%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE026+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 : n016.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 0.19s 0.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 22:44:07 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.57 % Refutation found
% 0.19/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.57 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.57 fof(f1,axiom,(
% 0.19/0.57 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f2,axiom,(
% 0.19/0.57 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f4,axiom,(
% 0.19/0.57 (! [A] : addition(A,A) = A )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f5,axiom,(
% 0.19/0.57 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f7,axiom,(
% 0.19/0.57 (! [A] : multiplication(one,A) = A )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f9,axiom,(
% 0.19/0.57 (! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f12,axiom,(
% 0.19/0.57 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f14,axiom,(
% 0.19/0.57 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f15,axiom,(
% 0.19/0.57 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f19,conjecture,(
% 0.19/0.57 (! [X0,X1,X2] :( ( test(X1)& test(X2) )=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ) )),
% 0.19/0.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.57 fof(f20,negated_conjecture,(
% 0.19/0.57 ~((! [X0,X1,X2] :( ( test(X1)& test(X2) )=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ) ))),
% 0.19/0.57 inference(negated_conjecture,[status(cth)],[f19])).
% 0.19/0.57 fof(f21,plain,(
% 0.19/0.57 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f1])).
% 0.19/0.57 fof(f22,plain,(
% 0.19/0.57 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f2])).
% 0.19/0.57 fof(f24,plain,(
% 0.19/0.57 ![X0]: (addition(X0,X0)=X0)),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f4])).
% 0.19/0.57 fof(f25,plain,(
% 0.19/0.57 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f5])).
% 0.19/0.57 fof(f27,plain,(
% 0.19/0.57 ![X0]: (multiplication(one,X0)=X0)),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f7])).
% 0.19/0.57 fof(f29,plain,(
% 0.19/0.57 ![X0,X1,X2]: (multiplication(addition(X0,X1),X2)=addition(multiplication(X0,X2),multiplication(X1,X2)))),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f9])).
% 0.19/0.57 fof(f32,plain,(
% 0.19/0.57 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.19/0.57 inference(NNF_transformation,[status(thm)],[f12])).
% 0.19/0.57 fof(f33,plain,(
% 0.19/0.57 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.19/0.57 inference(miniscoping,[status(thm)],[f32])).
% 0.19/0.57 fof(f35,plain,(
% 0.19/0.57 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f33])).
% 0.19/0.57 fof(f41,plain,(
% 0.19/0.57 ![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)))),
% 0.19/0.57 inference(NNF_transformation,[status(thm)],[f14])).
% 0.19/0.57 fof(f42,plain,(
% 0.19/0.57 (![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)))),
% 0.19/0.57 inference(miniscoping,[status(thm)],[f41])).
% 0.19/0.57 fof(f45,plain,(
% 0.19/0.57 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 0.19/0.57 inference(cnf_transformation,[status(thm)],[f42])).
% 0.19/0.57 fof(f47,plain,(
% 0.19/0.57 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.19/0.57 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.19/0.57 fof(f48,plain,(
% 0.19/0.57 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.19/0.58 inference(NNF_transformation,[status(thm)],[f47])).
% 0.19/0.58 fof(f49,plain,(
% 0.19/0.58 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.19/0.58 inference(miniscoping,[status(thm)],[f48])).
% 0.19/0.58 fof(f50,plain,(
% 0.19/0.58 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f49])).
% 0.19/0.58 fof(f58,plain,(
% 0.19/0.58 (?[X0,X1,X2]: ((test(X1)&test(X2))&(multiplication(X1,X0)=multiplication(multiplication(X1,X0),X2)&~leq(multiplication(X1,X0),multiplication(X0,X2)))))),
% 0.19/0.58 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.19/0.58 fof(f59,plain,(
% 0.19/0.58 ?[X1,X2]: ((test(X1)&test(X2))&(?[X0]: (multiplication(X1,X0)=multiplication(multiplication(X1,X0),X2)&~leq(multiplication(X1,X0),multiplication(X0,X2)))))),
% 0.19/0.58 inference(miniscoping,[status(thm)],[f58])).
% 0.19/0.58 fof(f60,plain,(
% 0.19/0.58 ((test(sK1_skl)&test(sK2_skl))&(multiplication(sK1_skl,sK3_skl)=multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)&~leq(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))))),
% 0.19/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl),skolemize(X0,sK3_skl)],[f59])).
% 0.19/0.58 fof(f61,plain,(
% 0.19/0.58 test(sK1_skl)),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f60])).
% 0.19/0.58 fof(f63,plain,(
% 0.19/0.58 multiplication(sK1_skl,sK3_skl)=multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f60])).
% 0.19/0.58 fof(f64,plain,(
% 0.19/0.58 ~leq(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))),
% 0.19/0.58 inference(cnf_transformation,[status(thm)],[f60])).
% 0.19/0.58 fof(f65,plain,(
% 0.19/0.58 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 0.19/0.58 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 0.19/0.58 fof(f66,plain,(
% 0.19/0.58 multiplication(sK1_skl,sK3_skl)=multiplication(sK1_skl,multiplication(sK3_skl,sK2_skl))),
% 0.19/0.58 inference(forward_demodulation,[status(thm)],[f25,f63])).
% 0.19/0.58 fof(f78,plain,(
% 0.19/0.58 ~addition(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))=multiplication(sK3_skl,sK2_skl)),
% 0.19/0.58 inference(resolution,[status(thm)],[f35,f64])).
% 0.19/0.58 fof(f109,plain,(
% 0.19/0.58 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 0.19/0.58 inference(paramodulation,[status(thm)],[f24,f22])).
% 0.19/0.58 fof(f145,plain,(
% 0.19/0.58 complement(sK1_skl,c(sK1_skl))),
% 0.19/0.58 inference(resolution,[status(thm)],[f65,f61])).
% 0.19/0.58 fof(f199,plain,(
% 0.19/0.58 ![X0]: (multiplication(addition(sK1_skl,X0),multiplication(sK3_skl,sK2_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(X0,multiplication(sK3_skl,sK2_skl))))),
% 0.19/0.58 inference(paramodulation,[status(thm)],[f66,f29])).
% 0.19/0.58 fof(f226,plain,(
% 0.19/0.58 addition(c(sK1_skl),sK1_skl)=one),
% 0.19/0.58 inference(resolution,[status(thm)],[f145,f45])).
% 0.19/0.58 fof(f299,plain,(
% 0.19/0.58 addition(sK1_skl,c(sK1_skl))=one),
% 0.19/0.58 inference(paramodulation,[status(thm)],[f21,f226])).
% 0.19/0.58 fof(f486,plain,(
% 0.19/0.58 addition(sK1_skl,one)=addition(sK1_skl,c(sK1_skl))),
% 0.19/0.58 inference(paramodulation,[status(thm)],[f299,f109])).
% 0.19/0.58 fof(f506,plain,(
% 0.19/0.58 addition(sK1_skl,one)=one),
% 0.19/0.58 inference(forward_demodulation,[status(thm)],[f299,f486])).
% 0.19/0.58 fof(f661,plain,(
% 0.19/0.58 multiplication(addition(sK1_skl,one),multiplication(sK3_skl,sK2_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))),
% 0.19/0.58 inference(paramodulation,[status(thm)],[f27,f199])).
% 0.19/0.58 fof(f672,plain,(
% 0.19/0.58 multiplication(one,multiplication(sK3_skl,sK2_skl))=addition(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))),
% 0.19/0.58 inference(forward_demodulation,[status(thm)],[f506,f661])).
% 0.19/0.58 fof(f673,plain,(
% 0.19/0.58 multiplication(sK3_skl,sK2_skl)=addition(multiplication(sK1_skl,sK3_skl),multiplication(sK3_skl,sK2_skl))),
% 0.19/0.58 inference(forward_demodulation,[status(thm)],[f27,f672])).
% 0.19/0.58 fof(f674,plain,(
% 0.19/0.58 $false),
% 0.19/0.58 inference(forward_subsumption_resolution,[status(thm)],[f673,f78])).
% 0.19/0.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.63 % Elapsed time: 0.160826 seconds
% 0.19/0.63 % CPU time: 0.782290 seconds
% 0.19/0.63 % Total memory used: 114.332 MB
% 0.19/0.63 % Net memory used: 113.969 MB
%------------------------------------------------------------------------------