%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE066+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 : n014.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 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
<= multiplication(X0,domain(X1)) = zero ),
file('/export/starexec/sandbox/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(f66,plain,
domain(multiplication(sK0_skl,sK1_skl)) = domain(zero),
inference(paramodulation,[status(thm)],[f43,f36]) ).
fof(f70,plain,
domain(multiplication(sK0_skl,sK1_skl)) = zero,
inference(forward_demodulation,[status(thm)],[f38,f66]) ).
fof(f118,plain,
addition(multiplication(sK0_skl,sK1_skl),multiplication(zero,multiplication(sK0_skl,sK1_skl))) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,sK1_skl)),
inference(paramodulation,[status(thm)],[f70,f35]) ).
fof(f128,plain,
addition(multiplication(sK0_skl,sK1_skl),zero) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,sK1_skl)),
inference(forward_demodulation,[status(thm)],[f30,f118]) ).
fof(f129,plain,
multiplication(sK0_skl,sK1_skl) = multiplication(domain(multiplication(sK0_skl,sK1_skl)),multiplication(sK0_skl,sK1_skl)),
inference(forward_demodulation,[status(thm)],[f22,f128]) ).
fof(f130,plain,
multiplication(sK0_skl,sK1_skl) = multiplication(zero,multiplication(sK0_skl,sK1_skl)),
inference(forward_demodulation,[status(thm)],[f70,f129]) ).
fof(f131,plain,
multiplication(sK0_skl,sK1_skl) = zero,
inference(forward_demodulation,[status(thm)],[f30,f130]) ).
fof(f132,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f131,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE066+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:41:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.066979 seconds
% 0.09/0.44 % CPU time: 0.202923 seconds
% 0.09/0.44 % Total memory used: 67.214 MB
% 0.09/0.44 % Net memory used: 66.878 MB
%------------------------------------------------------------------------------