%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN366+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 : n020.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 03:15:54 PM UTC 2026
% Result : Theorem 0.11s 0.58s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 66 ( 21 ~; 15 |; 20 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 51 ( 43 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) )
=> ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) )
=> ( ? [X] : big_r(X,X)
=> ! [Y] : big_r(Y,Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [Y] : ~ big_r(Y,Y)
& ? [X] : big_r(X,X)
& ! [W,Z] :
( big_r(W,W)
<=> big_r(Z,W) )
& ! [U,V] :
( big_r(U,U)
<=> big_r(U,V) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ? [Y] : ~ big_r(Y,Y)
& ? [X] : big_r(X,X)
& ! [W,Z] :
( ( ~ big_r(Z,W)
| big_r(W,W) )
& ( big_r(Z,W)
| ~ big_r(W,W) ) )
& ! [U,V] :
( ( ~ big_r(U,V)
| big_r(U,U) )
& ( big_r(U,V)
| ~ big_r(U,U) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ? [Y] : ~ big_r(Y,Y)
& ? [X] : big_r(X,X)
& ! [W] :
( ! [Z] : ~ big_r(Z,W)
| big_r(W,W) )
& ! [W] :
( ! [Z] : big_r(Z,W)
| ~ big_r(W,W) )
& ! [U] :
( ! [V] : ~ big_r(U,V)
| big_r(U,U) )
& ! [U] :
( ! [V] : big_r(U,V)
| ~ big_r(U,U) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ~ big_r(sK1_skl,sK1_skl)
& big_r(sK0_skl,sK0_skl)
& ! [W] :
( ! [Z] : ~ big_r(Z,W)
| big_r(W,W) )
& ! [W] :
( ! [Z] : big_r(Z,W)
| ~ big_r(W,W) )
& ! [U] :
( ! [V] : ~ big_r(U,V)
| big_r(U,U) )
& ! [U] :
( ! [V] : big_r(U,V)
| ~ big_r(U,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( big_r(X0,X1)
| ~ big_r(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ big_r(X0,X1)
| big_r(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( big_r(X1,X0)
| ~ big_r(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
big_r(sK0_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,plain,
~ big_r(sK1_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,plain,
! [X0] : big_r(sK0_skl,X0),
inference(resolution,[status(thm)],[f7,f11]) ).
fof(f16,plain,
! [X0] : big_r(X0,sK0_skl),
inference(resolution,[status(thm)],[f9,f13]) ).
fof(f18,plain,
! [X0] : big_r(X0,X0),
inference(resolution,[status(thm)],[f16,f8]) ).
fof(f21,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f12,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN366+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.55 % Computer : n020.cluster.edu
% 0.11/0.55 % Model : x86_64 x86_64
% 0.11/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.55 % Memory : 8046.5625MB
% 0.11/0.55 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Mon Sep 21 10:52:49 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.57 % Drodi V4.1.1
% 0.11/0.58 % Refutation found
% 0.11/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.60 % Elapsed time: 0.037304 seconds
% 0.11/0.60 % CPU time: 0.095526 seconds
% 0.11/0.60 % Total memory used: 24.215 MB
% 0.11/0.60 % Net memory used: 23.979 MB
%------------------------------------------------------------------------------