc_1]) ).
cnf(c_24,plain,
( B = D
| empty_set = D
| empty_set = C
| cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(clausify,[status(thm)],[t134_zfmisc_1]) ).
cnf(c_25,plain,
subset(set_intersection2(A,B),A),
inference(clausify,[status(thm)],[t17_xboole_1]) ).
cnf(c_26,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
fof(nnf_11,plain,
? [A,B,C,D] :
( ( ~ subset(B,D)
| ~ subset(A,C) )
& cartesian_product2(A,B) != empty_set
& subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(fof_nnf,[status(thm)],[t138_zfmisc_1_neg]) ).
fof(sk_t138_zfmisc_1_neg,plain,
( ( ~ subset(sK1,sK3)
| ~ subset(sK0,sK2) )
& cartesian_product2(sK0,sK1) != empty_set
& subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_11]) ).
cnf(c_27,negated_conjecture,
subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t138_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
cartesian_product2(sK0,sK1) != empty_set,
inference(split_conjunct,[status(thm)],[sk_t138_zfmisc_1_neg]) ).
cnf(c_29,negated_conjecture,
( ~ subset(sK1,sK3)
| ~ subset(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t138_zfmisc_1_neg]) ).
cnf(c_39,plain,
subset(set_intersection2(A,B),B),
inference(paramod,[status(thm)],[c_12,c_25]) ).
cnf(c_195,negated_conjecture,
set_intersection2(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) = cartesian_product2(sK0,sK1),
inference(resolve,[status(thm)],[c_27,c_26]) ).
cnf(c_42,negated_conjecture,
cartesian_product2(set_intersection2(sK0,sK2),set_intersection2(sK1,sK3)) = cartesian_product2(sK0,sK1),
inference(paramod,[status(thm)],[c_22,c_195]) ).
cnf(c_196,negated_conjecture,
empty_set != sK1,
inference(resolve,[status(thm)],[c_20,c_28]) ).
cnf(c_43,negated_conjecture,
sK1 != empty_set,
inference(copy,[status(thm)],[c_196]) ).
cnf(c_197,negated_conjecture,
empty_set != sK0,
inference(resolve,[status(thm)],[c_19,c_28]) ).
cnf(c_44,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_197]) ).
cnf(c_198,plain,
( set_intersection2(sK1,sK3) = sK1
| empty_set = sK1
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_42,c_24]) ).
cnf(c_199,plain,
( set_intersection2(sK1,sK3) = sK1
| empty_set = sK1
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_198]) ).
cnf(c_200,plain,
( set_intersection2(sK1,sK3) = sK1
| sK1 = empty_set
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_201,plain,
( set_intersection2(sK1,sK3) = sK1
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_44,c_200]) ).
cnf(c_103,plain,
set_intersection2(sK1,sK3) = sK1,
inference(resolve,[status(thm)],[c_43,c_201]) ).
cnf(c_202,plain,
( set_intersection2(sK0,sK2) = sK0
| empty_set = sK1
| empty_set = sK0 ),
inference(resolve,[status(thm)],[c_42,c_23]) ).
cnf(c_203,plain,
( set_intersection2(sK0,sK2) = sK0
| empty_set = sK1
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_204,plain,
( set_intersection2(sK0,sK2) = sK0
| sK1 = empty_set
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_205,plain,
( set_intersection2(sK0,sK2) = sK0
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_44,c_204]) ).
cnf(c_104,plain,
set_intersection2(sK0,sK2) = sK0,
inference(resolve,[status(thm)],[c_43,c_205]) ).
cnf(c_192,plain,
subset(sK1,sK3),
inference(paramod,[status(thm)],[c_103,c_39]) ).
cnf(c_193,negated_conjecture,
~ subset(sK0,sK2),
inference(resolve,[status(thm)],[c_192,c_29]) ).
cnf(c_206,plain,
subset(sK0,sK2),
inference(paramod,[status(thm)],[c_104,c_39]) ).
cnf(c_194,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_193,c_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 08:30:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2446968 was started by sandbox2 on n003,
% 0.08/0.37 % Sat Sep 26 08:30:24 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.13/0.44 % Length of proof is 28.
% 0.13/0.44 % Level of proof is 7.
% 0.13/0.44 % Maximum clause weight is 30.000.
% 0.13/0.44 % Given clauses 43.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------