%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE068+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 : 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 12:58:17 PM UTC 2026
% Result : Theorem 25.38s 8.68s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE068+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
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 22:41:34 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 25.38/8.68 % Refutation found
% 25.38/8.68 % SZS status Theorem for theBenchmark: Theorem is valid
% 25.38/8.68 % SZS output start CNFRefutation for theBenchmark
% 25.38/8.68 fof(f1,axiom,(
% 25.38/8.68 (! [A,B] : addition(A,B) = addition(B,A) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f2,axiom,(
% 25.38/8.68 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f4,axiom,(
% 25.38/8.68 (! [A] : addition(A,A) = A )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f6,axiom,(
% 25.38/8.68 (! [A] : multiplication(A,one) = A )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f7,axiom,(
% 25.38/8.68 (! [A] : multiplication(one,A) = A )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f8,axiom,(
% 25.38/8.68 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f9,axiom,(
% 25.38/8.68 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f13,axiom,(
% 25.38/8.68 (! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f14,axiom,(
% 25.38/8.68 (! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f15,axiom,(
% 25.38/8.68 (! [X0] : addition(domain(X0),one) = one )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f17,axiom,(
% 25.38/8.68 (! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f18,conjecture,(
% 25.38/8.68 (! [X0,X1] : domain(multiplication(domain(X0),domain(X1))) = multiplication(domain(X0),domain(X1)) )),
% 25.38/8.68 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 25.38/8.68 fof(f19,negated_conjecture,(
% 25.38/8.68 ~((! [X0,X1] : domain(multiplication(domain(X0),domain(X1))) = multiplication(domain(X0),domain(X1)) ))),
% 25.38/8.68 inference(negated_conjecture,[status(cth)],[f18])).
% 25.38/8.68 fof(f20,plain,(
% 25.38/8.68 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f1])).
% 25.38/8.68 fof(f21,plain,(
% 25.38/8.68 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f2])).
% 25.38/8.68 fof(f23,plain,(
% 25.38/8.68 ![X0]: (addition(X0,X0)=X0)),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f4])).
% 25.38/8.68 fof(f25,plain,(
% 25.38/8.68 ![X0]: (multiplication(X0,one)=X0)),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f6])).
% 25.38/8.68 fof(f26,plain,(
% 25.38/8.68 ![X0]: (multiplication(one,X0)=X0)),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f7])).
% 25.38/8.68 fof(f27,plain,(
% 25.38/8.68 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f8])).
% 25.38/8.68 fof(f28,plain,(
% 25.38/8.68 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f9])).
% 25.38/8.68 fof(f35,plain,(
% 25.38/8.68 ![X0]: (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f13])).
% 25.38/8.68 fof(f36,plain,(
% 25.38/8.68 ![X0,X1]: (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f14])).
% 25.38/8.68 fof(f37,plain,(
% 25.38/8.68 ![X0]: (addition(domain(X0),one)=one)),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f15])).
% 25.38/8.68 fof(f39,plain,(
% 25.38/8.68 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X0),domain(X1)))),
% 25.38/8.68 inference(cnf_transformation,[status(thm)],[f17])).
% 25.38/8.68 fof(f40,plain,(
% 25.38/8.68 (?[X0,X1]: ~domain(multiplication(domain(X0),domain(X1)))=multiplication(domain(X0),domain(X1)))),
% 25.38/8.68 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 25.38/8.68 fof(f41,plain,(
% 25.38/8.68 ~domain(multiplication(domain(sK0_skl),domain(sK1_skl)))=multiplication(domain(sK0_skl),domain(sK1_skl))),
% 25.38/8.68 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f40])).
% 25.38/8.68 fof(f42,plain,(
% 25.38/8.68 ~domain(multiplication(domain(sK0_skl),domain(sK1_skl)))=multiplication(domain(sK0_skl),domain(sK1_skl))),
% 25.38/8.69 inference(cnf_transformation,[status(thm)],[f41])).
% 25.38/8.69 fof(f43,plain,(
% 25.38/8.69 ~domain(multiplication(domain(sK0_skl),sK1_skl))=multiplication(domain(sK0_skl),domain(sK1_skl))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f36,f42])).
% 25.38/8.69 fof(f71,plain,(
% 25.38/8.69 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f20,f21])).
% 25.38/8.69 fof(f160,plain,(
% 25.38/8.69 ![X0]: (domain(multiplication(one,X0))=domain(domain(X0)))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f26,f36])).
% 25.38/8.69 fof(f164,plain,(
% 25.38/8.69 ![X0]: (domain(X0)=domain(domain(X0)))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f26,f160])).
% 25.38/8.69 fof(f208,plain,(
% 25.38/8.69 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X1,X0))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f23,f71])).
% 25.38/8.69 fof(f338,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f25,f27])).
% 25.38/8.69 fof(f343,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f25,f27])).
% 25.38/8.69 fof(f1142,plain,(
% 25.38/8.69 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X1,X2),multiplication(X0,X2)))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f20,f28])).
% 25.38/8.69 fof(f1152,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(addition(X0,one),X1)=addition(multiplication(X0,X1),X1))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f26,f28])).
% 25.38/8.69 fof(f2056,plain,(
% 25.38/8.69 ![X0]: (addition(X0,multiplication(domain(X0),X0))=addition(multiplication(domain(X0),X0),X0))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f35,f208])).
% 25.38/8.69 fof(f2072,plain,(
% 25.38/8.69 ![X0]: (multiplication(domain(X0),X0)=addition(multiplication(domain(X0),X0),X0))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f35,f2056])).
% 25.38/8.69 fof(f2094,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(X0,multiplication(X0,X1)))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f20,f338])).
% 25.38/8.69 fof(f2512,plain,(
% 25.38/8.69 ![X0]: (multiplication(domain(X0),X0)=multiplication(addition(domain(X0),one),X0))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f1152,f2072])).
% 25.38/8.69 fof(f2563,plain,(
% 25.38/8.69 ![X0]: (multiplication(domain(X0),X0)=multiplication(one,X0))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f37,f2512])).
% 25.38/8.69 fof(f2575,plain,(
% 25.38/8.69 ![X0]: (multiplication(domain(X0),X0)=X0)),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f26,f2563])).
% 25.38/8.69 fof(f2787,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(addition(X0,domain(X1)),X1)=addition(multiplication(X0,X1),X1))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f2575,f28])).
% 25.38/8.69 fof(f2790,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(domain(X0),addition(X0,X1))=addition(X0,multiplication(domain(X0),X1)))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f2575,f27])).
% 25.38/8.69 fof(f3207,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(X0,one)=addition(X0,multiplication(X0,domain(X1))))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f37,f2094])).
% 25.38/8.69 fof(f3208,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(one,X0)=addition(multiplication(domain(X1),X0),X0))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f37,f1152])).
% 25.38/8.69 fof(f3209,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(X0,one)=addition(multiplication(X0,domain(X1)),X0))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f37,f343])).
% 25.38/8.69 fof(f3232,plain,(
% 25.38/8.69 ![X0,X1]: (X0=addition(X0,multiplication(X0,domain(X1))))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f25,f3207])).
% 25.38/8.69 fof(f3233,plain,(
% 25.38/8.69 ![X0,X1]: (X0=addition(multiplication(domain(X1),X0),X0))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f26,f3208])).
% 25.38/8.69 fof(f3234,plain,(
% 25.38/8.69 ![X0,X1]: (X0=addition(multiplication(X0,domain(X1)),X0))),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f25,f3209])).
% 25.38/8.69 fof(f4343,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(domain(addition(X0,X1)),X1)=addition(multiplication(domain(X0),X1),X1))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f39,f2787])).
% 25.38/8.69 fof(f4398,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(domain(addition(X0,X1)),X1)=X1)),
% 25.38/8.69 inference(forward_demodulation,[status(thm)],[f3233,f4343])).
% 25.38/8.69 fof(f4497,plain,(
% 25.38/8.69 ![X0,X1]: (multiplication(domain(domain(addition(X0,X1))),domain(X1))=domain(X1))),
% 25.38/8.69 inference(paramodulation,[status(thm)],[f39,f4398])).
% 22.10/8.73 fof(f4560,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(addition(X0,X1)),domain(X1))=domain(X1))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f164,f4497])).
% 22.10/8.73 fof(f4721,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(X0,domain(X1))))=domain(multiplication(X0,domain(X1))))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f3232,f4560])).
% 22.10/8.73 fof(f4777,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(X0,X1)))=domain(multiplication(X0,domain(X1))))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f36,f4721])).
% 22.10/8.73 fof(f4778,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(X0,X1)))=domain(multiplication(X0,X1)))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f36,f4777])).
% 22.10/8.73 fof(f9336,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(multiplication(domain(X0),X1)))=domain(multiplication(domain(X0),X1)))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f164,f4778])).
% 22.10/8.73 fof(f9549,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(domain(X0)),domain(addition(X0,X1)))=addition(domain(X0),multiplication(domain(domain(X0)),domain(X1))))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f39,f2790])).
% 22.10/8.73 fof(f9556,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=addition(multiplication(domain(X0),X1),multiplication(domain(multiplication(domain(X0),X1)),X1)))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f3233,f2790])).
% 22.10/8.73 fof(f9656,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=addition(domain(X0),multiplication(domain(domain(X0)),domain(X1))))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f164,f9549])).
% 22.10/8.73 fof(f9657,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=addition(domain(X0),multiplication(domain(X0),domain(X1))))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f164,f9656])).
% 22.10/8.73 fof(f9658,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(addition(X0,X1)))=domain(X0))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f3232,f9657])).
% 22.10/8.73 fof(f9668,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=multiplication(addition(domain(multiplication(domain(X0),X1)),domain(X0)),X1))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f1142,f9556])).
% 22.10/8.73 fof(f9669,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=multiplication(domain(addition(multiplication(domain(X0),X1),X0)),X1))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f39,f9668])).
% 22.10/8.73 fof(f9848,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),domain(X1))=domain(multiplication(domain(X0),X1)))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f3233,f9658])).
% 22.10/8.73 fof(f18789,plain,(
% 22.10/8.73 ![X0,X1]: (domain(X0)=addition(domain(multiplication(domain(X0),X1)),domain(X0)))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f9336,f3234])).
% 22.10/8.73 fof(f18972,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),X1)),X1)=multiplication(domain(X0),X1))),
% 22.10/8.73 inference(backward_demodulation,[status(thm)],[f18973,f9669])).
% 22.10/8.73 fof(f18973,plain,(
% 22.10/8.73 ![X0,X1]: (domain(X0)=domain(addition(multiplication(domain(X0),X1),X0)))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f39,f18789])).
% 22.10/8.73 fof(f19131,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(multiplication(domain(X0),domain(X1))),domain(X1))=domain(multiplication(domain(X0),domain(X1))))),
% 22.10/8.73 inference(paramodulation,[status(thm)],[f164,f9848])).
% 22.10/8.73 fof(f19312,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(X1))=domain(multiplication(domain(X0),domain(X1))))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f18972,f19131])).
% 22.10/8.73 fof(f19317,plain,(
% 22.10/8.73 ~domain(multiplication(domain(sK0_skl),sK1_skl))=domain(multiplication(domain(sK0_skl),sK1_skl))),
% 22.10/8.73 inference(backward_demodulation,[status(thm)],[f19460,f43])).
% 22.10/8.73 fof(f19460,plain,(
% 22.10/8.73 ![X0,X1]: (multiplication(domain(X0),domain(X1))=domain(multiplication(domain(X0),X1)))),
% 22.10/8.73 inference(forward_demodulation,[status(thm)],[f36,f19312])).
% 22.10/8.73 fof(f19607,plain,(
% 22.10/8.73 $false),
% 22.10/8.73 inference(trivial_equality_resolution,[status(thm)],[f19317])).
% 22.10/8.73 % SZS output end CNFRefutation for theBenchmark.p
% 22.10/8.74 % Elapsed time: 3.349351 seconds
% 22.10/8.74 % CPU time: 26.360323 seconds
% 22.10/8.74 % Total memory used: 312.398 MB
% 22.10/8.74 % Net memory used: 302.148 MB
%------------------------------------------------------------------------------