%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET985+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 : n006.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 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 87 ( 49 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 16 ~; 42 |; 5 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 3 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(t138_zfmisc_1,axiom,
! [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(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t139_zfmisc_1,conjecture,
! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) )
=> subset(B,D) ) ),
file('theBenchmark.p',t139_zfmisc_1) ).
fof(t139_zfmisc_1_neg,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) )
=> subset(B,D) ) ),
inference(assume_negation,[status(cth)],[t139_zfmisc_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_8,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_12,plain,
( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ),
inference(clausify,[status(thm)],[t113_zfmisc_1]) ).
cnf(c_41,plain,
( B = empty_set
| empty_set = A
| cartesian_product2(A,B) != empty_set ),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_13,plain,
( empty_set = B
| empty_set = A
| cartesian_product2(A,B) != empty_set ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_18,plain,
( subset(A,C)
| cartesian_product2(A,B) = empty_set
| ~ subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[t138_zfmisc_1]) ).
cnf(c_19,plain,
( subset(B,D)
| cartesian_product2(A,B) = empty_set
| ~ subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[t138_zfmisc_1]) ).
cnf(c_20,plain,
subset(empty_set,A),
inference(clausify,[status(thm)],[t2_xboole_1]) ).
fof(nnf_7,plain,
? [A] :
( ? [B,C,D] :
( ~ subset(B,D)
& ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) ) )
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t139_zfmisc_1_neg]) ).
fof(sk_t139_zfmisc_1_neg,plain,
( ~ subset(sK1,sK3)
& ( subset(cartesian_product2(sK1,sK0),cartesian_product2(sK3,sK2))
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) )
& ~ empty(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_7]) ).
cnf(c_21,negated_conjecture,
~ empty(sK0),
inference(split_conjunct,[status(thm)],[sk_t139_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
( subset(cartesian_product2(sK1,sK0),cartesian_product2(sK3,sK2))
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(split_conjunct,[status(thm)],[sk_t139_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
~ subset(sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t139_zfmisc_1_neg]) ).
cnf(c_42,negated_conjecture,
( subset(sK1,sK3)
| cartesian_product2(sK1,sK0) = empty_set
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_28,negated_conjecture,
( cartesian_product2(sK1,sK0) = empty_set
| subset(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)) ),
inference(resolve,[status(thm)],[c_23,c_42]) ).
cnf(c_43,plain,
( subset(sK1,sK3)
| cartesian_product2(sK0,sK1) = empty_set
| cartesian_product2(sK1,sK0) = empty_set ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_32,negated_conjecture,
( cartesian_product2(sK0,sK1) = empty_set
| cartesian_product2(sK1,sK0) = empty_set ),
inference(resolve,[status(thm)],[c_23,c_43]) ).
cnf(c_44,plain,
( empty_set = sK0
| empty_set = sK1
| cartesian_product2(sK0,sK1) = empty_set ),
inference(resolve,[status(thm)],[c_32,c_13]) ).
cnf(c_45,plain,
( empty_set = sK0
| sK1 = empty_set
| cartesian_product2(sK0,sK1) = empty_set ),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_33,plain,
( sK0 = empty_set
| sK1 = empty_set
| cartesian_product2(sK0,sK1) = empty_set ),
inference(copy,[status(thm)],[c_45]) ).
cnf(c_46,plain,
( empty_set = sK1
| empty_set = sK0
| sK0 = empty_set
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_33,c_13]) ).
cnf(c_47,plain,
( empty_set = sK1
| sK0 = empty_set
| sK0 = empty_set
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_46]) ).
cnf(c_48,plain,
( sK1 = empty_set
| sK0 = empty_set
| sK0 = empty_set
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_49,plain,
( sK1 = empty_set
| sK0 = empty_set
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_36,plain,
( sK0 = empty_set
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_50,plain,
( ~ subset(empty_set,sK3)
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_36,c_23]) ).
cnf(c_39,plain,
sK0 = empty_set,
inference(resolve,[status(thm)],[c_20,c_50]) ).
cnf(c_51,negated_conjecture,
~ empty(empty_set),
inference(paramod,[status(thm)],[c_39,c_21]) ).
cnf(c_40,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_8,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:28:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 819505 was started by sandbox on n006,
% 0.09/0.36 % Sat Sep 26 08:28:27 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 19.
% 0.09/0.38 % Level of proof is 7.
% 0.09/0.38 % Maximum clause weight is 15.000.
% 0.09/0.38 % Given clauses 21.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------