%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET985+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 : n001.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 6.26s 6.55s
% Output : Proof 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 96 ( 44 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 83 ( 22 ~; 44 |; 11 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 44 ( 3 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B,C,D] :
( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set
| ~ subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set
| ~ subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( subset(X0,X2)
| cartesian_product2(X0,X1) = empty_set
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(f6_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(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,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(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ~ subset(sk3,sk5)
& ( subset(cartesian_product2(sk3,sk2),cartesian_product2(sk5,sk4))
| subset(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk5)) )
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f6_nnf]) ).
cnf(c10,plain,
( subset(cartesian_product2(sk3,sk2),cartesian_product2(sk5,sk4))
| subset(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk5)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p18,plain,
( subset(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk5))
| subset(sk3,sk5)
| cartesian_product2(sk3,sk2) = empty_set ),
inference(resolution,[status(thm)],[c7,c10]) ).
cnf(c8,plain,
( subset(X1,X3)
| cartesian_product2(X0,X1) = empty_set
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p22,plain,
( subset(sk3,sk5)
| cartesian_product2(sk2,sk3) = empty_set
| subset(sk3,sk5)
| cartesian_product2(sk3,sk2) = empty_set ),
inference(resolution,[status(thm)],[p18,c8]) ).
cnf(p27,plain,
( cartesian_product2(sk2,sk3) = empty_set
| subset(sk3,sk5)
| cartesian_product2(sk3,sk2) = empty_set ),
inference(factoring,[status(thm)],[p22]) ).
fof(f4,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ( B != empty_set
& A != empty_set )
| cartesian_product2(A,B) = empty_set )
& ( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( ( B != empty_set
& A != empty_set )
| cartesian_product2(A,B) = empty_set )
& ( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != empty_set ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p29,plain,
( sk2 = empty_set
| sk3 = empty_set
| cartesian_product2(sk2,sk3) = empty_set
| subset(sk3,sk5) ),
inference(resolution,[status(thm)],[p27,c4]) ).
cnf(p38,plain,
( sk3 = empty_set
| sk2 = empty_set
| sk2 = empty_set
| sk3 = empty_set
| subset(sk3,sk5) ),
inference(resolution,[status(thm)],[p29,c4]) ).
cnf(p55,plain,
( sk2 = empty_set
| sk2 = empty_set
| sk3 = empty_set
| subset(sk3,sk5) ),
inference(factoring,[status(thm)],[p38]) ).
cnf(p57,plain,
( sk2 = empty_set
| sk3 = empty_set
| subset(sk3,sk5) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(c11,plain,
~ subset(sk3,sk5),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p58,plain,
( sk2 = empty_set
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p57,c11]) ).
cnf(p59,plain,
( ~ subset(empty_set,sk5)
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p58,c11]) ).
fof(f7,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f7_nnf,plain,
! [A] : subset(empty_set,A),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] : subset(empty_set,A),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c12,plain,
subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p62,plain,
sk2 = empty_set,
inference(resolution,[status(thm)],[p59,c12]) ).
cnf(c9,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p63,plain,
~ empty(empty_set),
inference(demodulation,[status(thm)],[p62,c9]) ).
fof(f0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f0_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p65,plain,
$false,
inference(resolution,[status(thm)],[p63,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/5.46 % Computer : n001.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Thu Sep 24 12:36:58 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.26/6.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.26/6.55 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------