%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE150+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 12:58:04 PM UTC 2026
% Result : Theorem 6.64s 1.45s
% Output : CNFRefutation 6.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 20 ( 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
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(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,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
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,
? [X0] : strong_iteration(multiplication(X0,zero)) != addition(one,multiplication(X0,zero)),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
strong_iteration(multiplication(sK0_skl,zero)) != addition(one,multiplication(sK0_skl,zero)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f45]) ).
fof(f47,plain,
strong_iteration(multiplication(sK0_skl,zero)) != addition(one,multiplication(sK0_skl,zero)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,plain,
strong_iteration(multiplication(sK0_skl,zero)) != addition(multiplication(sK0_skl,zero),one),
inference(paramodulation,[status(thm)],[f21,f47]) ).
fof(f121,plain,
! [X0,X1] : multiplication(X0,zero) = multiplication(multiplication(X0,zero),X1),
inference(paramodulation,[status(thm)],[f30,f25]) ).
fof(f1704,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(multiplication(X0,zero),one),
inference(paramodulation,[status(thm)],[f121,f37]) ).
fof(f1721,plain,
strong_iteration(multiplication(sK0_skl,zero)) != strong_iteration(multiplication(sK0_skl,zero)),
inference(backward_demodulation,[status(thm)],[f1704,f52]) ).
fof(f1731,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE150+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n010.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 20 22:47:09 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.47 % Drodi V4.1.1
% 6.64/1.45 % Refutation found
% 6.64/1.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.64/1.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.17/1.47 % Elapsed time: 1.000083 seconds
% 2.17/1.47 % CPU time: 7.413923 seconds
% 2.17/1.47 % Total memory used: 120.183 MB
% 2.17/1.47 % Net memory used: 118.649 MB
%------------------------------------------------------------------------------