%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN412+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 03:16:01 PM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 1 unt; 3 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 30 ~; 23 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 17 ( 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X] :
! [Y] :
( f(X,Y)
<=> ~ f(X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ? [X] :
! [Y] :
( f(X,Y)
<=> ~ f(X,X) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X] :
! [Y] :
( ( f(X,X)
| f(X,Y) )
& ( ~ f(X,X)
| ~ f(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [X] :
( ( f(X,X)
| ! [Y] : f(X,Y) )
& ( ~ f(X,X)
| ! [Y] : ~ f(X,Y) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f5,plain,
( ( f(sK0_skl,sK0_skl)
| ! [Y] : f(sK0_skl,Y) )
& ( ~ f(sK0_skl,sK0_skl)
| ! [Y] : ~ f(sK0_skl,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f4]) ).
fof(f6,plain,
! [X0] :
( ~ f(sK0_skl,sK0_skl)
| ~ f(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0] :
( f(sK0_skl,sK0_skl)
| f(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,definition,
! [X0] :
( sQ0_spl
<=> ~ f(sK0_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f9,plain,
! [X0] :
( ~ sQ0_spl
| ~ f(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f8]) ).
fof(f11,definition,
( sQ1_spl
<=> f(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f12,plain,
( ~ sQ1_spl
| f(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f13,plain,
( sQ1_spl
| ~ f(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f8,f11]) ).
fof(f15,definition,
! [X0] :
( sQ2_spl
<=> f(sK0_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f16,plain,
! [X0] :
( ~ sQ2_spl
| f(sK0_skl,X0) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f7,f15,f11]) ).
fof(f19,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9,f16]) ).
fof(f20,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f19]) ).
fof(f21,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12,f9]) ).
fof(f22,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f21]) ).
fof(f23,plain,
( sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13,f16]) ).
fof(f24,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f23]) ).
fof(f25,plain,
$false,
inference(sat_refutation,[status(thm)],[f14,f18,f20,f22,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN412+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 10:54:24 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.041947 seconds
% 0.11/0.41 % CPU time: 0.112323 seconds
% 0.11/0.41 % Total memory used: 16.399 MB
% 0.11/0.41 % Net memory used: 15.765 MB
%------------------------------------------------------------------------------