%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE022+4 : 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 : n013.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 0.14s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE022+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.43 % Computer : n013.cluster.edu
% 0.14/0.43 % Model : x86_64 x86_64
% 0.14/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.43 % Memory : 8046.5625MB
% 0.14/0.43 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Sun Sep 20 22:38:20 UTC 2026
% 0.14/0.44 % CPUTime :
% 0.14/0.45 % Drodi V4.1.1
% 0.14/0.53 % Refutation found
% 0.14/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.53 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.53 fof(f1,axiom,(
% 0.14/0.53 (! [A,B] : addition(A,B) = addition(B,A) )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f4,axiom,(
% 0.14/0.53 (! [A] : addition(A,A) = A )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f6,axiom,(
% 0.14/0.53 (! [A] : multiplication(A,one) = A )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f8,axiom,(
% 0.14/0.53 (! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f12,axiom,(
% 0.14/0.53 (! [A,B] :( leq(A,B)<=> addition(A,B) = B ) )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f14,axiom,(
% 0.14/0.53 (! [X0,X1] :( complement(X1,X0)<=> ( multiplication(X0,X1) = zero& multiplication(X1,X0) = zero& addition(X0,X1) = one ) ) )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f15,axiom,(
% 0.14/0.53 (! [X0,X1] :( test(X0)=> ( c(X0) = X1<=> complement(X0,X1) ) ) )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f19,conjecture,(
% 0.14/0.53 (! [X0,X1] :( test(X1)=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ) )),
% 0.14/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.53 fof(f20,negated_conjecture,(
% 0.14/0.53 ~((! [X0,X1] :( test(X1)=> ( leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))& leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0) ) ) ))),
% 0.14/0.53 inference(negated_conjecture,[status(cth)],[f19])).
% 0.14/0.53 fof(f21,plain,(
% 0.14/0.53 ![X0,X1]: (addition(X0,X1)=addition(X1,X0))),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.53 fof(f24,plain,(
% 0.14/0.53 ![X0]: (addition(X0,X0)=X0)),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.53 fof(f26,plain,(
% 0.14/0.53 ![X0]: (multiplication(X0,one)=X0)),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.53 fof(f28,plain,(
% 0.14/0.53 ![X0,X1,X2]: (multiplication(X0,addition(X1,X2))=addition(multiplication(X0,X1),multiplication(X0,X2)))),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.53 fof(f32,plain,(
% 0.14/0.53 ![A,B]: ((~leq(A,B)|addition(A,B)=B)&(leq(A,B)|~addition(A,B)=B))),
% 0.14/0.53 inference(NNF_transformation,[status(thm)],[f12])).
% 0.14/0.53 fof(f33,plain,(
% 0.14/0.53 (![A,B]: (~leq(A,B)|addition(A,B)=B))&(![A,B]: (leq(A,B)|~addition(A,B)=B))),
% 0.14/0.53 inference(miniscoping,[status(thm)],[f32])).
% 0.14/0.53 fof(f35,plain,(
% 0.14/0.53 ![X0,X1]: (leq(X0,X1)|~addition(X0,X1)=X1)),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f33])).
% 0.14/0.53 fof(f41,plain,(
% 0.14/0.53 ![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)))),
% 0.14/0.53 inference(NNF_transformation,[status(thm)],[f14])).
% 0.14/0.53 fof(f42,plain,(
% 0.14/0.53 (![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)))),
% 0.14/0.53 inference(miniscoping,[status(thm)],[f41])).
% 0.14/0.53 fof(f45,plain,(
% 0.14/0.53 ![X0,X1]: (~complement(X0,X1)|addition(X1,X0)=one)),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f42])).
% 0.14/0.53 fof(f47,plain,(
% 0.14/0.53 ![X0,X1]: (~test(X0)|(c(X0)=X1<=>complement(X0,X1)))),
% 0.14/0.53 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.14/0.53 fof(f48,plain,(
% 0.14/0.53 ![X0,X1]: (~test(X0)|((~c(X0)=X1|complement(X0,X1))&(c(X0)=X1|~complement(X0,X1))))),
% 0.14/0.53 inference(NNF_transformation,[status(thm)],[f47])).
% 0.14/0.53 fof(f49,plain,(
% 0.14/0.53 ![X0]: (~test(X0)|((![X1]: (~c(X0)=X1|complement(X0,X1)))&(![X1]: (c(X0)=X1|~complement(X0,X1)))))),
% 0.14/0.53 inference(miniscoping,[status(thm)],[f48])).
% 0.14/0.53 fof(f50,plain,(
% 0.14/0.53 ![X0,X1]: (~test(X0)|~c(X0)=X1|complement(X0,X1))),
% 0.14/0.53 inference(cnf_transformation,[status(thm)],[f49])).
% 0.14/0.53 fof(f58,plain,(
% 0.14/0.53 (?[X0,X1]: (test(X1)&(~leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))|~leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))))),
% 0.14/0.53 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.14/0.53 fof(f59,plain,(
% 0.14/0.53 ?[X1]: (test(X1)&((?[X0]: ~leq(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1)))))|(?[X0]: ~leq(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))))),
% 0.14/0.54 inference(miniscoping,[status(thm)],[f58])).
% 0.14/0.54 fof(f60,plain,(
% 0.14/0.54 (test(sK1_skl)&(~leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl))))|~leq(addition(multiplication(sK3_skl,sK1_skl),multiplication(sK3_skl,c(sK1_skl))),sK3_skl)))),
% 0.14/0.54 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X0,sK3_skl)],[f59])).
% 0.14/0.54 fof(f61,plain,(
% 0.14/0.54 test(sK1_skl)),
% 0.14/0.54 inference(cnf_transformation,[status(thm)],[f60])).
% 0.14/0.54 fof(f62,plain,(
% 0.14/0.54 ~leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl))))|~leq(addition(multiplication(sK3_skl,sK1_skl),multiplication(sK3_skl,c(sK1_skl))),sK3_skl)),
% 0.14/0.54 inference(cnf_transformation,[status(thm)],[f60])).
% 0.14/0.54 fof(f63,definition,(
% 0.14/0.54 sQ0_spl <=> (leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl)))))),
% 0.14/0.54 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.54 fof(f65,plain,(
% 0.14/0.54 ~leq(sK2_skl,addition(multiplication(sK2_skl,sK1_skl),multiplication(sK2_skl,c(sK1_skl))))|sQ0_spl),
% 0.14/0.54 inference(component_clause,[status(thm)],[f63])).
% 0.14/0.54 fof(f66,definition,(
% 0.14/0.54 sQ1_spl <=> (leq(addition(multiplication(sK3_skl,sK1_skl),multiplication(sK3_skl,c(sK1_skl))),sK3_skl))),
% 0.14/0.54 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.54 fof(f68,plain,(
% 0.14/0.54 ~leq(addition(multiplication(sK3_skl,sK1_skl),multiplication(sK3_skl,c(sK1_skl))),sK3_skl)|sQ1_spl),
% 0.14/0.54 inference(component_clause,[status(thm)],[f66])).
% 0.14/0.54 fof(f69,plain,(
% 0.14/0.54 ~sQ0_spl|~sQ1_spl),
% 0.14/0.54 inference(split_clause,[status(thm)],[f62,f63,f66])).
% 0.14/0.54 fof(f70,plain,(
% 0.14/0.54 ![X0]: (~test(X0)|complement(X0,c(X0)))),
% 0.14/0.54 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 0.14/0.54 fof(f87,plain,(
% 0.14/0.54 ![X0]: (leq(X0,X0))),
% 0.14/0.54 inference(resolution,[status(thm)],[f35,f24])).
% 0.14/0.54 fof(f135,plain,(
% 0.14/0.54 ~leq(sK2_skl,multiplication(sK2_skl,addition(sK1_skl,c(sK1_skl))))|sQ0_spl),
% 0.14/0.55 inference(backward_demodulation,[status(thm)],[f28,f65])).
% 0.14/0.55 fof(f515,plain,(
% 0.14/0.55 complement(sK1_skl,c(sK1_skl))),
% 0.14/0.55 inference(resolution,[status(thm)],[f70,f61])).
% 0.14/0.55 fof(f526,plain,(
% 0.14/0.55 addition(c(sK1_skl),sK1_skl)=one),
% 0.14/0.55 inference(resolution,[status(thm)],[f45,f515])).
% 0.14/0.55 fof(f560,plain,(
% 0.14/0.55 addition(sK1_skl,c(sK1_skl))=one),
% 0.14/0.55 inference(paramodulation,[status(thm)],[f21,f526])).
% 0.14/0.55 fof(f1499,plain,(
% 0.14/0.55 ~leq(sK2_skl,multiplication(sK2_skl,one))|sQ0_spl),
% 0.14/0.55 inference(backward_demodulation,[status(thm)],[f560,f135])).
% 0.14/0.55 fof(f1517,plain,(
% 0.14/0.55 ~leq(sK2_skl,sK2_skl)|sQ0_spl),
% 0.14/0.55 inference(forward_demodulation,[status(thm)],[f26,f1499])).
% 0.14/0.55 fof(f1518,plain,(
% 0.14/0.55 $false|sQ0_spl),
% 0.14/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1517,f87])).
% 0.14/0.55 fof(f1519,plain,(
% 0.14/0.55 sQ0_spl),
% 0.14/0.55 inference(contradiction_clause,[status(thm)],[f1518])).
% 0.14/0.55 fof(f1532,plain,(
% 0.14/0.55 ~leq(multiplication(sK3_skl,addition(sK1_skl,c(sK1_skl))),sK3_skl)|sQ1_spl),
% 0.14/0.55 inference(forward_demodulation,[status(thm)],[f28,f68])).
% 0.14/0.55 fof(f1533,plain,(
% 0.14/0.55 ~leq(multiplication(sK3_skl,one),sK3_skl)|sQ1_spl),
% 0.14/0.55 inference(forward_demodulation,[status(thm)],[f560,f1532])).
% 0.14/0.55 fof(f1534,plain,(
% 0.14/0.55 ~leq(sK3_skl,sK3_skl)|sQ1_spl),
% 0.14/0.55 inference(forward_demodulation,[status(thm)],[f26,f1533])).
% 0.14/0.55 fof(f1535,plain,(
% 0.14/0.55 $false|sQ1_spl),
% 0.14/0.55 inference(forward_subsumption_resolution,[status(thm)],[f1534,f87])).
% 0.14/0.55 fof(f1536,plain,(
% 0.14/0.55 sQ1_spl),
% 0.14/0.55 inference(contradiction_clause,[status(thm)],[f1535])).
% 0.14/0.55 fof(f1537,plain,(
% 0.14/0.55 $false),
% 0.14/0.55 inference(sat_refutation,[status(thm)],[f69,f1519,f1536])).
% 0.14/0.55 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.56 % Elapsed time: 0.104931 seconds
% 0.14/0.56 % CPU time: 0.246728 seconds
% 0.14/0.56 % Total memory used: 40.295 MB
% 0.14/0.56 % Net memory used: 40.212 MB
%------------------------------------------------------------------------------