%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU118+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 : n001.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 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 9 unt; 2 def)
% Number of atoms : 139 ( 9 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 158 ( 61 ~; 59 |; 23 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 57 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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(f8,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f49,plain,
! [A,B] :
( ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) )
| ~ preboolean(B) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f52,plain,
! [B] :
( ( ! [A] :
( ( ( ( finite(sK0_skl(A,B))
& subset(sK0_skl(A,B),A) )
| in(sK0_skl(A,B),B) )
& ( ~ finite(sK0_skl(A,B))
| ~ subset(sK0_skl(A,B),A)
| ~ in(sK0_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,[sK0_skl]),skolemize(C,sK0_skl(A,B))],[f51]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ finite(X2)
| ~ subset(X2,X1)
| in(X2,X0)
| X0 != finite_subsets(X1)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f59,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f120,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f121,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f124,plain,
? [A,B] :
( ~ element(B,finite_subsets(A))
& finite(A)
& element(B,powerset(A)) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f125,plain,
( ~ element(sK12_skl,finite_subsets(sK11_skl))
& finite(sK11_skl)
& element(sK12_skl,powerset(sK11_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f124]) ).
fof(f126,plain,
element(sK12_skl,powerset(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
finite(sK11_skl),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
~ element(sK12_skl,finite_subsets(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f130,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f149,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ subset(X1,X0)
| in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f55]) ).
fof(f152,plain,
! [X0,X1] :
( ~ finite(X0)
| ~ subset(X0,X1)
| in(X0,finite_subsets(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f59]) ).
fof(f183,plain,
~ in(sK12_skl,finite_subsets(sK11_skl)),
inference(resolution,[status(thm)],[f121,f128]) ).
fof(f186,plain,
! [X0,X1] :
( ~ finite(X0)
| in(X0,finite_subsets(X1))
| ~ element(X0,powerset(X1)) ),
inference(resolution,[status(thm)],[f131,f152]) ).
fof(f187,plain,
( ~ finite(sK12_skl)
| ~ element(sK12_skl,powerset(sK11_skl)) ),
inference(resolution,[status(thm)],[f186,f183]) ).
fof(f191,definition,
( sQ0_spl
<=> element(sK12_skl,powerset(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ0_spl
| ~ element(sK12_skl,powerset(sK11_skl)) ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,definition,
( sQ1_spl
<=> finite(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ1_spl
| ~ finite(sK12_skl) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f187,f191,f194]) ).
fof(f198,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f126]) ).
fof(f199,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f204,plain,
! [X0] :
( sQ1_spl
| ~ element(sK12_skl,powerset(X0))
| ~ finite(X0) ),
inference(resolution,[status(thm)],[f196,f43]) ).
fof(f216,plain,
( sQ1_spl
| ~ finite(sK11_skl) ),
inference(resolution,[status(thm)],[f204,f126]) ).
fof(f219,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f216,f127]) ).
fof(f220,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f221,plain,
$false,
inference(sat_refutation,[status(thm)],[f197,f199,f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n001.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 05:57:04 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.44 % Elapsed time: 0.053838 seconds
% 0.14/5.44 % CPU time: 0.158499 seconds
% 0.14/5.44 % Total memory used: 82.245 MB
% 0.14/5.44 % Net memory used: 82.183 MB
%------------------------------------------------------------------------------