%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE063+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 12:58:16 PM UTC 2026
% Result : Theorem 2.57s 0.80s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE063+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
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:42:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 2.57/0.80 % Refutation found
% 2.57/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.57/0.80 % SZS output start CNFRefutation for theBenchmark
% 2.57/0.80 fof(f1,axiom,(
% 2.57/0.80 (! [A,B] : addition(A,B) = addition(B,A) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f2,axiom,(
% 2.57/0.80 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f4,axiom,(
% 2.57/0.80 (! [A] : addition(A,A) = A )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f6,axiom,(
% 2.57/0.80 (! [A] : multiplication(A,one) = A )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f7,axiom,(
% 2.57/0.80 (! [A] : multiplication(one,A) = A )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f8,axiom,(
% 2.57/0.80 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f9,axiom,(
% 2.57/0.80 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f12,axiom,(
% 2.57/0.80 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f14,axiom,(
% 2.57/0.80 (! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f15,axiom,(
% 2.57/0.80 (! [X0] : addition(domain(X0),one) = one )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f17,axiom,(
% 2.57/0.80 (! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f18,conjecture,(
% 2.57/0.80 (! [X0,X1] :( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)=> addition(domain(X0),domain(X1)) = domain(X1) ) )),
% 2.57/0.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 2.57/0.80 fof(f19,negated_conjecture,(
% 2.57/0.80 ~((! [X0,X1] :( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)=> addition(domain(X0),domain(X1)) = domain(X1) ) ))),
% 2.57/0.80 inference(negated_conjecture,[status(cth)],[f18])).
% 2.57/0.80 fof(f20,plain,(
% 2.57/0.80 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f1])).
% 2.57/0.80 fof(f21,plain,(
% 2.57/0.80 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f2])).
% 2.57/0.80 fof(f23,plain,(
% 2.57/0.80 ![X0]: (addition(X0,X0)=X0)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f4])).
% 2.57/0.80 fof(f25,plain,(
% 2.57/0.80 ![X0]: (multiplication(X0,one)=X0)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f6])).
% 2.57/0.80 fof(f26,plain,(
% 2.57/0.80 ![X0]: (multiplication(one,X0)=X0)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f7])).
% 2.57/0.80 fof(f27,plain,(
% 2.57/0.80 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f8])).
% 2.57/0.80 fof(f28,plain,(
% 2.57/0.80 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f9])).
% 2.57/0.80 fof(f31,plain,(
% 2.57/0.80 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 2.57/0.80 inference(NNF_transformation,[status(thm)],[f12])).
% 2.57/0.80 fof(f32,plain,(
% 2.57/0.80 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 2.57/0.80 inference(miniscoping,[status(thm)],[f31])).
% 2.57/0.80 fof(f33,plain,(
% 2.57/0.80 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f32])).
% 2.57/0.80 fof(f34,plain,(
% 2.57/0.80 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f32])).
% 2.57/0.80 fof(f36,plain,(
% 2.57/0.80 ![X0,X1]: (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))))),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f14])).
% 2.57/0.80 fof(f37,plain,(
% 2.57/0.80 ![X0]: (addition(domain(X0),one)=one)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f15])).
% 2.57/0.80 fof(f39,plain,(
% 2.57/0.80 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X0),domain(X1)))),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f17])).
% 2.57/0.80 fof(f40,plain,(
% 2.57/0.80 (?[X0,X1]: (addition(X0,multiplication(domain(X1),X0))=multiplication(domain(X1),X0)&~addition(domain(X0),domain(X1))=domain(X1)))),
% 2.57/0.80 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 2.57/0.80 fof(f41,plain,(
% 2.57/0.80 (addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl))=multiplication(domain(sK1_skl),sK0_skl)&~addition(domain(sK0_skl),domain(sK1_skl))=domain(sK1_skl))),
% 2.57/0.80 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f40])).
% 2.57/0.80 fof(f42,plain,(
% 2.57/0.80 addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl))=multiplication(domain(sK1_skl),sK0_skl)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f41])).
% 2.57/0.80 fof(f43,plain,(
% 2.57/0.80 ~addition(domain(sK0_skl),domain(sK1_skl))=domain(sK1_skl)),
% 2.57/0.80 inference(cnf_transformation,[status(thm)],[f41])).
% 2.57/0.80 fof(f75,plain,(
% 2.57/0.80 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f23,f21])).
% 2.57/0.80 fof(f132,plain,(
% 2.57/0.80 ![X0]: (addition(one,domain(X0))=one)),
% 2.57/0.80 inference(forward_demodulation,[status(thm)],[f20,f37])).
% 2.57/0.80 fof(f143,plain,(
% 2.57/0.80 ![X0,X1]: (multiplication(X0,addition(one,X1))=addition(X0,multiplication(X0,X1)))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f25,f27])).
% 2.57/0.80 fof(f193,plain,(
% 2.57/0.80 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 2.57/0.80 inference(resolution,[status(thm)],[f75,f34])).
% 2.57/0.80 fof(f266,plain,(
% 2.57/0.80 ![X0,X1]: (leq(X0,addition(X1,X0)))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f20,f193])).
% 2.57/0.80 fof(f270,plain,(
% 2.57/0.80 ![X0,X1,X2]: (leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f28,f266])).
% 2.57/0.80 fof(f356,plain,(
% 2.57/0.80 ![X0]: (domain(multiplication(one,X0))=domain(domain(X0)))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f26,f36])).
% 2.57/0.80 fof(f365,plain,(
% 2.57/0.80 ![X0]: (domain(X0)=domain(domain(X0)))),
% 2.57/0.80 inference(forward_demodulation,[status(thm)],[f26,f356])).
% 2.57/0.80 fof(f402,plain,(
% 2.57/0.80 ![X0,X1]: (leq(domain(X0),domain(addition(X1,X0))))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f39,f266])).
% 2.57/0.80 fof(f716,plain,(
% 2.57/0.80 ~domain(addition(sK0_skl,sK1_skl))=domain(sK1_skl)),
% 2.57/0.80 inference(forward_demodulation,[status(thm)],[f39,f43])).
% 2.57/0.80 fof(f3234,plain,(
% 2.57/0.80 ![X0,X1]: (multiplication(X0,one)=addition(X0,multiplication(X0,domain(X1))))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f132,f143])).
% 2.57/0.80 fof(f3300,plain,(
% 2.57/0.80 ![X0,X1]: (X0=addition(X0,multiplication(X0,domain(X1))))),
% 2.57/0.80 inference(forward_demodulation,[status(thm)],[f25,f3234])).
% 2.57/0.80 fof(f3409,plain,(
% 2.57/0.80 ![X0,X1]: (leq(domain(multiplication(X0,domain(X1))),domain(X0)))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f3300,f402])).
% 2.57/0.80 fof(f3451,plain,(
% 2.57/0.80 ![X0,X1]: (leq(domain(multiplication(X0,X1)),domain(X0)))),
% 2.57/0.80 inference(forward_demodulation,[status(thm)],[f36,f3409])).
% 2.57/0.80 fof(f4321,plain,(
% 2.57/0.80 ![X0,X1]: (leq(multiplication(domain(X0),X1),multiplication(one,X1)))),
% 2.57/0.80 inference(paramodulation,[status(thm)],[f132,f270])).
% 2.57/0.80 fof(f4351,plain,(
% 2.57/0.80 ![X0,X1]: (leq(multiplication(domain(X0),X1),X1))),
% 2.57/0.80 inference(forward_demodulation,[status(thm)],[f26,f4321])).
% 2.57/0.80 fof(f4366,plain,(
% 2.57/0.80 ![X0,X1]: (addition(multiplication(domain(X0),X1),X1)=X1)),
% 2.57/0.80 inference(resolution,[status(thm)],[f4351,f33])).
% 2.57/0.80 fof(f4378,plain,(
% 2.57/0.80 ![X0,X1]: (addition(X0,multiplication(domain(X1),X0))=X0)),
% 1.05/0.80 inference(forward_demodulation,[status(thm)],[f20,f4366])).
% 1.05/0.80 fof(f4385,plain,(
% 1.05/0.80 sK0_skl=multiplication(domain(sK1_skl),sK0_skl)),
% 1.05/0.80 inference(backward_demodulation,[status(thm)],[f4378,f42])).
% 1.05/0.80 fof(f4588,plain,(
% 1.05/0.80 leq(domain(sK0_skl),domain(domain(sK1_skl)))),
% 1.05/0.80 inference(paramodulation,[status(thm)],[f4385,f3451])).
% 1.05/0.80 fof(f4602,plain,(
% 1.05/0.80 leq(domain(sK0_skl),domain(sK1_skl))),
% 1.05/0.80 inference(forward_demodulation,[status(thm)],[f365,f4588])).
% 1.05/0.80 fof(f4609,plain,(
% 1.05/0.80 addition(domain(sK0_skl),domain(sK1_skl))=domain(sK1_skl)),
% 1.05/0.80 inference(resolution,[status(thm)],[f4602,f33])).
% 1.05/0.80 fof(f4610,plain,(
% 1.05/0.80 domain(addition(sK0_skl,sK1_skl))=domain(sK1_skl)),
% 1.05/0.80 inference(forward_demodulation,[status(thm)],[f39,f4609])).
% 1.05/0.80 fof(f4611,plain,(
% 1.05/0.80 $false),
% 1.05/0.80 inference(forward_subsumption_resolution,[status(thm)],[f4610,f716])).
% 1.05/0.80 % SZS output end CNFRefutation for theBenchmark.p
% 1.05/0.81 % Elapsed time: 0.427875 seconds
% 1.05/0.81 % CPU time: 3.149255 seconds
% 1.05/0.81 % Total memory used: 100.153 MB
% 1.05/0.81 % Net memory used: 98.493 MB
%------------------------------------------------------------------------------