%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE027+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 12:58:12 PM UTC 2026
% Result : Theorem 4.69s 1.10s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE027+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n026.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sun Sep 20 22:42:06 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 4.69/1.10 % Refutation found
% 4.69/1.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.69/1.10 % SZS output start CNFRefutation for theBenchmark
% 4.69/1.10 fof(f1,axiom,(
% 4.69/1.10 (! [A,B] : addition(A,B) = addition(B,A) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f3,axiom,(
% 4.69/1.10 (! [A] : addition(A,zero) = A )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f5,axiom,(
% 4.69/1.10 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f7,axiom,(
% 4.69/1.10 (! [A] : multiplication(one,A) = A )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f8,axiom,(
% 4.69/1.10 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f9,axiom,(
% 4.69/1.10 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f11,axiom,(
% 4.69/1.10 (! [A] : multiplication(zero,A) = zero )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f14,axiom,(
% 4.69/1.10 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f15,axiom,(
% 4.69/1.10 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f17,conjecture,(
% 4.69/1.10 (! [X0,X1,X2,X3,X4] :( ( test(X3)& test(X4) )=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ) )),
% 4.69/1.10 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 4.69/1.10 fof(f18,negated_conjecture,(
% 4.69/1.10 ~((! [X0,X1,X2,X3,X4] :( ( test(X3)& test(X4) )=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ) ))),
% 4.69/1.10 inference(negated_conjecture,[status(cth)],[f17])).
% 4.69/1.10 fof(f19,plain,(
% 4.69/1.10 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f1])).
% 4.69/1.10 fof(f21,plain,(
% 4.69/1.10 ![X0]: (addition(X0,zero)=X0)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f3])).
% 4.69/1.10 fof(f23,plain,(
% 4.69/1.10 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f5])).
% 4.69/1.10 fof(f25,plain,(
% 4.69/1.10 ![X0]: (multiplication(one,X0)=X0)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f7])).
% 4.69/1.10 fof(f26,plain,(
% 4.69/1.10 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f8])).
% 4.69/1.10 fof(f27,plain,(
% 4.69/1.10 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f9])).
% 4.69/1.10 fof(f29,plain,(
% 4.69/1.10 ![X0]: (multiplication(zero,X0)=zero)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f11])).
% 4.69/1.10 fof(f39,plain,(
% 4.69/1.10 ![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)))),
% 4.69/1.10 inference(NNF_transformation,[status(thm)],[f14])).
% 4.69/1.10 fof(f40,plain,(
% 4.69/1.10 (![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)))),
% 4.69/1.10 inference(miniscoping,[status(thm)],[f39])).
% 4.69/1.10 fof(f41,plain,(
% 4.69/1.10 ![X0,X1]: (~complement(X0,X1)|multiplication(X1,X0)=zero)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f40])).
% 4.69/1.10 fof(f42,plain,(
% 4.69/1.10 ![X0,X1]: (~complement(X0,X1)|multiplication(X0,X1)=zero)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f40])).
% 4.69/1.10 fof(f43,plain,(
% 4.69/1.10 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f40])).
% 4.69/1.10 fof(f45,plain,(
% 4.69/1.10 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 4.69/1.10 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 4.69/1.10 fof(f46,plain,(
% 4.69/1.10 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 4.69/1.10 inference(NNF_transformation,[status(thm)],[f45])).
% 4.69/1.10 fof(f47,plain,(
% 4.69/1.10 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 4.69/1.10 inference(miniscoping,[status(thm)],[f46])).
% 4.69/1.10 fof(f48,plain,(
% 4.69/1.10 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f47])).
% 4.69/1.10 fof(f52,plain,(
% 4.69/1.10 (?[X0,X1,X2,X3,X4]: ((test(X3)&test(X4))&~addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))=addition(multiplication(X3,X0),multiplication(c(X3),X2))))),
% 4.69/1.10 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 4.69/1.10 fof(f53,plain,(
% 4.69/1.10 ?[X3]: ((test(X3)&(?[X4]: test(X4)))&(?[X0,X1,X2]: ~addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))=addition(multiplication(X3,X0),multiplication(c(X3),X2))))),
% 4.69/1.10 inference(miniscoping,[status(thm)],[f52])).
% 4.69/1.10 fof(f54,plain,(
% 4.69/1.10 ((test(sK1_skl)&test(sK2_skl))&~addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)))),
% 4.69/1.10 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X3,sK1_skl),skolemize(X4,sK2_skl),skolemize(X0,sK3_skl),skolemize(X1,sK4_skl),skolemize(X2,sK5_skl)],[f53])).
% 4.69/1.10 fof(f55,plain,(
% 4.69/1.10 test(sK1_skl)),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f54])).
% 4.69/1.10 fof(f57,plain,(
% 4.69/1.10 ~addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 4.69/1.10 inference(cnf_transformation,[status(thm)],[f54])).
% 4.69/1.10 fof(f58,plain,(
% 4.69/1.10 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 4.69/1.10 inference(destructive_equality_resolution,[status(thm)],[f48])).
% 4.69/1.10 fof(f63,plain,(
% 4.69/1.10 ~addition(multiplication(c(sK1_skl),sK5_skl),multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 4.69/1.10 inference(paramodulation,[status(thm)],[f19,f57])).
% 4.69/1.10 fof(f126,plain,(
% 4.69/1.10 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X2),multiplication(X0,X1)))),
% 4.69/1.10 inference(paramodulation,[status(thm)],[f19,f26])).
% 4.69/1.10 fof(f148,plain,(
% 4.69/1.10 ![X0]: (addition(zero,X0)=X0)),
% 4.69/1.10 inference(paramodulation,[status(thm)],[f19,f21])).
% 4.69/1.10 fof(f218,plain,(
% 4.69/1.10 ![X0]: (multiplication(c(X0),X0)=zero|~test(X0))),
% 4.69/1.10 inference(resolution,[status(thm)],[f41,f58])).
% 4.69/1.10 fof(f220,plain,(
% 4.69/1.10 ![X0]: (multiplication(X0,c(X0))=zero|~test(X0))),
% 4.69/1.10 inference(resolution,[status(thm)],[f42,f58])).
% 4.69/1.10 fof(f222,plain,(
% 4.69/1.10 ![X0]: (addition(c(X0),X0)=one|~test(X0))),
% 4.69/1.10 inference(resolution,[status(thm)],[f43,f58])).
% 4.69/1.10 fof(f265,plain,(
% 4.69/1.10 multiplication(c(sK1_skl),sK1_skl)=zero),
% 4.69/1.10 inference(resolution,[status(thm)],[f218,f55])).
% 4.69/1.10 fof(f277,plain,(
% 4.69/1.10 ![X0]: (multiplication(addition(X0,c(sK1_skl)),sK1_skl)=addition(multiplication(X0,sK1_skl),zero))),
% 4.69/1.10 inference(paramodulation,[status(thm)],[f265,f27])).
% 4.69/1.10 fof(f282,plain,(
% 4.69/1.10 ![X0]: (multiplication(addition(X0,c(sK1_skl)),sK1_skl)=multiplication(X0,sK1_skl))),
% 4.69/1.10 inference(forward_demodulation,[status(thm)],[f21,f277])).
% 4.69/1.10 fof(f317,plain,(
% 4.69/1.10 multiplication(sK1_skl,c(sK1_skl))=zero),
% 4.69/1.10 inference(resolution,[status(thm)],[f220,f55])).
% 4.69/1.10 fof(f334,plain,(
% 4.69/1.10 ![X0]: (multiplication(sK1_skl,multiplication(c(sK1_skl),X0))=multiplication(zero,X0))),
% 4.69/1.10 inference(paramodulation,[status(thm)],[f317,f23])).
% 4.69/1.10 fof(f339,plain,(
% 4.69/1.10 ![X0]: (multiplication(sK1_skl,multiplication(c(sK1_skl),X0))=zero)),
% 4.69/1.10 inference(forward_demodulation,[status(thm)],[f29,f334])).
% 4.69/1.10 fof(f342,plain,(
% 4.69/1.10 addition(c(sK1_skl),sK1_skl)=one),
% 4.69/1.10 inference(resolution,[status(thm)],[f222,f55])).
% 4.69/1.10 fof(f365,plain,(
% 4.69/1.10 addition(sK1_skl,c(sK1_skl))=one),
% 4.69/1.10 inference(paramodulation,[status(thm)],[f19,f342])).
% 4.31/1.11 fof(f6146,plain,(
% 4.31/1.11 ![X0,X1]: (multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1)))=addition(zero,multiplication(sK1_skl,X0)))),
% 4.31/1.11 inference(paramodulation,[status(thm)],[f339,f126])).
% 4.31/1.11 fof(f6176,plain,(
% 4.31/1.11 ~addition(multiplication(c(sK1_skl),sK5_skl),multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 4.31/1.11 inference(backward_demodulation,[status(thm)],[f6178,f63])).
% 4.31/1.11 fof(f6178,plain,(
% 4.31/1.11 ![X0,X1]: (multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1)))=multiplication(sK1_skl,X0))),
% 4.31/1.11 inference(forward_demodulation,[status(thm)],[f148,f6146])).
% 4.31/1.11 fof(f12107,plain,(
% 4.31/1.11 multiplication(one,sK1_skl)=multiplication(sK1_skl,sK1_skl)),
% 4.31/1.11 inference(paramodulation,[status(thm)],[f365,f282])).
% 4.31/1.11 fof(f12152,plain,(
% 4.31/1.11 sK1_skl=multiplication(sK1_skl,sK1_skl)),
% 4.31/1.11 inference(forward_demodulation,[status(thm)],[f25,f12107])).
% 4.31/1.11 fof(f12229,plain,(
% 4.31/1.11 ![X0]: (multiplication(sK1_skl,multiplication(sK1_skl,X0))=multiplication(sK1_skl,X0))),
% 4.31/1.11 inference(paramodulation,[status(thm)],[f12152,f23])).
% 4.31/1.11 fof(f12258,plain,(
% 4.31/1.11 ~addition(multiplication(c(sK1_skl),sK5_skl),multiplication(sK1_skl,sK3_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))),
% 4.31/1.11 inference(backward_demodulation,[status(thm)],[f12229,f6176])).
% 4.31/1.11 fof(f12264,plain,(
% 4.31/1.11 $false),
% 4.31/1.11 inference(forward_subsumption_resolution,[status(thm)],[f12258,f19])).
% 4.31/1.11 % SZS output end CNFRefutation for theBenchmark.p
% 4.31/1.13 % Elapsed time: 0.762109 seconds
% 4.31/1.13 % CPU time: 5.660007 seconds
% 4.31/1.13 % Total memory used: 171.301 MB
% 4.31/1.13 % Net memory used: 167.505 MB
%------------------------------------------------------------------------------