%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET932+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 : n013.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 02:44:19 PM UTC 2026
% Result : Theorem 4.76s 1.08s
% Output : Proof 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 87 ( 7 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 92 ( 34 ~; 36 |; 15 &)
% ( 3 <=>; 4 =>; 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; 2 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/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(c1,plain,
( subset(X2,X0)
| ~ in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p22,plain,
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c1]) ).
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/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]) ).
cnf(p23,plain,
( subset(powerset(X0),X1)
| subset(sk1(powerset(X0),X1),X0) ),
inference(resolution,[status(thm)],[p22,c8]) ).
fof(f6,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f6_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c13,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p25,plain,
( subset(sk1(powerset(X0),X1),X2)
| ~ subset(X0,X2)
| subset(powerset(X0),X1) ),
inference(resolution,[status(thm)],[p23,c13]) ).
fof(f7,conjecture,
! [A,B] :
( subset(A,B)
=> subset(powerset(A),powerset(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(powerset(A),powerset(B)) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B] :
( ~ subset(powerset(A),powerset(B))
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( ~ subset(powerset(sk4),powerset(sk5))
& subset(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f7_nnf]) ).
cnf(c14,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p32,plain,
( subset(sk1(powerset(sk4),X0),sk5)
| subset(powerset(sk4),X0) ),
inference(resolution,[status(thm)],[p25,c14]) ).
cnf(c2,plain,
( ~ subset(X2,X0)
| in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p26,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p36,plain,
( in(sk1(powerset(sk4),X0),powerset(sk5))
| subset(powerset(sk4),X0) ),
inference(resolution,[status(thm)],[p32,p26]) ).
cnf(c9,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p39,plain,
( subset(powerset(sk4),powerset(sk5))
| subset(powerset(sk4),powerset(sk5)) ),
inference(resolution,[status(thm)],[p36,c9]) ).
cnf(p40,plain,
subset(powerset(sk4),powerset(sk5)),
inference(factoring,[status(thm)],[p39]) ).
cnf(c15,plain,
~ subset(powerset(sk4),powerset(sk5)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p41,plain,
$false,
inference(resolution,[status(thm)],[p40,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET932+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 12:23:21 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.76/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.76/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------