%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET947+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 : n002.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 02:44:21 PM UTC 2026
% Result : Theorem 4.55s 1.07s
% Output : Proof 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 68 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 27 |; 12 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
& ~ in(C,B) )
| ( ~ subset(C,A)
& in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,A,C] :
( ( ( subset(sk0(A,B),A)
& ~ in(sk0(A,B),B) )
| ( ~ subset(sk0(A,B),A)
& in(sk0(A,B),B) )
| B = powerset(A) )
& ( ( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( ~ subset(X2,X0)
| in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p21,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk1(A,B),B)
& in(sk1(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c8,plain,
( in(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f3,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c10,plain,
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p17,plain,
( subset(sk1(X0,X1),union(X0))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c8,c10]) ).
cnf(p23,plain,
( subset(X0,X1)
| in(sk1(X0,X1),powerset(union(X0))) ),
inference(resolution,[status(thm)],[p21,p17]) ).
cnf(c9,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p86,plain,
( subset(X0,powerset(union(X0)))
| subset(X0,powerset(union(X0))) ),
inference(resolution,[status(thm)],[p23,c9]) ).
cnf(p192,plain,
subset(X0,powerset(union(X0))),
inference(factoring,[status(thm)],[p86]) ).
fof(f7,conjecture,
! [A] : subset(A,powerset(union(A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A] : subset(A,powerset(union(A))),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A] : ~ subset(A,powerset(union(A))),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
~ subset(sk4,powerset(union(sk4))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f7_nnf]) ).
cnf(c14,plain,
~ subset(sk4,powerset(union(sk4))),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p193,plain,
$false,
inference(resolution,[status(thm)],[p192,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET947+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:28:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.55/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.55/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------