%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 03:15:11 PM UTC 2026
% Result : Theorem 0.14s 0.57s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 1 unt; 5 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 106 ( 44 ~; 43 |; 9 &)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 25 ( 18 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X] :
( big_f(X,f(X))
<=> ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,Y)
=> big_f(Z,f(X)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [X] :
( big_f(X,f(X))
<=> ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,Y)
=> big_f(Z,f(X)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X] :
( big_f(X,f(X))
<~> ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,f(X))
| ~ big_f(Z,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [X] :
( ( ! [Y] :
( ~ big_f(X,Y)
| ? [Z] :
( ~ big_f(Z,f(X))
& big_f(Z,Y) ) )
| ~ big_f(X,f(X)) )
& ( ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,f(X))
| ~ big_f(Z,Y) ) )
| big_f(X,f(X)) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ! [Y] :
( ~ big_f(sK0_skl,Y)
| ( ~ big_f(sK2_skl(Y),f(sK0_skl))
& big_f(sK2_skl(Y),Y) ) )
| ~ big_f(sK0_skl,f(sK0_skl)) )
& ( ( big_f(sK0_skl,sK1_skl)
& ! [Z] :
( big_f(Z,f(sK0_skl))
| ~ big_f(Z,sK1_skl) ) )
| big_f(sK0_skl,f(sK0_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Z,sK2_skl(Y))],[f4]) ).
fof(f6,plain,
! [X0] :
( big_f(X0,f(sK0_skl))
| ~ big_f(X0,sK1_skl)
| big_f(sK0_skl,f(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( big_f(sK0_skl,sK1_skl)
| big_f(sK0_skl,f(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0] :
( ~ big_f(sK0_skl,X0)
| big_f(sK2_skl(X0),X0)
| ~ big_f(sK0_skl,f(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0] :
( ~ big_f(sK0_skl,X0)
| ~ big_f(sK2_skl(X0),f(sK0_skl))
| ~ big_f(sK0_skl,f(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,definition,
( sQ0_spl
<=> big_f(sK0_skl,f(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
( sQ0_spl
| ~ big_f(sK0_skl,f(sK0_skl)) ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,definition,
! [X0] :
( sQ1_spl
<=> ( big_f(X0,f(sK0_skl))
| ~ big_f(X0,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f14,plain,
! [X0] :
( ~ sQ1_spl
| big_f(X0,f(sK0_skl))
| ~ big_f(X0,sK1_skl) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f10,f13]) ).
fof(f17,definition,
( sQ2_spl
<=> big_f(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f18,plain,
( ~ sQ2_spl
| big_f(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f10,f17]) ).
fof(f21,definition,
! [X0] :
( sQ3_spl
<=> ( ~ big_f(sK0_skl,X0)
| big_f(sK2_skl(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_f(sK0_skl,X0)
| big_f(sK2_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f10,f21]) ).
fof(f25,definition,
! [X0] :
( sQ4_spl
<=> ( ~ big_f(sK0_skl,X0)
| ~ big_f(sK2_skl(X0),f(sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ4_spl
| ~ big_f(sK0_skl,X0)
| ~ big_f(sK2_skl(X0),f(sK0_skl)) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f10,f25]) ).
fof(f29,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ big_f(sK0_skl,f(sK0_skl))
| ~ big_f(sK0_skl,f(sK0_skl)) ),
inference(resolution,[status(thm)],[f26,f22]) ).
fof(f31,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f10,f25,f21]) ).
fof(f32,plain,
( ~ sQ1_spl
| sQ0_spl
| ~ big_f(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f12,f14]) ).
fof(f33,plain,
( ~ sQ1_spl
| sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f18]) ).
fof(f34,plain,
( ~ sQ1_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f33]) ).
fof(f35,plain,
$false,
inference(sat_refutation,[status(thm)],[f16,f20,f24,f28,f31,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n004.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Mon Sep 21 10:42:36 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.10/0.56 % Drodi V4.1.1
% 0.14/0.57 % Refutation found
% 0.14/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.59 % Elapsed time: 0.031677 seconds
% 0.14/0.59 % CPU time: 0.082472 seconds
% 0.14/0.59 % Total memory used: 9.806 MB
% 0.14/0.59 % Net memory used: 9.480 MB
%------------------------------------------------------------------------------