%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN960+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 03:18:35 PM UTC 2026
% Result : Theorem 0.02s 0.38s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 2 unt; 3 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 44 ( 20 ~; 16 |; 2 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 32 ( 16 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X,Y] : a(X,Y)
<=> ? [Y,X] : a(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X,Y] : a(X,Y)
<=> ? [Y,X] : a(X,Y) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ! [Y,X] : ~ a(X,Y)
| ! [X,Y] : ~ a(X,Y) )
& ( ? [Y,X] : a(X,Y)
| ? [X,Y] : a(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ( ! [Y,X] : ~ a(X,Y)
| ! [X,Y] : ~ a(X,Y) )
& ( a(sK3_skl,sK2_skl)
| a(sK0_skl,sK1_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(Y,sK2_skl),skolemize(X,sK3_skl)],[f4]) ).
fof(f6,plain,
( a(sK3_skl,sK2_skl)
| a(sK0_skl,sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( ~ a(X2,X3)
| ~ a(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,definition,
( sQ0_spl
<=> a(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f9,plain,
( ~ sQ0_spl
| a(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f8]) ).
fof(f11,definition,
( sQ1_spl
<=> a(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f12,plain,
( ~ sQ1_spl
| a(sK3_skl,sK2_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,X1] :
( sQ2_spl
<=> ~ a(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f16,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ a(X0,X1) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f7,f15]) ).
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
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12,f16]) ).
fof(f22,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f21]) ).
fof(f23,plain,
$false,
inference(sat_refutation,[status(thm)],[f14,f18,f20,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN960+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 11:31:12 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.02/0.38 % Refutation found
% 0.02/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.40 % Elapsed time: 0.032844 seconds
% 0.02/0.40 % CPU time: 0.038368 seconds
% 0.02/0.40 % Total memory used: 1.543 MB
% 0.02/0.40 % Net memory used: 1.486 MB
%------------------------------------------------------------------------------