%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE004+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 : n007.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 0.09s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE004+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:35:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.41 fof(f1,axiom,(
% 0.09/0.41 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f3,axiom,(
% 0.09/0.41 (! [A] : addition(A,zero) = A )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f10,axiom,(
% 0.09/0.41 (! [A] : multiplication(A,zero) = zero )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f11,axiom,(
% 0.09/0.41 (! [A] : multiplication(zero,A) = zero )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f13,axiom,(
% 0.09/0.41 (! [X0] :( test(X0)<=> (? [X1] : complement(X1,X0) )) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f14,axiom,(
% 0.09/0.41 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f15,axiom,(
% 0.09/0.41 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f17,conjecture,(
% 0.09/0.41 c(zero) = one ),
% 0.09/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.41 fof(f18,negated_conjecture,(
% 0.09/0.41 ~(c(zero) = one )),
% 0.09/0.41 inference(negated_conjecture,[status(cth)],[f17])).
% 0.09/0.41 fof(f19,plain,(
% 0.09/0.41 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.41 fof(f21,plain,(
% 0.09/0.41 ![X0]: (addition(X0,zero)=X0)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.41 fof(f28,plain,(
% 0.09/0.41 ![X0]: (multiplication(X0,zero)=zero)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/0.41 fof(f29,plain,(
% 0.09/0.41 ![X0]: (multiplication(zero,X0)=zero)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/0.41 fof(f34,plain,(
% 0.09/0.41 ![X0]: ((~test(X0)|(?[X1]: complement(X1,X0)))&(test(X0)|(![X1]: ~complement(X1,X0))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f13])).
% 0.09/0.41 fof(f35,plain,(
% 0.09/0.41 (![X0]: (~test(X0)|(?[X1]: complement(X1,X0))))&(![X0]: (test(X0)|(![X1]: ~complement(X1,X0))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f34])).
% 0.09/0.41 fof(f36,plain,(
% 0.09/0.41 (![X0]: (~test(X0)|complement(sK0_skl(X0),X0)))&(![X0]: (test(X0)|(![X1]: ~complement(X1,X0))))),
% 0.09/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl(X0))],[f35])).
% 0.09/0.41 fof(f38,plain,(
% 0.09/0.41 ![X0,X1]: (test(X0)|~complement(X1,X0))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f36])).
% 0.09/0.41 fof(f39,plain,(
% 0.09/0.41 ![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)))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f14])).
% 0.09/0.41 fof(f40,plain,(
% 0.09/0.41 (![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)))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f39])).
% 0.09/0.41 fof(f44,plain,(
% 0.09/0.41 ![X0,X1]: (complement(X0,X1)|~multiplication(X1,X0)=zero|~multiplication(X0,X1)=zero|~addition(X1,X0)=one)),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.41 fof(f45,plain,(
% 0.09/0.41 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.09/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.09/0.41 fof(f46,plain,(
% 0.09/0.41 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.09/0.41 inference(NNF_transformation,[status(thm)],[f45])).
% 0.09/0.41 fof(f47,plain,(
% 0.09/0.41 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.09/0.41 inference(miniscoping,[status(thm)],[f46])).
% 0.09/0.41 fof(f49,plain,(
% 0.09/0.41 ![X0,X1]: (~test(X0)|c(X0)=X1|~complement(X0,X1))),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f47])).
% 0.09/0.41 fof(f52,plain,(
% 0.09/0.41 ~c(zero)=one),
% 0.09/0.41 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.41 fof(f70,definition,(
% 0.09/0.41 sQ1_spl <=> (c(zero)=one)),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f71,plain,(
% 0.09/0.41 c(zero)=one|~sQ1_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f70])).
% 0.09/0.41 fof(f89,plain,(
% 0.09/0.41 ![X0]: (complement(zero,X0)|~multiplication(X0,zero)=zero|~multiplication(zero,X0)=zero|~X0=one)),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f21,f44])).
% 0.09/0.41 fof(f107,plain,(
% 0.09/0.41 ![X0]: (complement(zero,X0)|~zero=zero|~multiplication(zero,X0)=zero|~X0=one)),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f28,f89])).
% 0.09/0.41 fof(f108,plain,(
% 0.09/0.41 ![X0]: (complement(zero,X0)|~zero=zero|~zero=zero|~X0=one)),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f29,f107])).
% 0.09/0.41 fof(f109,plain,(
% 0.09/0.41 ![X0]: (complement(zero,X0)|~zero=zero|~X0=one)),
% 0.09/0.41 inference(duplicate_literals_removal,[status(thm)],[f108])).
% 0.09/0.41 fof(f110,plain,(
% 0.09/0.41 ![X0]: (complement(zero,X0)|~X0=one)),
% 0.09/0.41 inference(trivial_equality_resolution,[status(thm)],[f109])).
% 0.09/0.41 fof(f111,plain,(
% 0.09/0.41 complement(zero,one)),
% 0.09/0.41 inference(destructive_equality_resolution,[status(thm)],[f110])).
% 0.09/0.41 fof(f117,plain,(
% 0.09/0.41 ~test(zero)|c(zero)=one),
% 0.09/0.41 inference(resolution,[status(thm)],[f111,f49])).
% 0.09/0.41 fof(f119,definition,(
% 0.09/0.41 sQ9_spl <=> (test(zero))),
% 0.09/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.09/0.41 fof(f121,plain,(
% 0.09/0.41 ~test(zero)|sQ9_spl),
% 0.09/0.41 inference(component_clause,[status(thm)],[f119])).
% 0.09/0.41 fof(f122,plain,(
% 0.09/0.41 ~sQ9_spl|sQ1_spl),
% 0.09/0.41 inference(split_clause,[status(thm)],[f117,f119,f70])).
% 0.09/0.41 fof(f136,plain,(
% 0.09/0.41 $false|~sQ1_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f71,f52])).
% 0.09/0.41 fof(f137,plain,(
% 0.09/0.41 ~sQ1_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f136])).
% 0.09/0.41 fof(f186,plain,(
% 0.09/0.41 ![X0]: (X0=addition(zero,X0))),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f21,f19])).
% 0.09/0.41 fof(f249,plain,(
% 0.09/0.41 ![X0]: (complement(X0,zero)|~multiplication(zero,X0)=zero|~multiplication(X0,zero)=zero|~X0=one)),
% 0.09/0.41 inference(paramodulation,[status(thm)],[f186,f44])).
% 0.09/0.41 fof(f251,plain,(
% 0.09/0.41 ![X0]: (complement(X0,zero)|~zero=zero|~multiplication(X0,zero)=zero|~X0=one)),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f29,f249])).
% 0.09/0.41 fof(f252,plain,(
% 0.09/0.41 ![X0]: (complement(X0,zero)|~zero=zero|~zero=zero|~X0=one)),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f28,f251])).
% 0.09/0.41 fof(f253,plain,(
% 0.09/0.41 ![X0]: (complement(X0,zero)|~zero=zero|~X0=one)),
% 0.09/0.41 inference(duplicate_literals_removal,[status(thm)],[f252])).
% 0.09/0.41 fof(f254,plain,(
% 0.09/0.41 ![X0]: (complement(X0,zero)|~X0=one)),
% 0.09/0.41 inference(trivial_equality_resolution,[status(thm)],[f253])).
% 0.09/0.41 fof(f255,plain,(
% 0.09/0.41 complement(one,zero)),
% 0.09/0.41 inference(destructive_equality_resolution,[status(thm)],[f254])).
% 0.09/0.41 fof(f260,plain,(
% 0.09/0.41 test(zero)),
% 0.09/0.41 inference(resolution,[status(thm)],[f255,f38])).
% 0.09/0.41 fof(f263,plain,(
% 0.09/0.41 $false|sQ9_spl),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f260,f121])).
% 0.09/0.41 fof(f264,plain,(
% 0.09/0.41 sQ9_spl),
% 0.09/0.41 inference(contradiction_clause,[status(thm)],[f263])).
% 0.09/0.41 fof(f265,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(sat_refutation,[status(thm)],[f122,f137,f264])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.052320 seconds
% 0.09/0.43 % CPU time: 0.165458 seconds
% 0.09/0.43 % Total memory used: 102.200 MB
% 0.09/0.43 % Net memory used: 101.892 MB
%------------------------------------------------------------------------------