%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET983+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 : n011.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 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 36 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 6 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 20 !; 5 ?)
% 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(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
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(t137_zfmisc_1,conjecture,
! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
file('theBenchmark.p',t137_zfmisc_1) ).
fof(t137_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
inference(assume_negation,[status(cth)],[t137_zfmisc_1]) ).
cnf(c_10,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_13,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_20,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]) ).
fof(nnf_8,plain,
? [A,B,C,D,E] :
( ~ in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E)))
& in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[t137_zfmisc_1_neg]) ).
fof(sk_t137_zfmisc_1_neg,plain,
( ~ in(sK0,cartesian_product2(set_intersection2(sK1,sK3),set_intersection2(sK2,sK4)))
& in(sK0,cartesian_product2(sK3,sK4))
& in(sK0,cartesian_product2(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3),skolemize(E,sK4)],[nnf_8]) ).
cnf(c_21,negated_conjecture,
in(sK0,cartesian_product2(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t137_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
in(sK0,cartesian_product2(sK3,sK4)),
inference(split_conjunct,[status(thm)],[sk_t137_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
~ in(sK0,cartesian_product2(set_intersection2(sK1,sK3),set_intersection2(sK2,sK4))),
inference(split_conjunct,[status(thm)],[sk_t137_zfmisc_1_neg]) ).
cnf(c_24,negated_conjecture,
~ in(sK0,set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),
inference(paramod,[status(thm)],[c_20,c_23]) ).
cnf(c_87,negated_conjecture,
( ~ in(sK0,B)
| ~ in(sK0,A)
| set_intersection2(A,B) != set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) ),
inference(resolve,[status(thm)],[c_13,c_24]) ).
cnf(c_88,negated_conjecture,
( ~ in(sK0,A)
| set_intersection2(cartesian_product2(sK3,sK4),A) != set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) ),
inference(resolve,[status(thm)],[c_87,c_22]) ).
cnf(c_89,negated_conjecture,
set_intersection2(cartesian_product2(sK3,sK4),cartesian_product2(sK1,sK2)) != set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),
inference(resolve,[status(thm)],[c_88,c_21]) ).
cnf(c_90,negated_conjecture,
set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) != set_intersection2(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),
inference(paramod,[status(thm)],[c_10,c_89]) ).
cnf(c_86,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:28:45 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 45549 was started by sandbox2 on n011,
% 0.11/0.38 % Sat Sep 26 08:28:45 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.40
% 0.11/0.40 % SZS status Theorem for theBenchmark
% 0.11/0.40
% 0.11/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.40 % Length of proof is 12.
% 0.11/0.40 % Level of proof is 3.
% 0.11/0.40 % Maximum clause weight is 15.000.
% 0.11/0.40 % Given clauses 15.
% 0.11/0.40
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------