TSTP Solution File: SET796+4 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET796+4 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:35:12 EDT 2023
% Result : Theorem 58.09s 7.70s
% Output : CNFRefutation 58.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET796+4 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.04/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 10:21:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.36 % Drodi V3.5.1
% 58.09/7.70 % Refutation found
% 58.09/7.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 58.09/7.70 % SZS output start CNFRefutation for theBenchmark
% 58.09/7.70 fof(f1,axiom,(
% 58.09/7.70 (! [A,B] :( subset(A,B)<=> (! [X] :( member(X,A)=> member(X,B) ) )) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f3,axiom,(
% 58.09/7.70 (! [X,A] :( member(X,power_set(A))<=> subset(X,A) ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f6,axiom,(
% 58.09/7.70 (! [X] : ~ member(X,empty_set) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f7,axiom,(
% 58.09/7.70 (! [B,A,E] :( member(B,difference(E,A))<=> ( member(B,E)& ~ member(B,A) ) ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f8,axiom,(
% 58.09/7.70 (! [X,A] :( member(X,singleton(A))<=> X = A ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f9,axiom,(
% 58.09/7.70 (! [X,A,B] :( member(X,unordered_pair(A,B))<=> ( X = A| X = B ) ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f11,axiom,(
% 58.09/7.70 (! [X,A] :( member(X,product(A))<=> (! [Y] :( member(Y,A)=> member(X,Y) ) )) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f12,axiom,(
% 58.09/7.70 (! [R,E] :( order(R,E)<=> ( (! [X] :( member(X,E)=> apply(R,X,X) ))& (! [X,Y] :( ( member(X,E)& member(Y,E) )=> ( ( apply(R,X,Y)& apply(R,Y,X) )=> X = Y ) ))& (! [X,Y,Z] :( ( member(X,E)& member(Y,E)& member(Z,E) )=> ( ( apply(R,X,Y)& apply(R,Y,Z) )=> apply(R,X,Z) ) ) )) ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f15,axiom,(
% 58.09/7.70 (! [R,E,M] :( lower_bound(M,R,E)<=> (! [X] :( member(X,E)=> apply(R,M,X) ) )) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f21,axiom,(
% 58.09/7.70 (! [A,X,R,E] :( greatest_lower_bound(A,X,R,E)<=> ( member(A,X)& lower_bound(A,R,X)& (! [M] :( ( member(M,E)& lower_bound(M,R,X) )=> apply(R,M,A) ) )) ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f22,conjecture,(
% 58.09/7.70 (! [R,E,A,B] :( ( order(R,E)& member(A,E)& member(B,E)& apply(R,A,B) )=> greatest_lower_bound(A,unordered_pair(A,B),R,E) ) )),
% 58.09/7.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 58.09/7.70 fof(f23,negated_conjecture,(
% 58.09/7.70 ~((! [R,E,A,B] :( ( order(R,E)& member(A,E)& member(B,E)& apply(R,A,B) )=> greatest_lower_bound(A,unordered_pair(A,B),R,E) ) ))),
% 58.09/7.70 inference(negated_conjecture,[status(cth)],[f22])).
% 58.09/7.70 fof(f24,plain,(
% 58.09/7.70 ![A,B]: (subset(A,B)<=>(![X]: (~member(X,A)|member(X,B))))),
% 58.09/7.70 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 58.09/7.70 fof(f25,plain,(
% 58.09/7.70 ![A,B]: ((~subset(A,B)|(![X]: (~member(X,A)|member(X,B))))&(subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f24])).
% 58.09/7.70 fof(f26,plain,(
% 58.09/7.70 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(?[X]: (member(X,A)&~member(X,B)))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f25])).
% 58.09/7.70 fof(f27,plain,(
% 58.09/7.70 (![A,B]: (~subset(A,B)|(![X]: (~member(X,A)|member(X,B)))))&(![A,B]: (subset(A,B)|(member(sk0_0(B,A),A)&~member(sk0_0(B,A),B))))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f26])).
% 58.09/7.70 fof(f28,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~subset(X0,X1)|~member(X2,X0)|member(X2,X1))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f27])).
% 58.09/7.70 fof(f29,plain,(
% 58.09/7.70 ![X0,X1]: (subset(X0,X1)|member(sk0_0(X1,X0),X0))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f27])).
% 58.09/7.70 fof(f36,plain,(
% 58.09/7.70 ![X,A]: ((~member(X,power_set(A))|subset(X,A))&(member(X,power_set(A))|~subset(X,A)))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f3])).
% 58.09/7.70 fof(f37,plain,(
% 58.09/7.70 (![X,A]: (~member(X,power_set(A))|subset(X,A)))&(![X,A]: (member(X,power_set(A))|~subset(X,A)))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f36])).
% 58.09/7.70 fof(f39,plain,(
% 58.09/7.70 ![X0,X1]: (member(X0,power_set(X1))|~subset(X0,X1))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f37])).
% 58.09/7.70 fof(f50,plain,(
% 58.09/7.70 ![X0]: (~member(X0,empty_set))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f6])).
% 58.09/7.70 fof(f51,plain,(
% 58.09/7.70 ![B,A,E]: ((~member(B,difference(E,A))|(member(B,E)&~member(B,A)))&(member(B,difference(E,A))|(~member(B,E)|member(B,A))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f7])).
% 58.09/7.70 fof(f52,plain,(
% 58.09/7.70 (![B,A,E]: (~member(B,difference(E,A))|(member(B,E)&~member(B,A))))&(![B,A,E]: (member(B,difference(E,A))|(~member(B,E)|member(B,A))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f51])).
% 58.09/7.70 fof(f54,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~member(X0,difference(X1,X2))|~member(X0,X2))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f52])).
% 58.09/7.70 fof(f56,plain,(
% 58.09/7.70 ![X,A]: ((~member(X,singleton(A))|X=A)&(member(X,singleton(A))|~X=A))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f8])).
% 58.09/7.70 fof(f57,plain,(
% 58.09/7.70 (![X,A]: (~member(X,singleton(A))|X=A))&(![X,A]: (member(X,singleton(A))|~X=A))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f56])).
% 58.09/7.70 fof(f58,plain,(
% 58.09/7.70 ![X0,X1]: (~member(X0,singleton(X1))|X0=X1)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f57])).
% 58.09/7.70 fof(f59,plain,(
% 58.09/7.70 ![X0,X1]: (member(X0,singleton(X1))|~X0=X1)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f57])).
% 58.09/7.70 fof(f60,plain,(
% 58.09/7.70 ![X,A,B]: ((~member(X,unordered_pair(A,B))|(X=A|X=B))&(member(X,unordered_pair(A,B))|(~X=A&~X=B)))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f9])).
% 58.09/7.70 fof(f61,plain,(
% 58.09/7.70 (![X,A,B]: (~member(X,unordered_pair(A,B))|(X=A|X=B)))&(![X,A,B]: (member(X,unordered_pair(A,B))|(~X=A&~X=B)))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f60])).
% 58.09/7.70 fof(f62,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~member(X0,unordered_pair(X1,X2))|X0=X1|X0=X2)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f61])).
% 58.09/7.70 fof(f63,plain,(
% 58.09/7.70 ![X0,X1,X2]: (member(X0,unordered_pair(X1,X2))|~X0=X1)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f61])).
% 58.09/7.70 fof(f64,plain,(
% 58.09/7.70 ![X0,X1,X2]: (member(X0,unordered_pair(X1,X2))|~X0=X2)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f61])).
% 58.09/7.70 fof(f71,plain,(
% 58.09/7.70 ![X,A]: (member(X,product(A))<=>(![Y]: (~member(Y,A)|member(X,Y))))),
% 58.09/7.70 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 58.09/7.70 fof(f72,plain,(
% 58.09/7.70 ![X,A]: ((~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y))))&(member(X,product(A))|(?[Y]: (member(Y,A)&~member(X,Y)))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f71])).
% 58.09/7.70 fof(f73,plain,(
% 58.09/7.70 (![X,A]: (~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y)))))&(![X,A]: (member(X,product(A))|(?[Y]: (member(Y,A)&~member(X,Y)))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f72])).
% 58.09/7.70 fof(f74,plain,(
% 58.09/7.70 (![X,A]: (~member(X,product(A))|(![Y]: (~member(Y,A)|member(X,Y)))))&(![X,A]: (member(X,product(A))|(member(sk0_2(A,X),A)&~member(X,sk0_2(A,X)))))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f73])).
% 58.09/7.70 fof(f75,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~member(X0,product(X1))|~member(X2,X1)|member(X0,X2))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f74])).
% 58.09/7.70 fof(f76,plain,(
% 58.09/7.70 ![X0,X1]: (member(X0,product(X1))|member(sk0_2(X1,X0),X1))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f74])).
% 58.09/7.70 fof(f78,plain,(
% 58.09/7.70 ![R,E]: (order(R,E)<=>(((![X]: (~member(X,E)|apply(R,X,X)))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 58.09/7.70 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 58.09/7.70 fof(f79,plain,(
% 58.09/7.70 ![R,E]: (pd0_0(E,R)<=>((![X]: (~member(X,E)|apply(R,X,X)))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))),
% 58.09/7.70 introduced(predicate_definition,[f78])).
% 58.09/7.70 fof(f80,plain,(
% 58.09/7.70 ![R,E]: (order(R,E)<=>(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))),
% 58.09/7.70 inference(formula_renaming,[status(thm)],[f78,f79])).
% 58.09/7.70 fof(f81,plain,(
% 58.09/7.70 ![R,E]: ((~order(R,E)|(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z))))))&(order(R,E)|(~pd0_0(E,R)|(?[X,Y,Z]: (((member(X,E)&member(Y,E))&member(Z,E))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f80])).
% 58.09/7.70 fof(f82,plain,(
% 58.09/7.70 (![R,E]: (~order(R,E)|(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![R,E]: (order(R,E)|(~pd0_0(E,R)|(?[X,Y,Z]: (((member(X,E)&member(Y,E))&member(Z,E))&((apply(R,X,Y)&apply(R,Y,Z))&~apply(R,X,Z)))))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f81])).
% 58.09/7.70 fof(f83,plain,(
% 58.09/7.70 (![R,E]: (~order(R,E)|(pd0_0(E,R)&(![X,Y,Z]: (((~member(X,E)|~member(Y,E))|~member(Z,E))|((~apply(R,X,Y)|~apply(R,Y,Z))|apply(R,X,Z)))))))&(![R,E]: (order(R,E)|(~pd0_0(E,R)|(((member(sk0_3(E,R),E)&member(sk0_4(E,R),E))&member(sk0_5(E,R),E))&((apply(R,sk0_3(E,R),sk0_4(E,R))&apply(R,sk0_4(E,R),sk0_5(E,R)))&~apply(R,sk0_3(E,R),sk0_5(E,R)))))))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f82])).
% 58.09/7.70 fof(f84,plain,(
% 58.09/7.70 ![X0,X1]: (~order(X0,X1)|pd0_0(X1,X0))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f83])).
% 58.09/7.70 fof(f109,plain,(
% 58.09/7.70 ![R,E,M]: (lower_bound(M,R,E)<=>(![X]: (~member(X,E)|apply(R,M,X))))),
% 58.09/7.70 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 58.09/7.70 fof(f110,plain,(
% 58.09/7.70 ![R,E,M]: ((~lower_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,M,X))))&(lower_bound(M,R,E)|(?[X]: (member(X,E)&~apply(R,M,X)))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f109])).
% 58.09/7.70 fof(f111,plain,(
% 58.09/7.70 (![R,E,M]: (~lower_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,M,X)))))&(![R,E,M]: (lower_bound(M,R,E)|(?[X]: (member(X,E)&~apply(R,M,X)))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f110])).
% 58.09/7.70 fof(f112,plain,(
% 58.09/7.70 (![R,E,M]: (~lower_bound(M,R,E)|(![X]: (~member(X,E)|apply(R,M,X)))))&(![R,E,M]: (lower_bound(M,R,E)|(member(sk0_9(M,E,R),E)&~apply(R,M,sk0_9(M,E,R)))))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f111])).
% 58.09/7.70 fof(f113,plain,(
% 58.09/7.70 ![X0,X1,X2,X3]: (~lower_bound(X0,X1,X2)|~member(X3,X2)|apply(X1,X0,X3))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f112])).
% 58.09/7.70 fof(f114,plain,(
% 58.09/7.70 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|member(sk0_9(X0,X2,X1),X2))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f112])).
% 58.09/7.70 fof(f115,plain,(
% 58.09/7.70 ![X0,X1,X2]: (lower_bound(X0,X1,X2)|~apply(X1,X0,sk0_9(X0,X2,X1)))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f112])).
% 58.09/7.70 fof(f160,plain,(
% 58.09/7.70 ![A,X,R,E]: (greatest_lower_bound(A,X,R,E)<=>((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A)))))),
% 58.09/7.70 inference(pre_NNF_transformation,[status(esa)],[f21])).
% 58.09/7.70 fof(f161,plain,(
% 58.09/7.70 ![A,X,R,E]: ((~greatest_lower_bound(A,X,R,E)|((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A)))))&(greatest_lower_bound(A,X,R,E)|((~member(A,X)|~lower_bound(A,R,X))|(?[M]: ((member(M,E)&lower_bound(M,R,X))&~apply(R,M,A))))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f160])).
% 58.09/7.70 fof(f162,plain,(
% 58.09/7.70 (![A,X,R,E]: (~greatest_lower_bound(A,X,R,E)|((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A))))))&(![A,X,R,E]: (greatest_lower_bound(A,X,R,E)|((~member(A,X)|~lower_bound(A,R,X))|(?[M]: ((member(M,E)&lower_bound(M,R,X))&~apply(R,M,A))))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f161])).
% 58.09/7.70 fof(f163,plain,(
% 58.09/7.70 (![A,X,R,E]: (~greatest_lower_bound(A,X,R,E)|((member(A,X)&lower_bound(A,R,X))&(![M]: ((~member(M,E)|~lower_bound(M,R,X))|apply(R,M,A))))))&(![A,X,R,E]: (greatest_lower_bound(A,X,R,E)|((~member(A,X)|~lower_bound(A,R,X))|((member(sk0_15(E,R,X,A),E)&lower_bound(sk0_15(E,R,X,A),R,X))&~apply(R,sk0_15(E,R,X,A),A)))))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f162])).
% 58.09/7.70 fof(f168,plain,(
% 58.09/7.70 ![X0,X1,X2,X3]: (greatest_lower_bound(X0,X1,X2,X3)|~member(X0,X1)|~lower_bound(X0,X2,X1)|lower_bound(sk0_15(X3,X2,X1,X0),X2,X1))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f163])).
% 58.09/7.70 fof(f169,plain,(
% 58.09/7.70 ![X0,X1,X2,X3]: (greatest_lower_bound(X0,X1,X2,X3)|~member(X0,X1)|~lower_bound(X0,X2,X1)|~apply(X2,sk0_15(X3,X2,X1,X0),X0))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f163])).
% 58.09/7.70 fof(f170,plain,(
% 58.09/7.70 (?[R,E,A,B]: ((((order(R,E)&member(A,E))&member(B,E))&apply(R,A,B))&~greatest_lower_bound(A,unordered_pair(A,B),R,E)))),
% 58.09/7.70 inference(pre_NNF_transformation,[status(esa)],[f23])).
% 58.09/7.70 fof(f171,plain,(
% 58.09/7.70 ((((order(sk0_16,sk0_17)&member(sk0_18,sk0_17))&member(sk0_19,sk0_17))&apply(sk0_16,sk0_18,sk0_19))&~greatest_lower_bound(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16,sk0_17))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f170])).
% 58.09/7.70 fof(f172,plain,(
% 58.09/7.70 order(sk0_16,sk0_17)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f171])).
% 58.09/7.70 fof(f173,plain,(
% 58.09/7.70 member(sk0_18,sk0_17)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f171])).
% 58.09/7.70 fof(f174,plain,(
% 58.09/7.70 member(sk0_19,sk0_17)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f171])).
% 58.09/7.70 fof(f175,plain,(
% 58.09/7.70 apply(sk0_16,sk0_18,sk0_19)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f171])).
% 58.09/7.70 fof(f176,plain,(
% 58.09/7.70 ~greatest_lower_bound(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16,sk0_17)),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f171])).
% 58.09/7.70 fof(f177,plain,(
% 58.09/7.70 ![R,E,X]: (pd0_1(X,E,R)<=>(~member(X,E)|apply(R,X,X)))),
% 58.09/7.70 introduced(predicate_definition,[f79])).
% 58.09/7.70 fof(f178,plain,(
% 58.09/7.70 ![R,E]: (pd0_0(E,R)<=>((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))),
% 58.09/7.70 inference(formula_renaming,[status(thm)],[f79,f177])).
% 58.09/7.70 fof(f179,plain,(
% 58.09/7.70 ![R,E]: ((~pd0_0(E,R)|((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y)))))&(pd0_0(E,R)|((?[X]: ~pd0_1(X,E,R))|(?[X,Y]: ((member(X,E)&member(Y,E))&((apply(R,X,Y)&apply(R,Y,X))&~X=Y))))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f178])).
% 58.09/7.70 fof(f180,plain,(
% 58.09/7.70 (![R,E]: (~pd0_0(E,R)|((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))))&(![R,E]: (pd0_0(E,R)|((?[X]: ~pd0_1(X,E,R))|(?[X,Y]: ((member(X,E)&member(Y,E))&((apply(R,X,Y)&apply(R,Y,X))&~X=Y))))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f179])).
% 58.09/7.70 fof(f181,plain,(
% 58.09/7.70 (![R,E]: (~pd0_0(E,R)|((![X]: pd0_1(X,E,R))&(![X,Y]: ((~member(X,E)|~member(Y,E))|((~apply(R,X,Y)|~apply(R,Y,X))|X=Y))))))&(![R,E]: (pd0_0(E,R)|(~pd0_1(sk0_20(E,R),E,R)|((member(sk0_21(E,R),E)&member(sk0_22(E,R),E))&((apply(R,sk0_21(E,R),sk0_22(E,R))&apply(R,sk0_22(E,R),sk0_21(E,R)))&~sk0_21(E,R)=sk0_22(E,R))))))),
% 58.09/7.70 inference(skolemization,[status(esa)],[f180])).
% 58.09/7.70 fof(f182,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~pd0_0(X0,X1)|pd0_1(X2,X0,X1))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f181])).
% 58.09/7.70 fof(f189,plain,(
% 58.09/7.70 ![R,E,X]: ((~pd0_1(X,E,R)|(~member(X,E)|apply(R,X,X)))&(pd0_1(X,E,R)|(member(X,E)&~apply(R,X,X))))),
% 58.09/7.70 inference(NNF_transformation,[status(esa)],[f177])).
% 58.09/7.70 fof(f190,plain,(
% 58.09/7.70 (![R,E,X]: (~pd0_1(X,E,R)|(~member(X,E)|apply(R,X,X))))&(![R,E,X]: (pd0_1(X,E,R)|(member(X,E)&~apply(R,X,X))))),
% 58.09/7.70 inference(miniscoping,[status(esa)],[f189])).
% 58.09/7.70 fof(f191,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~pd0_1(X0,X1,X2)|~member(X0,X1)|apply(X2,X0,X0))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f190])).
% 58.09/7.70 fof(f193,plain,(
% 58.09/7.70 ![X0,X1,X2]: (pd0_1(X0,X1,X2)|~apply(X2,X0,X0))),
% 58.09/7.70 inference(cnf_transformation,[status(esa)],[f190])).
% 58.09/7.70 fof(f194,plain,(
% 58.09/7.70 ![X0]: (member(X0,singleton(X0)))),
% 58.09/7.70 inference(destructive_equality_resolution,[status(esa)],[f59])).
% 58.09/7.70 fof(f195,plain,(
% 58.09/7.70 ![X0,X1]: (member(X0,unordered_pair(X0,X1)))),
% 58.09/7.70 inference(destructive_equality_resolution,[status(esa)],[f63])).
% 58.09/7.70 fof(f196,plain,(
% 58.09/7.70 ![X0,X1]: (member(X0,unordered_pair(X1,X0)))),
% 58.09/7.70 inference(destructive_equality_resolution,[status(esa)],[f64])).
% 58.09/7.70 fof(f198,plain,(
% 58.09/7.70 ![X0]: (subset(empty_set,X0))),
% 58.09/7.70 inference(resolution,[status(thm)],[f50,f29])).
% 58.09/7.70 fof(f204,plain,(
% 58.09/7.70 ![X0]: (member(empty_set,power_set(X0)))),
% 58.09/7.70 inference(resolution,[status(thm)],[f39,f198])).
% 58.09/7.70 fof(f311,plain,(
% 58.09/7.70 spl0_7 <=> ~member(X0,power_set(empty_set))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f312,plain,(
% 58.09/7.70 ![X0]: (~member(X0,power_set(empty_set))|~spl0_7)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f311])).
% 58.09/7.70 fof(f318,plain,(
% 58.09/7.70 ![X0]: (subset(power_set(empty_set),X0)|~spl0_7)),
% 58.09/7.70 inference(resolution,[status(thm)],[f312,f29])).
% 58.09/7.70 fof(f323,plain,(
% 58.09/7.70 ![X0]: (member(power_set(empty_set),power_set(X0))|~spl0_7)),
% 58.09/7.70 inference(resolution,[status(thm)],[f318,f39])).
% 58.09/7.70 fof(f326,plain,(
% 58.09/7.70 $false|~spl0_7),
% 58.09/7.70 inference(resolution,[status(thm)],[f323,f312])).
% 58.09/7.70 fof(f327,plain,(
% 58.09/7.70 ~spl0_7),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f326])).
% 58.09/7.70 fof(f340,plain,(
% 58.09/7.70 spl0_8 <=> ~member(X1,sk0_17)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f341,plain,(
% 58.09/7.70 ![X0]: (~member(X0,sk0_17)|~spl0_8)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f340])).
% 58.09/7.70 fof(f349,plain,(
% 58.09/7.70 $false|~spl0_8),
% 58.09/7.70 inference(backward_subsumption_resolution,[status(thm)],[f174,f341])).
% 58.09/7.70 fof(f350,plain,(
% 58.09/7.70 ~spl0_8),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f349])).
% 58.09/7.70 fof(f506,plain,(
% 58.09/7.70 ![X0,X1]: (sk0_0(X0,singleton(X1))=X1|subset(singleton(X1),X0))),
% 58.09/7.70 inference(resolution,[status(thm)],[f58,f29])).
% 58.09/7.70 fof(f1084,plain,(
% 58.09/7.70 spl0_50 <=> ~member(X0,unordered_pair(sk0_17,sk0_17))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f1085,plain,(
% 58.09/7.70 ![X0]: (~member(X0,unordered_pair(sk0_17,sk0_17))|~spl0_50)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f1084])).
% 58.09/7.70 fof(f1179,plain,(
% 58.09/7.70 ![X0,X1,X2]: (sk0_0(X0,singleton(X1))=X1|~member(X2,singleton(X1))|member(X2,X0))),
% 58.09/7.70 inference(resolution,[status(thm)],[f506,f28])).
% 58.09/7.70 fof(f1186,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~member(X0,X1)|member(X2,X0)|member(sk0_2(X1,X2),X1))),
% 58.09/7.70 inference(resolution,[status(thm)],[f75,f76])).
% 58.09/7.70 fof(f1202,plain,(
% 58.09/7.70 $false|~spl0_50),
% 58.09/7.70 inference(resolution,[status(thm)],[f1085,f196])).
% 58.09/7.70 fof(f1203,plain,(
% 58.09/7.70 ~spl0_50),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f1202])).
% 58.09/7.70 fof(f1847,plain,(
% 58.09/7.70 ![X0,X1,X2,X3]: (~member(X0,unordered_pair(X1,X2))|member(X3,X0)|sk0_2(unordered_pair(X1,X2),X3)=X1|sk0_2(unordered_pair(X1,X2),X3)=X2)),
% 58.09/7.70 inference(resolution,[status(thm)],[f1186,f62])).
% 58.09/7.70 fof(f2761,plain,(
% 58.09/7.70 ![X0,X1,X2]: (member(X0,X1)|sk0_2(unordered_pair(X2,X1),X0)=X2|sk0_2(unordered_pair(X2,X1),X0)=X1)),
% 58.09/7.70 inference(resolution,[status(thm)],[f1847,f196])).
% 58.09/7.70 fof(f2821,plain,(
% 58.09/7.70 ![X0,X1]: (sk0_0(X0,singleton(X1))=X1|member(X1,X0))),
% 58.09/7.70 inference(resolution,[status(thm)],[f1179,f194])).
% 58.09/7.70 fof(f2845,plain,(
% 58.09/7.70 ![X0,X1,X2]: (sk0_0(difference(X0,X1),singleton(X2))=X2|~member(X2,X1))),
% 58.09/7.70 inference(resolution,[status(thm)],[f2821,f54])).
% 58.09/7.70 fof(f2883,plain,(
% 58.09/7.70 ![X0,X1]: (sk0_0(difference(X0,power_set(X1)),singleton(empty_set))=empty_set)),
% 58.09/7.70 inference(resolution,[status(thm)],[f2845,f204])).
% 58.09/7.70 fof(f3093,plain,(
% 58.09/7.70 spl0_126 <=> ~member(X0,singleton(sk0_17))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f3094,plain,(
% 58.09/7.70 ![X0]: (~member(X0,singleton(sk0_17))|~spl0_126)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f3093])).
% 58.09/7.70 fof(f3266,plain,(
% 58.09/7.70 ![X0,X1]: (sk0_2(unordered_pair(X0,empty_set),X1)=X0|sk0_2(unordered_pair(X0,empty_set),X1)=empty_set)),
% 58.09/7.70 inference(resolution,[status(thm)],[f2761,f50])).
% 58.09/7.70 fof(f3283,plain,(
% 58.09/7.70 ![X0,X1]: (~empty_set=X0|sk0_2(unordered_pair(X0,empty_set),X1)=X0)),
% 58.09/7.70 inference(equality_factoring,[status(esa)],[f3266])).
% 58.09/7.70 fof(f3284,plain,(
% 58.09/7.70 ![X0]: (sk0_2(unordered_pair(empty_set,empty_set),X0)=empty_set)),
% 58.09/7.70 inference(destructive_equality_resolution,[status(esa)],[f3283])).
% 58.09/7.70 fof(f3295,plain,(
% 58.09/7.70 spl0_132 <=> ~member(X0,unordered_pair(empty_set,empty_set))|member(X1,X0)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f3296,plain,(
% 58.09/7.70 ![X0,X1]: (~member(X0,unordered_pair(empty_set,empty_set))|member(X1,X0)|~spl0_132)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f3295])).
% 58.09/7.70 fof(f3298,plain,(
% 58.09/7.70 spl0_133 <=> member(empty_set,unordered_pair(empty_set,empty_set))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f3301,plain,(
% 58.09/7.70 ![X0,X1]: (~member(X0,unordered_pair(empty_set,empty_set))|member(X1,X0)|member(empty_set,unordered_pair(empty_set,empty_set)))),
% 58.09/7.70 inference(paramodulation,[status(thm)],[f3284,f1186])).
% 58.09/7.70 fof(f3302,plain,(
% 58.09/7.70 spl0_132|spl0_133),
% 58.09/7.70 inference(split_clause,[status(thm)],[f3301,f3295,f3298])).
% 58.09/7.70 fof(f3456,plain,(
% 58.09/7.70 spl0_134 <=> subset(singleton(empty_set),difference(X0,power_set(X1)))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f3457,plain,(
% 58.09/7.70 ![X0,X1]: (subset(singleton(empty_set),difference(X0,power_set(X1)))|~spl0_134)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f3456])).
% 58.09/7.70 fof(f3459,plain,(
% 58.09/7.70 spl0_135 <=> member(empty_set,singleton(empty_set))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f3462,plain,(
% 58.09/7.70 ![X0,X1]: (subset(singleton(empty_set),difference(X0,power_set(X1)))|member(empty_set,singleton(empty_set)))),
% 58.09/7.70 inference(paramodulation,[status(thm)],[f2883,f29])).
% 58.09/7.70 fof(f3463,plain,(
% 58.09/7.70 spl0_134|spl0_135),
% 58.09/7.70 inference(split_clause,[status(thm)],[f3462,f3456,f3459])).
% 58.09/7.70 fof(f3921,plain,(
% 58.09/7.70 $false|~spl0_126),
% 58.09/7.70 inference(resolution,[status(thm)],[f3094,f194])).
% 58.09/7.70 fof(f3922,plain,(
% 58.09/7.70 ~spl0_126),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f3921])).
% 58.09/7.70 fof(f3927,plain,(
% 58.09/7.70 ![X0]: (member(X0,empty_set)|~spl0_132)),
% 58.09/7.70 inference(resolution,[status(thm)],[f3296,f196])).
% 58.09/7.70 fof(f3928,plain,(
% 58.09/7.70 $false|~spl0_132),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f3927,f50])).
% 58.09/7.70 fof(f3929,plain,(
% 58.09/7.70 ~spl0_132),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f3928])).
% 58.09/7.70 fof(f3949,plain,(
% 58.09/7.70 ![X0,X1,X2]: (~member(X0,singleton(empty_set))|member(X0,difference(X1,power_set(X2)))|~spl0_134)),
% 58.09/7.70 inference(resolution,[status(thm)],[f3457,f28])).
% 58.09/7.70 fof(f3955,plain,(
% 58.09/7.70 ![X0,X1]: (member(empty_set,difference(X0,power_set(X1)))|~spl0_134)),
% 58.09/7.70 inference(resolution,[status(thm)],[f3949,f194])).
% 58.09/7.70 fof(f4054,plain,(
% 58.09/7.70 spl0_144 <=> member(sk0_18,sk0_17)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4056,plain,(
% 58.09/7.70 ~member(sk0_18,sk0_17)|spl0_144),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4054])).
% 58.09/7.70 fof(f4098,plain,(
% 58.09/7.70 spl0_145 <=> member(sk0_18,unordered_pair(sk0_18,sk0_19))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4100,plain,(
% 58.09/7.70 ~member(sk0_18,unordered_pair(sk0_18,sk0_19))|spl0_145),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4098])).
% 58.09/7.70 fof(f4101,plain,(
% 58.09/7.70 spl0_146 <=> lower_bound(sk0_18,sk0_16,unordered_pair(sk0_18,sk0_19))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4103,plain,(
% 58.09/7.70 ~lower_bound(sk0_18,sk0_16,unordered_pair(sk0_18,sk0_19))|spl0_146),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4101])).
% 58.09/7.70 fof(f4109,plain,(
% 58.09/7.70 $false|spl0_145),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f4100,f195])).
% 58.09/7.70 fof(f4110,plain,(
% 58.09/7.70 spl0_145),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f4109])).
% 58.09/7.70 fof(f4134,plain,(
% 58.09/7.70 ~apply(sk0_16,sk0_18,sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16))|spl0_146),
% 58.09/7.70 inference(resolution,[status(thm)],[f4103,f115])).
% 58.09/7.70 fof(f4135,plain,(
% 58.09/7.70 member(sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16),unordered_pair(sk0_18,sk0_19))|spl0_146),
% 58.09/7.70 inference(resolution,[status(thm)],[f4103,f114])).
% 58.09/7.70 fof(f4203,plain,(
% 58.09/7.70 spl0_155 <=> member(sk0_17,unordered_pair(sk0_17,sk0_19))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4205,plain,(
% 58.09/7.70 ~member(sk0_17,unordered_pair(sk0_17,sk0_19))|spl0_155),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4203])).
% 58.09/7.70 fof(f4209,plain,(
% 58.09/7.70 spl0_157 <=> member(sk0_15(X0,sk0_16,unordered_pair(sk0_17,sk0_19),sk0_17),X0)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4210,plain,(
% 58.09/7.70 ![X0]: (member(sk0_15(X0,sk0_16,unordered_pair(sk0_17,sk0_19),sk0_17),X0)|~spl0_157)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4209])).
% 58.09/7.70 fof(f4214,plain,(
% 58.09/7.70 $false|spl0_155),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f4205,f195])).
% 58.09/7.70 fof(f4215,plain,(
% 58.09/7.70 spl0_155),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f4214])).
% 58.09/7.70 fof(f4254,plain,(
% 58.09/7.70 ![X0]: (~member(empty_set,power_set(X0))|~spl0_134)),
% 58.09/7.70 inference(resolution,[status(thm)],[f3955,f54])).
% 58.09/7.70 fof(f4255,plain,(
% 58.09/7.70 $false|~spl0_134),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f4254,f204])).
% 58.09/7.70 fof(f4256,plain,(
% 58.09/7.70 ~spl0_134),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f4255])).
% 58.09/7.70 fof(f4275,plain,(
% 58.09/7.70 $false|~spl0_157),
% 58.09/7.70 inference(resolution,[status(thm)],[f4210,f50])).
% 58.09/7.70 fof(f4276,plain,(
% 58.09/7.70 ~spl0_157),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f4275])).
% 58.09/7.70 fof(f4542,plain,(
% 58.09/7.70 spl0_175 <=> apply(sk0_16,sk0_15(sk0_17,sk0_16,unordered_pair(sk0_18,sk0_19),sk0_18),sk0_18)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4544,plain,(
% 58.09/7.70 ~apply(sk0_16,sk0_15(sk0_17,sk0_16,unordered_pair(sk0_18,sk0_19),sk0_18),sk0_18)|spl0_175),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4542])).
% 58.09/7.70 fof(f4545,plain,(
% 58.09/7.70 ~member(sk0_18,unordered_pair(sk0_18,sk0_19))|~lower_bound(sk0_18,sk0_16,unordered_pair(sk0_18,sk0_19))|~apply(sk0_16,sk0_15(sk0_17,sk0_16,unordered_pair(sk0_18,sk0_19),sk0_18),sk0_18)),
% 58.09/7.70 inference(resolution,[status(thm)],[f169,f176])).
% 58.09/7.70 fof(f4546,plain,(
% 58.09/7.70 ~spl0_145|~spl0_146|~spl0_175),
% 58.09/7.70 inference(split_clause,[status(thm)],[f4545,f4098,f4101,f4542])).
% 58.09/7.70 fof(f4570,plain,(
% 58.09/7.70 ![X0]: (~lower_bound(sk0_15(sk0_17,sk0_16,unordered_pair(sk0_18,sk0_19),sk0_18),sk0_16,X0)|~member(sk0_18,X0)|spl0_175)),
% 58.09/7.70 inference(resolution,[status(thm)],[f4544,f113])).
% 58.09/7.70 fof(f4664,plain,(
% 58.09/7.70 spl0_180 <=> sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16)=sk0_18),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4665,plain,(
% 58.09/7.70 sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16)=sk0_18|~spl0_180),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4664])).
% 58.09/7.70 fof(f4667,plain,(
% 58.09/7.70 spl0_181 <=> sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16)=sk0_19),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4668,plain,(
% 58.09/7.70 sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16)=sk0_19|~spl0_181),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4667])).
% 58.09/7.70 fof(f4670,plain,(
% 58.09/7.70 sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16)=sk0_18|sk0_9(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16)=sk0_19|spl0_146),
% 58.09/7.70 inference(resolution,[status(thm)],[f62,f4135])).
% 58.09/7.70 fof(f4671,plain,(
% 58.09/7.70 spl0_180|spl0_181|spl0_146),
% 58.09/7.70 inference(split_clause,[status(thm)],[f4670,f4664,f4667,f4101])).
% 58.09/7.70 fof(f4850,plain,(
% 58.09/7.70 spl0_182 <=> member(sk0_17,unordered_pair(sk0_17,sk0_18))),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f4852,plain,(
% 58.09/7.70 ~member(sk0_17,unordered_pair(sk0_17,sk0_18))|spl0_182),
% 58.09/7.70 inference(component_clause,[status(thm)],[f4850])).
% 58.09/7.70 fof(f4866,plain,(
% 58.09/7.70 $false|spl0_182),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f4852,f195])).
% 58.09/7.70 fof(f4867,plain,(
% 58.09/7.70 spl0_182),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f4866])).
% 58.09/7.70 fof(f4965,plain,(
% 58.09/7.70 $false|spl0_144),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f4056,f173])).
% 58.09/7.70 fof(f4966,plain,(
% 58.09/7.70 spl0_144),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f4965])).
% 58.09/7.70 fof(f4969,plain,(
% 58.09/7.70 ~apply(sk0_16,sk0_18,sk0_18)|~spl0_180|spl0_146),
% 58.09/7.70 inference(forward_demodulation,[status(thm)],[f4665,f4134])).
% 58.09/7.70 fof(f5206,plain,(
% 58.09/7.70 ![X0]: (~pd0_1(sk0_18,X0,sk0_16)|~member(sk0_18,X0)|~spl0_180|spl0_146)),
% 58.09/7.70 inference(resolution,[status(thm)],[f4969,f191])).
% 58.09/7.70 fof(f5211,plain,(
% 58.09/7.70 spl0_193 <=> ~member(sk0_18,X0)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f5212,plain,(
% 58.09/7.70 ![X0]: (~member(sk0_18,X0)|~spl0_193)),
% 58.09/7.70 inference(component_clause,[status(thm)],[f5211])).
% 58.09/7.70 fof(f5214,plain,(
% 58.09/7.70 spl0_194 <=> apply(sk0_16,sk0_18,sk0_18)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f5216,plain,(
% 58.09/7.70 ~apply(sk0_16,sk0_18,sk0_18)|spl0_194),
% 58.09/7.70 inference(component_clause,[status(thm)],[f5214])).
% 58.09/7.70 fof(f5217,plain,(
% 58.09/7.70 ![X0]: (~member(sk0_18,X0)|~apply(sk0_16,sk0_18,sk0_18)|~spl0_180|spl0_146)),
% 58.09/7.70 inference(resolution,[status(thm)],[f5206,f193])).
% 58.09/7.70 fof(f5218,plain,(
% 58.09/7.70 spl0_193|~spl0_194|~spl0_180|spl0_146),
% 58.09/7.70 inference(split_clause,[status(thm)],[f5217,f5211,f5214,f4664,f4101])).
% 58.09/7.70 fof(f5222,plain,(
% 58.09/7.70 ~apply(sk0_16,sk0_18,sk0_19)|~spl0_181|spl0_146),
% 58.09/7.70 inference(forward_demodulation,[status(thm)],[f4668,f4134])).
% 58.09/7.70 fof(f5223,plain,(
% 58.09/7.70 $false|~spl0_181|spl0_146),
% 58.09/7.70 inference(forward_subsumption_resolution,[status(thm)],[f5222,f175])).
% 58.09/7.70 fof(f5224,plain,(
% 58.09/7.70 ~spl0_181|spl0_146),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f5223])).
% 58.09/7.70 fof(f5225,plain,(
% 58.09/7.70 $false|~spl0_193),
% 58.09/7.70 inference(backward_subsumption_resolution,[status(thm)],[f173,f5212])).
% 58.09/7.70 fof(f5226,plain,(
% 58.09/7.70 ~spl0_193),
% 58.09/7.70 inference(contradiction_clause,[status(thm)],[f5225])).
% 58.09/7.70 fof(f5253,plain,(
% 58.09/7.70 ![X0]: (~pd0_1(sk0_18,X0,sk0_16)|~member(sk0_18,X0)|spl0_194)),
% 58.09/7.70 inference(resolution,[status(thm)],[f5216,f191])).
% 58.09/7.70 fof(f5257,plain,(
% 58.09/7.70 ![X0]: (~member(sk0_18,X0)|~pd0_0(X0,sk0_16)|spl0_194)),
% 58.09/7.70 inference(resolution,[status(thm)],[f5253,f182])).
% 58.09/7.70 fof(f5260,plain,(
% 58.09/7.70 ![X0]: (~member(sk0_18,X0)|~order(sk0_16,X0)|spl0_194)),
% 58.09/7.70 inference(resolution,[status(thm)],[f5257,f84])).
% 58.09/7.70 fof(f5261,plain,(
% 58.09/7.70 ~member(sk0_18,sk0_17)|spl0_194),
% 58.09/7.70 inference(resolution,[status(thm)],[f5260,f172])).
% 58.09/7.70 fof(f5262,plain,(
% 58.09/7.70 ~spl0_144|spl0_194),
% 58.09/7.70 inference(split_clause,[status(thm)],[f5261,f4054,f5214])).
% 58.09/7.70 fof(f5356,plain,(
% 58.09/7.70 spl0_201 <=> greatest_lower_bound(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16,sk0_17)),
% 58.09/7.70 introduced(split_symbol_definition)).
% 58.09/7.70 fof(f5357,plain,(
% 58.09/7.70 greatest_lower_bound(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16,sk0_17)|~spl0_201),
% 58.09/7.70 inference(component_clause,[status(thm)],[f5356])).
% 58.09/7.70 fof(f5359,plain,(
% 58.09/7.70 ~member(sk0_18,unordered_pair(sk0_18,sk0_19))|greatest_lower_bound(sk0_18,unordered_pair(sk0_18,sk0_19),sk0_16,sk0_17)|~member(sk0_18,unordered_pair(sk0_18,sk0_19))|~lower_bound(sk0_18,sk0_16,unordered_pair(sk0_18,sk0_19))|spl0_175),
% 58.09/7.70 inference(resolution,[status(thm)],[f4570,f168])).
% 58.09/7.70 fof(f5360,plain,(
% 58.09/7.70 ~spl0_145|spl0_201|~spl0_146|spl0_175),
% 58.09/7.70 inference(split_clause,[status(thm)],[f5359,f4098,f5356,f4101,f4542])).
% 58.09/7.72 fof(f5364,plain,(
% 58.09/7.72 $false|~spl0_201),
% 58.09/7.72 inference(forward_subsumption_resolution,[status(thm)],[f5357,f176])).
% 58.09/7.72 fof(f5365,plain,(
% 58.09/7.72 ~spl0_201),
% 58.09/7.72 inference(contradiction_clause,[status(thm)],[f5364])).
% 58.09/7.72 fof(f5366,plain,(
% 58.09/7.72 $false),
% 58.09/7.72 inference(sat_refutation,[status(thm)],[f327,f350,f1203,f3302,f3463,f3922,f3929,f4110,f4215,f4256,f4276,f4546,f4671,f4867,f4966,f5218,f5224,f5226,f5262,f5360,f5365])).
% 58.09/7.72 % SZS output end CNFRefutation for theBenchmark.p
% 58.77/7.76 % Elapsed time: 7.388255 seconds
% 58.77/7.76 % CPU time: 58.566135 seconds
% 58.77/7.76 % Memory used: 278.741 MB
%------------------------------------------------------------------------------