%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET867+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 02:44:11 PM UTC 2026
% Result : Theorem 3.27s 0.94s
% Output : Proof 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 62 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 72 ( 30 ~; 24 |; 15 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 33 ( 2 sgn 18 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
& ~ in(C,B) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C,D] :
( ( ( in(sk3(A,B),A)
& in(sk2(A,B),sk3(A,B))
& ~ in(sk2(A,B),B) )
| ( ( ~ in(D,A)
| ~ in(sk2(A,B),D) )
& in(sk2(A,B),B) )
| B = union(A) )
& ( ( ( ~ in(D,A)
| ~ in(C,D)
| in(C,B) )
& ( ( in(sk1(A,B,C),A)
& in(C,sk1(A,B,C)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f2_nnf]) ).
cnf(c4,plain,
( in(sk1(X0,X1,X2),X0)
| ~ in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p21,plain,
( in(sk1(X1,union(X1),X0),X1)
| ~ in(X0,union(X1)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
fof(f1,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f1_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_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])],[f1_nnf]) ).
cnf(c2,plain,
( in(sk0(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p22,plain,
( union(X0) = empty_set
| in(sk1(X0,union(X0),sk0(union(X0))),X0) ),
inference(resolution,[status(thm)],[p21,c2]) ).
cnf(c1,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p17,plain,
~ in(X0,empty_set),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p27,plain,
union(empty_set) = empty_set,
inference(resolution,[status(thm)],[p22,p17]) ).
fof(f6,conjecture,
union(empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
union(empty_set) != empty_set,
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
union(empty_set) != empty_set,
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
union(empty_set) != empty_set,
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c15,plain,
union(empty_set) != empty_set,
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p28,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p27,c15]) ).
cnf(p33,plain,
$false,
inference(equality_resolution,[status(thm)],[p28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n012.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 12:17:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.27/0.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.27/0.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------