%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:11:00 PM UTC 2026
% Result : Theorem 0.10s 0.56s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 61 ( 8 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 69 ( 29 ~; 26 |; 11 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 42 ( 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A] : subset(singleton(A),powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A] : subset(singleton(A),powerset(A)),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,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)],[f2]) ).
fof(f12,plain,
( ! [A,B] :
( ? [C] :
( ( subset(C,A)
| in(C,B) )
& ( ~ subset(C,A)
| ~ in(C,B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
( ! [A,B] :
( ( ( subset(sK0_skl(B,A),A)
| in(sK0_skl(B,A),B) )
& ( ~ subset(sK0_skl(B,A),A)
| ~ in(sK0_skl(B,A),B) ) )
| B = powerset(A) )
& ! [A,B] :
( ( ! [C] :
( ~ subset(C,A)
| in(C,B) )
& ! [C] :
( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
? [A] : ~ subset(singleton(A),powerset(A)),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
~ subset(singleton(sK3_skl),powerset(sK3_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f28]) ).
fof(f30,plain,
~ subset(singleton(sK3_skl),powerset(sK3_skl)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f15]) ).
fof(f35,plain,
~ in(sK3_skl,powerset(sK3_skl)),
inference(resolution,[status(thm)],[f21,f30]) ).
fof(f37,plain,
~ subset(sK3_skl,sK3_skl),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f38,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f37,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET933+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n013.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Mon Sep 21 05:43:21 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.54 % Drodi V4.1.1
% 0.10/0.56 % Refutation found
% 0.10/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.58 % Elapsed time: 0.041193 seconds
% 0.10/0.58 % CPU time: 0.103231 seconds
% 0.10/0.58 % Total memory used: 44.907 MB
% 0.10/0.58 % Net memory used: 44.635 MB
%------------------------------------------------------------------------------