%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE007+2 : 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 : n012.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 12:58:09 PM UTC 2026
% Result : Theorem 0.08s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE007+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.51 % Computer : n012.cluster.edu
% 0.04/0.51 % Model : x86_64 x86_64
% 0.04/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.51 % Memory : 8046.5625MB
% 0.04/0.51 % OS : Linux 6.8.0-71-generic
% 0.04/0.51 % CPULimit : 300
% 0.04/0.51 % WCLimit : 300
% 0.04/0.51 % DateTime : Sun Sep 20 22:37:52 UTC 2026
% 0.04/0.51 % CPUTime :
% 0.04/0.52 % Drodi V4.1.1
% 0.08/0.53 % Refutation found
% 0.08/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.53 fof(f1,axiom,(
% 0.08/0.53 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f4,axiom,(
% 0.08/0.53 (! [A] : addition(A,A) = A )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f7,axiom,(
% 0.08/0.53 (! [A] : multiplication(one,A) = A )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f8,axiom,(
% 0.08/0.53 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f12,axiom,(
% 0.08/0.53 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f14,axiom,(
% 0.08/0.53 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f15,axiom,(
% 0.08/0.53 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f17,conjecture,(
% 0.08/0.53 (! [X0,X1] :( ( test(X1)& test(X0) )=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ) )),
% 0.08/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.53 fof(f18,negated_conjecture,(
% 0.08/0.53 ~((! [X0,X1] :( ( test(X1)& test(X0) )=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ) ))),
% 0.08/0.53 inference(negated_conjecture,[status(cth)],[f17])).
% 0.08/0.53 fof(f19,plain,(
% 0.08/0.53 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.53 fof(f22,plain,(
% 0.08/0.53 ![X0]: (addition(X0,X0)=X0)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f4])).
% 0.08/0.53 fof(f25,plain,(
% 0.08/0.53 ![X0]: (multiplication(one,X0)=X0)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.53 fof(f26,plain,(
% 0.08/0.53 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f8])).
% 0.08/0.53 fof(f30,plain,(
% 0.08/0.53 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.08/0.53 inference(NNF_transformation,[status(thm)],[f12])).
% 0.08/0.53 fof(f31,plain,(
% 0.08/0.53 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.08/0.53 inference(miniscoping,[status(thm)],[f30])).
% 0.08/0.53 fof(f33,plain,(
% 0.08/0.53 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f31])).
% 0.08/0.53 fof(f39,plain,(
% 0.08/0.53 ![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)))),
% 0.08/0.53 inference(NNF_transformation,[status(thm)],[f14])).
% 0.08/0.53 fof(f40,plain,(
% 0.08/0.53 (![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)))),
% 0.08/0.53 inference(miniscoping,[status(thm)],[f39])).
% 0.08/0.53 fof(f43,plain,(
% 0.08/0.53 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f40])).
% 0.08/0.53 fof(f45,plain,(
% 0.08/0.53 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.08/0.53 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.08/0.53 fof(f46,plain,(
% 0.08/0.53 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.08/0.53 inference(NNF_transformation,[status(thm)],[f45])).
% 0.08/0.53 fof(f47,plain,(
% 0.08/0.53 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.08/0.53 inference(miniscoping,[status(thm)],[f46])).
% 0.08/0.53 fof(f48,plain,(
% 0.08/0.53 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f47])).
% 0.08/0.53 fof(f52,plain,(
% 0.08/0.53 (?[X0,X1]: ((test(X1)&test(X0))&(~leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))|~leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one))))),
% 0.08/0.53 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.08/0.53 fof(f53,plain,(
% 0.08/0.53 ((test(sK2_skl)&test(sK1_skl))&(~leq(one,addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))))|~leq(addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))),one)))),
% 0.08/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl)],[f52])).
% 0.08/0.53 fof(f54,plain,(
% 0.08/0.53 test(sK2_skl)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f53])).
% 0.08/0.53 fof(f55,plain,(
% 0.08/0.53 test(sK1_skl)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f53])).
% 0.08/0.53 fof(f56,plain,(
% 0.08/0.53 ~leq(one,addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))))|~leq(addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))),one)),
% 0.08/0.53 inference(cnf_transformation,[status(thm)],[f53])).
% 0.08/0.53 fof(f57,plain,(
% 0.08/0.53 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 0.08/0.53 inference(destructive_equality_resolution,[status(thm)],[f48])).
% 0.08/0.53 fof(f58,plain,(
% 0.08/0.53 ~leq(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))|~leq(addition(multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl),multiplication(addition(sK1_skl,c(sK1_skl)),c(sK2_skl))),one)),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f26,f56])).
% 0.08/0.53 fof(f59,plain,(
% 0.08/0.53 ~leq(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))|~leq(multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))),one)),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f26,f58])).
% 0.08/0.53 fof(f178,plain,(
% 0.08/0.53 ~addition(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))=multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))|~leq(multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))),one)),
% 0.08/0.53 inference(resolution,[status(thm)],[f33,f59])).
% 0.08/0.53 fof(f180,plain,(
% 0.08/0.53 ~addition(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))=multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))|~addition(multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))),one)=one),
% 0.08/0.53 inference(resolution,[status(thm)],[f178,f33])).
% 0.08/0.53 fof(f181,plain,(
% 0.08/0.53 ~addition(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))=multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))|~addition(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))=one),
% 0.08/0.53 inference(paramodulation,[status(thm)],[f19,f180])).
% 0.08/0.53 fof(f184,plain,(
% 0.08/0.53 ![X0]: (addition(c(X0),X0)=one|~test(X0))),
% 0.08/0.53 inference(resolution,[status(thm)],[f43,f57])).
% 0.08/0.53 fof(f312,plain,(
% 0.08/0.53 addition(c(sK1_skl),sK1_skl)=one),
% 0.08/0.53 inference(resolution,[status(thm)],[f184,f55])).
% 0.08/0.53 fof(f313,plain,(
% 0.08/0.53 addition(c(sK2_skl),sK2_skl)=one),
% 0.08/0.53 inference(resolution,[status(thm)],[f184,f54])).
% 0.08/0.53 fof(f315,plain,(
% 0.08/0.53 addition(sK1_skl,c(sK1_skl))=one),
% 0.08/0.53 inference(paramodulation,[status(thm)],[f19,f312])).
% 0.08/0.53 fof(f326,plain,(
% 0.08/0.53 ~addition(one,multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl))))=multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))|~addition(one,multiplication(one,addition(sK2_skl,c(sK2_skl))))=one),
% 0.08/0.53 inference(backward_demodulation,[status(thm)],[f315,f181])).
% 0.08/0.53 fof(f342,plain,(
% 0.08/0.53 ~addition(one,multiplication(one,addition(sK2_skl,c(sK2_skl))))=multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))|~addition(one,multiplication(one,addition(sK2_skl,c(sK2_skl))))=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f315,f326])).
% 0.08/0.53 fof(f343,plain,(
% 0.08/0.53 ~addition(one,addition(sK2_skl,c(sK2_skl)))=multiplication(addition(sK1_skl,c(sK1_skl)),addition(sK2_skl,c(sK2_skl)))|~addition(one,multiplication(one,addition(sK2_skl,c(sK2_skl))))=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f25,f342])).
% 0.08/0.53 fof(f344,plain,(
% 0.08/0.53 ~addition(one,addition(sK2_skl,c(sK2_skl)))=multiplication(one,addition(sK2_skl,c(sK2_skl)))|~addition(one,multiplication(one,addition(sK2_skl,c(sK2_skl))))=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f315,f343])).
% 0.08/0.53 fof(f345,plain,(
% 0.08/0.53 ~addition(one,addition(sK2_skl,c(sK2_skl)))=addition(sK2_skl,c(sK2_skl))|~addition(one,multiplication(one,addition(sK2_skl,c(sK2_skl))))=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f25,f344])).
% 0.08/0.53 fof(f346,plain,(
% 0.08/0.53 ~addition(one,addition(sK2_skl,c(sK2_skl)))=addition(sK2_skl,c(sK2_skl))|~addition(one,addition(sK2_skl,c(sK2_skl)))=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f25,f345])).
% 0.08/0.53 fof(f464,plain,(
% 0.08/0.53 addition(sK2_skl,c(sK2_skl))=one),
% 0.08/0.53 inference(paramodulation,[status(thm)],[f19,f313])).
% 0.08/0.53 fof(f474,plain,(
% 0.08/0.53 ~addition(one,addition(sK2_skl,c(sK2_skl)))=addition(sK2_skl,c(sK2_skl))|~addition(one,one)=one),
% 0.08/0.53 inference(backward_demodulation,[status(thm)],[f464,f346])).
% 0.08/0.53 fof(f480,plain,(
% 0.08/0.53 ~addition(one,one)=addition(sK2_skl,c(sK2_skl))|~addition(one,one)=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f464,f474])).
% 0.08/0.53 fof(f481,plain,(
% 0.08/0.53 ~one=addition(sK2_skl,c(sK2_skl))|~addition(one,one)=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f22,f480])).
% 0.08/0.53 fof(f482,plain,(
% 0.08/0.53 ~one=one|~addition(one,one)=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f464,f481])).
% 0.08/0.53 fof(f483,plain,(
% 0.08/0.53 ~one=one|~one=one),
% 0.08/0.53 inference(forward_demodulation,[status(thm)],[f22,f482])).
% 0.08/0.53 fof(f484,plain,(
% 0.08/0.53 ~one=one),
% 0.08/0.53 inference(duplicate_literals_removal,[status(thm)],[f483])).
% 0.08/0.53 fof(f485,plain,(
% 0.08/0.53 $false),
% 0.08/0.53 inference(trivial_equality_resolution,[status(thm)],[f484])).
% 0.08/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.54 % Elapsed time: 0.026591 seconds
% 0.08/0.54 % CPU time: 0.087292 seconds
% 0.08/0.54 % Total memory used: 27.502 MB
% 0.08/0.54 % Net memory used: 27.389 MB
%------------------------------------------------------------------------------