%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:57:42 PM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 27 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 5 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(addition(X0,X2),addition(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f18,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ~ leq(addition(X0,X2),addition(X0,X2))
& leq(X0,X1) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
? [X0] :
( ? [X2] : ~ leq(addition(X0,X2),addition(X0,X2))
& ? [X1] : leq(X0,X1) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
( ~ leq(addition(sK0_skl,sK2_skl),addition(sK0_skl,sK2_skl))
& leq(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f31]) ).
fof(f34,plain,
~ leq(addition(sK0_skl,sK2_skl),addition(sK0_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f41,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f29,f18]) ).
fof(f47,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f34,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n005.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 22:37:49 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.39 % Elapsed time: 0.051099 seconds
% 0.11/0.39 % CPU time: 0.142580 seconds
% 0.11/0.39 % Total memory used: 66.549 MB
% 0.11/0.39 % Net memory used: 66.116 MB
%------------------------------------------------------------------------------