%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN413+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 : n004.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 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 52 ( 20 ~; 14 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 38 ( 28 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) )
=> ~ ? [V] :
! [U] : f(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) )
=> ~ ? [V] :
! [U] : f(U,V) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [V] :
! [U] : f(U,V)
& ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ? [V] :
! [U] : f(U,V)
& ! [Z] :
? [Y] :
! [X] :
( ( f(X,X)
| ~ f(X,Z)
| f(X,Y) )
& ( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,Y) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ? [V] :
! [U] : f(U,V)
& ! [Z] :
? [Y] :
( ! [X] :
( f(X,X)
| ~ f(X,Z)
| f(X,Y) )
& ! [X] :
( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ! [U] : f(U,sK1_skl)
& ! [Z] :
( ! [X] :
( f(X,X)
| ~ f(X,Z)
| f(X,sK0_skl(Z)) )
& ! [X] :
( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,sK0_skl(Z)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl(Z)),skolemize(V,sK1_skl)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( ~ f(X0,X0)
| ~ f(X0,sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( f(X0,X0)
| ~ f(X0,X1)
| f(X0,sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0] : f(X0,sK1_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
! [X0] :
( f(X0,X0)
| f(X0,sK0_skl(sK1_skl)) ),
inference(resolution,[status(thm)],[f9,f10]) ).
fof(f18,plain,
! [X0] :
( ~ f(sK0_skl(X0),sK0_skl(X0))
| f(sK0_skl(X0),sK0_skl(sK1_skl)) ),
inference(resolution,[status(thm)],[f11,f8]) ).
fof(f29,plain,
! [X0] : ~ f(sK0_skl(X0),sK0_skl(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f18,f8]) ).
fof(f30,plain,
$false,
inference(resolution,[status(thm)],[f29,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 10:53:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.041849 seconds
% 0.12/0.41 % CPU time: 0.098226 seconds
% 0.12/0.41 % Total memory used: 14.437 MB
% 0.12/0.41 % Net memory used: 13.905 MB
%------------------------------------------------------------------------------