%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE010+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 : n019.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 12:58:09 PM UTC 2026
% Result : Theorem 0.10s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE010+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
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 22:38:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.53 fof(f1,axiom,(
% 0.10/0.53 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f2,axiom,(
% 0.10/0.53 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f4,axiom,(
% 0.10/0.53 (! [A] : addition(A,A) = A )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f6,axiom,(
% 0.10/0.53 (! [A] : multiplication(A,one) = A )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f7,axiom,(
% 0.10/0.53 (! [A] : multiplication(one,A) = A )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f8,axiom,(
% 0.10/0.53 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f9,axiom,(
% 0.10/0.53 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f14,axiom,(
% 0.10/0.53 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f15,axiom,(
% 0.10/0.53 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f17,conjecture,(
% 0.10/0.53 (! [X0,X1] :( ( test(X1)& test(X0) )=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ) )),
% 0.10/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.53 fof(f18,negated_conjecture,(
% 0.10/0.53 ~((! [X0,X1] :( ( test(X1)& test(X0) )=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ) ))),
% 0.10/0.53 inference(negated_conjecture,[status(cth)],[f17])).
% 0.10/0.53 fof(f19,plain,(
% 0.10/0.53 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.53 fof(f20,plain,(
% 0.10/0.53 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.53 fof(f22,plain,(
% 0.10/0.53 ![X0]: (addition(X0,X0)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.53 fof(f24,plain,(
% 0.10/0.53 ![X0]: (multiplication(X0,one)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.53 fof(f25,plain,(
% 0.10/0.53 ![X0]: (multiplication(one,X0)=X0)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.53 fof(f26,plain,(
% 0.10/0.53 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f8])).
% 0.10/0.53 fof(f27,plain,(
% 0.10/0.53 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f9])).
% 0.10/0.53 fof(f39,plain,(
% 0.10/0.53 ![X0,X1]: ((~complement(X1,X0)|((multiplication(X0,X1)=zero&multiplication(X1,X0)=zero)&addition(X0,X1)=one))&(complement(X1,X0)|((~multiplication(X0,X1)=zero|~multiplication(X1,X0)=zero)|~addition(X0,X1)=one)))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f14])).
% 0.10/0.53 fof(f40,plain,(
% 0.10/0.53 (![X0,X1]: (~complement(X1,X0)|((multiplication(X0,X1)=zero&multiplication(X1,X0)=zero)&addition(X0,X1)=one)))&(![X0,X1]: (complement(X1,X0)|((~multiplication(X0,X1)=zero|~multiplication(X1,X0)=zero)|~addition(X0,X1)=one)))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f39])).
% 0.10/0.53 fof(f43,plain,(
% 0.10/0.53 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.53 fof(f45,plain,(
% 0.10/0.53 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.10/0.53 fof(f46,plain,(
% 0.10/0.53 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.10/0.53 inference(NNF_transformation,[status(thm)],[f45])).
% 0.10/0.53 fof(f47,plain,(
% 0.10/0.53 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.10/0.53 inference(miniscoping,[status(thm)],[f46])).
% 0.10/0.53 fof(f48,plain,(
% 0.10/0.53 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f47])).
% 0.10/0.53 fof(f52,plain,(
% 0.10/0.53 (?[X0,X1]: ((test(X1)&test(X0))&~one=addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))))),
% 0.10/0.53 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.10/0.53 fof(f53,plain,(
% 0.10/0.53 ((test(sK2_skl)&test(sK1_skl))&~one=addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))))),
% 0.10/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl)],[f52])).
% 0.10/0.53 fof(f54,plain,(
% 0.10/0.53 test(sK2_skl)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f53])).
% 0.10/0.53 fof(f55,plain,(
% 0.10/0.53 test(sK1_skl)),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f53])).
% 0.10/0.53 fof(f56,plain,(
% 0.10/0.53 ~one=addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))),
% 0.10/0.53 inference(cnf_transformation,[status(thm)],[f53])).
% 0.10/0.53 fof(f57,plain,(
% 0.10/0.53 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 0.10/0.53 inference(destructive_equality_resolution,[status(thm)],[f48])).
% 0.10/0.53 fof(f58,plain,(
% 0.10/0.53 ~one=addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl))))),
% 0.10/0.53 inference(forward_demodulation,[status(thm)],[f20,f56])).
% 0.10/0.53 fof(f59,plain,(
% 0.10/0.53 ~one=addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl)))))),
% 0.10/0.53 inference(forward_demodulation,[status(thm)],[f20,f58])).
% 0.10/0.53 fof(f60,plain,(
% 0.10/0.53 ~one=addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(c(sK2_skl),sK1_skl),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl))))))),
% 0.10/0.53 inference(forward_demodulation,[status(thm)],[f20,f59])).
% 0.10/0.53 fof(f61,plain,(
% 0.10/0.53 ~one=addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(c(sK2_skl),sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))))),
% 0.10/0.53 inference(forward_demodulation,[status(thm)],[f26,f60])).
% 0.10/0.53 fof(f68,plain,(
% 0.10/0.53 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f19,f20])).
% 0.10/0.53 fof(f74,plain,(
% 0.10/0.53 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f22,f20])).
% 0.10/0.53 fof(f127,plain,(
% 0.10/0.53 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f24,f26])).
% 0.10/0.53 fof(f166,plain,(
% 0.10/0.53 ![X0,X1,X2,X3]: (addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3))=addition(multiplication(addition(X0,X2),X1),X3))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f27,f20])).
% 0.10/0.53 fof(f180,plain,(
% 0.10/0.53 ~one=addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))))),
% 0.10/0.53 inference(backward_demodulation,[status(thm)],[f166,f61])).
% 0.10/0.53 fof(f182,plain,(
% 0.10/0.53 ![X0]: (addition(c(X0),X0)=one|~test(X0))),
% 0.10/0.53 inference(resolution,[status(thm)],[f43,f57])).
% 0.10/0.53 fof(f213,plain,(
% 0.10/0.53 addition(c(sK1_skl),sK1_skl)=one),
% 0.10/0.53 inference(resolution,[status(thm)],[f182,f55])).
% 0.10/0.53 fof(f214,plain,(
% 0.10/0.53 addition(c(sK2_skl),sK2_skl)=one),
% 0.10/0.53 inference(resolution,[status(thm)],[f182,f54])).
% 0.10/0.53 fof(f319,plain,(
% 0.10/0.53 ![X0]: (addition(c(sK1_skl),addition(sK1_skl,X0))=addition(X0,one))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f213,f68])).
% 0.10/0.53 fof(f320,plain,(
% 0.10/0.53 ![X0]: (addition(X0,one)=addition(sK1_skl,addition(X0,c(sK1_skl))))),
% 0.10/0.53 inference(paramodulation,[status(thm)],[f213,f68])).
% 0.10/0.54 fof(f326,plain,(
% 0.10/0.54 addition(sK2_skl,c(sK2_skl))=one),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f19,f214])).
% 0.10/0.54 fof(f334,plain,(
% 0.10/0.54 ~one=addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),one)))),
% 0.10/0.54 inference(backward_demodulation,[status(thm)],[f326,f180])).
% 0.10/0.54 fof(f337,plain,(
% 0.10/0.54 ~one=addition(multiplication(one,sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),one)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f326,f334])).
% 0.10/0.54 fof(f338,plain,(
% 0.10/0.54 ~one=addition(sK1_skl,addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),one)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f25,f337])).
% 0.10/0.54 fof(f339,plain,(
% 0.10/0.54 ~one=addition(sK1_skl,addition(multiplication(sK1_skl,sK2_skl),c(sK1_skl)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f338])).
% 0.10/0.54 fof(f340,plain,(
% 0.10/0.54 ~one=addition(multiplication(sK1_skl,sK2_skl),one)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f320,f339])).
% 0.10/0.54 fof(f499,plain,(
% 0.10/0.54 addition(sK2_skl,one)=addition(sK2_skl,c(sK2_skl))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f326,f74])).
% 0.10/0.54 fof(f501,plain,(
% 0.10/0.54 addition(sK2_skl,one)=one),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f326,f499])).
% 0.10/0.54 fof(f502,plain,(
% 0.10/0.54 addition(one,sK2_skl)=one),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f19,f501])).
% 0.10/0.54 fof(f667,plain,(
% 0.10/0.54 ![X0]: (multiplication(X0,one)=addition(X0,multiplication(X0,sK2_skl)))),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f502,f127])).
% 0.10/0.54 fof(f673,plain,(
% 0.10/0.54 ![X0]: (X0=addition(X0,multiplication(X0,sK2_skl)))),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f24,f667])).
% 0.10/0.54 fof(f1190,plain,(
% 0.10/0.54 addition(c(sK1_skl),sK1_skl)=addition(multiplication(sK1_skl,sK2_skl),one)),
% 0.10/0.54 inference(paramodulation,[status(thm)],[f673,f319])).
% 0.10/0.54 fof(f1207,plain,(
% 0.10/0.54 one=addition(multiplication(sK1_skl,sK2_skl),one)),
% 0.10/0.54 inference(forward_demodulation,[status(thm)],[f213,f1190])).
% 0.10/0.54 fof(f1208,plain,(
% 0.10/0.54 $false),
% 0.10/0.54 inference(forward_subsumption_resolution,[status(thm)],[f1207,f340])).
% 0.10/0.54 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.57 % Elapsed time: 0.170117 seconds
% 0.15/0.57 % CPU time: 1.016115 seconds
% 0.15/0.57 % Total memory used: 114.948 MB
% 0.15/0.57 % Net memory used: 114.335 MB
%------------------------------------------------------------------------------