%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE005+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 : 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 12:58:08 PM UTC 2026
% Result : Theorem 0.11s 0.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE005+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
% 0.11/0.52 % Computer : n019.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Sun Sep 20 22:37:50 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.53 % Drodi V4.1.1
% 0.11/0.56 % Refutation found
% 0.11/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.56 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.56 fof(f1,axiom,(
% 0.11/0.56 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f3,axiom,(
% 0.11/0.56 (! [A] : addition(A,zero) = A )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f10,axiom,(
% 0.11/0.56 (! [A] : multiplication(A,zero) = zero )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f11,axiom,(
% 0.11/0.56 (! [A] : multiplication(zero,A) = zero )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f14,axiom,(
% 0.11/0.56 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f15,axiom,(
% 0.11/0.56 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f16,axiom,(
% 0.11/0.56 (! [X0] :( ~ test(X0)=> c(X0) = zero ) )),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f17,conjecture,(
% 0.11/0.56 c(one) = zero ),
% 0.11/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.56 fof(f18,negated_conjecture,(
% 0.11/0.56 ~(c(one) = zero )),
% 0.11/0.56 inference(negated_conjecture,[status(cth)],[f17])).
% 0.11/0.56 fof(f19,plain,(
% 0.11/0.56 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f1])).
% 0.11/0.56 fof(f21,plain,(
% 0.11/0.56 ![X0]: (addition(X0,zero)=X0)),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f3])).
% 0.11/0.56 fof(f28,plain,(
% 0.11/0.56 ![X0]: (multiplication(X0,zero)=zero)),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f10])).
% 0.11/0.56 fof(f29,plain,(
% 0.11/0.56 ![X0]: (multiplication(zero,X0)=zero)),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f11])).
% 0.11/0.56 fof(f39,plain,(
% 0.11/0.56 ![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)))),
% 0.11/0.56 inference(NNF_transformation,[status(thm)],[f14])).
% 0.11/0.56 fof(f40,plain,(
% 0.11/0.56 (![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)))),
% 0.11/0.56 inference(miniscoping,[status(thm)],[f39])).
% 0.11/0.56 fof(f44,plain,(
% 0.11/0.56 ![X0,X1]: (complement(X0,X1)|~multiplication(X1,X0)=zero|~multiplication(X0,X1)=zero|~addition(X1,X0)=one)),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f40])).
% 0.11/0.56 fof(f45,plain,(
% 0.11/0.56 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.11/0.56 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.11/0.56 fof(f46,plain,(
% 0.11/0.56 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.11/0.56 inference(NNF_transformation,[status(thm)],[f45])).
% 0.11/0.56 fof(f47,plain,(
% 0.11/0.56 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.11/0.56 inference(miniscoping,[status(thm)],[f46])).
% 0.11/0.56 fof(f49,plain,(
% 0.11/0.56 ![X0,X1]: (~test(X0)|c(X0)=X1|~complement(X0,X1))),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f47])).
% 0.11/0.56 fof(f50,plain,(
% 0.11/0.56 ![X0]: (test(X0)|c(X0)=zero)),
% 0.11/0.56 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.11/0.56 fof(f51,plain,(
% 0.11/0.56 ![X0]: (test(X0)|c(X0)=zero)),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f50])).
% 0.11/0.56 fof(f52,plain,(
% 0.11/0.56 ~c(one)=zero),
% 0.11/0.56 inference(cnf_transformation,[status(thm)],[f18])).
% 0.11/0.56 fof(f149,definition,(
% 0.11/0.56 sQ13_spl <=> (test(one))),
% 0.11/0.56 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.11/0.56 fof(f151,plain,(
% 0.11/0.56 ~test(one)|sQ13_spl),
% 0.11/0.56 inference(component_clause,[status(thm)],[f149])).
% 0.11/0.56 fof(f160,definition,(
% 0.11/0.56 sQ15_spl <=> (c(one)=zero)),
% 0.11/0.56 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.11/0.56 fof(f161,plain,(
% 0.11/0.56 c(one)=zero|~sQ15_spl),
% 0.11/0.56 inference(component_clause,[status(thm)],[f160])).
% 0.11/0.56 fof(f168,plain,(
% 0.11/0.56 c(one)=zero|sQ13_spl),
% 0.11/0.56 inference(resolution,[status(thm)],[f151,f51])).
% 0.11/0.56 fof(f182,plain,(
% 0.11/0.56 ~zero=zero|~sQ15_spl),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f161,f52])).
% 0.11/0.56 fof(f183,plain,(
% 0.11/0.56 $false|~sQ15_spl),
% 0.11/0.56 inference(trivial_equality_resolution,[status(thm)],[f182])).
% 0.11/0.56 fof(f184,plain,(
% 0.11/0.56 ~sQ15_spl),
% 0.11/0.56 inference(contradiction_clause,[status(thm)],[f183])).
% 0.11/0.56 fof(f189,plain,(
% 0.11/0.56 ~zero=zero|sQ13_spl),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f168,f52])).
% 0.11/0.56 fof(f190,plain,(
% 0.11/0.56 $false|sQ13_spl),
% 0.11/0.56 inference(trivial_equality_resolution,[status(thm)],[f189])).
% 0.11/0.56 fof(f191,plain,(
% 0.11/0.56 sQ13_spl),
% 0.11/0.56 inference(contradiction_clause,[status(thm)],[f190])).
% 0.11/0.56 fof(f194,plain,(
% 0.11/0.56 ![X0]: (X0=addition(zero,X0))),
% 0.11/0.56 inference(paramodulation,[status(thm)],[f21,f19])).
% 0.11/0.56 fof(f255,plain,(
% 0.11/0.56 ![X0]: (complement(X0,zero)|~multiplication(zero,X0)=zero|~multiplication(X0,zero)=zero|~X0=one)),
% 0.11/0.56 inference(paramodulation,[status(thm)],[f194,f44])).
% 0.11/0.56 fof(f257,plain,(
% 0.11/0.56 ![X0]: (complement(X0,zero)|~zero=zero|~multiplication(X0,zero)=zero|~X0=one)),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f29,f255])).
% 0.11/0.56 fof(f258,plain,(
% 0.11/0.56 ![X0]: (complement(X0,zero)|~zero=zero|~zero=zero|~X0=one)),
% 0.11/0.56 inference(forward_demodulation,[status(thm)],[f28,f257])).
% 0.11/0.56 fof(f259,plain,(
% 0.11/0.56 ![X0]: (complement(X0,zero)|~zero=zero|~X0=one)),
% 0.11/0.56 inference(duplicate_literals_removal,[status(thm)],[f258])).
% 0.11/0.56 fof(f260,plain,(
% 0.11/0.56 ![X0]: (complement(X0,zero)|~X0=one)),
% 0.11/0.56 inference(trivial_equality_resolution,[status(thm)],[f259])).
% 0.11/0.56 fof(f261,plain,(
% 0.11/0.56 complement(one,zero)),
% 0.11/0.56 inference(destructive_equality_resolution,[status(thm)],[f260])).
% 0.11/0.56 fof(f263,plain,(
% 0.11/0.56 ~test(one)|c(one)=zero),
% 0.11/0.56 inference(resolution,[status(thm)],[f261,f49])).
% 0.11/0.56 fof(f265,plain,(
% 0.11/0.56 ~sQ13_spl|sQ15_spl),
% 0.11/0.56 inference(split_clause,[status(thm)],[f263,f149,f160])).
% 0.11/0.56 fof(f266,plain,(
% 0.11/0.56 $false),
% 0.11/0.56 inference(sat_refutation,[status(thm)],[f184,f191,f265])).
% 0.11/0.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.59 % Elapsed time: 0.057641 seconds
% 0.16/0.59 % CPU time: 0.158869 seconds
% 0.16/0.59 % Total memory used: 102.160 MB
% 0.16/0.59 % Net memory used: 101.817 MB
%------------------------------------------------------------------------------