%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 280.73s 36.91s
% Output : CNFRefutation 280.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 102 ( 31 unt; 0 def)
% Number of atoms : 236 ( 114 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 198 ( 64 ~; 113 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 119 ( 15 sgn 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t134_zfmisc_1,conjecture,
! [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(t134_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( ( B = D
& A = C )
| B = empty_set
| A = empty_set ) ),
inference(assume_negation,[status(cth)],[t134_zfmisc_1]) ).
cnf(c_13,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
fof(nnf_3,plain,
! [A] :
( ( ? [B] : in(B,A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(sk_d1_xboole_0_sk,plain,
! [A] :
( ( in(sK0(A),A)
| empty_set = A )
& ( ! [X0] : ~ in(X0,A)
| empty_set != A ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0(A))],[nnf_3]) ).
fof(sk_d1_xboole_0,plain,
( ! [VAR_0] :
( in(sK0(VAR_0),VAR_0)
| empty_set = VAR_0 )
& ! [VAR_0,VAR_1] :
( ~ in(VAR_1,VAR_0)
| empty_set != VAR_0 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_xboole_0_sk]) ).
cnf(c_14,plain,
( ~ in(B,A)
| empty_set != A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_15,plain,
( in(sK0(A),A)
| empty_set = A ),
inference(split_conjunct,[status(thm)],[sk_d1_xboole_0]) ).
cnf(c_16,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_20,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_21,plain,
( in(A,C)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_16,c_20]) ).
cnf(c_22,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_23,plain,
( in(B,D)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_16,c_22]) ).
cnf(c_24,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[l55_zfmisc_1]) ).
cnf(c_25,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_16,c_24]) ).
fof(nnf_10,plain,
! [A,B] :
( B = A
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(sk_t2_tarski_sk,plain,
! [A,B] :
( B = A
| ( ( ~ in(sK1(A,B),B)
| ~ in(sK1(A,B),A) )
& ( in(sK1(A,B),B)
| in(sK1(A,B),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1(A,B))],[nnf_10]) ).
fof(sk_t2_tarski,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ in(sK1(VAR_0,VAR_1),VAR_1)
| ~ in(sK1(VAR_0,VAR_1),VAR_0) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| in(sK1(VAR_0,VAR_1),VAR_1)
| in(sK1(VAR_0,VAR_1),VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t2_tarski_sk]) ).
cnf(c_31,plain,
( B = A
| in(sK1(A,B),B)
| in(sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
cnf(c_32,plain,
( B = A
| ~ in(sK1(A,B),B)
| ~ in(sK1(A,B),A) ),
inference(split_conjunct,[status(thm)],[sk_t2_tarski]) ).
fof(nnf_11,plain,
? [A,B,C,D] :
( ( D != B
| C != A )
& empty_set != B
& empty_set != A
& cartesian_product2(C,D) = cartesian_product2(A,B) ),
inference(fof_nnf,[status(thm)],[t134_zfmisc_1_neg]) ).
fof(sk_t134_zfmisc_1_neg,plain,
( ( sK3 != sK5
| sK2 != sK4 )
& empty_set != sK5
& empty_set != sK4
& cartesian_product2(sK2,sK3) = cartesian_product2(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(A,sK4),skolemize(B,sK5),skolemize(C,sK2),skolemize(D,sK3)],[nnf_11]) ).
cnf(c_33,negated_conjecture,
cartesian_product2(sK2,sK3) = cartesian_product2(sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_t134_zfmisc_1_neg]) ).
cnf(c_34,negated_conjecture,
empty_set != sK4,
inference(split_conjunct,[status(thm)],[sk_t134_zfmisc_1_neg]) ).
cnf(c_35,negated_conjecture,
sK4 != empty_set,
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,negated_conjecture,
empty_set != sK5,
inference(split_conjunct,[status(thm)],[sk_t134_zfmisc_1_neg]) ).
cnf(c_37,negated_conjecture,
sK5 != empty_set,
inference(copy,[status(thm)],[c_36]) ).
cnf(c_38,negated_conjecture,
( sK3 != sK5
| sK2 != sK4 ),
inference(split_conjunct,[status(thm)],[sk_t134_zfmisc_1_neg]) ).
cnf(c_47,plain,
( in(A,C)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_13,c_21]) ).
cnf(c_48,plain,
( in(A,D)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(B)),cartesian_product2(C,D)) ),
inference(paramod,[status(thm)],[c_13,c_23]) ).
cnf(c_50,plain,
( empty_set = A
| ~ in(B,C)
| in(unordered_pair(unordered_pair(sK0(A),B),singleton(sK0(A))),cartesian_product2(A,C)) ),
inference(resolve,[status(thm)],[c_25,c_15]) ).
cnf(c_51,plain,
( empty_set = B
| ~ in(A,C)
| in(unordered_pair(unordered_pair(A,sK0(B)),singleton(A)),cartesian_product2(C,B)) ),
inference(resolve,[status(thm)],[c_25,c_15]) ).
cnf(c_62,plain,
( in(A,sK2)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(sK4,sK5)) ),
inference(paramod,[status(thm)],[c_33,c_21]) ).
cnf(c_63,plain,
( in(B,sK3)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),cartesian_product2(sK4,sK5)) ),
inference(paramod,[status(thm)],[c_33,c_23]) ).
cnf(c_179,plain,
( in(A,sK2)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(sK4,sK5)) ),
inference(paramod,[status(thm)],[c_33,c_47]) ).
cnf(c_193,plain,
( C = B
| in(sK1(B,C),B)
| empty_set = A
| in(unordered_pair(unordered_pair(sK0(A),sK1(B,C)),singleton(sK0(A))),cartesian_product2(A,C)) ),
inference(resolve,[status(thm)],[c_50,c_31]) ).
cnf(c_195,plain,
( empty_set = B
| empty_set = A
| in(unordered_pair(unordered_pair(sK0(A),sK0(B)),singleton(sK0(A))),cartesian_product2(A,B)) ),
inference(resolve,[status(thm)],[c_50,c_15]) ).
cnf(c_286,plain,
( B = A
| in(sK1(A,B),A)
| empty_set = C
| in(unordered_pair(unordered_pair(sK1(A,B),sK0(C)),singleton(sK1(A,B))),cartesian_product2(B,C)) ),
inference(resolve,[status(thm)],[c_51,c_31]) ).
cnf(c_34035,plain,
( in(sK0(sK5),sK3)
| empty_set = sK5
| empty_set = sK4 ),
inference(resolve,[status(thm)],[c_195,c_63]) ).
cnf(c_34036,plain,
( in(sK0(sK5),sK3)
| empty_set = sK5
| sK4 = empty_set ),
inference(copy,[status(thm)],[c_34035]) ).
cnf(c_34037,plain,
( in(sK0(sK5),sK3)
| sK5 = empty_set
| sK4 = empty_set ),
inference(copy,[status(thm)],[c_34036]) ).
cnf(c_34038,negated_conjecture,
( in(sK0(sK5),sK3)
| sK5 = empty_set ),
inference(resolve,[status(thm)],[c_35,c_34037]) ).
cnf(c_1461,negated_conjecture,
in(sK0(sK5),sK3),
inference(resolve,[status(thm)],[c_37,c_34038]) ).
cnf(c_34039,plain,
( in(sK0(sK4),sK2)
| empty_set = sK5
| empty_set = sK4 ),
inference(resolve,[status(thm)],[c_195,c_62]) ).
cnf(c_34040,plain,
( in(sK0(sK4),sK2)
| empty_set = sK5
| sK4 = empty_set ),
inference(copy,[status(thm)],[c_34039]) ).
cnf(c_34041,plain,
( in(sK0(sK4),sK2)
| sK5 = empty_set
| sK4 = empty_set ),
inference(copy,[status(thm)],[c_34040]) ).
cnf(c_34042,negated_conjecture,
( in(sK0(sK4),sK2)
| sK5 = empty_set ),
inference(resolve,[status(thm)],[c_35,c_34041]) ).
cnf(c_1462,negated_conjecture,
in(sK0(sK4),sK2),
inference(resolve,[status(thm)],[c_37,c_34042]) ).
cnf(c_34043,plain,
( empty_set = sK3
| empty_set = sK2
| in(unordered_pair(unordered_pair(sK0(sK2),sK0(sK3)),singleton(sK0(sK2))),cartesian_product2(sK4,sK5)) ),
inference(paramod,[status(thm)],[c_33,c_195]) ).
cnf(c_34044,plain,
( empty_set = sK3
| empty_set = sK2
| in(unordered_pair(singleton(sK0(sK2)),unordered_pair(sK0(sK2),sK0(sK3))),cartesian_product2(sK4,sK5)) ),
inference(paramod,[status(thm)],[c_13,c_34043]) ).
cnf(c_34045,plain,
( empty_set = sK3
| sK2 = empty_set
| in(unordered_pair(singleton(sK0(sK2)),unordered_pair(sK0(sK2),sK0(sK3))),cartesian_product2(sK4,sK5)) ),
inference(copy,[status(thm)],[c_34044]) ).
cnf(c_1475,plain,
( sK3 = empty_set
| sK2 = empty_set
| in(unordered_pair(singleton(sK0(sK2)),unordered_pair(sK0(sK2),sK0(sK3))),cartesian_product2(sK4,sK5)) ),
inference(copy,[status(thm)],[c_34045]) ).
cnf(c_1495,plain,
( ~ in(A,B)
| in(unordered_pair(unordered_pair(A,sK0(sK5)),singleton(A)),cartesian_product2(B,sK3)) ),
inference(resolve,[status(thm)],[c_1461,c_25]) ).
cnf(c_34046,plain,
empty_set != sK3,
inference(resolve,[status(thm)],[c_1461,c_14]) ).
cnf(c_1497,plain,
sK3 != empty_set,
inference(copy,[status(thm)],[c_34046]) ).
cnf(c_1499,plain,
( sK2 = empty_set
| in(unordered_pair(singleton(sK0(sK2)),unordered_pair(sK0(sK2),sK0(sK3))),cartesian_product2(sK4,sK5)) ),
inference(resolve,[status(thm)],[c_1497,c_1475]) ).
cnf(c_34047,plain,
empty_set != sK2,
inference(resolve,[status(thm)],[c_1462,c_14]) ).
cnf(c_1606,plain,
sK2 != empty_set,
inference(copy,[status(thm)],[c_34047]) ).
cnf(c_1608,plain,
in(unordered_pair(singleton(sK0(sK2)),unordered_pair(sK0(sK2),sK0(sK3))),cartesian_product2(sK4,sK5)),
inference(resolve,[status(thm)],[c_1606,c_1499]) ).
cnf(c_1635,plain,
in(sK0(sK2),sK2),
inference(resolve,[status(thm)],[c_1608,c_179]) ).
cnf(c_1773,plain,
( ~ in(A,B)
| in(unordered_pair(unordered_pair(sK0(sK2),A),singleton(sK0(sK2))),cartesian_product2(sK2,B)) ),
inference(resolve,[status(thm)],[c_1635,c_25]) ).
cnf(c_34048,plain,
in(unordered_pair(unordered_pair(sK0(sK2),sK0(sK5)),singleton(sK0(sK2))),cartesian_product2(sK2,sK3)),
inference(resolve,[status(thm)],[c_1495,c_1635]) ).
cnf(c_34049,plain,
in(unordered_pair(unordered_pair(sK0(sK5),sK0(sK2)),singleton(sK0(sK2))),cartesian_product2(sK2,sK3)),
inference(paramod,[status(thm)],[c_13,c_34048]) ).
cnf(c_2430,plain,
in(unordered_pair(unordered_pair(sK0(sK5),sK0(sK2)),singleton(sK0(sK2))),cartesian_product2(sK4,sK5)),
inference(paramod,[status(thm)],[c_33,c_34049]) ).
cnf(c_2762,plain,
in(sK0(sK5),sK5),
inference(resolve,[status(thm)],[c_2430,c_48]) ).
cnf(c_2777,plain,
( ~ in(A,B)
| in(unordered_pair(unordered_pair(A,sK0(sK5)),singleton(A)),cartesian_product2(B,sK5)) ),
inference(resolve,[status(thm)],[c_2762,c_25]) ).
cnf(c_34050,plain,
( in(sK1(A,sK5),sK3)
| sK5 = A
| in(sK1(A,sK5),A)
| empty_set = sK4 ),
inference(resolve,[status(thm)],[c_193,c_63]) ).
cnf(c_34051,plain,
( in(sK1(A,sK5),sK3)
| sK5 = A
| in(sK1(A,sK5),A)
| sK4 = empty_set ),
inference(copy,[status(thm)],[c_34050]) ).
cnf(c_18521,negated_conjecture,
( in(sK1(A,sK5),sK3)
| sK5 = A
| in(sK1(A,sK5),A) ),
inference(resolve,[status(thm)],[c_35,c_34051]) ).
cnf(c_34052,plain,
( sK5 = sK3
| in(sK1(sK3,sK5),sK3) ),
inference(factor,[status(thm)],[c_18521]) ).
cnf(c_18531,plain,
( sK3 = sK5
| in(sK1(sK3,sK5),sK3) ),
inference(copy,[status(thm)],[c_34052]) ).
cnf(c_34053,plain,
( in(unordered_pair(unordered_pair(sK0(sK2),sK1(sK3,sK5)),singleton(sK0(sK2))),cartesian_product2(sK2,sK3))
| sK3 = sK5 ),
inference(resolve,[status(thm)],[c_18531,c_1773]) ).
cnf(c_34054,plain,
( in(unordered_pair(unordered_pair(sK1(sK3,sK5),sK0(sK2)),singleton(sK0(sK2))),cartesian_product2(sK2,sK3))
| sK3 = sK5 ),
inference(paramod,[status(thm)],[c_13,c_34053]) ).
cnf(c_18567,plain,
( in(unordered_pair(unordered_pair(sK1(sK3,sK5),sK0(sK2)),singleton(sK0(sK2))),cartesian_product2(sK4,sK5))
| sK3 = sK5 ),
inference(paramod,[status(thm)],[c_33,c_34054]) ).
cnf(c_34055,plain,
( sK5 = sK3
| ~ in(sK1(sK3,sK5),sK5)
| sK3 = sK5 ),
inference(resolve,[status(thm)],[c_18531,c_32]) ).
cnf(c_34056,plain,
( sK3 = sK5
| ~ in(sK1(sK3,sK5),sK5)
| sK3 = sK5 ),
inference(copy,[status(thm)],[c_34055]) ).
cnf(c_18586,plain,
( ~ in(sK1(sK3,sK5),sK5)
| sK3 = sK5 ),
inference(copy,[status(thm)],[c_34056]) ).
cnf(c_24998,plain,
( in(sK1(sK3,sK5),sK5)
| sK3 = sK5 ),
inference(resolve,[status(thm)],[c_18567,c_48]) ).
cnf(c_34057,plain,
( sK3 = sK5
| sK3 = sK5 ),
inference(resolve,[status(thm)],[c_24998,c_18586]) ).
cnf(c_25019,plain,
sK3 = sK5,
inference(copy,[status(thm)],[c_34057]) ).
cnf(c_34058,negated_conjecture,
( sK5 != sK5
| sK2 != sK4 ),
inference(paramod,[status(thm)],[c_25019,c_38]) ).
cnf(c_25525,negated_conjecture,
sK2 != sK4,
inference(copy,[status(thm)],[c_34058]) ).
cnf(c_25526,negated_conjecture,
cartesian_product2(sK2,sK5) = cartesian_product2(sK4,sK5),
inference(paramod,[status(thm)],[c_25019,c_33]) ).
cnf(c_34059,plain,
( in(sK1(A,sK4),sK2)
| sK4 = A
| in(sK1(A,sK4),A)
| empty_set = sK5 ),
inference(resolve,[status(thm)],[c_286,c_62]) ).
cnf(c_34060,plain,
( in(sK1(A,sK4),sK2)
| sK4 = A
| in(sK1(A,sK4),A)
| sK5 = empty_set ),
inference(copy,[status(thm)],[c_34059]) ).
cnf(c_33738,negated_conjecture,
( in(sK1(A,sK4),sK2)
| sK4 = A
| in(sK1(A,sK4),A) ),
inference(resolve,[status(thm)],[c_37,c_34060]) ).
cnf(c_34061,plain,
( sK4 = sK2
| in(sK1(sK2,sK4),sK2) ),
inference(factor,[status(thm)],[c_33738]) ).
cnf(c_34062,plain,
( sK2 = sK4
| in(sK1(sK2,sK4),sK2) ),
inference(copy,[status(thm)],[c_34061]) ).
cnf(c_33757,negated_conjecture,
in(sK1(sK2,sK4),sK2),
inference(resolve,[status(thm)],[c_25525,c_34062]) ).
cnf(c_34063,plain,
in(unordered_pair(unordered_pair(sK1(sK2,sK4),sK0(sK5)),singleton(sK1(sK2,sK4))),cartesian_product2(sK2,sK5)),
inference(resolve,[status(thm)],[c_33757,c_2777]) ).
cnf(c_34064,plain,
in(unordered_pair(singleton(sK1(sK2,sK4)),unordered_pair(sK1(sK2,sK4),sK0(sK5))),cartesian_product2(sK2,sK5)),
inference(paramod,[status(thm)],[c_13,c_34063]) ).
cnf(c_33841,plain,
in(unordered_pair(singleton(sK1(sK2,sK4)),unordered_pair(sK1(sK2,sK4),sK0(sK5))),cartesian_product2(sK4,sK5)),
inference(paramod,[status(thm)],[c_25526,c_34064]) ).
cnf(c_34065,plain,
( sK4 = sK2
| ~ in(sK1(sK2,sK4),sK4) ),
inference(resolve,[status(thm)],[c_33757,c_32]) ).
cnf(c_34066,plain,
( sK2 = sK4
| ~ in(sK1(sK2,sK4),sK4) ),
inference(copy,[status(thm)],[c_34065]) ).
cnf(c_33859,negated_conjecture,
~ in(sK1(sK2,sK4),sK4),
inference(resolve,[status(thm)],[c_25525,c_34066]) ).
cnf(c_34033,plain,
~ in(unordered_pair(singleton(sK1(sK2,sK4)),unordered_pair(sK1(sK2,sK4),A)),cartesian_product2(sK4,B)),
inference(resolve,[status(thm)],[c_47,c_33859]) ).
cnf(c_34034,plain,
$false,
inference(resolve,[status(thm)],[c_34033,c_33841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET980+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:28:43 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 820094 was started by sandbox2 on n006,
% 0.09/0.36 % Sat Sep 26 08:28:43 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 280.73/36.91
% 280.73/36.91 % given #500 (T,wt=16): 14042 empty_set = A | -in(cartesian_product2(c6,A),unordered_pair(singleton(f1(c6)),unordered_pair(f1(c6),f1(A)))). [para(13(a,1),12122(b,2))].
% 280.73/36.91
% 280.73/36.91 % given #1000 (F,wt=9): 2659 cartesian_product2(cartesian_product2(c5,c5),cartesian_product2(c4,c5)) != empty_set. [ur(28,b,1632,a(flip),c,1702,a(flip))].
% 280.73/36.91
% 280.73/36.91 % SZS status Theorem for theBenchmark
% 280.73/36.91
% 280.73/36.91 % Proof 1 at 24.87 (+ 11.35) seconds.
% 280.73/36.91 % Length of proof is 61.
% 280.73/36.91 % Level of proof is 18.
% 280.73/36.91 % Maximum clause weight is 26.000.
% 280.73/36.91 % Given clauses 1394.
% 280.73/36.91
% 280.73/36.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------