%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 12:58:08 PM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.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 22:37:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.37 fof(f9,axiom,(
% 0.08/0.37 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f12,axiom,(
% 0.08/0.37 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f13,conjecture,(
% 0.08/0.37 (! [X0,X1,X2] :( leq(X0,X1)=> leq(multiplication(X0,X2),multiplication(X1,X2)) ) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f14,negated_conjecture,(
% 0.08/0.37 ~((! [X0,X1,X2] :( leq(X0,X1)=> leq(multiplication(X0,X2),multiplication(X1,X2)) ) ))),
% 0.08/0.37 inference(negated_conjecture,[status(cth)],[f13])).
% 0.08/0.37 fof(f23,plain,(
% 0.08/0.37 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.37 fof(f26,plain,(
% 0.08/0.37 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.08/0.37 inference(NNF_transformation,[status(thm)],[f12])).
% 0.08/0.37 fof(f27,plain,(
% 0.08/0.37 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.08/0.37 inference(miniscoping,[status(thm)],[f26])).
% 0.08/0.37 fof(f28,plain,(
% 0.08/0.37 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f27])).
% 0.08/0.37 fof(f29,plain,(
% 0.08/0.37 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f27])).
% 0.08/0.37 fof(f30,plain,(
% 0.08/0.37 (?[X0,X1,X2]: (leq(X0,X1)&~leq(multiplication(X0,X2),multiplication(X1,X2))))),
% 0.08/0.37 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.08/0.37 fof(f31,plain,(
% 0.08/0.37 ?[X0,X1]: (leq(X0,X1)&(?[X2]: ~leq(multiplication(X0,X2),multiplication(X1,X2))))),
% 0.08/0.37 inference(miniscoping,[status(thm)],[f30])).
% 0.08/0.37 fof(f32,plain,(
% 0.08/0.37 (leq(sK0_skl,sK1_skl)&~leq(multiplication(sK0_skl,sK2_skl),multiplication(sK1_skl,sK2_skl)))),
% 0.08/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f31])).
% 0.08/0.37 fof(f33,plain,(
% 0.08/0.37 leq(sK0_skl,sK1_skl)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f32])).
% 0.08/0.37 fof(f34,plain,(
% 0.08/0.37 ~leq(multiplication(sK0_skl,sK2_skl),multiplication(sK1_skl,sK2_skl))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f32])).
% 0.08/0.37 fof(f38,plain,(
% 0.08/0.37 addition(sK0_skl,sK1_skl)=sK1_skl),
% 0.08/0.37 inference(resolution,[status(thm)],[f28,f33])).
% 0.08/0.37 fof(f39,plain,(
% 0.08/0.37 ~addition(multiplication(sK0_skl,sK2_skl),multiplication(sK1_skl,sK2_skl))=multiplication(sK1_skl,sK2_skl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f29,f34])).
% 0.08/0.37 fof(f41,plain,(
% 0.08/0.37 ~multiplication(addition(sK0_skl,sK1_skl),sK2_skl)=multiplication(sK1_skl,sK2_skl)),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f23,f39])).
% 0.08/0.37 fof(f42,plain,(
% 0.08/0.37 ~multiplication(sK1_skl,sK2_skl)=multiplication(sK1_skl,sK2_skl)),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f38,f41])).
% 0.08/0.37 fof(f43,plain,(
% 0.08/0.37 $false),
% 0.08/0.37 inference(trivial_equality_resolution,[status(thm)],[f42])).
% 0.08/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.39 % Elapsed time: 0.035761 seconds
% 0.14/0.39 % CPU time: 0.078173 seconds
% 0.14/0.39 % Total memory used: 12.758 MB
% 0.14/0.39 % Net memory used: 12.738 MB
%------------------------------------------------------------------------------