%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:19:23 PM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 10 unt; 2 def)
% Number of atoms : 129 ( 53 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 139 ( 51 ~; 63 |; 18 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 61 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( sK0_skl(X0,X1) != X1
| ~ in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( sK0_skl(X0,X1) = X1
| in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,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)],[f3]) ).
fof(f25,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)],[f24]) ).
fof(f26,plain,
( ! [A,B] :
( ( ( subset(sK1_skl(B,A),A)
| in(sK1_skl(B,A),B) )
& ( ~ subset(sK1_skl(B,A),A)
| ~ in(sK1_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,[sK1_skl]),skolemize(C,sK1_skl(B,A))],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f36,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f27]) ).
fof(f49,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f59,plain,
! [X0,X1] :
( subset(sK0_skl(powerset(X0),X1),X0)
| sK0_skl(powerset(X0),X1) = X1
| powerset(X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f23,f48]) ).
fof(f70,plain,
! [X0] :
( sK0_skl(powerset(empty_set),X0) = empty_set
| sK0_skl(powerset(empty_set),X0) = X0
| powerset(empty_set) = singleton(X0) ),
inference(resolution,[status(thm)],[f59,f45]) ).
fof(f75,plain,
! [X0] :
( sK0_skl(powerset(empty_set),X0) = X0
| empty_set != X0
| powerset(empty_set) = singleton(X0) ),
inference(equality_factoring,[status(thm)],[f70]) ).
fof(f76,definition,
( sQ0_spl
<=> powerset(empty_set) = singleton(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ0_spl
| powerset(empty_set) = singleton(empty_set) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f82,definition,
( sQ2_spl
<=> in(sK0_skl(powerset(empty_set),empty_set),powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( sQ2_spl
| ~ in(sK0_skl(powerset(empty_set),empty_set),powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f100,plain,
( sK0_skl(powerset(empty_set),empty_set) = empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(destructive_equality_resolution,[status(thm)],[f75]) ).
fof(f101,plain,
sK0_skl(powerset(empty_set),empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[f100,f38]) ).
fof(f105,plain,
( ~ in(sK0_skl(powerset(empty_set),empty_set),powerset(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(resolution,[status(thm)],[f101,f22]) ).
fof(f111,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f105,f76,f82]) ).
fof(f120,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f38]) ).
fof(f121,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f122,plain,
( sQ2_spl
| ~ in(empty_set,powerset(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f101,f84]) ).
fof(f123,plain,
( sQ2_spl
| ~ subset(empty_set,empty_set) ),
inference(resolution,[status(thm)],[f122,f49]) ).
fof(f124,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f37]) ).
fof(f125,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f126,plain,
$false,
inference(sat_refutation,[status(thm)],[f111,f121,f125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:52:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.054332 seconds
% 0.10/0.43 % CPU time: 0.149676 seconds
% 0.10/0.43 % Total memory used: 80.476 MB
% 0.10/0.43 % Net memory used: 80.070 MB
%------------------------------------------------------------------------------