%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:19:31 PM UTC 2026
% Result : Theorem 0.27s 0.52s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 125 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 143 ( 50 ~; 51 |; 27 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 68 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f131,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)],[f9]) ).
fof(f132,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)],[f131]) ).
fof(f133,plain,
( ! [A,B] :
( ( ( subset(sK2_skl(B,A),A)
| in(sK2_skl(B,A),B) )
& ( ~ subset(sK2_skl(B,A),A)
| ~ in(sK2_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,[sK2_skl]),skolemize(C,sK2_skl(B,A))],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f139,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
( ! [A] :
( ( ! [B] :
( ~ empty(B)
| element(B,A) )
& ! [B] :
( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ! [A] :
( ( ! [B] :
( ~ in(B,A)
| element(B,A) )
& ! [B] :
( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(miniscoping,[status(thm)],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f172,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f173,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)],[f172]) ).
fof(f174,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f175,plain,
( ! [A,B] :
( ( ~ in(sK10_skl(B,A),B)
& in(sK10_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B,A))],[f174]) ).
fof(f176,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f218,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f248,plain,
? [A,B] :
( ? [C] :
( ~ in(C,A)
& in(C,B) )
& element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f249,plain,
( ~ in(sK19_skl,sK17_skl)
& in(sK19_skl,sK18_skl)
& element(sK18_skl,powerset(sK17_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl),skolemize(C,sK19_skl)],[f248]) ).
fof(f250,plain,
element(sK18_skl,powerset(sK17_skl)),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f251,plain,
in(sK19_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f252,plain,
~ in(sK19_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f425,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f456,plain,
( in(sK18_skl,powerset(sK17_skl))
| empty(powerset(sK17_skl)) ),
inference(resolution,[status(thm)],[f141,f250]) ).
fof(f457,plain,
in(sK18_skl,powerset(sK17_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f456,f218]) ).
fof(f467,plain,
subset(sK18_skl,sK17_skl),
inference(resolution,[status(thm)],[f457,f425]) ).
fof(f1098,plain,
! [X0] :
( in(X0,sK17_skl)
| ~ in(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f176,f467]) ).
fof(f1122,plain,
in(sK19_skl,sK17_skl),
inference(resolution,[status(thm)],[f1098,f251]) ).
fof(f1126,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1122,f252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 05:52:35 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.27/0.52 % Refutation found
% 0.27/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.27/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.56 % Elapsed time: 0.094779 seconds
% 0.27/0.56 % CPU time: 0.317476 seconds
% 0.27/0.56 % Total memory used: 109.887 MB
% 0.27/0.56 % Net memory used: 109.580 MB
%------------------------------------------------------------------------------