%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:44:15 PM UTC 2026
% Result : Theorem 2.76s 0.81s
% Output : Proof 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 5 unt; 0 def)
% Number of atoms : 53 ( 43 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 29 ~; 19 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_zfmisc_1) ).
fof(f5_nnf,plain,
! [A,B] :
( ? [C] :
( C != B
& in(C,A) )
| A = empty_set
| A = singleton(B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( ( sk4(A,B) != B
& in(sk4(A,B),A) )
| A = empty_set
| A = singleton(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f5_nnf]) ).
cnf(c7,plain,
( in(sk4(X0,X1),X0)
| X0 = empty_set
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f4,conjecture,
! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_zfmisc_1) ).
fof(f4_neg,negated_conjecture,
~ ! [A,B] :
~ ( ! [C] :
~ ( C != B
& in(C,A) )
& A != empty_set
& A != singleton(B) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [A,B] :
( ! [C] :
( C = B
| ~ in(C,A) )
& A != empty_set
& A != singleton(B) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
! [C] :
( ( C = sk3
| ~ in(C,sk2) )
& sk2 != empty_set
& sk2 != singleton(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f4_nnf]) ).
cnf(c6,plain,
( X2 = sk3
| ~ in(X2,sk2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p13,plain,
( sk4(sk2,X0) = sk3
| sk2 = empty_set
| sk2 = singleton(X0) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(c8,plain,
( sk4(X0,X1) != X1
| X0 = empty_set
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p21,plain,
( sk2 = empty_set
| sk2 = singleton(sk3)
| sk2 = empty_set
| sk2 = singleton(sk3) ),
inference(resolution,[status(thm)],[p13,c8]) ).
cnf(p30,plain,
( sk2 = empty_set
| sk2 = empty_set
| sk2 = singleton(sk3) ),
inference(factoring,[status(thm)],[p21]) ).
cnf(p32,plain,
( sk2 = empty_set
| sk2 = singleton(sk3) ),
inference(factoring,[status(thm)],[p30]) ).
cnf(c4,plain,
sk2 != singleton(sk3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p35,plain,
sk2 = empty_set,
inference(resolution,[status(thm)],[p32,c4]) ).
cnf(c5,plain,
sk2 != empty_set,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p37,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p35,c5]) ).
cnf(p41,plain,
$false,
inference(equality_resolution,[status(thm)],[p37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.30 % Computer : n012.cluster.edu
% 0.06/0.30 % Model : x86_64 x86_64
% 0.06/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.30 % Memory : 8046.5625MB
% 0.06/0.30 % OS : Linux 6.8.0-71-generic
% 0.06/0.30 % CPULimit : 300
% 0.06/0.30 % WCLimit : 300
% 0.06/0.30 % DateTime : Thu Sep 24 12:20:40 UTC 2026
% 0.06/0.31 % CPUTime :
% 0.06/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.76/0.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/0.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------