%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET984+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 : n020.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 127.57s 24.91s
% Output : Proof 127.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 28 unt; 0 def)
% Number of atoms : 128 ( 93 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 29 ~; 51 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 6 sgn 56 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f0_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f7,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f7_nnf,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p24,plain,
set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = set_intersection2(cartesian_product2(X2,X1),cartesian_product2(X0,X3)),
inference(superposition,[status(thm)],[c0,c9]) ).
fof(f11,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f11_nnf,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c16,plain,
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f9,conjecture,
! [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(f9_neg,negated_conjecture,
~ ! [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 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_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)],[f9_neg]) ).
fof(f9_sk,plain,
( ( ~ subset(sk3,sk5)
| ~ subset(sk2,sk4) )
& cartesian_product2(sk2,sk3) != empty_set
& subset(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4,sk5])],[f9_nnf]) ).
cnf(c12,plain,
subset(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk5)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p21,plain,
set_intersection2(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk5)) = cartesian_product2(sk2,sk3),
inference(resolution,[status(thm)],[c16,c12]) ).
cnf(p119,plain,
set_intersection2(cartesian_product2(sk2,sk5),cartesian_product2(sk4,sk3)) = cartesian_product2(sk2,sk3),
inference(superposition,[status(thm)],[p24,p21]) ).
fof(f10,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f10_nnf,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c15,plain,
subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p18,plain,
subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c0,c15]) ).
cnf(p146,plain,
subset(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk3)),
inference(superposition,[status(thm)],[p119,p18]) ).
cnf(p155,plain,
set_intersection2(cartesian_product2(sk2,sk3),cartesian_product2(sk4,sk3)) = cartesian_product2(sk2,sk3),
inference(resolution,[status(thm)],[p146,c16]) ).
cnf(p194,plain,
cartesian_product2(set_intersection2(sk2,sk4),sk3) = cartesian_product2(sk2,sk3),
inference(superposition,[status(thm)],[p155,c9]) ).
fof(f8,axiom,
! [A,B,C,D] :
( cartesian_product2(A,B) = cartesian_product2(C,D)
=> ( ( B = D
& A = C )
| B = empty_set
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f8_nnf,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| B = empty_set
| A = empty_set
| cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| B = empty_set
| A = empty_set
| cartesian_product2(A,B) != cartesian_product2(C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( X0 = X2
| X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p196,plain,
( set_intersection2(sk2,sk4) = sk2
| sk3 = empty_set
| set_intersection2(sk2,sk4) = empty_set ),
inference(resolution,[status(thm)],[p194,c10]) ).
cnf(p343,plain,
( subset(sk2,sk4)
| sk3 = empty_set
| set_intersection2(sk2,sk4) = empty_set ),
inference(superposition,[status(thm)],[p196,p18]) ).
cnf(p382,plain,
( empty_set = cartesian_product2(sk2,sk3)
| subset(sk2,sk4)
| sk3 = empty_set ),
inference(superposition,[status(thm)],[p343,p194]) ).
cnf(c13,plain,
cartesian_product2(sk2,sk3) != empty_set,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p424,plain,
( empty_set != empty_set
| subset(sk2,sk4)
| sk3 = empty_set ),
inference(superposition,[status(thm)],[p382,c13]) ).
cnf(p449,plain,
( subset(sk2,sk4)
| sk3 = empty_set ),
inference(equality_resolution,[status(thm)],[p424]) ).
cnf(c14,plain,
( ~ subset(sk3,sk5)
| ~ subset(sk2,sk4) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p450,plain,
( ~ subset(sk3,sk5)
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p449,c14]) ).
cnf(p22,plain,
set_intersection2(X0,set_intersection2(X0,X1)) = set_intersection2(X0,X1),
inference(resolution,[status(thm)],[c16,c15]) ).
cnf(p154,plain,
set_intersection2(cartesian_product2(sk2,sk3),cartesian_product2(sk2,sk5)) = cartesian_product2(sk2,sk3),
inference(superposition,[status(thm)],[p119,p22]) ).
cnf(p178,plain,
cartesian_product2(sk2,set_intersection2(sk3,sk5)) = cartesian_product2(sk2,sk3),
inference(superposition,[status(thm)],[p154,c9]) ).
cnf(c11,plain,
( X1 = X3
| X1 = empty_set
| X0 = empty_set
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p181,plain,
( set_intersection2(sk3,sk5) = sk3
| set_intersection2(sk3,sk5) = empty_set
| sk2 = empty_set ),
inference(resolution,[status(thm)],[p178,c11]) ).
cnf(p263,plain,
( subset(sk3,sk5)
| set_intersection2(sk3,sk5) = empty_set
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p181,p18]) ).
cnf(p284,plain,
( empty_set = cartesian_product2(sk2,sk3)
| subset(sk3,sk5)
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p263,p178]) ).
cnf(p294,plain,
( empty_set != empty_set
| subset(sk3,sk5)
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p284,c13]) ).
cnf(p317,plain,
( subset(sk3,sk5)
| sk2 = empty_set ),
inference(equality_resolution,[status(thm)],[p294]) ).
cnf(p452,plain,
( sk2 = empty_set
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p450,p317]) ).
cnf(p453,plain,
( empty_set != empty_set
| sk2 = empty_set ),
inference(superposition,[status(thm)],[p452,c13]) ).
cnf(p480,plain,
sk2 = empty_set,
inference(equality_resolution,[status(thm)],[p453]) ).
cnf(p482,plain,
cartesian_product2(empty_set,sk3) != empty_set,
inference(demodulation,[status(thm)],[p480,c13]) ).
fof(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c7,plain,
( X0 != empty_set
| cartesian_product2(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p19,plain,
cartesian_product2(empty_set,X0) = empty_set,
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(p649,plain,
$false,
inference(resolution,[status(thm)],[p482,p19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET984+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n020.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Thu Sep 24 12:31:54 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 127.57/24.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 127.57/24.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------