%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET960+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 : n011.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 02:44:22 PM UTC 2026
% Result : Theorem 4.49s 1.26s
% Output : Proof 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 6 unt; 0 def)
% Number of atoms : 158 ( 97 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 177 ( 62 ~; 84 |; 26 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 72 ( 5 sgn 28 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
& ~ in(D,C) )
| ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(D,C) ) )
| C = cartesian_product2(A,B) )
& ( ! [D] :
( ( ! [E,F] :
( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
| in(D,C) )
& ( ? [E,F] :
( D = ordered_pair(E,F)
& in(F,B)
& in(E,A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D,E,F] :
( ( ( sk3(A,B,C) = ordered_pair(sk4(A,B,C),sk5(A,B,C))
& in(sk5(A,B,C),B)
& in(sk4(A,B,C),A)
& ~ in(sk3(A,B,C),C) )
| ( ( sk3(A,B,C) != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A) )
& in(sk3(A,B,C),C) )
| C = cartesian_product2(A,B) )
& ( ( ( D != ordered_pair(E,F)
| ~ in(F,B)
| ~ in(E,A)
| in(D,C) )
& ( ( D = ordered_pair(sk1(A,B,C,D),sk2(A,B,C,D))
& in(sk2(A,B,C,D),B)
& in(sk1(A,B,C,D),A) )
| ~ in(D,C) ) )
| C != cartesian_product2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4,sk5])],[f3_nnf]) ).
cnf(c9,plain,
( in(sk4(X0,X1,X2),X0)
| in(sk3(X0,X1,X2),X2)
| X2 = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f2,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f2_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p28,plain,
~ in(X0,empty_set),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p117,plain,
( in(sk4(X0,X1,empty_set),X0)
| empty_set = cartesian_product2(X0,X1) ),
inference(resolution,[status(thm)],[c9,p28]) ).
cnf(p220,plain,
empty_set = cartesian_product2(empty_set,X0),
inference(resolution,[status(thm)],[p117,p28]) ).
cnf(c10,plain,
( in(sk5(X0,X1,X2),X1)
| in(sk3(X0,X1,X2),X2)
| X2 = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f9,conjecture,
! [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(f9_neg,negated_conjecture,
~ ! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_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)],[f9_neg]) ).
fof(f9_sk,plain,
( ( ( sk9 = empty_set
| sk8 = empty_set )
& cartesian_product2(sk8,sk9) != empty_set )
| ( sk9 != empty_set
& sk8 != empty_set
& cartesian_product2(sk8,sk9) = empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f9_nnf]) ).
cnf(c22,plain,
( sk9 = empty_set
| sk8 = empty_set
| cartesian_product2(sk8,sk9) = empty_set ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(c7,plain,
( X3 != ordered_pair(X4,X5)
| ~ in(X5,X1)
| ~ in(X4,X0)
| in(X3,X2)
| X2 != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p101,plain,
( X1 != ordered_pair(X2,X3)
| ~ in(X3,sk9)
| ~ in(X2,sk8)
| in(X1,X0)
| X0 != empty_set
| sk9 = empty_set
| sk8 = empty_set ),
inference(superposition,[status(thm)],[c22,c7]) ).
cnf(p102,plain,
( X0 != ordered_pair(X1,X2)
| ~ in(X2,sk9)
| ~ in(X1,sk8)
| in(X0,empty_set)
| sk9 = empty_set
| sk8 = empty_set ),
inference(equality_resolution,[status(thm)],[p101]) ).
cnf(p104,plain,
( ~ in(X1,sk9)
| ~ in(X0,sk8)
| in(ordered_pair(X0,X1),empty_set)
| sk9 = empty_set
| sk8 = empty_set ),
inference(equality_resolution,[status(thm)],[p102]) ).
cnf(c3,plain,
( in(sk0(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p106,plain,
( sk8 = empty_set
| ~ in(X0,sk9)
| in(ordered_pair(sk0(sk8),X0),empty_set)
| sk9 = empty_set
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p104,c3]) ).
cnf(p107,plain,
( ~ in(X0,sk9)
| in(ordered_pair(sk0(sk8),X0),empty_set)
| sk9 = empty_set
| sk8 = empty_set ),
inference(factoring,[status(thm)],[p106]) ).
cnf(p108,plain,
( sk9 = empty_set
| in(ordered_pair(sk0(sk8),sk0(sk9)),empty_set)
| sk9 = empty_set
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p107,c3]) ).
cnf(p109,plain,
( in(ordered_pair(sk0(sk8),sk0(sk9)),empty_set)
| sk9 = empty_set
| sk8 = empty_set ),
inference(factoring,[status(thm)],[p108]) ).
cnf(p111,plain,
( sk9 = empty_set
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p109,p28]) ).
cnf(p114,plain,
( ~ in(X0,sk9)
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p111,c2]) ).
cnf(p127,plain,
( sk8 = empty_set
| in(sk5(X0,X1,sk9),X1)
| sk9 = cartesian_product2(X0,X1) ),
inference(resolution,[status(thm)],[c10,p114]) ).
cnf(p182,plain,
( sk8 = empty_set
| sk9 = cartesian_product2(X0,empty_set) ),
inference(resolution,[status(thm)],[p127,p28]) ).
cnf(c25,plain,
( cartesian_product2(sk8,sk9) != empty_set
| sk9 != empty_set ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p112,plain,
( cartesian_product2(sk8,sk9) != empty_set
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p111,c25]) ).
cnf(p121,plain,
( cartesian_product2(sk8,empty_set) != empty_set
| sk8 = empty_set
| sk8 = empty_set ),
inference(superposition,[status(thm)],[p111,p112]) ).
cnf(p122,plain,
( cartesian_product2(sk8,empty_set) != empty_set
| sk8 = empty_set ),
inference(factoring,[status(thm)],[p121]) ).
cnf(p200,plain,
( sk9 != empty_set
| sk8 = empty_set
| sk8 = empty_set ),
inference(superposition,[status(thm)],[p182,p122]) ).
cnf(p201,plain,
( sk9 != empty_set
| sk8 = empty_set ),
inference(factoring,[status(thm)],[p200]) ).
cnf(p202,plain,
( sk8 = empty_set
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p201,p111]) ).
cnf(p203,plain,
sk8 = empty_set,
inference(factoring,[status(thm)],[p202]) ).
cnf(c23,plain,
( cartesian_product2(sk8,sk9) != empty_set
| sk8 != empty_set ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p204,plain,
( cartesian_product2(empty_set,sk9) != empty_set
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p203,c23]) ).
cnf(p213,plain,
cartesian_product2(empty_set,sk9) != empty_set,
inference(equality_resolution,[status(thm)],[p204]) ).
cnf(p226,plain,
empty_set != empty_set,
inference(superposition,[status(thm)],[p220,p213]) ).
cnf(p227,plain,
$false,
inference(equality_resolution,[status(thm)],[p226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:26:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.49/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.49/1.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------