%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 0.15s 0.41s
% Output : CNFRefutation 0.15s
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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(f15,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)],[f14]) ).
fof(f16,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))],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( sK0_skl(X0,X1) != X1
| ~ in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( sK0_skl(X0,X1) = X1
| in(sK0_skl(X0,X1),X0)
| X0 = singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f23,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))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f33,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f34,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f41,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f42,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f25]) ).
fof(f56,plain,
! [X0,X1] :
( subset(sK0_skl(powerset(X0),X1),X0)
| sK0_skl(powerset(X0),X1) = X1
| powerset(X0) = singleton(X1) ),
inference(resolution,[status(thm)],[f20,f45]) ).
fof(f67,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)],[f56,f42]) ).
fof(f72,plain,
! [X0] :
( sK0_skl(powerset(empty_set),X0) = X0
| empty_set != X0
| powerset(empty_set) = singleton(X0) ),
inference(equality_factoring,[status(thm)],[f67]) ).
fof(f73,definition,
( sQ0_spl
<=> powerset(empty_set) = singleton(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ0_spl
| powerset(empty_set) = singleton(empty_set) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f79,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(f81,plain,
( sQ2_spl
| ~ in(sK0_skl(powerset(empty_set),empty_set),powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f97,plain,
( sK0_skl(powerset(empty_set),empty_set) = empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(destructive_equality_resolution,[status(thm)],[f72]) ).
fof(f98,plain,
sK0_skl(powerset(empty_set),empty_set) = empty_set,
inference(forward_subsumption_resolution,[status(thm)],[f97,f35]) ).
fof(f102,plain,
( ~ in(sK0_skl(powerset(empty_set),empty_set),powerset(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(resolution,[status(thm)],[f98,f19]) ).
fof(f108,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f102,f73,f79]) ).
fof(f117,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f35]) ).
fof(f118,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ2_spl
| ~ in(empty_set,powerset(empty_set)) ),
inference(forward_demodulation,[status(thm)],[f98,f81]) ).
fof(f120,plain,
( sQ2_spl
| ~ subset(empty_set,empty_set) ),
inference(resolution,[status(thm)],[f119,f46]) ).
fof(f121,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f34]) ).
fof(f122,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f123,plain,
$false,
inference(sat_refutation,[status(thm)],[f108,f118,f122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:52:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.061895 seconds
% 0.15/0.44 % CPU time: 0.174938 seconds
% 0.15/0.44 % Total memory used: 60.365 MB
% 0.15/0.44 % Net memory used: 60.076 MB
%------------------------------------------------------------------------------