%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE139+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 : n013.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 146.85s 18.93s
% Output : CNFRefutation 146.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),X0),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(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f45,plain,
? [X0] : strong_iteration(X0) != addition(multiplication(strong_iteration(X0),X0),one),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
strong_iteration(sK0_skl) != addition(multiplication(strong_iteration(sK0_skl),sK0_skl),one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f45]) ).
fof(f47,plain,
strong_iteration(sK0_skl) != addition(multiplication(strong_iteration(sK0_skl),sK0_skl),one),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f54,plain,
strong_iteration(sK0_skl) != addition(one,multiplication(strong_iteration(sK0_skl),sK0_skl)),
inference(paramodulation,[status(thm)],[f21,f47]) ).
fof(f76,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f32,f22]) ).
fof(f1342,plain,
! [X0,X1] : addition(one,multiplication(addition(star(X0),X1),X0)) = addition(star(X0),multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f76]) ).
fof(f83343,plain,
! [X0] : addition(one,multiplication(strong_iteration(X0),X0)) = addition(star(X0),multiplication(multiplication(strong_iteration(X0),zero),X0)),
inference(paramodulation,[status(thm)],[f40,f1342]) ).
fof(f83616,plain,
! [X0] : addition(one,multiplication(strong_iteration(X0),X0)) = addition(star(X0),multiplication(strong_iteration(X0),multiplication(zero,X0))),
inference(forward_demodulation,[status(thm)],[f25,f83343]) ).
fof(f83617,plain,
! [X0] : addition(one,multiplication(strong_iteration(X0),X0)) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(forward_demodulation,[status(thm)],[f30,f83616]) ).
fof(f83618,plain,
! [X0] : addition(one,multiplication(strong_iteration(X0),X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f40,f83617]) ).
fof(f83777,plain,
strong_iteration(sK0_skl) != strong_iteration(sK0_skl),
inference(backward_demodulation,[status(thm)],[f83618,f54]) ).
fof(f84009,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f83777]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE139+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:45:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 146.85/18.93 % Refutation found
% 146.85/18.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 146.85/18.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.84/19.05 % Elapsed time: 18.670704 seconds
% 13.84/19.05 % CPU time: 147.730815 seconds
% 13.84/19.05 % Total memory used: 621.393 MB
% 13.84/19.05 % Net memory used: 597.832 MB
%------------------------------------------------------------------------------