%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 01:40:27 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 2 unt; 2 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 86 ( 36 ~; 34 |; 9 &)
% ( 4 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
~ ! [B] :
( ordinal(B)
=> in(B,A) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f119,plain,
! [A] :
? [B] :
! [C] :
( ( ~ ordinal(C)
| ~ in(C,A)
| in(C,B) )
& ( ( ordinal(C)
& in(C,A) )
| ~ in(C,B) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f120,plain,
! [A] :
? [B] :
( ! [C] :
( ~ ordinal(C)
| ~ in(C,A)
| in(C,B) )
& ! [C] :
( ( ordinal(C)
& in(C,A) )
| ~ in(C,B) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f121,plain,
! [A] :
( ! [C] :
( ~ ordinal(C)
| ~ in(C,A)
| in(C,sK14_skl(A)) )
& ! [C] :
( ( ordinal(C)
& in(C,A) )
| ~ in(C,sK14_skl(A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(B,sK14_skl(A))],[f120]) ).
fof(f123,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,sK14_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ in(X0,X1)
| in(X0,sK14_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f129,plain,
! [A] :
? [B] :
( in(B,A)
<~> ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f130,plain,
! [A] :
? [B] :
( ( ~ ordinal(B)
| ~ in(B,A) )
& ( ordinal(B)
| in(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [A] :
( ( ~ ordinal(sK15_skl(A))
| ~ in(sK15_skl(A),A) )
& ( ordinal(sK15_skl(A))
| in(sK15_skl(A),A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(B,sK15_skl(A))],[f130]) ).
fof(f132,plain,
! [X0] :
( ordinal(sK15_skl(X0))
| in(sK15_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0] :
( ~ ordinal(sK15_skl(X0))
| ~ in(sK15_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
? [A] :
! [B] :
( in(B,A)
| ~ ordinal(B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f135,plain,
! [B] :
( in(B,sK16_skl)
| ~ ordinal(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f134]) ).
fof(f136,plain,
! [X0] :
( in(X0,sK16_skl)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f205,plain,
! [X0] :
( ~ ordinal(X0)
| ~ ordinal(X0)
| in(X0,sK14_skl(sK16_skl)) ),
inference(resolution,[status(thm)],[f124,f136]) ).
fof(f206,plain,
! [X0] :
( ~ ordinal(X0)
| in(X0,sK14_skl(sK16_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f205]) ).
fof(f230,plain,
! [X0] :
( in(sK15_skl(X0),X0)
| in(sK15_skl(X0),sK14_skl(sK16_skl)) ),
inference(resolution,[status(thm)],[f206,f132]) ).
fof(f284,plain,
( ~ ordinal(sK15_skl(sK14_skl(sK16_skl)))
| in(sK15_skl(sK14_skl(sK16_skl)),sK14_skl(sK16_skl)) ),
inference(resolution,[status(thm)],[f230,f133]) ).
fof(f289,definition,
( sQ15_spl
<=> in(sK15_skl(sK14_skl(sK16_skl)),sK14_skl(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ15_spl
| in(sK15_skl(sK14_skl(sK16_skl)),sK14_skl(sK16_skl)) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,definition,
( sQ16_spl
<=> ordinal(sK15_skl(sK14_skl(sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ16_spl
| ~ ordinal(sK15_skl(sK14_skl(sK16_skl))) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( ~ sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f284,f289,f292]) ).
fof(f330,plain,
( ~ sQ15_spl
| ~ ordinal(sK15_skl(sK14_skl(sK16_skl))) ),
inference(resolution,[status(thm)],[f290,f133]) ).
fof(f339,plain,
( sQ16_spl
| in(sK15_skl(sK14_skl(sK16_skl)),sK14_skl(sK16_skl)) ),
inference(resolution,[status(thm)],[f294,f132]) ).
fof(f410,plain,
( sQ16_spl
| ordinal(sK15_skl(sK14_skl(sK16_skl))) ),
inference(resolution,[status(thm)],[f339,f123]) ).
fof(f413,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f294]) ).
fof(f414,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f330,f292,f289]) ).
fof(f416,plain,
$false,
inference(sat_refutation,[status(thm)],[f295,f414,f415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:26:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.057560 seconds
% 0.13/0.43 % CPU time: 0.189800 seconds
% 0.13/0.43 % Total memory used: 82.175 MB
% 0.13/0.43 % Net memory used: 82.085 MB
%------------------------------------------------------------------------------