%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE138+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:58:02 PM UTC 2026
% Result : Theorem 0.17s 0.52s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
strong_iteration(zero) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
strong_iteration(zero) != one,
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
strong_iteration(zero) != one,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
strong_iteration(zero) = addition(zero,one),
inference(paramodulation,[status(thm)],[f30,f37]) ).
fof(f65,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f76,plain,
strong_iteration(zero) = one,
inference(backward_demodulation,[status(thm)],[f65,f60]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f76,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE138+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % Computer : n010.cluster.edu
% 0.17/0.48 % Model : x86_64 x86_64
% 0.17/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.48 % Memory : 8046.5625MB
% 0.17/0.48 % OS : Linux 6.8.0-71-generic
% 0.17/0.48 % CPULimit : 300
% 0.17/0.48 % WCLimit : 300
% 0.17/0.48 % DateTime : Sun Sep 20 22:45:54 UTC 2026
% 0.17/0.48 % CPUTime :
% 0.17/0.51 % Drodi V4.1.1
% 0.17/0.52 % Refutation found
% 0.17/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.59 % Elapsed time: 0.092693 seconds
% 0.22/0.59 % CPU time: 0.096678 seconds
% 0.22/0.59 % Total memory used: 6.352 MB
% 0.22/0.59 % Net memory used: 6.334 MB
%------------------------------------------------------------------------------