%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN986+1.002 : TPTP v9.3.1. Released v4.0.0.
% 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 03:18:39 PM UTC 2026
% Result : Theorem 0.11s 5.58s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 62 ( 35 ~; 21 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 52 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Y] : r(Y,zero,succ(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Y,X,Z,Z1] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
? [Z2,Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,Z2,Z1)
& r(zero,zero,Z2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ? [Z2,Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,Z2,Z1)
& r(zero,zero,Z2) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] : r(X0,zero,succ(X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [Y,X,Z,Z1] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [Y,X,Z] :
( ! [Z1] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1) )
| ~ r(Y,X,Z) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( r(X0,succ(X1),X3)
| ~ r(X2,X1,X3)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [Z2,Z1,Z0] :
( ~ r(zero,Z1,Z0)
| ~ r(zero,Z2,Z1)
| ~ r(zero,zero,Z2) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
! [Z1] :
( ! [Z0] : ~ r(zero,Z1,Z0)
| ! [Z2] :
( ~ r(zero,Z2,Z1)
| ~ r(zero,zero,Z2) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ r(zero,X1,X2)
| ~ r(zero,X0,X1)
| ~ r(zero,zero,X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( ~ r(zero,X0,X1)
| ~ r(zero,succ(zero),X0) ),
inference(resolution,[status(thm)],[f5,f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ r(zero,X1,X2)
| ~ r(X0,zero,X1)
| ~ r(zero,zero,X0) ),
inference(resolution,[status(thm)],[f8,f12]) ).
fof(f14,plain,
! [X0,X1] :
( ~ r(zero,X0,X1)
| ~ r(succ(zero),zero,X0) ),
inference(resolution,[status(thm)],[f13,f5]) ).
fof(f15,plain,
! [X0] : ~ r(zero,succ(succ(zero)),X0),
inference(resolution,[status(thm)],[f14,f5]) ).
fof(f16,plain,
! [X0,X1] :
( ~ r(X0,succ(zero),X1)
| ~ r(zero,succ(zero),X0) ),
inference(resolution,[status(thm)],[f15,f8]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ r(X2,zero,X0)
| ~ r(zero,zero,X2)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[status(thm)],[f16,f8]) ).
fof(f18,plain,
! [X0,X1] :
( ~ r(succ(zero),zero,X0)
| ~ r(X0,succ(zero),X1) ),
inference(resolution,[status(thm)],[f17,f5]) ).
fof(f19,plain,
! [X0] : ~ r(succ(succ(zero)),succ(zero),X0),
inference(resolution,[status(thm)],[f18,f5]) ).
fof(f20,plain,
! [X0,X1] :
( ~ r(X0,zero,X1)
| ~ r(succ(succ(zero)),zero,X0) ),
inference(resolution,[status(thm)],[f19,f8]) ).
fof(f21,plain,
! [X0] : ~ r(succ(succ(succ(zero))),zero,X0),
inference(resolution,[status(thm)],[f20,f5]) ).
fof(f22,plain,
$false,
inference(resolution,[status(thm)],[f21,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.55 % Computer : n004.cluster.edu
% 0.11/5.55 % Model : x86_64 x86_64
% 0.11/5.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.55 % Memory : 8046.5625MB
% 0.11/5.55 % OS : Linux 6.8.0-71-generic
% 0.11/5.55 % CPULimit : 300
% 0.11/5.55 % WCLimit : 300
% 0.11/5.55 % DateTime : Mon Sep 21 11:31:58 UTC 2026
% 0.11/5.55 % CPUTime :
% 0.11/5.56 % Drodi V4.1.1
% 0.11/5.58 % Refutation found
% 0.11/5.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.60 % Elapsed time: 0.042550 seconds
% 0.14/5.60 % CPU time: 0.120130 seconds
% 0.14/5.60 % Total memory used: 39.776 MB
% 0.14/5.60 % Net memory used: 39.339 MB
%------------------------------------------------------------------------------