%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE021+3 : 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 : 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 12:58:11 PM UTC 2026
% Result : Theorem 0.08s 0.35s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE021+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 22:38:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.08/0.35 % Refutation found
% 0.08/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.35 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.35 fof(f1,axiom,(
% 0.08/0.35 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f7,axiom,(
% 0.08/0.35 (! [A] : multiplication(one,A) = A )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f9,axiom,(
% 0.08/0.35 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f14,axiom,(
% 0.08/0.35 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f15,axiom,(
% 0.08/0.35 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f19,conjecture,(
% 0.08/0.35 (! [X0,X1] :( test(X1)=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ) )),
% 0.08/0.35 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.08/0.35 fof(f20,negated_conjecture,(
% 0.08/0.35 ~((! [X0,X1] :( test(X1)=> X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ) ))),
% 0.08/0.35 inference(negated_conjecture,[status(cth)],[f19])).
% 0.08/0.35 fof(f21,plain,(
% 0.08/0.35 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.35 fof(f27,plain,(
% 0.08/0.35 ![X0]: (multiplication(one,X0)=X0)),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f7])).
% 0.08/0.35 fof(f29,plain,(
% 0.08/0.35 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f9])).
% 0.08/0.35 fof(f41,plain,(
% 0.08/0.35 ![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)))),
% 0.08/0.35 inference(NNF_transformation,[status(thm)],[f14])).
% 0.08/0.35 fof(f42,plain,(
% 0.08/0.35 (![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)))),
% 0.08/0.35 inference(miniscoping,[status(thm)],[f41])).
% 0.08/0.35 fof(f45,plain,(
% 0.08/0.35 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f42])).
% 0.08/0.35 fof(f47,plain,(
% 0.08/0.35 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.08/0.35 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.08/0.35 fof(f48,plain,(
% 0.08/0.35 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.08/0.35 inference(NNF_transformation,[status(thm)],[f47])).
% 0.08/0.35 fof(f49,plain,(
% 0.08/0.35 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.08/0.35 inference(miniscoping,[status(thm)],[f48])).
% 0.08/0.35 fof(f50,plain,(
% 0.08/0.35 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f49])).
% 0.08/0.35 fof(f58,plain,(
% 0.08/0.35 (?[X0,X1]: (test(X1)&~X0=addition(multiplication(X1,X0),multiplication(c(X1),X0))))),
% 0.08/0.35 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.08/0.35 fof(f59,plain,(
% 0.08/0.35 ?[X1]: (test(X1)&(?[X0]: ~X0=addition(multiplication(X1,X0),multiplication(c(X1),X0))))),
% 0.08/0.35 inference(miniscoping,[status(thm)],[f58])).
% 0.08/0.35 fof(f60,plain,(
% 0.08/0.35 (test(sK1_skl)&~sK2_skl=addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),sK2_skl)))),
% 0.08/0.35 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl)],[f59])).
% 0.08/0.35 fof(f61,plain,(
% 0.08/0.35 test(sK1_skl)),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f60])).
% 0.08/0.35 fof(f62,plain,(
% 0.08/0.35 ~sK2_skl=addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),sK2_skl))),
% 0.08/0.35 inference(cnf_transformation,[status(thm)],[f60])).
% 0.08/0.35 fof(f63,plain,(
% 0.08/0.35 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 0.08/0.35 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 0.08/0.35 fof(f338,plain,(
% 0.08/0.35 ~sK2_skl=multiplication(addition(sK1_skl,c(sK1_skl)),sK2_skl)),
% 0.08/0.35 inference(backward_demodulation,[status(thm)],[f29,f62])).
% 0.08/0.35 fof(f594,plain,(
% 0.08/0.35 complement(sK1_skl,c(sK1_skl))),
% 0.08/0.35 inference(resolution,[status(thm)],[f63,f61])).
% 0.08/0.35 fof(f623,plain,(
% 0.08/0.35 addition(c(sK1_skl),sK1_skl)=one),
% 0.08/0.35 inference(resolution,[status(thm)],[f45,f594])).
% 0.08/0.35 fof(f782,plain,(
% 0.08/0.35 addition(sK1_skl,c(sK1_skl))=one),
% 0.08/0.35 inference(paramodulation,[status(thm)],[f21,f623])).
% 0.08/0.35 fof(f1731,plain,(
% 0.08/0.35 ~sK2_skl=multiplication(one,sK2_skl)),
% 0.08/0.35 inference(backward_demodulation,[status(thm)],[f782,f338])).
% 0.08/0.35 fof(f1750,plain,(
% 0.08/0.35 ~sK2_skl=sK2_skl),
% 0.08/0.35 inference(forward_demodulation,[status(thm)],[f27,f1731])).
% 0.08/0.35 fof(f1751,plain,(
% 0.08/0.35 $false),
% 0.08/0.35 inference(trivial_equality_resolution,[status(thm)],[f1750])).
% 0.08/0.35 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/0.36 % Elapsed time: 0.058747 seconds
% 0.08/0.36 % CPU time: 0.229306 seconds
% 0.08/0.36 % Total memory used: 107.489 MB
% 0.08/0.36 % Net memory used: 107.061 MB
%------------------------------------------------------------------------------