%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE025+2 : 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 : n009.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 1.09s 0.76s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE025+2 : 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 : n009.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 22:39:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 1.09/0.76 % Refutation found
% 1.09/0.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.09/0.76 % SZS output start CNFRefutation for theBenchmark
% 1.09/0.76 fof(f1,axiom,(
% 1.09/0.76 (! [A,B] : addition(A,B) = addition(B,A) )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f3,axiom,(
% 1.09/0.76 (! [A] : addition(A,zero) = A )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f5,axiom,(
% 1.09/0.76 (! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f6,axiom,(
% 1.09/0.76 (! [A] : multiplication(A,one) = A )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f8,axiom,(
% 1.09/0.76 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f14,axiom,(
% 1.09/0.76 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f15,axiom,(
% 1.09/0.76 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f19,conjecture,(
% 1.09/0.76 (! [X0,X1,X2] :( ( test(X1)& test(X2) )=> ( multiplication(multiplication(X1,X0),c(X2)) = zero=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ) )),
% 1.09/0.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 1.09/0.76 fof(f20,negated_conjecture,(
% 1.09/0.76 ~((! [X0,X1,X2] :( ( test(X1)& test(X2) )=> ( multiplication(multiplication(X1,X0),c(X2)) = zero=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ) ))),
% 1.09/0.76 inference(negated_conjecture,[status(cth)],[f19])).
% 1.09/0.76 fof(f21,plain,(
% 1.09/0.76 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f1])).
% 1.09/0.76 fof(f23,plain,(
% 1.09/0.76 ![X0]: (addition(X0,zero)=X0)),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f3])).
% 1.09/0.76 fof(f25,plain,(
% 1.09/0.76 ![X0,X1,X2]: (multiplication(X0,multiplication(X1,X2))=multiplication(multiplication(X0,X1),X2))),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f5])).
% 1.09/0.76 fof(f26,plain,(
% 1.09/0.76 ![X0]: (multiplication(X0,one)=X0)),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f6])).
% 1.09/0.76 fof(f28,plain,(
% 1.09/0.76 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f8])).
% 1.09/0.76 fof(f41,plain,(
% 1.09/0.76 ![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)))),
% 1.09/0.76 inference(NNF_transformation,[status(thm)],[f14])).
% 1.09/0.76 fof(f42,plain,(
% 1.09/0.76 (![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)))),
% 1.09/0.76 inference(miniscoping,[status(thm)],[f41])).
% 1.09/0.76 fof(f45,plain,(
% 1.09/0.76 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f42])).
% 1.09/0.76 fof(f47,plain,(
% 1.09/0.76 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 1.09/0.76 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 1.09/0.76 fof(f48,plain,(
% 1.09/0.76 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 1.09/0.76 inference(NNF_transformation,[status(thm)],[f47])).
% 1.09/0.76 fof(f49,plain,(
% 1.09/0.76 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 1.09/0.76 inference(miniscoping,[status(thm)],[f48])).
% 1.09/0.76 fof(f50,plain,(
% 1.09/0.76 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 1.09/0.76 inference(cnf_transformation,[status(thm)],[f49])).
% 1.09/0.76 fof(f58,plain,(
% 1.09/0.76 (?[X0,X1,X2]: ((test(X1)&test(X2))&(multiplication(multiplication(X1,X0),c(X2))=zero&~multiplication(X1,X0)=multiplication(multiplication(X1,X0),X2))))),
% 1.09/0.76 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 1.09/0.76 fof(f59,plain,(
% 1.09/0.76 ?[X1,X2]: ((test(X1)&test(X2))&(?[X0]: (multiplication(multiplication(X1,X0),c(X2))=zero&~multiplication(X1,X0)=multiplication(multiplication(X1,X0),X2))))),
% 1.09/0.76 inference(miniscoping,[status(thm)],[f58])).
% 2.64/0.77 fof(f60,plain,(
% 2.64/0.77 ((test(sK1_skl)&test(sK2_skl))&(multiplication(multiplication(sK1_skl,sK3_skl),c(sK2_skl))=zero&~multiplication(sK1_skl,sK3_skl)=multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)))),
% 2.64/0.77 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])).
% 2.64/0.77 fof(f62,plain,(
% 2.64/0.77 test(sK2_skl)),
% 2.64/0.77 inference(cnf_transformation,[status(thm)],[f60])).
% 2.64/0.77 fof(f63,plain,(
% 2.64/0.77 multiplication(multiplication(sK1_skl,sK3_skl),c(sK2_skl))=zero),
% 2.64/0.77 inference(cnf_transformation,[status(thm)],[f60])).
% 2.64/0.77 fof(f64,plain,(
% 2.64/0.77 ~multiplication(sK1_skl,sK3_skl)=multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)),
% 2.64/0.77 inference(cnf_transformation,[status(thm)],[f60])).
% 2.64/0.77 fof(f65,plain,(
% 2.64/0.77 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 2.64/0.77 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 2.64/0.77 fof(f68,plain,(
% 2.64/0.77 ~multiplication(sK1_skl,sK3_skl)=multiplication(sK1_skl,multiplication(sK3_skl,sK2_skl))),
% 2.64/0.77 inference(backward_demodulation,[status(thm)],[f25,f64])).
% 2.64/0.77 fof(f69,plain,(
% 2.64/0.77 multiplication(sK1_skl,multiplication(sK3_skl,c(sK2_skl)))=zero),
% 2.64/0.77 inference(backward_demodulation,[status(thm)],[f25,f63])).
% 2.64/0.77 fof(f113,plain,(
% 2.64/0.77 ![X0]: (X0=addition(zero,X0))),
% 2.64/0.77 inference(paramodulation,[status(thm)],[f23,f21])).
% 2.64/0.77 fof(f163,plain,(
% 2.64/0.77 ![X0]: (multiplication(sK1_skl,addition(multiplication(sK3_skl,c(sK2_skl)),X0))=addition(zero,multiplication(sK1_skl,X0)))),
% 2.64/0.77 inference(paramodulation,[status(thm)],[f69,f28])).
% 2.64/0.77 fof(f182,plain,(
% 2.64/0.77 ![X0]: (multiplication(sK1_skl,addition(multiplication(sK3_skl,c(sK2_skl)),X0))=multiplication(sK1_skl,X0))),
% 2.64/0.77 inference(forward_demodulation,[status(thm)],[f113,f163])).
% 2.64/0.77 fof(f286,plain,(
% 2.64/0.77 complement(sK2_skl,c(sK2_skl))),
% 2.64/0.77 inference(resolution,[status(thm)],[f65,f62])).
% 2.64/0.77 fof(f333,plain,(
% 2.64/0.77 addition(c(sK2_skl),sK2_skl)=one),
% 2.64/0.77 inference(resolution,[status(thm)],[f45,f286])).
% 2.64/0.77 fof(f420,plain,(
% 2.64/0.77 ![X0]: (multiplication(sK1_skl,multiplication(sK3_skl,addition(c(sK2_skl),X0)))=multiplication(sK1_skl,multiplication(sK3_skl,X0)))),
% 2.64/0.77 inference(paramodulation,[status(thm)],[f28,f182])).
% 2.64/0.77 fof(f5651,plain,(
% 2.64/0.77 multiplication(sK1_skl,multiplication(sK3_skl,one))=multiplication(sK1_skl,multiplication(sK3_skl,sK2_skl))),
% 2.64/0.77 inference(paramodulation,[status(thm)],[f333,f420])).
% 2.64/0.77 fof(f5693,plain,(
% 2.64/0.77 multiplication(sK1_skl,sK3_skl)=multiplication(sK1_skl,multiplication(sK3_skl,sK2_skl))),
% 2.64/0.77 inference(forward_demodulation,[status(thm)],[f26,f5651])).
% 2.64/0.77 fof(f5694,plain,(
% 2.64/0.77 $false),
% 2.64/0.77 inference(forward_subsumption_resolution,[status(thm)],[f5693,f68])).
% 2.64/0.77 % SZS output end CNFRefutation for theBenchmark.p
% 2.64/0.81 % Elapsed time: 0.423385 seconds
% 2.64/0.81 % CPU time: 3.058249 seconds
% 2.64/0.81 % Total memory used: 162.853 MB
% 2.64/0.81 % Net memory used: 160.335 MB
%------------------------------------------------------------------------------