%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE064+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 12:58:16 PM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE064+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
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:44:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.15/0.52 % Refutation found
% 0.15/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.52 fof(f1,axiom,(
% 0.15/0.52 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f2,axiom,(
% 0.15/0.52 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f4,axiom,(
% 0.15/0.52 (! [A] : addition(A,A) = A )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f9,axiom,(
% 0.15/0.52 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f12,axiom,(
% 0.15/0.52 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f13,axiom,(
% 0.15/0.52 (! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f17,axiom,(
% 0.15/0.52 (! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f18,conjecture,(
% 0.15/0.52 (! [X0,X1] :( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)<= addition(domain(X0),domain(X1)) = domain(X1) ) )),
% 0.15/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.15/0.52 fof(f19,negated_conjecture,(
% 0.15/0.52 ~((! [X0,X1] :( addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0)<= addition(domain(X0),domain(X1)) = domain(X1) ) ))),
% 0.15/0.52 inference(negated_conjecture,[status(cth)],[f18])).
% 0.15/0.52 fof(f20,plain,(
% 0.15/0.52 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f1])).
% 0.15/0.52 fof(f21,plain,(
% 0.15/0.52 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f2])).
% 0.15/0.52 fof(f23,plain,(
% 0.15/0.52 ![X0]: (addition(X0,X0)=X0)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f4])).
% 0.15/0.52 fof(f28,plain,(
% 0.15/0.52 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f9])).
% 0.15/0.52 fof(f31,plain,(
% 0.15/0.52 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.15/0.52 inference(NNF_transformation,[status(thm)],[f12])).
% 0.15/0.52 fof(f32,plain,(
% 0.15/0.52 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.15/0.52 inference(miniscoping,[status(thm)],[f31])).
% 0.15/0.52 fof(f33,plain,(
% 0.15/0.52 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f32])).
% 0.15/0.52 fof(f34,plain,(
% 0.15/0.52 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f32])).
% 0.15/0.52 fof(f35,plain,(
% 0.15/0.52 ![X0]: (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f13])).
% 0.15/0.52 fof(f39,plain,(
% 0.15/0.52 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X0),domain(X1)))),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f17])).
% 0.15/0.52 fof(f40,plain,(
% 0.15/0.52 (?[X0,X1]: (~addition(X0,multiplication(domain(X1),X0))=multiplication(domain(X1),X0)&addition(domain(X0),domain(X1))=domain(X1)))),
% 0.15/0.52 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.15/0.52 fof(f41,plain,(
% 0.15/0.52 (~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))),
% 0.15/0.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f40])).
% 0.15/0.52 fof(f42,plain,(
% 0.15/0.52 ~addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl))=multiplication(domain(sK1_skl),sK0_skl)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f41])).
% 0.15/0.52 fof(f43,plain,(
% 0.15/0.52 addition(domain(sK0_skl),domain(sK1_skl))=domain(sK1_skl)),
% 0.15/0.52 inference(cnf_transformation,[status(thm)],[f41])).
% 0.15/0.52 fof(f48,plain,(
% 0.15/0.52 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(X2,addition(X0,X1)))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f20,f21])).
% 0.15/0.52 fof(f55,plain,(
% 0.15/0.52 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f23,f21])).
% 0.15/0.52 fof(f156,plain,(
% 0.15/0.52 domain(addition(sK0_skl,sK1_skl))=domain(sK1_skl)),
% 0.15/0.52 inference(backward_demodulation,[status(thm)],[f39,f43])).
% 0.15/0.52 fof(f157,plain,(
% 0.15/0.52 ![X0,X1]: (domain(addition(X0,X1))=addition(domain(X1),domain(X0)))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f20,f39])).
% 0.15/0.52 fof(f619,plain,(
% 0.15/0.52 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 0.15/0.52 inference(resolution,[status(thm)],[f34,f55])).
% 0.15/0.52 fof(f807,plain,(
% 0.15/0.52 ![X0,X1,X2]: (leq(X0,addition(X1,addition(X0,X2))))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f48,f619])).
% 0.15/0.52 fof(f1129,plain,(
% 0.15/0.52 ![X0,X1]: (leq(X0,addition(X1,multiplication(domain(X0),X0))))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f35,f807])).
% 0.15/0.52 fof(f2283,plain,(
% 0.15/0.52 ![X0,X1]: (leq(X0,multiplication(addition(X1,domain(X0)),X0)))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f28,f1129])).
% 0.15/0.52 fof(f2956,plain,(
% 0.15/0.52 ![X0,X1]: (leq(X0,multiplication(domain(addition(X0,X1)),X0)))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f157,f2283])).
% 0.15/0.52 fof(f3187,plain,(
% 0.15/0.52 leq(sK0_skl,multiplication(domain(sK1_skl),sK0_skl))),
% 0.15/0.52 inference(paramodulation,[status(thm)],[f156,f2956])).
% 0.15/0.52 fof(f3402,plain,(
% 0.15/0.52 addition(sK0_skl,multiplication(domain(sK1_skl),sK0_skl))=multiplication(domain(sK1_skl),sK0_skl)),
% 0.15/0.52 inference(resolution,[status(thm)],[f3187,f33])).
% 0.15/0.52 fof(f3403,plain,(
% 0.15/0.52 $false),
% 0.15/0.52 inference(forward_subsumption_resolution,[status(thm)],[f3402,f42])).
% 0.15/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.55 % Elapsed time: 0.175678 seconds
% 0.15/0.55 % CPU time: 1.137541 seconds
% 0.15/0.55 % Total memory used: 77.875 MB
% 0.15/0.55 % Net memory used: 77.394 MB
%------------------------------------------------------------------------------