%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU294+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:20:03 PM UTC 2026
% Result : Theorem 7.02s 1.66s
% Output : CNFRefutation 9.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 9 unt; 2 def)
% Number of atoms : 129 ( 8 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 143 ( 52 ~; 52 |; 25 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f249,conjecture,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f250,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
inference(negated_conjecture,[status(cth)],[f249]) ).
fof(f422,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f423,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f422]) ).
fof(f623,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)],[f42]) ).
fof(f624,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)],[f623]) ).
fof(f625,plain,
( ! [A,B] :
( ( ( subset(sK34_skl(B,A),A)
| in(sK34_skl(B,A),B) )
& ( ~ subset(sK34_skl(B,A),A)
| ~ in(sK34_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,[sK34_skl]),skolemize(C,sK34_skl(B,A))],[f624]) ).
fof(f627,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| in(X2,X0)
| X0 != powerset(X1) ),
inference(cnf_transformation,[status(thm)],[f625]) ).
fof(f652,plain,
! [A,B] :
( ( ( element(B,A)
<=> empty(B) )
| ~ empty(A) )
& ( ( element(B,A)
<=> in(B,A) )
| empty(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f653,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)],[f652]) ).
fof(f654,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)],[f653]) ).
fof(f656,plain,
! [X0,X1] :
( ~ in(X1,X0)
| element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f654]) ).
fof(f982,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f1497,plain,
? [A,B] :
( ~ finite(A)
& finite(B)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f250]) ).
fof(f1498,plain,
? [A] :
( ~ finite(A)
& ? [B] :
( finite(B)
& subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f1497]) ).
fof(f1499,plain,
( ~ finite(sK200_skl)
& finite(sK201_skl)
& subset(sK200_skl,sK201_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200_skl,sK201_skl]),skolemize(A,sK200_skl),skolemize(B,sK201_skl)],[f1498]) ).
fof(f1500,plain,
subset(sK200_skl,sK201_skl),
inference(cnf_transformation,[status(thm)],[f1499]) ).
fof(f1501,plain,
finite(sK201_skl),
inference(cnf_transformation,[status(thm)],[f1499]) ).
fof(f1502,plain,
~ finite(sK200_skl),
inference(cnf_transformation,[status(thm)],[f1499]) ).
fof(f2260,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f627]) ).
fof(f4124,plain,
in(sK200_skl,powerset(sK201_skl)),
inference(resolution,[status(thm)],[f2260,f1500]) ).
fof(f4396,plain,
! [X0,X1] :
( finite(X1)
| ~ finite(X0)
| ~ in(X1,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f656,f423]) ).
fof(f4486,plain,
! [X0] :
( ~ finite(X0)
| ~ in(sK200_skl,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f4396,f1502]) ).
fof(f4520,plain,
( ~ finite(sK201_skl)
| empty(powerset(sK201_skl)) ),
inference(resolution,[status(thm)],[f4486,f4124]) ).
fof(f4522,definition,
( sQ194_spl
<=> empty(powerset(sK201_skl)) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f4523,plain,
( ~ sQ194_spl
| empty(powerset(sK201_skl)) ),
inference(component_clause,[status(thm)],[f4522]) ).
fof(f4525,definition,
( sQ195_spl
<=> finite(sK201_skl) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f4527,plain,
( sQ195_spl
| ~ finite(sK201_skl) ),
inference(component_clause,[status(thm)],[f4525]) ).
fof(f4528,plain,
( ~ sQ195_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f4520,f4522,f4525]) ).
fof(f4536,plain,
( sQ195_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4527,f1501]) ).
fof(f4537,plain,
sQ195_spl,
inference(contradiction_clause,[status(thm)],[f4536]) ).
fof(f5647,plain,
( ~ sQ194_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4523,f982]) ).
fof(f5648,plain,
~ sQ194_spl,
inference(contradiction_clause,[status(thm)],[f5647]) ).
fof(f5649,plain,
$false,
inference(sat_refutation,[status(thm)],[f4528,f4537,f5648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU294+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:08:08 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.40 % Drodi V4.1.1
% 7.02/1.66 % Refutation found
% 7.02/1.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.02/1.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.57/1.69 % Elapsed time: 1.325628 seconds
% 9.57/1.69 % CPU time: 9.984334 seconds
% 9.57/1.69 % Total memory used: 198.528 MB
% 9.57/1.69 % Net memory used: 186.538 MB
%------------------------------------------------------------------------------