%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE141+2 : 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 : n001.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 12:58:23 PM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE141+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:51:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.41 fof(f2,axiom,(
% 0.10/0.41 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f4,axiom,(
% 0.10/0.41 (! [A] : addition(A,A) = A )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f6,axiom,(
% 0.10/0.41 (! [A] : multiplication(A,one) = A )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f7,axiom,(
% 0.10/0.41 (! [A] : multiplication(one,A) = A )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f16,axiom,(
% 0.10/0.41 (! [A,B,C] :( leq(C,addition(multiplication(A,C),B))=> leq(C,multiplication(strong_iteration(A),B)) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f18,axiom,(
% 0.10/0.41 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f19,conjecture,(
% 0.10/0.41 (! [X0] :( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))& leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ) )),
% 0.10/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.41 fof(f20,negated_conjecture,(
% 0.10/0.41 ~((! [X0] :( leq(multiplication(strong_iteration(one),X0),strong_iteration(one))& leq(strong_iteration(one),multiplication(strong_iteration(one),X0)) ) ))),
% 0.10/0.41 inference(negated_conjecture,[status(cth)],[f19])).
% 0.10/0.41 fof(f22,plain,(
% 0.10/0.41 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.41 fof(f24,plain,(
% 0.10/0.41 ![X0]: (addition(X0,X0)=X0)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.41 fof(f26,plain,(
% 0.10/0.41 ![X0]: (multiplication(X0,one)=X0)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.41 fof(f27,plain,(
% 0.10/0.41 ![X0]: (multiplication(one,X0)=X0)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.41 fof(f38,plain,(
% 0.10/0.41 ![A,B,C]: (~leq(C,addition(multiplication(A,C),B))|leq(C,multiplication(strong_iteration(A),B)))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.10/0.41 fof(f39,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),X2))|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f38])).
% 0.10/0.41 fof(f41,plain,(
% 0.10/0.41 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.10/0.41 inference(NNF_transformation,[status(thm)],[f18])).
% 0.10/0.41 fof(f42,plain,(
% 0.10/0.41 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.10/0.41 inference(miniscoping,[status(thm)],[f41])).
% 0.10/0.41 fof(f44,plain,(
% 0.10/0.41 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f42])).
% 0.10/0.41 fof(f45,plain,(
% 0.10/0.41 (?[X0]: (~leq(multiplication(strong_iteration(one),X0),strong_iteration(one))|~leq(strong_iteration(one),multiplication(strong_iteration(one),X0))))),
% 0.10/0.41 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.10/0.41 fof(f46,plain,(
% 0.10/0.41 (?[X0]: ~leq(multiplication(strong_iteration(one),X0),strong_iteration(one)))|(?[X0]: ~leq(strong_iteration(one),multiplication(strong_iteration(one),X0)))),
% 0.10/0.41 inference(miniscoping,[status(thm)],[f45])).
% 0.10/0.41 fof(f47,plain,(
% 0.10/0.41 ~leq(multiplication(strong_iteration(one),sK0_skl),strong_iteration(one))|~leq(strong_iteration(one),multiplication(strong_iteration(one),sK1_skl))),
% 0.10/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46])).
% 0.10/0.41 fof(f48,plain,(
% 0.10/0.41 ~leq(multiplication(strong_iteration(one),sK0_skl),strong_iteration(one))|~leq(strong_iteration(one),multiplication(strong_iteration(one),sK1_skl))),
% 0.10/0.41 inference(cnf_transformation,[status(thm)],[f47])).
% 0.10/0.41 fof(f64,plain,(
% 0.10/0.41 ![X0,X1]: (~leq(X0,addition(X0,X1))|leq(X0,multiplication(strong_iteration(one),X1)))),
% 0.10/0.41 inference(paramodulation,[status(thm)],[f27,f39])).
% 0.10/0.41 fof(f312,plain,(
% 0.10/0.41 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.10/0.41 inference(paramodulation,[status(thm)],[f24,f22])).
% 0.10/0.41 fof(f439,plain,(
% 0.10/0.41 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 0.10/0.41 inference(resolution,[status(thm)],[f312,f44])).
% 0.10/0.41 fof(f485,plain,(
% 0.10/0.41 ![X0,X1]: (leq(X0,multiplication(strong_iteration(one),X1)))),
% 0.10/0.41 inference(backward_subsumption_resolution,[status(thm)],[f64,f439])).
% 0.10/0.41 fof(f544,plain,(
% 0.10/0.41 ~leq(multiplication(strong_iteration(one),sK0_skl),strong_iteration(one))),
% 0.10/0.41 inference(backward_subsumption_resolution,[status(thm)],[f48,f485])).
% 0.10/0.41 fof(f548,plain,(
% 0.10/0.41 ![X0]: (leq(X0,strong_iteration(one)))),
% 0.10/0.41 inference(paramodulation,[status(thm)],[f26,f485])).
% 0.10/0.41 fof(f661,plain,(
% 0.10/0.41 $false),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f544,f548])).
% 0.10/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.064563 seconds
% 0.10/0.43 % CPU time: 0.254103 seconds
% 0.10/0.43 % Total memory used: 69.600 MB
% 0.10/0.43 % Net memory used: 69.165 MB
%------------------------------------------------------------------------------