%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM341+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 01:39:00 PM UTC 2026
% Result : Theorem 0.23s 5.50s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 4 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 49 ( 20 ~; 16 |; 9 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 54 ( 48 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f296,axiom,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f743,plain,
! [X,Y,Z] :
( ( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ( difference(X,Y,Z)
| ~ sum(Y,Z,X) ) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f744,plain,
( ! [X,Y,Z] :
( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ! [X,Y,Z] :
( difference(X,Y,Z)
| ~ sum(Y,Z,X) ) ),
inference(miniscoping,[status(thm)],[f743]) ).
fof(f745,plain,
! [X0,X1,X2] :
( difference(X2,X0,X1)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f744]) ).
fof(f746,plain,
! [X0,X1,X2] :
( ~ difference(X2,X0,X1)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f744]) ).
fof(f861,plain,
! [X,Y,Z] :
( sum(X,Y,Z)
<~> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X,Y,Z] :
( ( ~ difference(Z,X,Y)
| ~ difference(Z,Y,X)
| ~ sum(X,Y,Z) )
& ( ( difference(Z,X,Y)
& difference(Z,Y,X) )
| sum(X,Y,Z) ) ),
inference(NNF_transformation,[status(thm)],[f861]) ).
fof(f863,plain,
( ! [X,Y,Z] :
( ~ difference(Z,X,Y)
| ~ difference(Z,Y,X)
| ~ sum(X,Y,Z) )
& ! [X,Y,Z] :
( ( difference(Z,X,Y)
& difference(Z,Y,X) )
| sum(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f862]) ).
fof(f865,plain,
! [X0,X1,X2] :
( difference(X2,X0,X1)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f863]) ).
fof(f866,plain,
! [X0,X1,X2] :
( ~ difference(X2,X0,X1)
| ~ difference(X2,X1,X0)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f863]) ).
fof(f869,plain,
! [X0,X1,X2] :
( ~ difference(X2,X1,X0)
| ~ sum(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f866,f870]) ).
fof(f870,plain,
! [X0,X1,X2] : difference(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f745,f865]) ).
fof(f871,plain,
! [X0,X1,X2] : ~ sum(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f869,f870]) ).
fof(f874,plain,
! [X0,X1,X2] : ~ difference(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[f746,f871]) ).
fof(f875,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f870,f874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM341+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n011.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Mon Sep 21 02:23:15 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.48 % Drodi V4.1.1
% 0.23/5.50 % Refutation found
% 0.23/5.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.55 % Elapsed time: 0.085609 seconds
% 0.23/5.55 % CPU time: 0.121457 seconds
% 0.23/5.55 % Total memory used: 6.059 MB
% 0.23/5.55 % Net memory used: 6.051 MB
%------------------------------------------------------------------------------