%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN321+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 : n003.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 03:15:44 PM UTC 2026
% Result : Theorem 0.13s 0.57s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 60 ( 20 ~; 18 |; 11 &)
% ( 2 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 62 ( 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ? [X,Y] :
( ( ? [Z] : big_f(X,Z)
=> ! [Z] : big_g(X,Z) )
=> ( ! [Z] :
( big_g(Z,Z)
=> big_f(Z,Y) )
=> ( big_f(X,Y)
<=> ! [Z] : big_g(X,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X,Y] :
( ( big_f(X,Y)
<~> ! [Z] : big_g(X,Z) )
& ! [Z] :
( big_f(Z,Y)
| ~ big_g(Z,Z) )
& ( ! [Z] : big_g(X,Z)
| ! [Z] : ~ big_f(X,Z) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
! [X,Y] :
( ( ? [Z] : ~ big_g(X,Z)
| ~ big_f(X,Y) )
& ( ! [Z] : big_g(X,Z)
| big_f(X,Y) )
& ! [Z] :
( big_f(Z,Y)
| ~ big_g(Z,Z) )
& ( ! [Z] : big_g(X,Z)
| ! [Z] : ~ big_f(X,Z) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ! [X] :
( ? [Z] : ~ big_g(X,Z)
| ! [Y] : ~ big_f(X,Y) )
& ! [X] :
( ! [Z] : big_g(X,Z)
| ! [Y] : big_f(X,Y) )
& ! [Z] :
( ! [Y] : big_f(Z,Y)
| ~ big_g(Z,Z) )
& ! [X] :
( ! [Z] : big_g(X,Z)
| ! [Z] : ~ big_f(X,Z) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ! [X] :
( ~ big_g(X,sK0_skl(X))
| ! [Y] : ~ big_f(X,Y) )
& ! [X] :
( ! [Z] : big_g(X,Z)
| ! [Y] : big_f(X,Y) )
& ! [Z] :
( ! [Y] : big_f(Z,Y)
| ~ big_g(Z,Z) )
& ! [X] :
( ! [Z] : big_g(X,Z)
| ! [Z] : ~ big_f(X,Z) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Z,sK0_skl(X))],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( big_g(X0,X2)
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(X0,X1)
| ~ big_g(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1,X2] :
( big_g(X0,X2)
| big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_g(X0,sK0_skl(X0))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
! [X0,X1] : big_f(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f8,f12]) ).
fof(f12,plain,
! [X0,X1] : big_g(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f9,f7]) ).
fof(f13,plain,
! [X0,X1] : ~ big_f(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f10,f12]) ).
fof(f14,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN321+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.54 % Computer : n003.cluster.edu
% 0.08/0.54 % Model : x86_64 x86_64
% 0.08/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.54 % Memory : 8046.5625MB
% 0.08/0.54 % OS : Linux 6.8.0-71-generic
% 0.08/0.54 % CPULimit : 300
% 0.08/0.54 % WCLimit : 300
% 0.08/0.54 % DateTime : Mon Sep 21 10:50:32 UTC 2026
% 0.08/0.54 % CPUTime :
% 0.08/0.55 % Drodi V4.1.1
% 0.13/0.57 % Refutation found
% 0.13/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.59 % Elapsed time: 0.039969 seconds
% 0.13/0.59 % CPU time: 0.103015 seconds
% 0.13/0.59 % Total memory used: 13.950 MB
% 0.13/0.59 % Net memory used: 13.434 MB
%------------------------------------------------------------------------------