%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU117+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 : n019.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 02:19:15 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 9 unt; 2 def)
% Number of atoms : 128 ( 9 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 142 ( 53 ~; 51 |; 27 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 54 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f55,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f61,plain,
( ! [A] : preboolean(finite_subsets(A))
& ! [A] : diff_closed(finite_subsets(A))
& ! [A] : cup_closed(finite_subsets(A))
& ! [A] : ~ empty(finite_subsets(A)) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f62,plain,
! [X0] : ~ empty(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f118,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f119,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f121,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f128,plain,
? [A,B] :
( ~ element(B,powerset(A))
& element(B,finite_subsets(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f129,plain,
( ~ element(sK11_skl,powerset(sK10_skl))
& element(sK11_skl,finite_subsets(sK10_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl]),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f128]) ).
fof(f130,plain,
element(sK11_skl,finite_subsets(sK10_skl)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
~ element(sK11_skl,powerset(sK10_skl)),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,plain,
! [A,B] :
( ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) )
| ~ preboolean(B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f133,plain,
! [A,B] :
( ( ( ? [C] :
( ( ( finite(C)
& subset(C,A) )
| in(C,B) )
& ( ~ finite(C)
| ~ subset(C,A)
| ~ in(C,B) ) )
| B = finite_subsets(A) )
& ( ! [C] :
( ( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(NNF_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [B] :
( ( ! [A] :
( ? [C] :
( ( ( finite(C)
& subset(C,A) )
| in(C,B) )
& ( ~ finite(C)
| ~ subset(C,A)
| ~ in(C,B) ) )
| B = finite_subsets(A) )
& ! [A] :
( ( ! [C] :
( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ! [C] :
( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(miniscoping,[status(thm)],[f133]) ).
fof(f135,plain,
! [B] :
( ( ! [A] :
( ( ( ( finite(sK12_skl(A,B))
& subset(sK12_skl(A,B),A) )
| in(sK12_skl(A,B),B) )
& ( ~ finite(sK12_skl(A,B))
| ~ subset(sK12_skl(A,B),A)
| ~ in(sK12_skl(A,B),B) ) )
| B = finite_subsets(A) )
& ! [A] :
( ( ! [C] :
( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ! [C] :
( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(C,sK12_skl(A,B))],[f134]) ).
fof(f136,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f142,plain,
! [X1,X2] :
( subset(X2,X1)
| ~ in(X2,finite_subsets(X1))
| ~ preboolean(finite_subsets(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f136]) ).
fof(f143,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f55]) ).
fof(f151,plain,
( in(sK11_skl,finite_subsets(sK10_skl))
| empty(finite_subsets(sK10_skl)) ),
inference(resolution,[status(thm)],[f40,f130]) ).
fof(f152,definition,
( sQ0_spl
<=> empty(finite_subsets(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ0_spl
| empty(finite_subsets(sK10_skl)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ1_spl
<=> in(sK11_skl,finite_subsets(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ1_spl
| in(sK11_skl,finite_subsets(sK10_skl)) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f151,f152,f155]) ).
fof(f159,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f62]) ).
fof(f160,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f177,plain,
( ~ sQ1_spl
| subset(sK11_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f156,f143]) ).
fof(f250,plain,
~ subset(sK11_skl,sK10_skl),
inference(resolution,[status(thm)],[f121,f131]) ).
fof(f253,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f250,f177]) ).
fof(f254,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f255,plain,
$false,
inference(sat_refutation,[status(thm)],[f158,f160,f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU117+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:51:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.049897 seconds
% 0.11/0.44 % CPU time: 0.145792 seconds
% 0.11/0.44 % Total memory used: 82.022 MB
% 0.11/0.44 % Net memory used: 81.936 MB
%------------------------------------------------------------------------------