%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET974+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 : 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 08:37:23 AM UTC 2026
% Result : Theorem 0.22s 15.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 74 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 29 ~; 22 |; 17 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 87 ( 3 sgn 58 !; 8 ?)
% 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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t104_zfmisc_1,axiom,
! [A,B,C,D,E] :
~ ( ! [F,G] :
~ ( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& A = ordered_pair(F,G) )
& in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
file('theBenchmark.p',t104_zfmisc_1) ).
fof(t4_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t127_zfmisc_1,conjecture,
! [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(t127_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(assume_negation,[status(cth)],[t127_zfmisc_1]) ).
cnf(c_15,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_23,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(nnf_10,plain,
! [A,B,C,D,E] :
( ? [F,G] :
( in(G,set_intersection2(C,E))
& in(F,set_intersection2(B,D))
& ordered_pair(F,G) = A )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(fof_nnf,[status(thm)],[t104_zfmisc_1]) ).
fof(sk_t104_zfmisc_1_sk,plain,
! [A,B,C,D,E] :
( ( in(sK1(A,B,C,D,E),set_intersection2(C,E))
& in(sK0(A,B,C,D,E),set_intersection2(B,D))
& ordered_pair(sK0(A,B,C,D,E),sK1(A,B,C,D,E)) = A )
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(F,sK0(A,B,C,D,E)),skolemize(G,sK1(A,B,C,D,E))],[nnf_10]) ).
fof(sk_t104_zfmisc_1,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( in(sK1(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),set_intersection2(VAR_2,VAR_4))
| ~ in(VAR_0,set_intersection2(cartesian_product2(VAR_1,VAR_2),cartesian_product2(VAR_3,VAR_4))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( in(sK0(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),set_intersection2(VAR_1,VAR_3))
| ~ in(VAR_0,set_intersection2(cartesian_product2(VAR_1,VAR_2),cartesian_product2(VAR_3,VAR_4))) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ordered_pair(sK0(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),sK1(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4)) = VAR_0
| ~ in(VAR_0,set_intersection2(cartesian_product2(VAR_1,VAR_2),cartesian_product2(VAR_3,VAR_4))) ) ),
inference(cnf_transformation,[status(thm)],[sk_t104_zfmisc_1_sk]) ).
cnf(c_26,plain,
( in(sK0(A,B,C,D,E),set_intersection2(B,D))
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(split_conjunct,[status(thm)],[sk_t104_zfmisc_1]) ).
cnf(c_27,plain,
( in(sK1(A,B,C,D,E),set_intersection2(C,E))
| ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
inference(split_conjunct,[status(thm)],[sk_t104_zfmisc_1]) ).
fof(nnf_11,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [X0] : in(X0,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(sk_t4_xboole_0_sk,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( in(sK2(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2(A,B))],[nnf_11]) ).
fof(sk_t4_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ disjoint(VAR_1,VAR_2)
| ~ in(VAR_0,set_intersection2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),set_intersection2(VAR_0,VAR_1))
| disjoint(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_t4_xboole_0_sk]) ).
cnf(c_28,plain,
( in(sK2(A,B),set_intersection2(A,B))
| disjoint(A,B) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
cnf(c_29,plain,
( ~ disjoint(B,C)
| ~ in(A,set_intersection2(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_t4_xboole_0]) ).
fof(nnf_12,plain,
? [A,B,C,D] :
( ~ disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
& ( disjoint(C,D)
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t127_zfmisc_1_neg]) ).
fof(sk_t127_zfmisc_1_neg,plain,
( ~ disjoint(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6))
& ( disjoint(sK5,sK6)
| disjoint(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(A,sK3),skolemize(B,sK4),skolemize(C,sK5),skolemize(D,sK6)],[nnf_12]) ).
cnf(c_30,negated_conjecture,
( disjoint(sK5,sK6)
| disjoint(sK3,sK4) ),
inference(split_conjunct,[status(thm)],[sk_t127_zfmisc_1_neg]) ).
cnf(c_31,negated_conjecture,
~ disjoint(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6)),
inference(split_conjunct,[status(thm)],[sk_t127_zfmisc_1_neg]) ).
cnf(c_36,plain,
( ~ in(A,set_intersection2(sK5,sK6))
| disjoint(sK3,sK4) ),
inference(resolve,[status(thm)],[c_30,c_29]) ).
cnf(c_38,plain,
in(sK2(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6)),set_intersection2(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6))),
inference(resolve,[status(thm)],[c_31,c_28]) ).
cnf(c_39,negated_conjecture,
~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK3,sK5)),
inference(resolve,[status(thm)],[c_23,c_31]) ).
cnf(c_57,plain,
in(sK2(cartesian_product2(sK4,sK6),cartesian_product2(sK3,sK5)),set_intersection2(cartesian_product2(sK4,sK6),cartesian_product2(sK3,sK5))),
inference(resolve,[status(thm)],[c_39,c_28]) ).
cnf(c_40,plain,
in(sK2(cartesian_product2(sK4,sK6),cartesian_product2(sK3,sK5)),set_intersection2(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6))),
inference(paramod,[status(thm)],[c_15,c_57]) ).
cnf(c_42,plain,
in(sK1(sK2(cartesian_product2(sK3,sK5),cartesian_product2(sK4,sK6)),sK3,sK5,sK4,sK6),set_intersection2(sK5,sK6)),
inference(resolve,[status(thm)],[c_38,c_27]) ).
cnf(c_47,plain,
in(sK0(sK2(cartesian_product2(sK4,sK6),cartesian_product2(sK3,sK5)),sK3,sK5,sK4,sK6),set_intersection2(sK3,sK4)),
inference(resolve,[status(thm)],[c_40,c_26]) ).
cnf(c_51,plain,
disjoint(sK3,sK4),
inference(resolve,[status(thm)],[c_42,c_36]) ).
cnf(c_55,plain,
~ in(A,set_intersection2(sK3,sK4)),
inference(resolve,[status(thm)],[c_51,c_29]) ).
cnf(c_56,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/15.47 % Computer : n013.cluster.edu
% 0.17/15.47 % Model : x86_64 x86_64
% 0.17/15.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.47 % Memory : 8046.5625MB
% 0.17/15.47 % OS : Linux 6.8.0-71-generic
% 0.17/15.47 % CPULimit : 300
% 0.17/15.47 % WCLimit : 300
% 0.17/15.47 % DateTime : Sat Sep 26 08:28:07 UTC 2026
% 0.17/15.47 % CPUTime :
% 0.17/15.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/15.47 % Process 2332880 was started by sandbox2 on n013,
% 0.17/15.47 % Sat Sep 26 08:28:07 2026
% 0.17/15.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/15.48
% 0.17/15.48 % From the command line: assign(max_seconds, 300).
% 0.22/15.50
% 0.22/15.50 % Assigning unary symbol singleton kb_weight 0 and highest precedence (18).
% 0.22/15.50
% 0.22/15.50 % SZS status Theorem for theBenchmark
% 0.22/15.50
% 0.22/15.50 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.22/15.50 % Length of proof is 22.
% 0.22/15.50 % Level of proof is 6.
% 0.22/15.50 % Maximum clause weight is 36.000.
% 0.22/15.50 % Given clauses 30.
% 0.22/15.50
% 0.22/15.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------