TSTP Solution File: GEO462+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GEO462+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 20:18:06 EDT 2024
% Result : Theorem 5.69s 1.93s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO462+1 : TPTP v8.1.2. Released v7.0.0.
% 0.08/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 01:30:11 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.08/1.31 % Drodi V3.6.0
% 5.69/1.93 % Refutation found
% 5.69/1.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.69/1.93 % SZS output start CNFRefutation for theBenchmark
% 5.69/1.93 fof(f5,axiom,(
% 5.69/1.93 (! [X,XI_] :( ( p(s(bool,X))=> p(s(bool,XI_)) )<=> ( ( p(s(bool,X))& p(s(bool,XI_)) )<=> p(s(bool,X)) ) ) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f43,axiom,(
% 5.69/1.93 ~ p(s(bool,f0)) ),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f1673,axiom,(
% 5.69/1.93 (! [A] : p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),empty)))) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f1700,axiom,(
% 5.69/1.93 (! [A,S0] :( (? [X] : p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))<=> s(fun(A,bool),S0) != s(fun(A,bool),empty) ) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f1830,axiom,(
% 5.69/1.93 (! [Q47899,Q47903,F0,S0] :( s(fun(Q47899,bool),i(s(fun(fun(Q47903,bool),fun(Q47899,bool)),i(s(fun(fun(Q47903,Q47899),fun(fun(Q47903,bool),fun(Q47899,bool))),image),s(fun(Q47903,Q47899),F0))),s(fun(Q47903,bool),S0))) = s(fun(Q47899,bool),empty)<=> s(fun(Q47903,bool),S0) = s(fun(Q47903,bool),empty) ) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f1929,axiom,(
% 5.69/1.93 (! [A] : s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),empty))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f3294,axiom,(
% 5.69/1.93 (! [Q121390,S0] :( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))<=> ( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))& (! [X,Y] :( ( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))& p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),Y))),s(fun(cart(real,Q121390),bool),S0)))) )=> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(cart(real,Q121390),fun(cart(real,Q121390),cart(real,Q121390))),vectoru_add),s(cart(real,Q121390),X))),s(cart(real,Q121390),Y))))),s(fun(cart(real,Q121390),bool),S0)))) ))& (! [C0,X] :( p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))=> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0)))) ) )) ) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f3299,conjecture,(
% 5.69/1.93 (! [Q121443,S0] :( p(s(bool,i(s(fun(fun(cart(real,Q121443),bool),bool),subspace),s(fun(cart(real,Q121443),bool),S0))))=> s(fun(cart(real,Q121443),bool),S0) != s(fun(cart(real,Q121443),bool),empty) ) )),
% 5.69/1.93 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.69/1.93 fof(f3300,negated_conjecture,(
% 5.69/1.93 ~((! [Q121443,S0] :( p(s(bool,i(s(fun(fun(cart(real,Q121443),bool),bool),subspace),s(fun(cart(real,Q121443),bool),S0))))=> s(fun(cart(real,Q121443),bool),S0) != s(fun(cart(real,Q121443),bool),empty) ) ))),
% 5.69/1.93 inference(negated_conjecture,[status(cth)],[f3299])).
% 5.69/1.93 fof(f3310,plain,(
% 5.69/1.93 ![X,XI_]: ((~p(s(bool,X))|p(s(bool,XI_)))<=>((p(s(bool,X))&p(s(bool,XI_)))<=>p(s(bool,X))))),
% 5.69/1.93 inference(pre_NNF_transformation,[status(esa)],[f5])).
% 5.69/1.93 fof(f3311,plain,(
% 5.69/1.93 ![X,XI_]: (pd0_0(XI_,X)<=>((p(s(bool,X))&p(s(bool,XI_)))<=>p(s(bool,X))))),
% 5.69/1.93 introduced(predicate_definition,[f3310])).
% 5.69/1.93 fof(f3312,plain,(
% 5.69/1.93 ![X,XI_]: ((~p(s(bool,X))|p(s(bool,XI_)))<=>pd0_0(XI_,X))),
% 5.69/1.93 inference(formula_renaming,[status(thm)],[f3310,f3311])).
% 5.69/1.93 fof(f3313,plain,(
% 5.69/1.93 ![X,XI_]: (((p(s(bool,X))&~p(s(bool,XI_)))|pd0_0(XI_,X))&((~p(s(bool,X))|p(s(bool,XI_)))|~pd0_0(XI_,X)))),
% 5.69/1.93 inference(NNF_transformation,[status(esa)],[f3312])).
% 5.69/1.93 fof(f3314,plain,(
% 5.69/1.93 (![X,XI_]: ((p(s(bool,X))&~p(s(bool,XI_)))|pd0_0(XI_,X)))&(![X,XI_]: ((~p(s(bool,X))|p(s(bool,XI_)))|~pd0_0(XI_,X)))),
% 5.69/1.93 inference(miniscoping,[status(esa)],[f3313])).
% 5.69/1.93 fof(f3315,plain,(
% 5.69/1.93 ![X0,X1]: (p(s(bool,X0))|pd0_0(X1,X0))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f3314])).
% 5.69/1.93 fof(f3316,plain,(
% 5.69/1.93 ![X0,X1]: (~p(s(bool,X0))|pd0_0(X0,X1))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f3314])).
% 5.69/1.93 fof(f3317,plain,(
% 5.69/1.93 ![X0,X1]: (~p(s(bool,X0))|p(s(bool,X1))|~pd0_0(X1,X0))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f3314])).
% 5.69/1.93 fof(f3519,plain,(
% 5.69/1.93 ~p(s(bool,f0))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f43])).
% 5.69/1.93 fof(f7991,plain,(
% 5.69/1.93 ![X0]: (p(s(bool,i(s(fun(fun(X0,bool),bool),finite),s(fun(X0,bool),empty)))))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f1673])).
% 5.69/1.93 fof(f8135,plain,(
% 5.69/1.93 ![A,S0]: (((![X]: ~p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))|~s(fun(A,bool),S0)=s(fun(A,bool),empty))&((?[X]: p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))|s(fun(A,bool),S0)=s(fun(A,bool),empty)))),
% 5.69/1.93 inference(NNF_transformation,[status(esa)],[f1700])).
% 5.69/1.93 fof(f8136,plain,(
% 5.69/1.93 (![A,S0]: ((![X]: ~p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))|~s(fun(A,bool),S0)=s(fun(A,bool),empty)))&(![A,S0]: ((?[X]: p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))|s(fun(A,bool),S0)=s(fun(A,bool),empty)))),
% 5.69/1.93 inference(miniscoping,[status(esa)],[f8135])).
% 5.69/1.93 fof(f8137,plain,(
% 5.69/1.93 (![A,S0]: ((![X]: ~p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))|~s(fun(A,bool),S0)=s(fun(A,bool),empty)))&(![A,S0]: (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,sk0_832(S0,A)))),s(fun(A,bool),S0))))|s(fun(A,bool),S0)=s(fun(A,bool),empty)))),
% 5.69/1.93 inference(skolemization,[status(esa)],[f8136])).
% 5.69/1.93 fof(f8138,plain,(
% 5.69/1.93 ![X0,X1,X2]: (~p(s(bool,i(s(fun(fun(X0,bool),bool),i(s(fun(X0,fun(fun(X0,bool),bool)),in),s(X0,X1))),s(fun(X0,bool),X2))))|~s(fun(X0,bool),X2)=s(fun(X0,bool),empty))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f8137])).
% 5.69/1.93 fof(f8444,plain,(
% 5.69/1.93 ![Q47899,Q47903,F0,S0]: ((~s(fun(Q47899,bool),i(s(fun(fun(Q47903,bool),fun(Q47899,bool)),i(s(fun(fun(Q47903,Q47899),fun(fun(Q47903,bool),fun(Q47899,bool))),image),s(fun(Q47903,Q47899),F0))),s(fun(Q47903,bool),S0)))=s(fun(Q47899,bool),empty)|s(fun(Q47903,bool),S0)=s(fun(Q47903,bool),empty))&(s(fun(Q47899,bool),i(s(fun(fun(Q47903,bool),fun(Q47899,bool)),i(s(fun(fun(Q47903,Q47899),fun(fun(Q47903,bool),fun(Q47899,bool))),image),s(fun(Q47903,Q47899),F0))),s(fun(Q47903,bool),S0)))=s(fun(Q47899,bool),empty)|~s(fun(Q47903,bool),S0)=s(fun(Q47903,bool),empty)))),
% 5.69/1.93 inference(NNF_transformation,[status(esa)],[f1830])).
% 5.69/1.93 fof(f8445,plain,(
% 5.69/1.93 (![Q47903,S0]: ((![Q47899,F0]: ~s(fun(Q47899,bool),i(s(fun(fun(Q47903,bool),fun(Q47899,bool)),i(s(fun(fun(Q47903,Q47899),fun(fun(Q47903,bool),fun(Q47899,bool))),image),s(fun(Q47903,Q47899),F0))),s(fun(Q47903,bool),S0)))=s(fun(Q47899,bool),empty))|s(fun(Q47903,bool),S0)=s(fun(Q47903,bool),empty)))&(![Q47903,S0]: ((![Q47899,F0]: s(fun(Q47899,bool),i(s(fun(fun(Q47903,bool),fun(Q47899,bool)),i(s(fun(fun(Q47903,Q47899),fun(fun(Q47903,bool),fun(Q47899,bool))),image),s(fun(Q47903,Q47899),F0))),s(fun(Q47903,bool),S0)))=s(fun(Q47899,bool),empty))|~s(fun(Q47903,bool),S0)=s(fun(Q47903,bool),empty)))),
% 5.69/1.93 inference(miniscoping,[status(esa)],[f8444])).
% 5.69/1.93 fof(f8447,plain,(
% 5.69/1.93 ![X0,X1,X2,X3]: (s(fun(X0,bool),i(s(fun(fun(X1,bool),fun(X0,bool)),i(s(fun(fun(X1,X0),fun(fun(X1,bool),fun(X0,bool))),image),s(fun(X1,X0),X2))),s(fun(X1,bool),X3)))=s(fun(X0,bool),empty)|~s(fun(X1,bool),X3)=s(fun(X1,bool),empty))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f8445])).
% 5.69/1.93 fof(f9104,plain,(
% 5.69/1.93 ![X0]: (s(num,i(s(fun(fun(X0,bool),num),card),s(fun(X0,bool),empty)))=s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f1929])).
% 5.69/1.93 fof(f14382,plain,(
% 5.69/1.93 ![Q121390,S0]: (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))<=>((p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))&(![X,Y]: ((~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),Y))),s(fun(cart(real,Q121390),bool),S0)))))|p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(cart(real,Q121390),fun(cart(real,Q121390),cart(real,Q121390))),vectoru_add),s(cart(real,Q121390),X))),s(cart(real,Q121390),Y))))),s(fun(cart(real,Q121390),bool),S0)))))))&(![C0,X]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0))))))))),
% 5.69/1.93 inference(pre_NNF_transformation,[status(esa)],[f3294])).
% 5.69/1.93 fof(f14383,plain,(
% 5.69/1.93 ![Q121390,S0,X,Y]: (pd0_256(Y,X,S0,Q121390)<=>((~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),Y))),s(fun(cart(real,Q121390),bool),S0)))))|p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(cart(real,Q121390),fun(cart(real,Q121390),cart(real,Q121390))),vectoru_add),s(cart(real,Q121390),X))),s(cart(real,Q121390),Y))))),s(fun(cart(real,Q121390),bool),S0))))))),
% 5.69/1.93 introduced(predicate_definition,[f14382])).
% 5.69/1.93 fof(f14384,plain,(
% 5.69/1.93 ![Q121390,S0]: (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))<=>((p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))&(![X,Y]: pd0_256(Y,X,S0,Q121390)))&(![C0,X]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0))))))))),
% 5.69/1.93 inference(formula_renaming,[status(thm)],[f14382,f14383])).
% 5.69/1.93 fof(f14385,plain,(
% 5.69/1.93 ![Q121390,S0]: ((~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))|((p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))&(![X,Y]: pd0_256(Y,X,S0,Q121390)))&(![C0,X]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0))))))))&(p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))|((~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))|(?[X,Y]: ~pd0_256(Y,X,S0,Q121390)))|(?[C0,X]: (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))&~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0)))))))))),
% 5.69/1.93 inference(NNF_transformation,[status(esa)],[f14384])).
% 5.69/1.93 fof(f14386,plain,(
% 5.69/1.93 (![Q121390,S0]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))|((p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))&(![X,Y]: pd0_256(Y,X,S0,Q121390)))&(![X]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|(![C0]: p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0))))))))))&(![Q121390,S0]: (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))|((~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))|(?[X,Y]: ~pd0_256(Y,X,S0,Q121390)))|(?[X]: (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))&(?[C0]: ~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0))))))))))),
% 5.69/1.93 inference(miniscoping,[status(esa)],[f14385])).
% 5.69/1.93 fof(f14387,plain,(
% 5.69/1.93 (![Q121390,S0]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))|((p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))&(![X,Y]: pd0_256(Y,X,S0,Q121390)))&(![X]: (~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0))))|(![C0]: p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0))))))))))&(![Q121390,S0]: (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0))))|((~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0))))|~pd0_256(sk0_3450(S0,Q121390),sk0_3449(S0,Q121390),S0,Q121390))|(p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),sk0_3451(S0,Q121390)))),s(fun(cart(real,Q121390),bool),S0))))&~p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,sk0_3452(S0,Q121390)))),s(cart(real,Q121390),sk0_3451(S0,Q121390)))))),s(fun(cart(real,Q121390),bool),S0))))))))),
% 5.69/1.93 inference(skolemization,[status(esa)],[f14386])).
% 5.69/1.93 fof(f14388,plain,(
% 5.69/1.93 ![X0,X1]: (~p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),subspace),s(fun(cart(real,X0),bool),X1))))|p(s(bool,i(s(fun(fun(cart(real,X0),bool),bool),i(s(fun(cart(real,X0),fun(fun(cart(real,X0),bool),bool)),in),s(cart(real,X0),i(s(fun(num,cart(real,X0)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,X0),bool),X1)))))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f14387])).
% 5.69/1.93 fof(f14405,plain,(
% 5.69/1.93 (?[Q121443,S0]: (p(s(bool,i(s(fun(fun(cart(real,Q121443),bool),bool),subspace),s(fun(cart(real,Q121443),bool),S0))))&s(fun(cart(real,Q121443),bool),S0)=s(fun(cart(real,Q121443),bool),empty)))),
% 5.69/1.93 inference(pre_NNF_transformation,[status(esa)],[f3300])).
% 5.69/1.93 fof(f14406,plain,(
% 5.69/1.93 (p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),sk0_3455))))&s(fun(cart(real,sk0_3454),bool),sk0_3455)=s(fun(cart(real,sk0_3454),bool),empty))),
% 5.69/1.93 inference(skolemization,[status(esa)],[f14405])).
% 5.69/1.93 fof(f14407,plain,(
% 5.69/1.93 p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),sk0_3455))))),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f14406])).
% 5.69/1.93 fof(f14408,plain,(
% 5.69/1.93 s(fun(cart(real,sk0_3454),bool),sk0_3455)=s(fun(cart(real,sk0_3454),bool),empty)),
% 5.69/1.93 inference(cnf_transformation,[status(esa)],[f14406])).
% 5.69/1.93 fof(f16114,plain,(
% 5.69/1.93 spl0_3 <=> p(s(bool,X0))),
% 5.69/1.93 introduced(split_symbol_definition)).
% 5.69/1.93 fof(f16115,plain,(
% 5.69/1.93 ![X0]: (p(s(bool,X0))|~spl0_3)),
% 5.69/1.93 inference(component_clause,[status(thm)],[f16114])).
% 5.69/1.93 fof(f17064,plain,(
% 5.69/1.93 p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),empty))))),
% 5.69/1.93 inference(forward_demodulation,[status(thm)],[f14408,f14407])).
% 5.69/1.93 fof(f17089,plain,(
% 5.69/1.93 spl0_199 <=> s(fun(cart(real,sk0_3454),bool),empty)=s(fun(cart(real,sk0_3454),bool),empty)),
% 5.69/1.93 introduced(split_symbol_definition)).
% 5.69/1.93 fof(f17091,plain,(
% 5.69/1.93 ~s(fun(cart(real,sk0_3454),bool),empty)=s(fun(cart(real,sk0_3454),bool),empty)|spl0_199),
% 5.69/1.93 inference(component_clause,[status(thm)],[f17089])).
% 5.69/1.93 fof(f17095,plain,(
% 5.69/1.93 $false|spl0_199),
% 5.69/1.93 inference(trivial_equality_resolution,[status(esa)],[f17091])).
% 5.69/1.93 fof(f17096,plain,(
% 5.69/1.93 spl0_199),
% 5.69/1.93 inference(contradiction_clause,[status(thm)],[f17095])).
% 5.69/1.93 fof(f17133,plain,(
% 5.69/1.93 ![X0,X1,X2]: (pd0_0(X0,X1)|pd0_0(X2,X0))),
% 5.69/1.93 inference(resolution,[status(thm)],[f3316,f3315])).
% 5.69/1.94 fof(f17227,plain,(
% 5.69/1.94 spl0_205 <=> ~s(fun(X0,bool),i(s(fun(fun(cart(real,sk0_3454),bool),fun(X0,bool)),i(s(fun(fun(cart(real,sk0_3454),X0),fun(fun(cart(real,sk0_3454),bool),fun(X0,bool))),image),s(fun(cart(real,sk0_3454),X0),X1))),s(fun(cart(real,sk0_3454),bool),empty)))=s(fun(X0,bool),empty)),
% 5.69/1.94 introduced(split_symbol_definition)).
% 5.69/1.94 fof(f17228,plain,(
% 5.69/1.94 ![X0,X1]: (~s(fun(X0,bool),i(s(fun(fun(cart(real,sk0_3454),bool),fun(X0,bool)),i(s(fun(fun(cart(real,sk0_3454),X0),fun(fun(cart(real,sk0_3454),bool),fun(X0,bool))),image),s(fun(cart(real,sk0_3454),X0),X1))),s(fun(cart(real,sk0_3454),bool),empty)))=s(fun(X0,bool),empty)|~spl0_205)),
% 5.69/1.94 inference(component_clause,[status(thm)],[f17227])).
% 5.69/1.94 fof(f17373,plain,(
% 5.69/1.94 ![X0]: (p(s(bool,X0))|~pd0_0(X0,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),empty))))),
% 5.69/1.94 inference(resolution,[status(thm)],[f3317,f17064])).
% 5.69/1.94 fof(f17430,plain,(
% 5.69/1.94 $false|~spl0_3),
% 5.69/1.94 inference(backward_subsumption_resolution,[status(thm)],[f3519,f16115])).
% 5.69/1.94 fof(f17431,plain,(
% 5.69/1.94 ~spl0_3),
% 5.69/1.94 inference(contradiction_clause,[status(thm)],[f17430])).
% 5.69/1.94 fof(f17509,plain,(
% 5.69/1.94 ![X0,X1]: (p(s(bool,X0))|pd0_0(X1,X0))),
% 5.69/1.94 inference(resolution,[status(thm)],[f17373,f17133])).
% 5.69/1.94 fof(f17519,plain,(
% 5.69/1.94 spl0_212 <=> p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),empty))))),
% 5.69/1.94 introduced(split_symbol_definition)).
% 5.69/1.94 fof(f17522,plain,(
% 5.69/1.94 ![X0]: (p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),empty))))|p(s(bool,X0)))),
% 5.69/1.94 inference(resolution,[status(thm)],[f17509,f17373])).
% 5.69/1.94 fof(f17523,plain,(
% 5.69/1.94 spl0_212|spl0_3),
% 5.69/1.94 inference(split_clause,[status(thm)],[f17522,f17519,f16114])).
% 5.69/1.94 fof(f17551,plain,(
% 5.69/1.94 ![X0,X1]: (s(fun(X0,bool),i(s(fun(fun(cart(real,sk0_3454),bool),fun(X0,bool)),i(s(fun(fun(cart(real,sk0_3454),X0),fun(fun(cart(real,sk0_3454),bool),fun(X0,bool))),image),s(fun(cart(real,sk0_3454),X0),X1))),s(fun(cart(real,sk0_3454),bool),sk0_3455)))=s(fun(X0,bool),empty))),
% 5.69/1.94 inference(resolution,[status(thm)],[f8447,f14408])).
% 5.69/1.94 fof(f17552,plain,(
% 5.69/1.94 ![X0,X1]: (s(fun(X0,bool),i(s(fun(fun(cart(real,sk0_3454),bool),fun(X0,bool)),i(s(fun(fun(cart(real,sk0_3454),X0),fun(fun(cart(real,sk0_3454),bool),fun(X0,bool))),image),s(fun(cart(real,sk0_3454),X0),X1))),s(fun(cart(real,sk0_3454),bool),empty)))=s(fun(X0,bool),empty))),
% 5.69/1.94 inference(forward_demodulation,[status(thm)],[f14408,f17551])).
% 5.69/1.94 fof(f17553,plain,(
% 5.69/1.94 $false|~spl0_205),
% 5.69/1.94 inference(forward_subsumption_resolution,[status(thm)],[f17552,f17228])).
% 5.69/1.94 fof(f17554,plain,(
% 5.69/1.94 ~spl0_205),
% 5.69/1.94 inference(contradiction_clause,[status(thm)],[f17553])).
% 5.69/1.94 fof(f17571,plain,(
% 5.69/1.94 spl0_216 <=> p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),finite),s(fun(cart(real,sk0_3454),bool),empty))))),
% 5.69/1.94 introduced(split_symbol_definition)).
% 5.69/1.94 fof(f17573,plain,(
% 5.69/1.94 ~p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),finite),s(fun(cart(real,sk0_3454),bool),empty))))|spl0_216),
% 5.69/1.94 inference(component_clause,[status(thm)],[f17571])).
% 5.69/1.94 fof(f17574,plain,(
% 5.69/1.94 spl0_217 <=> s(num,i(s(fun(fun(cart(real,sk0_3454),bool),num),card),s(fun(cart(real,sk0_3454),bool),sk0_3455)))=s(num,i(s(fun(num,num),numeral),s(num,u_0)))),
% 5.69/1.94 introduced(split_symbol_definition)).
% 5.69/1.94 fof(f17576,plain,(
% 5.69/1.94 ~s(num,i(s(fun(fun(cart(real,sk0_3454),bool),num),card),s(fun(cart(real,sk0_3454),bool),sk0_3455)))=s(num,i(s(fun(num,num),numeral),s(num,u_0)))|spl0_217),
% 5.69/1.94 inference(component_clause,[status(thm)],[f17574])).
% 5.69/1.94 fof(f17585,plain,(
% 5.69/1.94 ~s(num,i(s(fun(fun(cart(real,sk0_3454),bool),num),card),s(fun(cart(real,sk0_3454),bool),empty)))=s(num,i(s(fun(num,num),numeral),s(num,u_0)))|spl0_217),
% 5.69/1.94 inference(forward_demodulation,[status(thm)],[f14408,f17576])).
% 5.69/1.94 fof(f17586,plain,(
% 5.69/1.94 ~s(num,i(s(fun(num,num),numeral),s(num,u_0)))=s(num,i(s(fun(num,num),numeral),s(num,u_0)))|spl0_217),
% 5.69/1.94 inference(forward_demodulation,[status(thm)],[f9104,f17585])).
% 5.69/1.94 fof(f17587,plain,(
% 5.69/1.94 $false|spl0_217),
% 5.69/1.94 inference(trivial_equality_resolution,[status(esa)],[f17586])).
% 5.69/1.94 fof(f17588,plain,(
% 5.69/1.94 spl0_217),
% 5.69/1.94 inference(contradiction_clause,[status(thm)],[f17587])).
% 6.24/2.02 fof(f17589,plain,(
% 6.24/2.02 $false|spl0_216),
% 6.24/2.02 inference(forward_subsumption_resolution,[status(thm)],[f17573,f7991])).
% 6.24/2.02 fof(f17590,plain,(
% 6.24/2.02 spl0_216),
% 6.24/2.02 inference(contradiction_clause,[status(thm)],[f17589])).
% 6.24/2.02 fof(f17783,plain,(
% 6.24/2.02 spl0_237 <=> ~s(fun(X0,bool),empty)=s(fun(X0,bool),empty)),
% 6.24/2.02 introduced(split_symbol_definition)).
% 6.24/2.02 fof(f17784,plain,(
% 6.24/2.02 ![X0]: (~s(fun(X0,bool),empty)=s(fun(X0,bool),empty)|~spl0_237)),
% 6.24/2.02 inference(component_clause,[status(thm)],[f17783])).
% 6.24/2.02 fof(f17807,plain,(
% 6.24/2.02 $false|~spl0_237),
% 6.24/2.02 inference(trivial_equality_resolution,[status(esa)],[f17784])).
% 6.24/2.02 fof(f17808,plain,(
% 6.24/2.02 ~spl0_237),
% 6.24/2.02 inference(contradiction_clause,[status(thm)],[f17807])).
% 6.24/2.02 fof(f18472,plain,(
% 6.24/2.02 spl0_282 <=> p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),i(s(fun(cart(real,sk0_3454),fun(fun(cart(real,sk0_3454),bool),bool)),in),s(cart(real,sk0_3454),i(s(fun(num,cart(real,sk0_3454)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,sk0_3454),bool),sk0_3455))))),
% 6.24/2.02 introduced(split_symbol_definition)).
% 6.24/2.02 fof(f18473,plain,(
% 6.24/2.02 p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),i(s(fun(cart(real,sk0_3454),fun(fun(cart(real,sk0_3454),bool),bool)),in),s(cart(real,sk0_3454),i(s(fun(num,cart(real,sk0_3454)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,sk0_3454),bool),sk0_3455))))|~spl0_282),
% 6.24/2.02 inference(component_clause,[status(thm)],[f18472])).
% 6.24/2.02 fof(f18475,plain,(
% 6.24/2.02 ~p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),subspace),s(fun(cart(real,sk0_3454),bool),empty))))|p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),i(s(fun(cart(real,sk0_3454),fun(fun(cart(real,sk0_3454),bool),bool)),in),s(cart(real,sk0_3454),i(s(fun(num,cart(real,sk0_3454)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,sk0_3454),bool),sk0_3455))))),
% 6.24/2.02 inference(paramodulation,[status(thm)],[f14408,f14388])).
% 6.24/2.02 fof(f18476,plain,(
% 6.24/2.02 ~spl0_212|spl0_282),
% 6.24/2.02 inference(split_clause,[status(thm)],[f18475,f17519,f18472])).
% 6.24/2.02 fof(f18483,plain,(
% 6.24/2.02 p(s(bool,i(s(fun(fun(cart(real,sk0_3454),bool),bool),i(s(fun(cart(real,sk0_3454),fun(fun(cart(real,sk0_3454),bool),bool)),in),s(cart(real,sk0_3454),i(s(fun(num,cart(real,sk0_3454)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,sk0_3454),bool),empty))))|~spl0_282),
% 6.24/2.02 inference(forward_demodulation,[status(thm)],[f14408,f18473])).
% 6.24/2.02 fof(f19303,plain,(
% 6.24/2.02 ~s(fun(cart(real,sk0_3454),bool),empty)=s(fun(cart(real,sk0_3454),bool),empty)|~spl0_282),
% 6.24/2.02 inference(resolution,[status(thm)],[f8138,f18483])).
% 6.24/2.02 fof(f19304,plain,(
% 6.24/2.02 ~spl0_199|~spl0_282),
% 6.24/2.02 inference(split_clause,[status(thm)],[f19303,f17089,f18472])).
% 6.24/2.02 fof(f19328,plain,(
% 6.24/2.02 $false),
% 6.24/2.02 inference(sat_refutation,[status(thm)],[f17096,f17431,f17523,f17554,f17588,f17590,f17808,f18476,f19304])).
% 6.24/2.02 % SZS output end CNFRefutation for theBenchmark.p
% 6.24/2.06 % Elapsed time: 1.695973 seconds
% 6.24/2.06 % CPU time: 6.223207 seconds
% 6.24/2.06 % Total memory used: 1.414 GB
% 6.24/2.06 % Net memory used: 1.411 GB
%------------------------------------------------------------------------------