%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE048+1 : 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 : n010.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 12:58:15 PM UTC 2026
% Result : Theorem 1.35s 0.78s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:40:54 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 1.35/0.78 % Refutation found
% 1.35/0.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.35/0.78 % SZS output start CNFRefutation for theBenchmark
% 1.35/0.78 fof(f1,axiom,(
% 1.35/0.78 (! [A,B] : addition(A,B) = addition(B,A) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f2,axiom,(
% 1.35/0.78 (! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f4,axiom,(
% 1.35/0.78 (! [A] : addition(A,A) = A )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f6,axiom,(
% 1.35/0.78 (! [A] : multiplication(A,one) = A )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f7,axiom,(
% 1.35/0.78 (! [A] : multiplication(one,A) = A )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f8,axiom,(
% 1.35/0.78 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f12,axiom,(
% 1.35/0.78 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f14,axiom,(
% 1.35/0.78 (! [A] : leq(addition(one,multiplication(star(A),A)),star(A)) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f16,axiom,(
% 1.35/0.78 (! [A,B,C] :( leq(addition(multiplication(A,B),C),A)=> leq(multiplication(C,star(B)),A) ) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f18,axiom,(
% 1.35/0.78 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f19,axiom,(
% 1.35/0.78 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f21,conjecture,(
% 1.35/0.78 (! [X0] :( test(X0)=> star(X0) = one ) )),
% 1.35/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 1.35/0.78 fof(f22,negated_conjecture,(
% 1.35/0.78 ~((! [X0] :( test(X0)=> star(X0) = one ) ))),
% 1.35/0.78 inference(negated_conjecture,[status(cth)],[f21])).
% 1.35/0.78 fof(f23,plain,(
% 1.35/0.78 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f1])).
% 1.35/0.78 fof(f24,plain,(
% 1.35/0.78 ![X0,X1,X2]: (addition(X0,addition(X1,X2))=addition(addition(X0,X1),X2))),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f2])).
% 1.35/0.78 fof(f26,plain,(
% 1.35/0.78 ![X0]: (addition(X0,X0)=X0)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f4])).
% 1.35/0.78 fof(f28,plain,(
% 1.35/0.78 ![X0]: (multiplication(X0,one)=X0)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f6])).
% 1.35/0.78 fof(f29,plain,(
% 1.35/0.78 ![X0]: (multiplication(one,X0)=X0)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f7])).
% 1.35/0.78 fof(f30,plain,(
% 1.35/0.78 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f8])).
% 1.35/0.78 fof(f34,plain,(
% 1.35/0.78 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 1.35/0.78 inference(NNF_transformation,[status(thm)],[f12])).
% 1.35/0.78 fof(f35,plain,(
% 1.35/0.78 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 1.35/0.78 inference(miniscoping,[status(thm)],[f34])).
% 1.35/0.78 fof(f36,plain,(
% 1.35/0.78 ![X0,X1]: (~leq(X0,X1)|addition(X0,X1)=X1)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f35])).
% 1.35/0.78 fof(f37,plain,(
% 1.35/0.78 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f35])).
% 1.35/0.78 fof(f39,plain,(
% 1.35/0.78 ![X0]: (leq(addition(one,multiplication(star(X0),X0)),star(X0)))),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f14])).
% 1.35/0.78 fof(f42,plain,(
% 1.35/0.78 ![A,B,C]: (~leq(addition(multiplication(A,B),C),A)|leq(multiplication(C,star(B)),A))),
% 1.35/0.78 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 1.35/0.78 fof(f43,plain,(
% 1.35/0.78 ![X0,X1,X2]: (~leq(addition(multiplication(X0,X1),X2),X0)|leq(multiplication(X2,star(X1)),X0))),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f42])).
% 1.35/0.78 fof(f49,plain,(
% 1.35/0.78 ![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)))),
% 1.35/0.78 inference(NNF_transformation,[status(thm)],[f18])).
% 1.35/0.78 fof(f50,plain,(
% 1.35/0.78 (![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)))),
% 1.35/0.78 inference(miniscoping,[status(thm)],[f49])).
% 1.35/0.78 fof(f53,plain,(
% 1.35/0.78 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f50])).
% 1.35/0.78 fof(f55,plain,(
% 1.35/0.78 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 1.35/0.78 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 1.35/0.78 fof(f56,plain,(
% 1.35/0.78 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 1.35/0.78 inference(NNF_transformation,[status(thm)],[f55])).
% 1.35/0.78 fof(f57,plain,(
% 1.35/0.78 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 1.35/0.78 inference(miniscoping,[status(thm)],[f56])).
% 1.35/0.78 fof(f58,plain,(
% 1.35/0.78 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f57])).
% 1.35/0.78 fof(f62,plain,(
% 1.35/0.78 (?[X0]: (test(X0)&~star(X0)=one))),
% 1.35/0.78 inference(pre_NNF_transformation,[status(thm)],[f22])).
% 1.35/0.78 fof(f63,plain,(
% 1.35/0.78 (test(sK1_skl)&~star(sK1_skl)=one)),
% 1.35/0.78 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X0,sK1_skl)],[f62])).
% 1.35/0.78 fof(f64,plain,(
% 1.35/0.78 test(sK1_skl)),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f63])).
% 1.35/0.78 fof(f65,plain,(
% 1.35/0.78 ~star(sK1_skl)=one),
% 1.35/0.78 inference(cnf_transformation,[status(thm)],[f63])).
% 1.35/0.78 fof(f66,plain,(
% 1.35/0.78 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 1.35/0.78 inference(destructive_equality_resolution,[status(thm)],[f58])).
% 1.35/0.78 fof(f73,plain,(
% 1.35/0.78 ![X0,X1]: (~leq(addition(X0,X1),one)|leq(multiplication(X1,star(X0)),one))),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f29,f43])).
% 1.35/0.78 fof(f171,plain,(
% 1.35/0.78 ![X0,X1]: (addition(X0,addition(X0,X1))=addition(X0,X1))),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f26,f24])).
% 1.35/0.78 fof(f213,plain,(
% 1.35/0.78 ![X0,X1]: (multiplication(X0,addition(X1,one))=addition(multiplication(X0,X1),X0))),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f28,f30])).
% 1.35/0.78 fof(f276,plain,(
% 1.35/0.78 ![X0]: (addition(addition(one,multiplication(star(X0),X0)),star(X0))=star(X0))),
% 1.35/0.78 inference(resolution,[status(thm)],[f36,f39])).
% 1.35/0.78 fof(f280,plain,(
% 1.35/0.78 ![X0]: (addition(one,addition(multiplication(star(X0),X0),star(X0)))=star(X0))),
% 1.35/0.78 inference(forward_demodulation,[status(thm)],[f24,f276])).
% 1.35/0.78 fof(f283,plain,(
% 1.35/0.78 ![X0]: (leq(X0,X0))),
% 1.35/0.78 inference(resolution,[status(thm)],[f37,f26])).
% 1.35/0.78 fof(f502,plain,(
% 1.35/0.78 complement(sK1_skl,c(sK1_skl))),
% 1.35/0.78 inference(resolution,[status(thm)],[f66,f64])).
% 1.35/0.78 fof(f517,plain,(
% 1.35/0.78 addition(c(sK1_skl),sK1_skl)=one),
% 1.35/0.78 inference(resolution,[status(thm)],[f502,f53])).
% 1.35/0.78 fof(f589,plain,(
% 1.35/0.78 addition(sK1_skl,c(sK1_skl))=one),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f23,f517])).
% 1.35/0.78 fof(f1020,plain,(
% 1.35/0.78 addition(sK1_skl,one)=addition(sK1_skl,c(sK1_skl))),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f589,f171])).
% 1.35/0.78 fof(f1045,plain,(
% 1.35/0.78 addition(sK1_skl,one)=one),
% 1.35/0.78 inference(forward_demodulation,[status(thm)],[f589,f1020])).
% 1.35/0.78 fof(f1109,plain,(
% 1.35/0.78 ~leq(one,one)|leq(multiplication(one,star(sK1_skl)),one)),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f1045,f73])).
% 1.35/0.78 fof(f1123,plain,(
% 1.35/0.78 ~leq(one,one)|leq(star(sK1_skl),one)),
% 1.35/0.78 inference(forward_demodulation,[status(thm)],[f29,f1109])).
% 1.35/0.78 fof(f1124,plain,(
% 1.35/0.78 leq(star(sK1_skl),one)),
% 1.35/0.78 inference(forward_subsumption_resolution,[status(thm)],[f1123,f283])).
% 1.35/0.78 fof(f1284,plain,(
% 1.35/0.78 addition(star(sK1_skl),one)=one),
% 1.35/0.78 inference(resolution,[status(thm)],[f1124,f36])).
% 1.35/0.78 fof(f1565,plain,(
% 1.35/0.78 addition(one,star(sK1_skl))=one),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f23,f1284])).
% 1.35/0.78 fof(f3967,plain,(
% 1.35/0.78 ![X0]: (addition(one,multiplication(star(X0),addition(X0,one)))=star(X0))),
% 1.35/0.78 inference(forward_demodulation,[status(thm)],[f213,f280])).
% 1.35/0.78 fof(f3972,plain,(
% 1.35/0.78 addition(one,multiplication(star(sK1_skl),one))=star(sK1_skl)),
% 1.35/0.78 inference(paramodulation,[status(thm)],[f1045,f3967])).
% 1.35/0.78 fof(f4020,plain,(
% 1.35/0.78 addition(one,star(sK1_skl))=star(sK1_skl)),
% 1.35/0.78 inference(forward_demodulation,[status(thm)],[f28,f3972])).
% 1.35/0.78 fof(f4021,plain,(
% 1.35/0.78 one=star(sK1_skl)),
% 1.35/0.78 inference(forward_demodulation,[status(thm)],[f1565,f4020])).
% 1.35/0.78 fof(f4022,plain,(
% 1.35/0.78 $false),
% 1.35/0.78 inference(forward_subsumption_resolution,[status(thm)],[f4021,f65])).
% 1.35/0.81 % SZS output end CNFRefutation for theBenchmark.p
% 1.35/0.83 % Elapsed time: 0.445385 seconds
% 1.35/0.83 % CPU time: 3.187428 seconds
% 1.35/0.83 % Total memory used: 139.051 MB
% 1.35/0.83 % Net memory used: 136.522 MB
%------------------------------------------------------------------------------