%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET978+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 : n013.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 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 42 ( 13 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 39 ( 18 ~; 12 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 44 ( 10 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t127_zfmisc_1,axiom,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t127_zfmisc_1) ).
fof(t17_zfmisc_1,axiom,
! [A,B] :
( A != B
=> disjoint(singleton(A),singleton(B)) ),
file('theBenchmark.p',t17_zfmisc_1) ).
fof(t131_zfmisc_1,conjecture,
! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ) ),
file('theBenchmark.p',t131_zfmisc_1) ).
fof(t131_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ) ),
inference(assume_negation,[status(cth)],[t131_zfmisc_1]) ).
cnf(c_9,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
cnf(c_10,plain,
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[t127_zfmisc_1]) ).
cnf(c_11,plain,
( disjoint(cartesian_product2(C,A),cartesian_product2(D,B))
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[t127_zfmisc_1]) ).
cnf(c_12,plain,
( disjoint(singleton(B),singleton(A))
| A = B ),
inference(clausify,[status(thm)],[t17_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B,C,D] :
( ( ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
| ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) )
& B != A ),
inference(fof_nnf,[status(thm)],[t131_zfmisc_1_neg]) ).
fof(sk_t131_zfmisc_1_neg,plain,
( ( ~ disjoint(cartesian_product2(sK2,singleton(sK1)),cartesian_product2(sK3,singleton(sK0)))
| ~ disjoint(cartesian_product2(singleton(sK1),sK2),cartesian_product2(singleton(sK0),sK3)) )
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2),skolemize(D,sK3)],[nnf_6]) ).
cnf(c_13,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_t131_zfmisc_1_neg]) ).
cnf(c_14,negated_conjecture,
( ~ disjoint(cartesian_product2(sK2,singleton(sK1)),cartesian_product2(sK3,singleton(sK0)))
| ~ disjoint(cartesian_product2(singleton(sK1),sK2),cartesian_product2(singleton(sK0),sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t131_zfmisc_1_neg]) ).
cnf(c_15,plain,
( disjoint(cartesian_product2(C,singleton(B)),cartesian_product2(D,singleton(A)))
| A = B ),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_16,plain,
( disjoint(cartesian_product2(singleton(B),C),cartesian_product2(singleton(A),D))
| A = B ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_20,plain,
( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
| A = B ),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_32,negated_conjecture,
( ~ disjoint(cartesian_product2(sK2,singleton(sK1)),cartesian_product2(sK3,singleton(sK0)))
| sK0 = sK1 ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_22,negated_conjecture,
~ disjoint(cartesian_product2(sK2,singleton(sK1)),cartesian_product2(sK3,singleton(sK0))),
inference(resolve,[status(thm)],[c_13,c_32]) ).
cnf(c_33,plain,
sK1 = sK0,
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_34,plain,
sK0 = sK1,
inference(copy,[status(thm)],[c_33]) ).
cnf(c_31,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_13,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.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 08:28:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2333414 was started by sandbox on n013,
% 0.12/0.36 % Sat Sep 26 08:28:23 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 15.
% 0.12/0.37 % Level of proof is 4.
% 0.12/0.37 % Maximum clause weight is 18.000.
% 0.12/0.37 % Given clauses 15.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------