%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE148+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 : n004.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 12:58:24 PM UTC 2026
% Result : Theorem 7.01s 1.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE148+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n004.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sun Sep 20 22:46:20 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 7.01/1.51 % Refutation found
% 7.01/1.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.01/1.51 % SZS output start CNFRefutation for theBenchmark
% 7.01/1.51 fof(f1,axiom,(
% 7.01/1.51 (! [A,B] : addition(A,B) = addition(B,A) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f2,axiom,(
% 7.01/1.51 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f3,axiom,(
% 7.01/1.51 (! [A] : addition(A,zero) = A )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f4,axiom,(
% 7.01/1.51 (! [A] : addition(A,A) = A )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f5,axiom,(
% 7.01/1.51 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f6,axiom,(
% 7.01/1.51 (! [A] : multiplication(A,one) = A )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f8,axiom,(
% 7.01/1.51 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f10,axiom,(
% 7.01/1.51 (! [A] : multiplication(zero,A) = zero )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f15,axiom,(
% 7.01/1.51 (! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f16,axiom,(
% 7.01/1.51 (! [A,B,C] :( leq(C,addition(multiplication(A,C),B))=> leq(C,multiplication(strong_iteration(A),B)) ) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f18,axiom,(
% 7.01/1.51 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f19,conjecture,(
% 7.01/1.51 (! [X0,X1] :( ( multiplication(X0,X1) = zero=> leq(multiplication(X0,strong_iteration(X1)),X0) )& leq(X0,multiplication(X0,strong_iteration(X1))) ) )),
% 7.01/1.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 7.01/1.51 fof(f20,negated_conjecture,(
% 7.01/1.51 ~((! [X0,X1] :( ( multiplication(X0,X1) = zero=> leq(multiplication(X0,strong_iteration(X1)),X0) )& leq(X0,multiplication(X0,strong_iteration(X1))) ) ))),
% 7.01/1.51 inference(negated_conjecture,[status(cth)],[f19])).
% 7.01/1.51 fof(f21,plain,(
% 7.01/1.51 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f1])).
% 7.01/1.51 fof(f22,plain,(
% 7.01/1.51 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f2])).
% 7.01/1.51 fof(f23,plain,(
% 7.01/1.51 ![X0]: (addition(X0,zero)=X0)),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f3])).
% 7.01/1.51 fof(f24,plain,(
% 7.01/1.51 ![X0]: (addition(X0,X0)=X0)),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f4])).
% 7.01/1.51 fof(f25,plain,(
% 7.01/1.51 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f5])).
% 7.01/1.51 fof(f26,plain,(
% 7.01/1.51 ![X0]: (multiplication(X0,one)=X0)),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f6])).
% 7.01/1.51 fof(f28,plain,(
% 7.01/1.51 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f8])).
% 7.01/1.51 fof(f30,plain,(
% 7.01/1.51 ![X0]: (multiplication(zero,X0)=zero)),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f10])).
% 7.01/1.51 fof(f37,plain,(
% 7.01/1.51 ![X0]: (strong_iteration(X0)=addition(multiplication(X0,strong_iteration(X0)),one))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f15])).
% 7.01/1.51 fof(f38,plain,(
% 7.01/1.51 ![A,B,C]: (~leq(C,addition(multiplication(A,C),B))|leq(C,multiplication(strong_iteration(A),B)))),
% 7.01/1.51 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 7.01/1.51 fof(f39,plain,(
% 7.01/1.51 ![X0,X1,X2]: (~leq(X0,addition(multiplication(X1,X0),X2))|leq(X0,multiplication(strong_iteration(X1),X2)))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f38])).
% 7.01/1.51 fof(f41,plain,(
% 7.01/1.51 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 7.01/1.51 inference(NNF_transformation,[status(thm)],[f18])).
% 7.01/1.51 fof(f42,plain,(
% 7.01/1.51 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 7.01/1.51 inference(miniscoping,[status(thm)],[f41])).
% 7.01/1.51 fof(f43,plain,(
% 7.01/1.51 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f42])).
% 7.01/1.51 fof(f44,plain,(
% 7.01/1.51 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f42])).
% 7.01/1.51 fof(f45,plain,(
% 7.01/1.51 (?[X0,X1]: ((multiplication(X0,X1)=zero&~leq(multiplication(X0,strong_iteration(X1)),X0))|~leq(X0,multiplication(X0,strong_iteration(X1)))))),
% 7.01/1.51 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 7.01/1.51 fof(f46,plain,(
% 7.01/1.51 (?[X0,X1]: (multiplication(X0,X1)=zero&~leq(multiplication(X0,strong_iteration(X1)),X0)))|(?[X0,X1]: ~leq(X0,multiplication(X0,strong_iteration(X1))))),
% 7.01/1.51 inference(miniscoping,[status(thm)],[f45])).
% 7.01/1.51 fof(f47,plain,(
% 7.01/1.51 (multiplication(sK0_skl,sK1_skl)=zero&~leq(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl))|~leq(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl)))),
% 7.01/1.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl)],[f46])).
% 7.01/1.51 fof(f48,plain,(
% 7.01/1.51 multiplication(sK0_skl,sK1_skl)=zero|~leq(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl)))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f47])).
% 7.01/1.51 fof(f49,plain,(
% 7.01/1.51 ~leq(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl)|~leq(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl)))),
% 7.01/1.51 inference(cnf_transformation,[status(thm)],[f47])).
% 7.01/1.51 fof(f86,plain,(
% 7.01/1.51 ![X0]: (leq(X0,X0))),
% 7.01/1.51 inference(resolution,[status(thm)],[f24,f44])).
% 7.01/1.51 fof(f103,plain,(
% 7.01/1.51 ![X0,X1]: (~leq(one,addition(X0,X1))|leq(one,multiplication(strong_iteration(X0),X1)))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f26,f39])).
% 7.01/1.51 fof(f186,plain,(
% 7.01/1.51 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f24,f22])).
% 7.01/1.51 fof(f213,plain,(
% 7.01/1.51 ![X0,X1,X2]: (leq(multiplication(X0,X1),multiplication(X0,X2))|~multiplication(X0,addition(X1,X2))=multiplication(X0,X2))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f28,f44])).
% 7.01/1.51 fof(f399,plain,(
% 7.01/1.51 ![X0,X1]: (leq(X0,addition(X0,X1)))),
% 7.01/1.51 inference(resolution,[status(thm)],[f186,f44])).
% 7.01/1.51 fof(f412,plain,(
% 7.01/1.51 ![X0,X1]: (addition(X0,addition(X1,X0))=addition(X0,X1))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f21,f186])).
% 7.01/1.51 fof(f461,plain,(
% 7.01/1.51 ![X0,X1]: (leq(X0,addition(X1,X0)))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f21,f399])).
% 7.01/1.51 fof(f467,plain,(
% 7.01/1.51 ![X0]: (leq(one,multiplication(strong_iteration(X0),one)))),
% 7.01/1.51 inference(resolution,[status(thm)],[f461,f103])).
% 7.01/1.51 fof(f485,plain,(
% 7.01/1.51 ![X0]: (leq(one,strong_iteration(X0)))),
% 7.01/1.51 inference(forward_demodulation,[status(thm)],[f26,f467])).
% 7.01/1.51 fof(f487,plain,(
% 7.01/1.51 ![X0]: (addition(one,strong_iteration(X0))=strong_iteration(X0))),
% 7.01/1.51 inference(resolution,[status(thm)],[f485,f43])).
% 7.01/1.51 fof(f1374,plain,(
% 7.01/1.51 ![X0]: (addition(one,strong_iteration(X0))=addition(one,multiplication(X0,strong_iteration(X0))))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f37,f412])).
% 7.01/1.51 fof(f1392,plain,(
% 7.01/1.51 ![X0]: (strong_iteration(X0)=addition(one,multiplication(X0,strong_iteration(X0))))),
% 7.01/1.51 inference(forward_demodulation,[status(thm)],[f487,f1374])).
% 7.01/1.51 fof(f1821,plain,(
% 7.01/1.51 ![X0,X1]: (leq(multiplication(X0,one),multiplication(X0,strong_iteration(X1)))|~multiplication(X0,strong_iteration(X1))=multiplication(X0,strong_iteration(X1)))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f487,f213])).
% 7.01/1.51 fof(f1855,plain,(
% 7.01/1.51 ![X0,X1]: (leq(X0,multiplication(X0,strong_iteration(X1)))|~multiplication(X0,strong_iteration(X1))=multiplication(X0,strong_iteration(X1)))),
% 7.01/1.51 inference(forward_demodulation,[status(thm)],[f26,f1821])).
% 7.01/1.51 fof(f1856,plain,(
% 7.01/1.51 ![X0,X1]: (leq(X0,multiplication(X0,strong_iteration(X1))))),
% 7.01/1.51 inference(trivial_equality_resolution,[status(thm)],[f1855])).
% 7.01/1.51 fof(f1876,plain,(
% 7.01/1.51 ~leq(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl)),
% 7.01/1.51 inference(backward_subsumption_resolution,[status(thm)],[f49,f1856])).
% 7.01/1.51 fof(f1877,plain,(
% 7.01/1.51 multiplication(sK0_skl,sK1_skl)=zero),
% 7.01/1.51 inference(backward_subsumption_resolution,[status(thm)],[f48,f1856])).
% 7.01/1.51 fof(f1898,plain,(
% 7.01/1.51 ![X0]: (multiplication(sK0_skl,multiplication(sK1_skl,X0))=multiplication(zero,X0))),
% 7.01/1.51 inference(paramodulation,[status(thm)],[f1877,f25])).
% 7.01/1.51 fof(f1913,plain,(
% 7.01/1.51 ![X0]: (multiplication(sK0_skl,multiplication(sK1_skl,X0))=zero)),
% 7.01/1.53 inference(forward_demodulation,[status(thm)],[f30,f1898])).
% 7.01/1.53 fof(f2116,plain,(
% 7.01/1.53 ![X0,X1]: (multiplication(sK0_skl,addition(X0,multiplication(sK1_skl,X1)))=addition(multiplication(sK0_skl,X0),zero))),
% 7.01/1.53 inference(paramodulation,[status(thm)],[f1913,f28])).
% 7.01/1.53 fof(f2138,plain,(
% 7.01/1.53 ![X0,X1]: (multiplication(sK0_skl,addition(X0,multiplication(sK1_skl,X1)))=multiplication(sK0_skl,X0))),
% 7.01/1.53 inference(forward_demodulation,[status(thm)],[f23,f2116])).
% 7.01/1.53 fof(f16211,plain,(
% 7.01/1.53 multiplication(sK0_skl,strong_iteration(sK1_skl))=multiplication(sK0_skl,one)),
% 7.01/1.53 inference(paramodulation,[status(thm)],[f1392,f2138])).
% 7.01/1.53 fof(f16297,plain,(
% 7.01/1.53 multiplication(sK0_skl,strong_iteration(sK1_skl))=sK0_skl),
% 7.01/1.53 inference(forward_demodulation,[status(thm)],[f26,f16211])).
% 7.01/1.53 fof(f16333,plain,(
% 7.01/1.53 ~leq(sK0_skl,sK0_skl)),
% 7.01/1.53 inference(backward_demodulation,[status(thm)],[f16297,f1876])).
% 7.01/1.53 fof(f16386,plain,(
% 7.01/1.53 $false),
% 7.01/1.53 inference(forward_subsumption_resolution,[status(thm)],[f16333,f86])).
% 7.01/1.53 % SZS output end CNFRefutation for theBenchmark.p
% 7.01/1.55 % Elapsed time: 0.966262 seconds
% 7.01/1.55 % CPU time: 7.383321 seconds
% 7.01/1.55 % Total memory used: 148.058 MB
% 7.01/1.55 % Net memory used: 143.549 MB
%------------------------------------------------------------------------------