%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 : Fri Sep 25 02:44:24 PM UTC 2026
% Result : Theorem 2.87s 0.74s
% Output : Proof 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 57 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 54 ( 24 ~; 19 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 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 : 58 ( 8 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( A != B
=> disjoint(singleton(A),singleton(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B] :
( disjoint(singleton(A),singleton(B))
| A = B ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( disjoint(singleton(A),singleton(B))
| A = B ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( disjoint(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f2,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8,plain,
( disjoint(singleton(X1),singleton(X0))
| X0 = X1 ),
inference(resolution,[status(thm)],[c7,c2]) ).
fof(f3,axiom,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(C,D)
& ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(C,D)
& ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p11,plain,
( disjoint(cartesian_product2(singleton(X1),X2),cartesian_product2(singleton(X0),X3))
| X0 = X1 ),
inference(resolution,[status(thm)],[p8,c3]) ).
fof(f4,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
fof(f4_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(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,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)) )
& A != B ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( ( ~ disjoint(cartesian_product2(sk4,singleton(sk2)),cartesian_product2(sk5,singleton(sk3)))
| ~ disjoint(cartesian_product2(singleton(sk2),sk4),cartesian_product2(singleton(sk3),sk5)) )
& sk2 != sk3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f4_nnf]) ).
cnf(c6,plain,
( ~ disjoint(cartesian_product2(sk4,singleton(sk2)),cartesian_product2(sk5,singleton(sk3)))
| ~ disjoint(cartesian_product2(singleton(sk2),sk4),cartesian_product2(singleton(sk3),sk5)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p20,plain,
( ~ disjoint(cartesian_product2(sk4,singleton(sk2)),cartesian_product2(sk5,singleton(sk3)))
| sk3 = sk2 ),
inference(resolution,[status(thm)],[p11,c6]) ).
cnf(c4,plain,
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p12,plain,
( disjoint(cartesian_product2(X2,singleton(X1)),cartesian_product2(X3,singleton(X0)))
| X0 = X1 ),
inference(resolution,[status(thm)],[p8,c4]) ).
cnf(p37,plain,
( sk3 = sk2
| sk3 = sk2 ),
inference(resolution,[status(thm)],[p20,p12]) ).
cnf(p67,plain,
sk3 = sk2,
inference(factoring,[status(thm)],[p37]) ).
cnf(c5,plain,
sk2 != sk3,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p68,plain,
sk2 != sk2,
inference(demodulation,[status(thm)],[p67,c5]) ).
cnf(p126,plain,
$false,
inference(equality_resolution,[status(thm)],[p68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 12:29:56 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.87/0.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.87/0.74 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------