TSTP Solution File: ITP023+2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ITP023+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 : Tue Apr 30 20:22:58 EDT 2024
% Result : Theorem 2.40s 0.67s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP023+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 22:42:29 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.6.0
% 2.40/0.67 % Refutation found
% 2.40/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.40/0.67 % SZS output start CNFRefutation for theBenchmark
% 2.40/0.67 fof(f4,axiom,(
% 2.40/0.67 (! [A,B,F] :( mem(F,arr(A,B))=> (! [X] :( mem(X,A)=> mem(ap(F,X),B) ) )) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f13,axiom,(
% 2.40/0.67 ne(ty_2Erealax_2Ereal) ),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f15,axiom,(
% 2.40/0.67 mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))) ),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f17,axiom,(
% 2.40/0.67 (! [A_27a] :( ne(A_27a)=> (! [A_27b] :( ne(A_27b)=> mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) )) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f18,axiom,(
% 2.40/0.67 mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))) ),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f20,axiom,(
% 2.40/0.67 mem(c_2Ebool_2EF,bool) ),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f21,axiom,(
% 2.40/0.67 ~ p(c_2Ebool_2EF) ),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f28,axiom,(
% 2.40/0.67 mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f29,axiom,(
% 2.40/0.67 (! [Q] :( mem(Q,bool)=> ( p(ap(c_2Ebool_2E_7E,Q))<=> ~ p(Q) ) ) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f46,axiom,(
% 2.40/0.67 (! [V0x] :( mem(V0x,ty_2Erealax_2Ereal)=> (! [V1e] :( mem(V1e,ty_2Erealax_2Ereal)=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) )) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f47,axiom,(
% 2.40/0.67 (! [V0s] :( mem(V0s,arr(ty_2Erealax_2Ereal,bool))=> (! [V1t] :( mem(V1t,arr(ty_2Erealax_2Ereal,bool))=> ( ( p(ap(c_2Ereal__topology_2Ebounded__def,V1t))& p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),V0s),V1t)) )=> p(ap(c_2Ereal__topology_2Ebounded__def,V0s)) ) ) )) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f48,axiom,(
% 2.40/0.67 (! [V0x] :( mem(V0x,ty_2Erealax_2Ereal)=> (! [V1e] :( mem(V1e,ty_2Erealax_2Ereal)=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) )) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f59,conjecture,(
% 2.40/0.67 (! [V0x] :( mem(V0x,ty_2Erealax_2Ereal)=> (! [V1e] :( mem(V1e,ty_2Erealax_2Ereal)=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) )) )),
% 2.40/0.67 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.40/0.67 fof(f60,negated_conjecture,(
% 2.40/0.67 ~((! [V0x] :( mem(V0x,ty_2Erealax_2Ereal)=> (! [V1e] :( mem(V1e,ty_2Erealax_2Ereal)=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) )) ))),
% 2.40/0.67 inference(negated_conjecture,[status(cth)],[f59])).
% 2.40/0.67 fof(f65,plain,(
% 2.40/0.67 ![A,B,F]: (~mem(F,arr(A,B))|(![X]: (~mem(X,A)|mem(ap(F,X),B))))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f4])).
% 2.40/0.67 fof(f66,plain,(
% 2.40/0.67 ![X0,X1,X2,X3]: (~mem(X0,arr(X1,X2))|~mem(X3,X1)|mem(ap(X0,X3),X2))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f65])).
% 2.40/0.67 fof(f90,plain,(
% 2.40/0.67 ne(ty_2Erealax_2Ereal)),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f13])).
% 2.40/0.67 fof(f93,plain,(
% 2.40/0.67 mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f15])).
% 2.40/0.67 fof(f96,plain,(
% 2.40/0.67 ![A_27a]: (~ne(A_27a)|(![A_27b]: (~ne(A_27b)|mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))))))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f17])).
% 2.40/0.67 fof(f97,plain,(
% 2.40/0.67 ![X0,X1]: (~ne(X0)|~ne(X1)|mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1)))))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f96])).
% 2.40/0.67 fof(f98,plain,(
% 2.40/0.67 mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool)))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f18])).
% 2.40/0.67 fof(f100,plain,(
% 2.40/0.67 mem(c_2Ebool_2EF,bool)),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f20])).
% 2.40/0.67 fof(f101,plain,(
% 2.40/0.67 ~p(c_2Ebool_2EF)),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f21])).
% 2.40/0.67 fof(f120,plain,(
% 2.40/0.67 mem(c_2Ebool_2E_7E,arr(bool,bool))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f28])).
% 2.40/0.67 fof(f121,plain,(
% 2.40/0.67 ![Q]: (~mem(Q,bool)|(p(ap(c_2Ebool_2E_7E,Q))<=>~p(Q)))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f29])).
% 2.40/0.67 fof(f122,plain,(
% 2.40/0.67 ![Q]: (~mem(Q,bool)|((~p(ap(c_2Ebool_2E_7E,Q))|~p(Q))&(p(ap(c_2Ebool_2E_7E,Q))|p(Q))))),
% 2.40/0.67 inference(NNF_transformation,[status(esa)],[f121])).
% 2.40/0.67 fof(f124,plain,(
% 2.40/0.67 ![X0]: (~mem(X0,bool)|p(ap(c_2Ebool_2E_7E,X0))|p(X0))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f122])).
% 2.40/0.67 fof(f212,plain,(
% 2.40/0.67 ![V0x]: (~mem(V0x,ty_2Erealax_2Ereal)|(![V1e]: (~mem(V1e,ty_2Erealax_2Ereal)|p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))))))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f46])).
% 2.40/0.67 fof(f213,plain,(
% 2.40/0.67 ![X0,X1]: (~mem(X0,ty_2Erealax_2Ereal)|~mem(X1,ty_2Erealax_2Ereal)|p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f212])).
% 2.40/0.67 fof(f214,plain,(
% 2.40/0.67 ![V0s]: (~mem(V0s,arr(ty_2Erealax_2Ereal,bool))|(![V1t]: (~mem(V1t,arr(ty_2Erealax_2Ereal,bool))|((~p(ap(c_2Ereal__topology_2Ebounded__def,V1t))|~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),V0s),V1t)))|p(ap(c_2Ereal__topology_2Ebounded__def,V0s))))))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f47])).
% 2.40/0.67 fof(f215,plain,(
% 2.40/0.67 ![X0,X1]: (~mem(X0,arr(ty_2Erealax_2Ereal,bool))|~mem(X1,arr(ty_2Erealax_2Ereal,bool))|~p(ap(c_2Ereal__topology_2Ebounded__def,X1))|~p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))|p(ap(c_2Ereal__topology_2Ebounded__def,X0)))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f214])).
% 2.40/0.67 fof(f216,plain,(
% 2.40/0.67 ![V0x]: (~mem(V0x,ty_2Erealax_2Ereal)|(![V1e]: (~mem(V1e,ty_2Erealax_2Ereal)|p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))))))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f48])).
% 2.40/0.67 fof(f217,plain,(
% 2.40/0.67 ![X0,X1]: (~mem(X0,ty_2Erealax_2Ereal)|~mem(X1,ty_2Erealax_2Ereal)|p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f216])).
% 2.40/0.67 fof(f298,plain,(
% 2.40/0.67 (?[V0x]: (mem(V0x,ty_2Erealax_2Ereal)&(?[V1e]: (mem(V1e,ty_2Erealax_2Ereal)&~p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))))))))),
% 2.40/0.67 inference(pre_NNF_transformation,[status(esa)],[f60])).
% 2.40/0.67 fof(f299,plain,(
% 2.40/0.67 (mem(sk0_5,ty_2Erealax_2Ereal)&(mem(sk0_6,ty_2Erealax_2Ereal)&~p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sk0_5),sk0_6))))))),
% 2.40/0.67 inference(skolemization,[status(esa)],[f298])).
% 2.40/0.67 fof(f300,plain,(
% 2.40/0.67 mem(sk0_5,ty_2Erealax_2Ereal)),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f299])).
% 2.40/0.67 fof(f301,plain,(
% 2.40/0.67 mem(sk0_6,ty_2Erealax_2Ereal)),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f299])).
% 2.40/0.67 fof(f302,plain,(
% 2.40/0.67 ~p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sk0_5),sk0_6))))),
% 2.40/0.67 inference(cnf_transformation,[status(esa)],[f299])).
% 2.40/0.67 fof(f488,plain,(
% 2.40/0.67 ![X0]: (~mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|mem(ap(c_2Ereal__topology_2Eball,X0),arr(ty_2Erealax_2Ereal,bool)))),
% 2.40/0.67 inference(resolution,[status(thm)],[f66,f93])).
% 2.40/0.67 fof(f538,plain,(
% 2.40/0.67 ![X0,X1,X2]: (~ne(X0)|~ne(X1)|~mem(X2,X0)|mem(ap(c_2Epair_2E_2C(X0,X1),X2),arr(X1,ty_2Epair_2Eprod(X0,X1))))),
% 2.40/0.67 inference(resolution,[status(thm)],[f97,f66])).
% 2.40/0.67 fof(f593,plain,(
% 2.40/0.67 ![X0,X1,X2,X3]: (~ne(X0)|~ne(X1)|~mem(X2,X0)|~mem(X3,X1)|mem(ap(ap(c_2Epair_2E_2C(X0,X1),X2),X3),ty_2Epair_2Eprod(X0,X1)))),
% 2.40/0.67 inference(resolution,[status(thm)],[f538,f66])).
% 2.40/0.67 fof(f595,plain,(
% 2.40/0.67 spl0_13 <=> ne(ty_2Erealax_2Ereal)),
% 2.40/0.67 introduced(split_symbol_definition)).
% 2.40/0.67 fof(f597,plain,(
% 2.40/0.67 ~ne(ty_2Erealax_2Ereal)|spl0_13),
% 2.40/0.67 inference(component_clause,[status(thm)],[f595])).
% 2.40/0.67 fof(f614,plain,(
% 2.40/0.67 $false|spl0_13),
% 2.40/0.67 inference(forward_subsumption_resolution,[status(thm)],[f597,f90])).
% 2.40/0.67 fof(f615,plain,(
% 2.40/0.67 spl0_13),
% 2.40/0.67 inference(contradiction_clause,[status(thm)],[f614])).
% 2.40/0.67 fof(f663,plain,(
% 2.40/0.67 ![X0,X1]: (~mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))|~mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))|~p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))|p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))|~mem(X0,ty_2Erealax_2Ereal)|~mem(X1,ty_2Erealax_2Ereal))),
% 2.40/0.67 inference(resolution,[status(thm)],[f215,f213])).
% 2.40/0.67 fof(f664,plain,(
% 2.40/0.67 ![X0,X1]: (~mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))|~mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))|p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))|~mem(X0,ty_2Erealax_2Ereal)|~mem(X1,ty_2Erealax_2Ereal))),
% 2.40/0.67 inference(forward_subsumption_resolution,[status(thm)],[f663,f217])).
% 2.40/0.67 fof(f907,plain,(
% 2.40/0.67 ![X0]: (~mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|mem(ap(c_2Ereal__topology_2Ecball,X0),arr(ty_2Erealax_2Ereal,bool)))),
% 2.40/0.67 inference(resolution,[status(thm)],[f98,f66])).
% 2.40/0.67 fof(f1047,plain,(
% 2.40/0.67 spl0_51 <=> mem(sk0_5,ty_2Erealax_2Ereal)),
% 2.40/0.67 introduced(split_symbol_definition)).
% 2.40/0.67 fof(f1049,plain,(
% 2.40/0.67 ~mem(sk0_5,ty_2Erealax_2Ereal)|spl0_51),
% 2.40/0.67 inference(component_clause,[status(thm)],[f1047])).
% 2.40/0.67 fof(f1050,plain,(
% 2.40/0.67 spl0_52 <=> mem(sk0_6,ty_2Erealax_2Ereal)),
% 2.40/0.67 introduced(split_symbol_definition)).
% 2.40/0.67 fof(f1052,plain,(
% 2.40/0.67 ~mem(sk0_6,ty_2Erealax_2Ereal)|spl0_52),
% 2.40/0.67 inference(component_clause,[status(thm)],[f1050])).
% 2.40/0.67 fof(f1055,plain,(
% 2.40/0.67 $false|spl0_52),
% 2.40/0.67 inference(forward_subsumption_resolution,[status(thm)],[f1052,f301])).
% 2.40/0.67 fof(f1056,plain,(
% 2.40/0.67 spl0_52),
% 2.40/0.67 inference(contradiction_clause,[status(thm)],[f1055])).
% 2.40/0.67 fof(f1057,plain,(
% 2.40/0.67 $false|spl0_51),
% 2.40/0.67 inference(forward_subsumption_resolution,[status(thm)],[f1049,f300])).
% 2.40/0.67 fof(f1058,plain,(
% 2.40/0.67 spl0_51),
% 2.40/0.67 inference(contradiction_clause,[status(thm)],[f1057])).
% 2.40/0.67 fof(f1110,plain,(
% 2.40/0.67 spl0_56 <=> mem(c_2Ebool_2EF,bool)),
% 2.40/0.67 introduced(split_symbol_definition)).
% 2.40/0.67 fof(f1112,plain,(
% 2.40/0.67 ~mem(c_2Ebool_2EF,bool)|spl0_56),
% 2.40/0.67 inference(component_clause,[status(thm)],[f1110])).
% 2.40/0.67 fof(f1120,plain,(
% 2.40/0.67 $false|spl0_56),
% 2.40/0.67 inference(forward_subsumption_resolution,[status(thm)],[f1112,f100])).
% 2.40/0.67 fof(f1121,plain,(
% 2.40/0.67 spl0_56),
% 2.40/0.67 inference(contradiction_clause,[status(thm)],[f1120])).
% 2.40/0.67 fof(f1317,plain,(
% 2.40/0.67 ![X0,X1]: (~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|~mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))|p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))|~mem(X0,ty_2Erealax_2Ereal)|~mem(X1,ty_2Erealax_2Ereal))),
% 2.40/0.68 inference(resolution,[status(thm)],[f907,f664])).
% 2.40/0.68 fof(f1318,plain,(
% 2.40/0.68 ![X0,X1]: (~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))|~mem(X0,ty_2Erealax_2Ereal)|~mem(X1,ty_2Erealax_2Ereal))),
% 2.40/0.68 inference(forward_subsumption_resolution,[status(thm)],[f1317,f488])).
% 2.40/0.68 fof(f1420,plain,(
% 2.40/0.68 spl0_81 <=> mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sk0_5),sk0_6),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))),
% 2.40/0.68 introduced(split_symbol_definition)).
% 2.40/0.68 fof(f1422,plain,(
% 2.40/0.68 ~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sk0_5),sk0_6),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|spl0_81),
% 2.40/0.68 inference(component_clause,[status(thm)],[f1420])).
% 2.40/0.68 fof(f1423,plain,(
% 2.40/0.68 ~mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sk0_5),sk0_6),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))|~mem(sk0_5,ty_2Erealax_2Ereal)|~mem(sk0_6,ty_2Erealax_2Ereal)),
% 2.40/0.68 inference(resolution,[status(thm)],[f1318,f302])).
% 2.40/0.68 fof(f1424,plain,(
% 2.40/0.68 ~spl0_81|~spl0_51|~spl0_52),
% 2.40/0.68 inference(split_clause,[status(thm)],[f1423,f1420,f1047,f1050])).
% 2.40/0.68 fof(f1453,plain,(
% 2.40/0.68 spl0_84 <=> ~mem(X0,bool)|~p(ap(c_2Ebool_2E_7E,X0))),
% 2.40/0.68 introduced(split_symbol_definition)).
% 2.40/0.68 fof(f1454,plain,(
% 2.40/0.68 ![X0]: (~mem(X0,bool)|~p(ap(c_2Ebool_2E_7E,X0))|~spl0_84)),
% 2.40/0.68 inference(component_clause,[status(thm)],[f1453])).
% 2.40/0.68 fof(f1482,plain,(
% 2.40/0.68 spl0_88 <=> mem(c_2Ebool_2E_7E,arr(bool,bool))),
% 2.40/0.68 introduced(split_symbol_definition)).
% 2.40/0.68 fof(f1484,plain,(
% 2.40/0.68 ~mem(c_2Ebool_2E_7E,arr(bool,bool))|spl0_88),
% 2.40/0.68 inference(component_clause,[status(thm)],[f1482])).
% 2.40/0.68 fof(f1490,plain,(
% 2.40/0.68 $false|spl0_88),
% 2.40/0.68 inference(forward_subsumption_resolution,[status(thm)],[f1484,f120])).
% 2.40/0.68 fof(f1491,plain,(
% 2.40/0.68 spl0_88),
% 2.40/0.68 inference(contradiction_clause,[status(thm)],[f1490])).
% 2.40/0.68 fof(f1555,plain,(
% 2.40/0.68 ![X0]: (~mem(X0,bool)|p(X0)|~spl0_84)),
% 2.40/0.68 inference(forward_subsumption_resolution,[status(thm)],[f124,f1454])).
% 2.40/0.68 fof(f1570,plain,(
% 2.40/0.68 p(c_2Ebool_2EF)|~spl0_84),
% 2.40/0.68 inference(resolution,[status(thm)],[f1555,f100])).
% 2.40/0.68 fof(f1571,plain,(
% 2.40/0.68 $false|~spl0_84),
% 2.40/0.68 inference(forward_subsumption_resolution,[status(thm)],[f1570,f101])).
% 2.40/0.68 fof(f1572,plain,(
% 2.40/0.68 ~spl0_84),
% 2.40/0.68 inference(contradiction_clause,[status(thm)],[f1571])).
% 2.40/0.68 fof(f1690,plain,(
% 2.40/0.68 ~ne(ty_2Erealax_2Ereal)|~ne(ty_2Erealax_2Ereal)|~mem(sk0_5,ty_2Erealax_2Ereal)|~mem(sk0_6,ty_2Erealax_2Ereal)|spl0_81),
% 2.40/0.68 inference(resolution,[status(thm)],[f1422,f593])).
% 2.40/0.68 fof(f1691,plain,(
% 2.40/0.68 ~spl0_13|~spl0_51|~spl0_52|spl0_81),
% 2.40/0.68 inference(split_clause,[status(thm)],[f1690,f595,f1047,f1050,f1420])).
% 2.40/0.68 fof(f1692,plain,(
% 2.40/0.68 $false),
% 2.40/0.68 inference(sat_refutation,[status(thm)],[f615,f1056,f1058,f1121,f1424,f1491,f1572,f1691])).
% 2.40/0.68 % SZS output end CNFRefutation for theBenchmark.p
% 2.40/0.68 % Elapsed time: 0.338242 seconds
% 2.40/0.68 % CPU time: 2.543909 seconds
% 2.40/0.68 % Total memory used: 103.080 MB
% 2.40/0.68 % Net memory used: 101.351 MB
%------------------------------------------------------------------------------