%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:58:17 PM UTC 2026
% Result : Theorem 22.73s 18.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.40 % Computer : n026.cluster.edu
% 0.11/15.40 % Model : x86_64 x86_64
% 0.11/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.40 % Memory : 8046.5625MB
% 0.11/15.40 % OS : Linux 6.8.0-71-generic
% 0.11/15.40 % CPULimit : 300
% 0.11/15.40 % WCLimit : 300
% 0.11/15.40 % DateTime : Sun Sep 20 22:45:09 UTC 2026
% 0.11/15.41 % CPUTime :
% 0.11/15.42 % Drodi V4.1.1
% 22.73/18.42 % Refutation found
% 22.73/18.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 22.73/18.42 % SZS output start CNFRefutation for theBenchmark
% 22.73/18.42 fof(f1,axiom,(
% 22.73/18.42 (! [A,B] : addition(A,B) = addition(B,A) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f5,axiom,(
% 22.73/18.42 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f6,axiom,(
% 22.73/18.42 (! [A] : multiplication(A,one) = A )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f7,axiom,(
% 22.73/18.42 (! [A] : multiplication(one,A) = A )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f8,axiom,(
% 22.73/18.42 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f9,axiom,(
% 22.73/18.42 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f13,axiom,(
% 22.73/18.42 (! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f14,axiom,(
% 22.73/18.42 (! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f15,axiom,(
% 22.73/18.42 (! [X0] : addition(domain(X0),one) = one )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f17,axiom,(
% 22.73/18.42 (! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f18,conjecture,(
% 22.73/18.42 (! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0) )),
% 22.73/18.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 22.73/18.42 fof(f19,negated_conjecture,(
% 22.73/18.42 ~((! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0) ))),
% 22.73/18.42 inference(negated_conjecture,[status(cth)],[f18])).
% 22.73/18.42 fof(f20,plain,(
% 22.73/18.42 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f1])).
% 22.73/18.42 fof(f24,plain,(
% 22.73/18.42 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f5])).
% 22.73/18.42 fof(f25,plain,(
% 22.73/18.42 ![X0]: (multiplication(X0,one)=X0)),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f6])).
% 22.73/18.42 fof(f26,plain,(
% 22.73/18.42 ![X0]: (multiplication(one,X0)=X0)),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f7])).
% 22.73/18.42 fof(f27,plain,(
% 22.73/18.42 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f8])).
% 22.73/18.42 fof(f28,plain,(
% 22.73/18.42 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f9])).
% 22.73/18.42 fof(f35,plain,(
% 22.73/18.42 ![X0]: (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f13])).
% 22.73/18.42 fof(f36,plain,(
% 22.73/18.42 ![X0,X1]: (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f14])).
% 22.73/18.42 fof(f37,plain,(
% 22.73/18.42 ![X0]: (addition(domain(X0),one)=one)),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f15])).
% 22.73/18.42 fof(f39,plain,(
% 22.73/18.42 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X0),domain(X1)))),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f17])).
% 22.73/18.42 fof(f40,plain,(
% 22.73/18.42 (?[X0,X1]: ~multiplication(domain(X0),addition(domain(X0),domain(X1)))=domain(X0))),
% 22.73/18.42 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 22.73/18.42 fof(f41,plain,(
% 22.73/18.42 ~multiplication(domain(sK0_skl),addition(domain(sK0_skl),domain(sK1_skl)))=domain(sK0_skl)),
% 22.73/18.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f40])).
% 22.73/18.42 fof(f42,plain,(
% 22.73/18.42 ~multiplication(domain(sK0_skl),addition(domain(sK0_skl),domain(sK1_skl)))=domain(sK0_skl)),
% 22.73/18.42 inference(cnf_transformation,[status(thm)],[f41])).
% 22.73/18.42 fof(f107,plain,(
% 22.73/18.42 ~multiplication(domain(sK0_skl),domain(addition(sK0_skl,sK1_skl)))=domain(sK0_skl)),
% 22.73/18.42 inference(backward_demodulation,[status(thm)],[f39,f42])).
% 20.93/18.46 fof(f108,plain,(
% 20.93/18.46 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X1),domain(X0)))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f20,f39])).
% 20.93/18.46 fof(f330,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f25,f27])).
% 20.93/18.46 fof(f337,plain,(
% 20.93/18.46 ![X0]: (domain(multiplication(one,X0))=domain(domain(X0)))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f26,f36])).
% 20.93/18.46 fof(f338,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(addition(X0,one),X1)=addition(multiplication(X0,X1),X1))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f26,f28])).
% 20.93/18.46 fof(f343,plain,(
% 20.93/18.46 ![X0]: (domain(X0)=domain(domain(X0)))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f26,f337])).
% 20.93/18.46 fof(f4465,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(X0,one)=addition(multiplication(X0,domain(X1)),X0))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f37,f330])).
% 20.93/18.46 fof(f4568,plain,(
% 20.93/18.46 ![X0,X1]: (X0=addition(multiplication(X0,domain(X1)),X0))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f25,f4465])).
% 20.93/18.46 fof(f5143,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(one,X0)=addition(multiplication(multiplication(one,domain(X1)),X0),X0))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f4568,f338])).
% 20.93/18.46 fof(f5251,plain,(
% 20.93/18.46 ![X0,X1]: (X0=addition(multiplication(multiplication(one,domain(X1)),X0),X0))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f26,f5143])).
% 20.93/18.46 fof(f5252,plain,(
% 20.93/18.46 ![X0,X1]: (X0=addition(multiplication(one,multiplication(domain(X1),X0)),X0))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f24,f5251])).
% 20.93/18.46 fof(f5253,plain,(
% 20.93/18.46 ![X0,X1]: (X0=addition(multiplication(domain(X1),X0),X0))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f26,f5252])).
% 20.93/18.46 fof(f5335,plain,(
% 20.93/18.46 ![X0,X1]: (X0=addition(X0,multiplication(domain(X1),X0)))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f20,f5253])).
% 20.93/18.46 fof(f5441,plain,(
% 20.93/18.46 ![X0]: (X0=multiplication(domain(X0),X0))),
% 20.93/18.46 inference(backward_demodulation,[status(thm)],[f5335,f35])).
% 20.93/18.46 fof(f5595,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(domain(X0),addition(X1,X0))=addition(multiplication(domain(X0),X1),X0))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f5441,f27])).
% 20.93/18.46 fof(f7530,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(domain(domain(X0)),domain(addition(X0,X1)))=addition(multiplication(domain(domain(X0)),domain(X1)),domain(X0)))),
% 20.93/18.46 inference(paramodulation,[status(thm)],[f108,f5595])).
% 20.93/18.46 fof(f7636,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=addition(multiplication(domain(domain(X0)),domain(X1)),domain(X0)))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f343,f7530])).
% 20.93/18.46 fof(f7637,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=addition(multiplication(domain(X0),domain(X1)),domain(X0)))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f343,f7636])).
% 20.93/18.46 fof(f7638,plain,(
% 20.93/18.46 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=domain(X0))),
% 20.93/18.46 inference(forward_demodulation,[status(thm)],[f4568,f7637])).
% 20.93/18.46 fof(f20104,plain,(
% 20.93/18.46 ~domain(sK0_skl)=domain(sK0_skl)),
% 20.93/18.46 inference(backward_demodulation,[status(thm)],[f7638,f107])).
% 20.93/18.46 fof(f20244,plain,(
% 20.93/18.46 $false),
% 20.93/18.46 inference(trivial_equality_resolution,[status(thm)],[f20104])).
% 20.93/18.46 % SZS output end CNFRefutation for theBenchmark.p
% 20.93/18.48 % Elapsed time: 3.058084 seconds
% 20.93/18.48 % CPU time: 23.802487 seconds
% 20.93/18.48 % Total memory used: 173.490 MB
% 20.93/18.48 % Net memory used: 169.450 MB
%------------------------------------------------------------------------------