%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE022+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 : 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 12:58:11 PM UTC 2026
% Result : Theorem 0.02s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE022+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
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:39:05 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.02/0.40 % Refutation found
% 0.02/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.02/0.40 fof(f1,axiom,(
% 0.02/0.40 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f4,axiom,(
% 0.02/0.40 (! [A] : addition(A,A) = A )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f6,axiom,(
% 0.02/0.40 (! [A] : multiplication(A,one) = A )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f8,axiom,(
% 0.02/0.40 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f12,axiom,(
% 0.02/0.40 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f14,axiom,(
% 0.02/0.40 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f15,axiom,(
% 0.02/0.40 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f17,conjecture,(
% 0.02/0.40 (! [X0,X1] :( test(X1)=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ) )),
% 0.02/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.02/0.40 fof(f18,negated_conjecture,(
% 0.02/0.40 ~((! [X0,X1] :( test(X1)=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ) ))),
% 0.02/0.40 inference(negated_conjecture,[status(cth)],[f17])).
% 0.02/0.40 fof(f19,plain,(
% 0.02/0.40 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.02/0.40 fof(f22,plain,(
% 0.02/0.40 ![X0]: (addition(X0,X0)=X0)),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.02/0.40 fof(f24,plain,(
% 0.02/0.40 ![X0]: (multiplication(X0,one)=X0)),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.02/0.40 fof(f26,plain,(
% 0.02/0.40 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.02/0.40 fof(f30,plain,(
% 0.02/0.40 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.02/0.40 inference(NNF_transformation,[status(thm)],[f12])).
% 0.02/0.40 fof(f31,plain,(
% 0.02/0.40 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.02/0.40 inference(miniscoping,[status(thm)],[f30])).
% 0.02/0.40 fof(f33,plain,(
% 0.02/0.40 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f31])).
% 0.02/0.40 fof(f39,plain,(
% 0.02/0.40 ![X0,X1]: ((~complement(X1,X0)|((multiplication(X0,X1)=zero&multiplication(X1,X0)=zero)&addition(X0,X1)=one))&(complement(X1,X0)|((~multiplication(X0,X1)=zero|~multiplication(X1,X0)=zero)|~addition(X0,X1)=one)))),
% 0.02/0.40 inference(NNF_transformation,[status(thm)],[f14])).
% 0.02/0.40 fof(f40,plain,(
% 0.02/0.40 (![X0,X1]: (~complement(X1,X0)|((multiplication(X0,X1)=zero&multiplication(X1,X0)=zero)&addition(X0,X1)=one)))&(![X0,X1]: (complement(X1,X0)|((~multiplication(X0,X1)=zero|~multiplication(X1,X0)=zero)|~addition(X0,X1)=one)))),
% 0.02/0.40 inference(miniscoping,[status(thm)],[f39])).
% 0.02/0.40 fof(f43,plain,(
% 0.02/0.40 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f40])).
% 0.02/0.40 fof(f45,plain,(
% 0.02/0.40 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.02/0.40 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.02/0.40 fof(f46,plain,(
% 0.02/0.40 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.02/0.40 inference(NNF_transformation,[status(thm)],[f45])).
% 0.02/0.40 fof(f47,plain,(
% 0.02/0.40 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.02/0.40 inference(miniscoping,[status(thm)],[f46])).
% 0.02/0.40 fof(f48,plain,(
% 0.02/0.40 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 0.02/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.02/0.40 fof(f52,plain,(
% 0.02/0.40 (?[X0,X1]: (test(X1)&(~leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))|~leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))))),
% 0.02/0.40 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.02/0.40 fof(f53,plain,(
% 0.02/0.40 ?[X1]: (test(X1)&((?[X0]: ~leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))))|(?[X0]: ~leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))))),
% 0.02/0.41 inference(miniscoping,[status(thm)],[f52])).
% 0.02/0.41 fof(f54,plain,(
% 0.02/0.41 (test(sK1_skl)&(~leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl))))|~leq(addition(multiplication(sK3_skl,sK1_skl),multiplication(sK3_skl,c(sK1_skl))),sK3_skl)))),
% 0.02/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X0,sK3_skl)],[f53])).
% 0.02/0.41 fof(f55,plain,(
% 0.02/0.41 test(sK1_skl)),
% 0.02/0.41 inference(cnf_transformation,[status(thm)],[f54])).
% 0.02/0.41 fof(f56,plain,(
% 0.02/0.41 ~leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl))))|~leq(addition(multiplication(sK3_skl,sK1_skl),multiplication(sK3_skl,c(sK1_skl))),sK3_skl)),
% 0.02/0.41 inference(cnf_transformation,[status(thm)],[f54])).
% 0.02/0.41 fof(f57,plain,(
% 0.02/0.41 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 0.02/0.41 inference(destructive_equality_resolution,[status(thm)],[f48])).
% 0.02/0.41 fof(f77,plain,(
% 0.02/0.41 ~leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl))))|~leq(multiplication(sK3_skl,addition(sK1_skl,c(sK1_skl))),sK3_skl)),
% 0.02/0.41 inference(backward_demodulation,[status(thm)],[f26,f56])).
% 0.02/0.41 fof(f87,plain,(
% 0.02/0.41 ~leq(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))|~leq(multiplication(sK3_skl,addition(sK1_skl,c(sK1_skl))),sK3_skl)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f26,f77])).
% 0.02/0.41 fof(f169,plain,(
% 0.02/0.41 ~leq(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))|~addition(multiplication(sK3_skl,addition(sK1_skl,c(sK1_skl))),sK3_skl)=sK3_skl),
% 0.02/0.41 inference(resolution,[status(thm)],[f87,f33])).
% 0.02/0.41 fof(f170,plain,(
% 0.02/0.41 ~addition(multiplication(sK3_skl,addition(sK1_skl,c(sK1_skl))),sK3_skl)=sK3_skl|~addition(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))=multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl)))),
% 0.02/0.41 inference(resolution,[status(thm)],[f169,f33])).
% 0.02/0.41 fof(f180,plain,(
% 0.02/0.41 complement(sK1_skl,c(sK1_skl))),
% 0.02/0.41 inference(resolution,[status(thm)],[f57,f55])).
% 0.02/0.41 fof(f232,plain,(
% 0.02/0.41 addition(c(sK1_skl),sK1_skl)=one),
% 0.02/0.41 inference(resolution,[status(thm)],[f43,f180])).
% 0.02/0.41 fof(f492,plain,(
% 0.02/0.41 addition(sK1_skl,c(sK1_skl))=one),
% 0.02/0.41 inference(paramodulation,[status(thm)],[f19,f232])).
% 0.02/0.41 fof(f742,plain,(
% 0.02/0.41 ~addition(multiplication(sK3_skl,addition(sK1_skl,c(sK1_skl))),sK3_skl)=sK3_skl|~addition(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(backward_demodulation,[status(thm)],[f492,f170])).
% 0.02/0.41 fof(f751,plain,(
% 0.02/0.41 ~addition(multiplication(sK3_skl,one),sK3_skl)=sK3_skl|~addition(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f492,f742])).
% 0.02/0.41 fof(f752,plain,(
% 0.02/0.41 ~addition(sK3_skl,sK3_skl)=sK3_skl|~addition(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f24,f751])).
% 0.02/0.41 fof(f753,plain,(
% 0.02/0.41 ~sK3_skl=sK3_skl|~addition(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f22,f752])).
% 0.02/0.41 fof(f754,plain,(
% 0.02/0.41 ~sK3_skl=sK3_skl|~addition(sK2_skl,multiplication(sK2_skl,one))=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f492,f753])).
% 0.02/0.41 fof(f755,plain,(
% 0.02/0.41 ~sK3_skl=sK3_skl|~addition(sK2_skl,sK2_skl)=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f24,f754])).
% 0.02/0.41 fof(f756,plain,(
% 0.02/0.41 ~sK3_skl=sK3_skl|~sK2_skl=multiplication(sK2_skl,one)),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f22,f755])).
% 0.02/0.41 fof(f757,plain,(
% 0.02/0.41 ~sK3_skl=sK3_skl|~sK2_skl=sK2_skl),
% 0.02/0.41 inference(forward_demodulation,[status(thm)],[f24,f756])).
% 0.02/0.41 fof(f758,plain,(
% 0.02/0.41 $false),
% 0.02/0.41 inference(trivial_equality_resolution,[status(thm)],[f757])).
% 0.02/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.02/0.43 % Elapsed time: 0.065185 seconds
% 0.02/0.43 % CPU time: 0.265401 seconds
% 0.02/0.43 % Total memory used: 104.835 MB
% 0.02/0.43 % Net memory used: 104.512 MB
%------------------------------------------------------------------------------