%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE035+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 : n009.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 12:58:13 PM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE035+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
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:39:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 (! [A] : addition(A,zero) = A )),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f5,axiom,(
% 0.09/0.39 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f8,axiom,(
% 0.09/0.39 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f9,axiom,(
% 0.09/0.39 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,axiom,(
% 0.09/0.39 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f17,conjecture,(
% 0.09/0.39 (! [X0,X1,X2,X3] :( ( test(X3)& test(X2)& leq(multiplication(multiplication(X2,X0),c(X3)),zero)& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ) )),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f18,negated_conjecture,(
% 0.09/0.39 ~((! [X0,X1,X2,X3] :( ( test(X3)& test(X2)& leq(multiplication(multiplication(X2,X0),c(X3)),zero)& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ) ))),
% 0.09/0.39 inference(negated_conjecture,[status(cth)],[f17])).
% 0.09/0.39 fof(f21,plain,(
% 0.09/0.39 ![X0]: (addition(X0,zero)=X0)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.39 fof(f23,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/0.39 fof(f26,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/0.39 fof(f27,plain,(
% 0.09/0.39 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/0.39 fof(f30,plain,(
% 0.15/0.39 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.15/0.39 inference(NNF_transformation,[status(thm)],[f12])).
% 0.15/0.39 fof(f31,plain,(
% 0.15/0.39 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.15/0.39 inference(miniscoping,[status(thm)],[f30])).
% 0.15/0.39 fof(f32,plain,(
% 0.15/0.39 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/0.39 fof(f33,plain,(
% 0.15/0.39 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f31])).
% 0.15/0.39 fof(f52,plain,(
% 0.15/0.39 (?[X0,X1,X2,X3]: ((((test(X3)&test(X2))&leq(multiplication(multiplication(X2,X0),c(X3)),zero))&leq(multiplication(multiplication(X2,X1),c(X3)),zero))&~leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)))),
% 0.15/0.39 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.15/0.39 fof(f53,plain,(
% 0.15/0.39 ((((test(sK4_skl)&test(sK3_skl))&leq(multiplication(multiplication(sK3_skl,sK1_skl),c(sK4_skl)),zero))&leq(multiplication(multiplication(sK3_skl,sK2_skl),c(sK4_skl)),zero))&~leq(multiplication(multiplication(sK3_skl,addition(sK1_skl,sK2_skl)),c(sK4_skl)),zero))),
% 0.15/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl),skolemize(X2,sK3_skl),skolemize(X3,sK4_skl)],[f52])).
% 0.15/0.39 fof(f56,plain,(
% 0.15/0.39 leq(multiplication(multiplication(sK3_skl,sK1_skl),c(sK4_skl)),zero)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f53])).
% 0.15/0.39 fof(f57,plain,(
% 0.15/0.39 leq(multiplication(multiplication(sK3_skl,sK2_skl),c(sK4_skl)),zero)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f53])).
% 0.15/0.39 fof(f58,plain,(
% 0.15/0.39 ~leq(multiplication(multiplication(sK3_skl,addition(sK1_skl,sK2_skl)),c(sK4_skl)),zero)),
% 0.15/0.39 inference(cnf_transformation,[status(thm)],[f53])).
% 0.15/0.39 fof(f85,plain,(
% 0.15/0.39 leq(multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl))),zero)),
% 0.15/0.39 inference(backward_demodulation,[status(thm)],[f23,f56])).
% 0.15/0.39 fof(f195,plain,(
% 0.15/0.39 leq(multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl))),zero)),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f23,f57])).
% 0.15/0.39 fof(f196,plain,(
% 0.15/0.39 addition(multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl))),zero)=zero),
% 0.15/0.39 inference(resolution,[status(thm)],[f195,f32])).
% 0.15/0.39 fof(f197,plain,(
% 0.15/0.39 multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl)))=zero),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f21,f196])).
% 0.15/0.39 fof(f198,plain,(
% 0.15/0.39 ~leq(multiplication(sK3_skl,multiplication(addition(sK1_skl,sK2_skl),c(sK4_skl))),zero)),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f23,f58])).
% 0.15/0.39 fof(f199,plain,(
% 0.15/0.39 ~addition(multiplication(sK3_skl,multiplication(addition(sK1_skl,sK2_skl),c(sK4_skl))),zero)=zero),
% 0.15/0.39 inference(resolution,[status(thm)],[f198,f33])).
% 0.15/0.39 fof(f200,plain,(
% 0.15/0.39 ~multiplication(sK3_skl,multiplication(addition(sK1_skl,sK2_skl),c(sK4_skl)))=zero),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f21,f199])).
% 0.15/0.39 fof(f201,plain,(
% 0.15/0.39 addition(multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl))),zero)=zero),
% 0.15/0.39 inference(resolution,[status(thm)],[f85,f32])).
% 0.15/0.39 fof(f202,plain,(
% 0.15/0.39 multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl)))=zero),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f21,f201])).
% 0.15/0.39 fof(f206,plain,(
% 0.15/0.39 ![X0]: (multiplication(sK3_skl,addition(X0,multiplication(sK2_skl,c(sK4_skl))))=addition(multiplication(sK3_skl,X0),zero))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f197,f26])).
% 0.15/0.39 fof(f211,plain,(
% 0.15/0.39 ![X0]: (multiplication(sK3_skl,addition(X0,multiplication(sK2_skl,c(sK4_skl))))=multiplication(sK3_skl,X0))),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f21,f206])).
% 0.15/0.39 fof(f276,plain,(
% 0.15/0.39 ![X0]: (multiplication(sK3_skl,multiplication(addition(X0,sK2_skl),c(sK4_skl)))=multiplication(sK3_skl,multiplication(X0,c(sK4_skl))))),
% 0.15/0.39 inference(paramodulation,[status(thm)],[f27,f211])).
% 0.15/0.39 fof(f983,plain,(
% 0.15/0.39 ~multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl)))=zero),
% 0.15/0.39 inference(backward_demodulation,[status(thm)],[f276,f200])).
% 0.15/0.39 fof(f995,plain,(
% 0.15/0.39 ~zero=zero),
% 0.15/0.39 inference(forward_demodulation,[status(thm)],[f202,f983])).
% 0.15/0.39 fof(f996,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(trivial_equality_resolution,[status(thm)],[f995])).
% 0.15/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.42 % Elapsed time: 0.055085 seconds
% 0.15/0.42 % CPU time: 0.147098 seconds
% 0.15/0.42 % Total memory used: 27.979 MB
% 0.15/0.42 % Net memory used: 27.904 MB
%------------------------------------------------------------------------------