%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE060+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 : n016.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 12:58:16 PM UTC 2026
% Result : Theorem 23.74s 3.65s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE060+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
% 0.09/0.57 % Computer : n016.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sun Sep 20 22:46:08 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 23.74/3.65 % Refutation found
% 23.74/3.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.74/3.65 % SZS output start CNFRefutation for theBenchmark
% 23.74/3.65 fof(f1,axiom,(
% 23.74/3.65 (! [A,B] : addition(A,B) = addition(B,A) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f2,axiom,(
% 23.74/3.65 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f4,axiom,(
% 23.74/3.65 (! [A] : addition(A,A) = A )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f6,axiom,(
% 23.74/3.65 (! [A] : multiplication(A,one) = A )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f7,axiom,(
% 23.74/3.65 (! [A] : multiplication(one,A) = A )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f8,axiom,(
% 23.74/3.65 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f9,axiom,(
% 23.74/3.65 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f13,axiom,(
% 23.74/3.65 (! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f14,axiom,(
% 23.74/3.65 (! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f15,axiom,(
% 23.74/3.65 (! [X0] : addition(domain(X0),one) = one )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f17,axiom,(
% 23.74/3.65 (! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f18,conjecture,(
% 23.74/3.65 (! [X0,X1] : domain(multiplication(domain(X0),X1)) = multiplication(domain(X0),domain(X1)) )),
% 23.74/3.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 23.74/3.65 fof(f19,negated_conjecture,(
% 23.74/3.65 ~((! [X0,X1] : domain(multiplication(domain(X0),X1)) = multiplication(domain(X0),domain(X1)) ))),
% 23.74/3.65 inference(negated_conjecture,[status(cth)],[f18])).
% 23.74/3.65 fof(f20,plain,(
% 23.74/3.65 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f1])).
% 23.74/3.65 fof(f21,plain,(
% 23.74/3.65 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f2])).
% 23.74/3.65 fof(f23,plain,(
% 23.74/3.65 ![X0]: (addition(X0,X0)=X0)),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f4])).
% 23.74/3.65 fof(f25,plain,(
% 23.74/3.65 ![X0]: (multiplication(X0,one)=X0)),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f6])).
% 23.74/3.65 fof(f26,plain,(
% 23.74/3.65 ![X0]: (multiplication(one,X0)=X0)),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f7])).
% 23.74/3.65 fof(f27,plain,(
% 23.74/3.65 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f8])).
% 23.74/3.65 fof(f28,plain,(
% 23.74/3.65 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f9])).
% 23.74/3.65 fof(f35,plain,(
% 23.74/3.65 ![X0]: (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f13])).
% 23.74/3.65 fof(f36,plain,(
% 23.74/3.65 ![X0,X1]: (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f14])).
% 23.74/3.65 fof(f37,plain,(
% 23.74/3.65 ![X0]: (addition(domain(X0),one)=one)),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f15])).
% 23.74/3.65 fof(f39,plain,(
% 23.74/3.65 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X0),domain(X1)))),
% 23.74/3.65 inference(cnf_transformation,[status(thm)],[f17])).
% 23.74/3.65 fof(f40,plain,(
% 23.74/3.65 (?[X0,X1]: ~domain(multiplication(domain(X0),X1))=multiplication(domain(X0),domain(X1)))),
% 23.74/3.65 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 23.74/3.65 fof(f41,plain,(
% 23.74/3.65 ~domain(multiplication(domain(sK0_skl),sK1_skl))=multiplication(domain(sK0_skl),domain(sK1_skl))),
% 23.74/3.65 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f40])).
% 23.74/3.65 fof(f42,plain,(
% 23.74/3.65 ~domain(multiplication(domain(sK0_skl),sK1_skl))=multiplication(domain(sK0_skl),domain(sK1_skl))),
% 23.74/3.66 inference(cnf_transformation,[status(thm)],[f41])).
% 23.74/3.66 fof(f70,plain,(
% 23.74/3.66 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f20,f21])).
% 23.74/3.66 fof(f159,plain,(
% 23.74/3.66 ![X0]: (domain(multiplication(one,X0))=domain(domain(X0)))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f26,f36])).
% 23.74/3.66 fof(f163,plain,(
% 23.74/3.66 ![X0]: (domain(X0)=domain(domain(X0)))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f26,f159])).
% 23.74/3.66 fof(f207,plain,(
% 23.74/3.66 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X1,X0))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f23,f70])).
% 23.74/3.66 fof(f337,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f25,f27])).
% 23.74/3.66 fof(f342,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f25,f27])).
% 23.74/3.66 fof(f1141,plain,(
% 23.74/3.66 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X1,X2),multiplication(X0,X2)))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f20,f28])).
% 23.74/3.66 fof(f1151,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(addition(X0,one),X1)=addition(multiplication(X0,X1),X1))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f26,f28])).
% 23.74/3.66 fof(f2055,plain,(
% 23.74/3.66 ![X0]: (addition(X0,multiplication(domain(X0),X0))=addition(multiplication(domain(X0),X0),X0))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f35,f207])).
% 23.74/3.66 fof(f2071,plain,(
% 23.74/3.66 ![X0]: (multiplication(domain(X0),X0)=addition(multiplication(domain(X0),X0),X0))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f35,f2055])).
% 23.74/3.66 fof(f2093,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(X0,multiplication(X0,X1)))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f20,f337])).
% 23.74/3.66 fof(f2511,plain,(
% 23.74/3.66 ![X0]: (multiplication(domain(X0),X0)=multiplication(addition(domain(X0),one),X0))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f1151,f2071])).
% 23.74/3.66 fof(f2562,plain,(
% 23.74/3.66 ![X0]: (multiplication(domain(X0),X0)=multiplication(one,X0))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f37,f2511])).
% 23.74/3.66 fof(f2574,plain,(
% 23.74/3.66 ![X0]: (multiplication(domain(X0),X0)=X0)),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f26,f2562])).
% 23.74/3.66 fof(f2786,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(addition(X0,domain(X1)),X1)=addition(multiplication(X0,X1),X1))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f2574,f28])).
% 23.74/3.66 fof(f2789,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(domain(X0),addition(X0,X1))=addition(X0,multiplication(domain(X0),X1)))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f2574,f27])).
% 23.74/3.66 fof(f3206,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(X0,one)=addition(X0,multiplication(X0,domain(X1))))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f37,f2093])).
% 23.74/3.66 fof(f3207,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(one,X0)=addition(multiplication(domain(X1),X0),X0))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f37,f1151])).
% 23.74/3.66 fof(f3208,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(X0,one)=addition(multiplication(X0,domain(X1)),X0))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f37,f342])).
% 23.74/3.66 fof(f3231,plain,(
% 23.74/3.66 ![X0,X1]: (X0=addition(X0,multiplication(X0,domain(X1))))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f25,f3206])).
% 23.74/3.66 fof(f3232,plain,(
% 23.74/3.66 ![X0,X1]: (X0=addition(multiplication(domain(X1),X0),X0))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f26,f3207])).
% 23.74/3.66 fof(f3233,plain,(
% 23.74/3.66 ![X0,X1]: (X0=addition(multiplication(X0,domain(X1)),X0))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f25,f3208])).
% 23.74/3.66 fof(f4342,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(domain(addition(X0,X1)),X1)=addition(multiplication(domain(X0),X1),X1))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f39,f2786])).
% 23.74/3.66 fof(f4397,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(domain(addition(X0,X1)),X1)=X1)),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f3232,f4342])).
% 23.74/3.66 fof(f4496,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(domain(domain(addition(X0,X1))),domain(X1))=domain(X1))),
% 23.74/3.66 inference(paramodulation,[status(thm)],[f39,f4397])).
% 23.74/3.66 fof(f4559,plain,(
% 23.74/3.66 ![X0,X1]: (multiplication(domain(addition(X0,X1)),domain(X1))=domain(X1))),
% 23.74/3.66 inference(forward_demodulation,[status(thm)],[f163,f4496])).
% 23.74/3.66 fof(f4720,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(X0,domain(X1))))=domain(multiplication(X0,domain(X1))))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f3231,f4559])).
% 23.74/3.70 fof(f4776,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(X0,X1)))=domain(multiplication(X0,domain(X1))))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f36,f4720])).
% 23.74/3.70 fof(f4777,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(X0,X1)))=domain(multiplication(X0,X1)))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f36,f4776])).
% 23.74/3.70 fof(f9335,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(domain(X0),X1)))=domain(multiplication(domain(X0),X1)))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f163,f4777])).
% 23.74/3.70 fof(f9548,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(domain(X0)),domain(addition(X0,X1)))=addition(domain(X0),multiplication(domain(domain(X0)),domain(X1))))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f39,f2789])).
% 23.74/3.70 fof(f9555,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=addition(multiplication(domain(X0),X1),multiplication(domain(multiplication(domain(X0),X1)),X1)))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f3232,f2789])).
% 23.74/3.70 fof(f9655,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=addition(domain(X0),multiplication(domain(domain(X0)),domain(X1))))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f163,f9548])).
% 23.74/3.70 fof(f9656,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=addition(domain(X0),multiplication(domain(X0),domain(X1))))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f163,f9655])).
% 23.74/3.70 fof(f9657,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=domain(X0))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f3231,f9656])).
% 23.74/3.70 fof(f9667,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=multiplication(addition(domain(multiplication(domain(X0),X1)),domain(X0)),X1))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f1141,f9555])).
% 23.74/3.70 fof(f9668,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=multiplication(domain(addition(multiplication(domain(X0),X1),X0)),X1))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f39,f9667])).
% 23.74/3.70 fof(f9847,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),domain(X1))=domain(multiplication(domain(X0),X1)))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f3232,f9657])).
% 23.74/3.70 fof(f18788,plain,(
% 23.74/3.70 ![X0,X1]: (domain(X0)=addition(domain(multiplication(domain(X0),X1)),domain(X0)))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f9335,f3233])).
% 23.74/3.70 fof(f18971,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=multiplication(domain(X0),X1))),
% 23.74/3.70 inference(backward_demodulation,[status(thm)],[f18972,f9668])).
% 23.74/3.70 fof(f18972,plain,(
% 23.74/3.70 ![X0,X1]: (domain(X0)=domain(addition(multiplication(domain(X0),X1),X0)))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f39,f18788])).
% 23.74/3.70 fof(f19130,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),domain(X1))),domain(X1))=domain(multiplication(domain(X0),domain(X1))))),
% 23.74/3.70 inference(paramodulation,[status(thm)],[f163,f9847])).
% 23.74/3.70 fof(f19311,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(X1))=domain(multiplication(domain(X0),domain(X1))))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f18971,f19130])).
% 23.74/3.70 fof(f19316,plain,(
% 23.74/3.70 ~domain(multiplication(domain(sK0_skl),sK1_skl))=domain(multiplication(domain(sK0_skl),sK1_skl))),
% 23.74/3.70 inference(backward_demodulation,[status(thm)],[f19459,f42])).
% 23.74/3.70 fof(f19459,plain,(
% 23.74/3.70 ![X0,X1]: (multiplication(domain(X0),domain(X1))=domain(multiplication(domain(X0),X1)))),
% 23.74/3.70 inference(forward_demodulation,[status(thm)],[f36,f19311])).
% 23.74/3.70 fof(f19606,plain,(
% 23.74/3.70 $false),
% 23.74/3.70 inference(trivial_equality_resolution,[status(thm)],[f19316])).
% 23.74/3.70 % SZS output end CNFRefutation for theBenchmark.p
% 2.35/3.71 % Elapsed time: 3.124697 seconds
% 2.35/3.71 % CPU time: 24.513736 seconds
% 2.35/3.71 % Total memory used: 296.797 MB
% 2.35/3.71 % Net memory used: 287.418 MB
%------------------------------------------------------------------------------