%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE148+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 : n001.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 24 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,strong_iteration(X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,strong_iteration(X1)) = X0 ),
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(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
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,X1] :
( multiplication(X0,strong_iteration(X1)) != X0
& multiplication(X0,X1) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( multiplication(sK0_skl,strong_iteration(sK1_skl)) != sK0_skl
& multiplication(sK0_skl,sK1_skl) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f45]) ).
fof(f47,plain,
multiplication(sK0_skl,sK1_skl) = zero,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
multiplication(sK0_skl,strong_iteration(sK1_skl)) != sK0_skl,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
! [X0] : multiplication(sK0_skl,multiplication(sK1_skl,X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f47,f25]) ).
fof(f55,plain,
! [X0] : multiplication(sK0_skl,multiplication(sK1_skl,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f51]) ).
fof(f59,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f124,plain,
! [X0,X1] : multiplication(sK0_skl,addition(multiplication(sK1_skl,X0),X1)) = addition(zero,multiplication(sK0_skl,X1)),
inference(paramodulation,[status(thm)],[f55,f28]) ).
fof(f144,plain,
! [X0,X1] : multiplication(sK0_skl,addition(multiplication(sK1_skl,X0),X1)) = multiplication(sK0_skl,X1),
inference(forward_demodulation,[status(thm)],[f59,f124]) ).
fof(f638,plain,
multiplication(sK0_skl,strong_iteration(sK1_skl)) = multiplication(sK0_skl,one),
inference(paramodulation,[status(thm)],[f37,f144]) ).
fof(f656,plain,
multiplication(sK0_skl,strong_iteration(sK1_skl)) = sK0_skl,
inference(forward_demodulation,[status(thm)],[f26,f638]) ).
fof(f657,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f656,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE148+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 22:51:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.065313 seconds
% 0.12/0.42 % CPU time: 0.246954 seconds
% 0.12/0.42 % Total memory used: 69.424 MB
% 0.12/0.42 % Net memory used: 69.093 MB
%------------------------------------------------------------------------------