%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN356+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 : n002.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 03:15:52 PM UTC 2026
% Result : Theorem 0.13s 0.80s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 2 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 57 ( 18 ~; 15 |; 16 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& ! [X,Y] :
( big_r(X,Y)
=> ( big_q(X,Y)
& big_r(Y,X) ) )
& big_r(a,b) )
=> ( big_q(b,b)
& big_q(a,a) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& ! [X,Y] :
( big_r(X,Y)
=> ( big_q(X,Y)
& big_r(Y,X) ) )
& big_r(a,b) )
=> ( big_q(b,b)
& big_q(a,a) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ~ big_q(b,b)
| ~ big_q(a,a) )
& ! [U,V] :
( big_q(U,U)
| ~ big_q(U,V) )
& ! [X,Y] :
( ( big_q(X,Y)
& big_r(Y,X) )
| ~ big_r(X,Y) )
& big_r(a,b) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ~ big_q(b,b)
| ~ big_q(a,a) )
& ! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) )
& ! [X,Y] :
( ( big_q(X,Y)
& big_r(Y,X) )
| ~ big_r(X,Y) )
& big_r(a,b) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f5,plain,
big_r(a,b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( big_r(X1,X0)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f7,plain,
! [X0,X1] :
( big_q(X0,X1)
| ~ big_r(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f8,plain,
! [X0,X1] :
( big_q(X0,X0)
| ~ big_q(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,plain,
( ~ big_q(b,b)
| ~ big_q(a,a) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,definition,
( sQ0_spl
<=> big_q(a,a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f12,plain,
( sQ0_spl
| ~ big_q(a,a) ),
inference(component_clause,[status(thm)],[f10]) ).
fof(f13,definition,
( sQ1_spl
<=> big_q(b,b) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f15,plain,
( sQ1_spl
| ~ big_q(b,b) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f10,f13]) ).
fof(f17,plain,
big_r(b,a),
inference(resolution,[status(thm)],[f6,f5]) ).
fof(f18,plain,
big_q(a,b),
inference(resolution,[status(thm)],[f7,f5]) ).
fof(f19,plain,
big_q(b,a),
inference(resolution,[status(thm)],[f17,f7]) ).
fof(f21,plain,
big_q(b,b),
inference(resolution,[status(thm)],[f8,f19]) ).
fof(f22,plain,
big_q(a,a),
inference(resolution,[status(thm)],[f8,f18]) ).
fof(f23,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f12]) ).
fof(f24,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15,f21]) ).
fof(f27,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f26]) ).
fof(f28,plain,
$false,
inference(sat_refutation,[status(thm)],[f16,f24,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : SYN356+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.24 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.76 % Computer : n002.cluster.edu
% 0.08/0.76 % Model : x86_64 x86_64
% 0.08/0.76 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.76 % Memory : 8046.5625MB
% 0.08/0.76 % OS : Linux 6.8.0-71-generic
% 0.08/0.76 % CPULimit : 300
% 0.08/0.76 % WCLimit : 300
% 0.08/0.76 % DateTime : Mon Sep 21 10:54:04 UTC 2026
% 0.08/0.77 % CPUTime :
% 0.08/0.78 % Drodi V4.1.1
% 0.13/0.80 % Refutation found
% 0.13/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.82 % Elapsed time: 0.050543 seconds
% 0.13/0.82 % CPU time: 0.141751 seconds
% 0.13/0.82 % Total memory used: 55.298 MB
% 0.13/0.82 % Net memory used: 54.714 MB
%------------------------------------------------------------------------------