%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE065+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 : n020.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 12:57:54 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 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 ( 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f22,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)],[f11]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
domain(zero) = zero,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f40,plain,
? [X0,X1] :
( multiplication(X0,domain(X1)) != zero
& multiplication(X0,X1) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( multiplication(sK0_skl,domain(sK1_skl)) != zero
& 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)],[f40]) ).
fof(f42,plain,
multiplication(sK0_skl,sK1_skl) = zero,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
multiplication(sK0_skl,domain(sK1_skl)) != zero,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
! [X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))) = multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f36,f35]) ).
fof(f94,plain,
! [X0,X1] : addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))) = multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f36,f88]) ).
fof(f451,plain,
addition(multiplication(sK0_skl,domain(sK1_skl)),multiplication(domain(zero),multiplication(sK0_skl,domain(sK1_skl)))) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,domain(sK1_skl))),
inference(paramodulation,[status(thm)],[f42,f94]) ).
fof(f541,plain,
addition(multiplication(sK0_skl,domain(sK1_skl)),multiplication(zero,multiplication(sK0_skl,domain(sK1_skl)))) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f38,f451]) ).
fof(f542,plain,
addition(multiplication(sK0_skl,domain(sK1_skl)),zero) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f30,f541]) ).
fof(f543,plain,
multiplication(sK0_skl,domain(sK1_skl)) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f22,f542]) ).
fof(f544,plain,
multiplication(sK0_skl,domain(sK1_skl)) = multiplication(domain(zero),multiplication(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f42,f543]) ).
fof(f545,plain,
multiplication(sK0_skl,domain(sK1_skl)) = multiplication(zero,multiplication(sK0_skl,domain(sK1_skl))),
inference(forward_demodulation,[status(thm)],[f38,f544]) ).
fof(f546,plain,
multiplication(sK0_skl,domain(sK1_skl)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f545]) ).
fof(f547,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f546,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE065+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:42:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.051514 seconds
% 0.14/0.41 % CPU time: 0.171102 seconds
% 0.14/0.41 % Total memory used: 64.227 MB
% 0.14/0.41 % Net memory used: 63.909 MB
%------------------------------------------------------------------------------