TSTP Solution File: SWW102+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWW102+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : Tue Apr 30 20:49:46 EDT 2024
% Result : Theorem 3.11s 0.79s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWW102+1 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 23:05:13 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.36 % Drodi V3.6.0
% 3.11/0.79 % Refutation found
% 3.11/0.79 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.11/0.79 % SZS output start CNFRefutation for theBenchmark
% 3.11/0.79 fof(f1,axiom,(
% 3.11/0.79 (! [X] :( bool(X)<=> ( X = false| X = true ) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f2,axiom,(
% 3.11/0.79 ( true != false& true != err& false != err ) ),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f3,axiom,(
% 3.11/0.79 ( d(true)& d(false)& d(err) ) ),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f4,axiom,(
% 3.11/0.79 (! [X,Y] :( forallprefers(X,Y)<=> ( ( ~ d(X)& d(Y) )| ( d(X)& d(Y)& ~ bool(X)& bool(Y) )| ( X = false& Y = true ) ) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f5,axiom,(
% 3.11/0.79 (! [X,Y] :( existsprefers(X,Y)<=> ( ( ~ d(X)& d(Y) )| ( d(X)& d(Y)& ~ bool(X)& bool(Y) )| ( X = true& Y = false ) ) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f6,axiom,(
% 3.11/0.79 (! [X] :( ( d(X)& phi(X) = X )| ( ~ d(X)& phi(X) = err ) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f7,axiom,(
% 3.11/0.79 (! [X] :( prop(X) = true<=> bool(X) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f8,axiom,(
% 3.11/0.79 (! [X] :( prop(X) = false<=> ~ bool(X) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f9,axiom,(
% 3.11/0.79 (! [A,B] :( ~ bool(A)=> impl(A,B) = phi(A) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f10,axiom,(
% 3.11/0.79 (! [A,B] :( ( bool(A)& ~ bool(B) )=> impl(A,B) = phi(B) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f11,axiom,(
% 3.11/0.79 (! [B] :( bool(B)=> impl(false,B) = true ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f12,axiom,(
% 3.11/0.79 (! [B] :( bool(B)=> impl(true,B) = B ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f13,axiom,(
% 3.11/0.79 (! [A,B] :( ~ bool(A)=> lazy_impl(A,B) = phi(A) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f14,axiom,(
% 3.11/0.79 (! [B] : lazy_impl(false,B) = true )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f15,axiom,(
% 3.11/0.79 (! [B] : lazy_impl(true,B) = phi(B) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f20,axiom,(
% 3.11/0.79 (! [P,Q,R] : f1(P,Q,R) = lazy_impl(prop(R),impl(impl(P,impl(Q,R)),R)) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f21,axiom,(
% 3.11/0.79 (! [P,Q] :(? [R] :( and2(P,Q) = phi(f1(P,Q,R))& ~ (? [R1] : forallprefers(f1(P,Q,R1),f1(P,Q,R)) )) ))),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f25,axiom,(
% 3.11/0.79 (! [P,Q,R] : f2(P,Q,R) = lazy_impl(prop(R),impl(lazy_impl(P,impl(Q,R)),R)) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f26,axiom,(
% 3.11/0.79 (! [P,Q] :(? [R] :( lazy_and2(P,Q) = phi(f2(P,Q,R))& ~ (? [R1] : forallprefers(f2(P,Q,R1),f2(P,Q,R)) )) ))),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f31,axiom,(
% 3.11/0.79 (! [P,Q,R] : f3(P,Q,R) = lazy_impl(prop(R),impl(impl(P,R),impl(impl(Q,R),R))) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f32,axiom,(
% 3.11/0.79 (! [P,Q] :(? [R] :( or2(P,Q) = phi(f3(P,Q,R))& ~ (? [R1] : forallprefers(f3(P,Q,R1),f3(P,Q,R)) )) ))),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f36,axiom,(
% 3.11/0.79 (! [P,R] : f6(P,R) = lazy_impl(prop(R),impl(f5(P,R),R)) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f37,axiom,(
% 3.11/0.79 (! [P] :(? [R] :( exists2(P) = phi(f6(P,R))& ~ (? [R1] : forallprefers(f6(P,R1),f6(P,R)) )) ))),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f39,axiom,(
% 3.11/0.79 (! [P] : f7(P) = lazy_impl(prop(P),P) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f40,axiom,(
% 3.11/0.79 (? [P] :( false2 = phi(f7(P))& ~ (? [P1] : forallprefers(f7(P1),f7(P)) )) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f41,axiom,(
% 3.11/0.79 (! [A] :( ~ bool(A)=> not1(A) = phi(A) ) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f42,axiom,(
% 3.11/0.79 not1(false) = true ),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f43,axiom,(
% 3.11/0.79 not1(true) = false ),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f44,axiom,(
% 3.11/0.79 (! [P] : not2(P) = impl(P,false2) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f45,conjecture,(
% 3.11/0.79 (! [P] : not1(P) = not2(P) )),
% 3.11/0.79 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 3.11/0.79 fof(f46,negated_conjecture,(
% 3.11/0.79 ~((! [P] : not1(P) = not2(P) ))),
% 3.11/0.79 inference(negated_conjecture,[status(cth)],[f45])).
% 3.11/0.79 fof(f47,plain,(
% 3.11/0.79 ![X]: ((~bool(X)|(X=false|X=true))&(bool(X)|(~X=false&~X=true)))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f1])).
% 3.11/0.79 fof(f48,plain,(
% 3.11/0.79 (![X]: (~bool(X)|(X=false|X=true)))&(![X]: (bool(X)|(~X=false&~X=true)))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f47])).
% 3.11/0.79 fof(f49,plain,(
% 3.11/0.79 ![X0]: (~bool(X0)|X0=false|X0=true)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f48])).
% 3.11/0.79 fof(f50,plain,(
% 3.11/0.79 ![X0]: (bool(X0)|~X0=false)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f48])).
% 3.11/0.79 fof(f51,plain,(
% 3.11/0.79 ![X0]: (bool(X0)|~X0=true)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f48])).
% 3.11/0.79 fof(f52,plain,(
% 3.11/0.79 ~true=false),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f2])).
% 3.11/0.79 fof(f53,plain,(
% 3.11/0.79 ~true=err),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f2])).
% 3.11/0.79 fof(f54,plain,(
% 3.11/0.79 ~false=err),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f2])).
% 3.11/0.79 fof(f55,plain,(
% 3.11/0.79 d(true)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f3])).
% 3.11/0.79 fof(f56,plain,(
% 3.11/0.79 d(false)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f3])).
% 3.11/0.79 fof(f57,plain,(
% 3.11/0.79 d(err)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f3])).
% 3.11/0.79 fof(f58,plain,(
% 3.11/0.79 ![X,Y]: (pd0_0(Y,X)<=>((~d(X)&d(Y))|(((d(X)&d(Y))&~bool(X))&bool(Y))))),
% 3.11/0.79 introduced(predicate_definition,[f4])).
% 3.11/0.79 fof(f59,plain,(
% 3.11/0.79 ![X,Y]: (forallprefers(X,Y)<=>(pd0_0(Y,X)|(X=false&Y=true)))),
% 3.11/0.79 inference(formula_renaming,[status(thm)],[f4,f58])).
% 3.11/0.79 fof(f60,plain,(
% 3.11/0.79 ![X,Y]: ((~forallprefers(X,Y)|(pd0_0(Y,X)|(X=false&Y=true)))&(forallprefers(X,Y)|(~pd0_0(Y,X)&(~X=false|~Y=true))))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f59])).
% 3.11/0.79 fof(f61,plain,(
% 3.11/0.79 (![X,Y]: (~forallprefers(X,Y)|(pd0_0(Y,X)|(X=false&Y=true))))&(![X,Y]: (forallprefers(X,Y)|(~pd0_0(Y,X)&(~X=false|~Y=true))))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f60])).
% 3.11/0.79 fof(f64,plain,(
% 3.11/0.79 ![X0,X1]: (forallprefers(X0,X1)|~pd0_0(X1,X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f61])).
% 3.11/0.79 fof(f65,plain,(
% 3.11/0.79 ![X0,X1]: (forallprefers(X0,X1)|~X0=false|~X1=true)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f61])).
% 3.11/0.79 fof(f66,plain,(
% 3.11/0.79 ![X,Y]: (pd0_1(Y,X)<=>((~d(X)&d(Y))|(((d(X)&d(Y))&~bool(X))&bool(Y))))),
% 3.11/0.79 introduced(predicate_definition,[f5])).
% 3.11/0.79 fof(f74,plain,(
% 3.11/0.79 ![X]: (pd0_2(X)=>(d(X)&phi(X)=X))),
% 3.11/0.79 introduced(predicate_definition,[f6])).
% 3.11/0.79 fof(f75,plain,(
% 3.11/0.79 ![X]: (pd0_2(X)|(~d(X)&phi(X)=err))),
% 3.11/0.79 inference(formula_renaming,[status(thm)],[f6,f74])).
% 3.11/0.79 fof(f76,plain,(
% 3.11/0.79 ![X0]: (pd0_2(X0)|~d(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f75])).
% 3.11/0.79 fof(f77,plain,(
% 3.11/0.79 ![X0]: (pd0_2(X0)|phi(X0)=err)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f75])).
% 3.11/0.79 fof(f78,plain,(
% 3.11/0.79 ![X]: ((~prop(X)=true|bool(X))&(prop(X)=true|~bool(X)))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f7])).
% 3.11/0.79 fof(f79,plain,(
% 3.11/0.79 (![X]: (~prop(X)=true|bool(X)))&(![X]: (prop(X)=true|~bool(X)))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f78])).
% 3.11/0.79 fof(f80,plain,(
% 3.11/0.79 ![X0]: (~prop(X0)=true|bool(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f79])).
% 3.11/0.79 fof(f81,plain,(
% 3.11/0.79 ![X0]: (prop(X0)=true|~bool(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f79])).
% 3.11/0.79 fof(f82,plain,(
% 3.11/0.79 ![X]: ((~prop(X)=false|~bool(X))&(prop(X)=false|bool(X)))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f8])).
% 3.11/0.79 fof(f83,plain,(
% 3.11/0.79 (![X]: (~prop(X)=false|~bool(X)))&(![X]: (prop(X)=false|bool(X)))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f82])).
% 3.11/0.79 fof(f84,plain,(
% 3.11/0.79 ![X0]: (~prop(X0)=false|~bool(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f83])).
% 3.11/0.79 fof(f85,plain,(
% 3.11/0.79 ![X0]: (prop(X0)=false|bool(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f83])).
% 3.11/0.79 fof(f86,plain,(
% 3.11/0.79 ![A,B]: (bool(A)|impl(A,B)=phi(A))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f9])).
% 3.11/0.79 fof(f87,plain,(
% 3.11/0.79 ![A]: (bool(A)|(![B]: impl(A,B)=phi(A)))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f86])).
% 3.11/0.79 fof(f88,plain,(
% 3.11/0.79 ![X0,X1]: (bool(X0)|impl(X0,X1)=phi(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f87])).
% 3.11/0.79 fof(f89,plain,(
% 3.11/0.79 ![A,B]: ((~bool(A)|bool(B))|impl(A,B)=phi(B))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 3.11/0.79 fof(f90,plain,(
% 3.11/0.79 ![X0,X1]: (~bool(X0)|bool(X1)|impl(X0,X1)=phi(X1))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f89])).
% 3.11/0.79 fof(f91,plain,(
% 3.11/0.79 ![B]: (~bool(B)|impl(false,B)=true)),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 3.11/0.79 fof(f92,plain,(
% 3.11/0.79 ![X0]: (~bool(X0)|impl(false,X0)=true)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f91])).
% 3.11/0.79 fof(f93,plain,(
% 3.11/0.79 ![B]: (~bool(B)|impl(true,B)=B)),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 3.11/0.79 fof(f94,plain,(
% 3.11/0.79 ![X0]: (~bool(X0)|impl(true,X0)=X0)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f93])).
% 3.11/0.79 fof(f95,plain,(
% 3.11/0.79 ![A,B]: (bool(A)|lazy_impl(A,B)=phi(A))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 3.11/0.79 fof(f96,plain,(
% 3.11/0.79 ![A]: (bool(A)|(![B]: lazy_impl(A,B)=phi(A)))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f95])).
% 3.11/0.79 fof(f97,plain,(
% 3.11/0.79 ![X0,X1]: (bool(X0)|lazy_impl(X0,X1)=phi(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f96])).
% 3.11/0.79 fof(f98,plain,(
% 3.11/0.79 ![X0]: (lazy_impl(false,X0)=true)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f14])).
% 3.11/0.79 fof(f99,plain,(
% 3.11/0.79 ![X0]: (lazy_impl(true,X0)=phi(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f15])).
% 3.11/0.79 fof(f109,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f1(X0,X1,X2)=lazy_impl(prop(X2),impl(impl(X0,impl(X1,X2)),X2)))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f20])).
% 3.11/0.79 fof(f110,plain,(
% 3.11/0.79 ![P,Q]: (?[R]: (and2(P,Q)=phi(f1(P,Q,R))&(![R1]: ~forallprefers(f1(P,Q,R1),f1(P,Q,R)))))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f21])).
% 3.11/0.79 fof(f111,plain,(
% 3.11/0.79 ![P,Q]: (and2(P,Q)=phi(f1(P,Q,sk0_0(Q,P)))&(![R1]: ~forallprefers(f1(P,Q,R1),f1(P,Q,sk0_0(Q,P)))))),
% 3.11/0.79 inference(skolemization,[status(esa)],[f110])).
% 3.11/0.79 fof(f113,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(f1(X0,X1,X2),f1(X0,X1,sk0_0(X1,X0))))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f111])).
% 3.11/0.79 fof(f119,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f2(X0,X1,X2)=lazy_impl(prop(X2),impl(lazy_impl(X0,impl(X1,X2)),X2)))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f25])).
% 3.11/0.79 fof(f120,plain,(
% 3.11/0.79 ![P,Q]: (?[R]: (lazy_and2(P,Q)=phi(f2(P,Q,R))&(![R1]: ~forallprefers(f2(P,Q,R1),f2(P,Q,R)))))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f26])).
% 3.11/0.79 fof(f121,plain,(
% 3.11/0.79 ![P,Q]: (lazy_and2(P,Q)=phi(f2(P,Q,sk0_1(Q,P)))&(![R1]: ~forallprefers(f2(P,Q,R1),f2(P,Q,sk0_1(Q,P)))))),
% 3.11/0.79 inference(skolemization,[status(esa)],[f120])).
% 3.11/0.79 fof(f123,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(f2(X0,X1,X2),f2(X0,X1,sk0_1(X1,X0))))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f121])).
% 3.11/0.79 fof(f133,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f3(X0,X1,X2)=lazy_impl(prop(X2),impl(impl(X0,X2),impl(impl(X1,X2),X2))))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f31])).
% 3.11/0.79 fof(f134,plain,(
% 3.11/0.79 ![P,Q]: (?[R]: (or2(P,Q)=phi(f3(P,Q,R))&(![R1]: ~forallprefers(f3(P,Q,R1),f3(P,Q,R)))))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f32])).
% 3.11/0.79 fof(f135,plain,(
% 3.11/0.79 ![P,Q]: (or2(P,Q)=phi(f3(P,Q,sk0_2(Q,P)))&(![R1]: ~forallprefers(f3(P,Q,R1),f3(P,Q,sk0_2(Q,P)))))),
% 3.11/0.79 inference(skolemization,[status(esa)],[f134])).
% 3.11/0.79 fof(f137,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(f3(X0,X1,X2),f3(X0,X1,sk0_2(X1,X0))))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f135])).
% 3.11/0.79 fof(f147,plain,(
% 3.11/0.79 ![X0,X1]: (f6(X0,X1)=lazy_impl(prop(X1),impl(f5(X0,X1),X1)))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f36])).
% 3.11/0.79 fof(f148,plain,(
% 3.11/0.79 ![P]: (?[R]: (exists2(P)=phi(f6(P,R))&(![R1]: ~forallprefers(f6(P,R1),f6(P,R)))))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f37])).
% 3.11/0.79 fof(f149,plain,(
% 3.11/0.79 ![P]: (exists2(P)=phi(f6(P,sk0_5(P)))&(![R1]: ~forallprefers(f6(P,R1),f6(P,sk0_5(P)))))),
% 3.11/0.79 inference(skolemization,[status(esa)],[f148])).
% 3.11/0.79 fof(f151,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(f6(X0,X1),f6(X0,sk0_5(X0))))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f149])).
% 3.11/0.79 fof(f153,plain,(
% 3.11/0.79 ![X0]: (f7(X0)=lazy_impl(prop(X0),X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f39])).
% 3.11/0.79 fof(f154,plain,(
% 3.11/0.79 ?[P]: (false2=phi(f7(P))&(![P1]: ~forallprefers(f7(P1),f7(P))))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f40])).
% 3.11/0.79 fof(f155,plain,(
% 3.11/0.79 (false2=phi(f7(sk0_6))&(![P1]: ~forallprefers(f7(P1),f7(sk0_6))))),
% 3.11/0.79 inference(skolemization,[status(esa)],[f154])).
% 3.11/0.79 fof(f156,plain,(
% 3.11/0.79 false2=phi(f7(sk0_6))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f155])).
% 3.11/0.79 fof(f157,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(f7(X0),f7(sk0_6)))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f155])).
% 3.11/0.79 fof(f158,plain,(
% 3.11/0.79 ![A]: (bool(A)|not1(A)=phi(A))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f41])).
% 3.11/0.79 fof(f159,plain,(
% 3.11/0.79 ![X0]: (bool(X0)|not1(X0)=phi(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f158])).
% 3.11/0.79 fof(f160,plain,(
% 3.11/0.79 not1(false)=true),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f42])).
% 3.11/0.79 fof(f161,plain,(
% 3.11/0.79 not1(true)=false),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f43])).
% 3.11/0.79 fof(f162,plain,(
% 3.11/0.79 ![X0]: (not2(X0)=impl(X0,false2))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f44])).
% 3.11/0.79 fof(f163,plain,(
% 3.11/0.79 (?[P]: ~not1(P)=not2(P))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f46])).
% 3.11/0.79 fof(f164,plain,(
% 3.11/0.79 ~not1(sk0_7)=not2(sk0_7)),
% 3.11/0.79 inference(skolemization,[status(esa)],[f163])).
% 3.11/0.79 fof(f165,plain,(
% 3.11/0.79 ~not1(sk0_7)=not2(sk0_7)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f164])).
% 3.11/0.79 fof(f166,plain,(
% 3.11/0.79 ![X,Y]: (pd0_3(Y,X)<=>(~d(X)&d(Y)))),
% 3.11/0.79 introduced(predicate_definition,[f58])).
% 3.11/0.79 fof(f167,plain,(
% 3.11/0.79 ![X,Y]: (pd0_0(Y,X)<=>(pd0_3(Y,X)|(((d(X)&d(Y))&~bool(X))&bool(Y))))),
% 3.11/0.79 inference(formula_renaming,[status(thm)],[f58,f166])).
% 3.11/0.79 fof(f168,plain,(
% 3.11/0.79 ![X,Y]: ((~pd0_0(Y,X)|(pd0_3(Y,X)|(((d(X)&d(Y))&~bool(X))&bool(Y))))&(pd0_0(Y,X)|(~pd0_3(Y,X)&(((~d(X)|~d(Y))|bool(X))|~bool(Y)))))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f167])).
% 3.11/0.79 fof(f169,plain,(
% 3.11/0.79 (![X,Y]: (~pd0_0(Y,X)|(pd0_3(Y,X)|(((d(X)&d(Y))&~bool(X))&bool(Y)))))&(![X,Y]: (pd0_0(Y,X)|(~pd0_3(Y,X)&(((~d(X)|~d(Y))|bool(X))|~bool(Y)))))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f168])).
% 3.11/0.79 fof(f174,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_0(X0,X1)|~pd0_3(X0,X1))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f169])).
% 3.11/0.79 fof(f175,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_0(X0,X1)|~d(X1)|~d(X0)|bool(X1)|~bool(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f169])).
% 3.11/0.79 fof(f176,plain,(
% 3.11/0.79 ![X,Y]: (pd0_4(Y,X)<=>(~d(X)&d(Y)))),
% 3.11/0.79 introduced(predicate_definition,[f66])).
% 3.11/0.79 fof(f177,plain,(
% 3.11/0.79 ![X,Y]: (pd0_1(Y,X)<=>(pd0_4(Y,X)|(((d(X)&d(Y))&~bool(X))&bool(Y))))),
% 3.11/0.79 inference(formula_renaming,[status(thm)],[f66,f176])).
% 3.11/0.79 fof(f178,plain,(
% 3.11/0.79 ![X,Y]: ((~pd0_1(Y,X)|(pd0_4(Y,X)|(((d(X)&d(Y))&~bool(X))&bool(Y))))&(pd0_1(Y,X)|(~pd0_4(Y,X)&(((~d(X)|~d(Y))|bool(X))|~bool(Y)))))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f177])).
% 3.11/0.79 fof(f179,plain,(
% 3.11/0.79 (![X,Y]: (~pd0_1(Y,X)|(pd0_4(Y,X)|(((d(X)&d(Y))&~bool(X))&bool(Y)))))&(![X,Y]: (pd0_1(Y,X)|(~pd0_4(Y,X)&(((~d(X)|~d(Y))|bool(X))|~bool(Y)))))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f178])).
% 3.11/0.79 fof(f181,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_1(X0,X1)|pd0_4(X0,X1)|d(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f179])).
% 3.11/0.79 fof(f182,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_1(X0,X1)|pd0_4(X0,X1)|~bool(X1))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f179])).
% 3.11/0.79 fof(f184,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_1(X0,X1)|~pd0_4(X0,X1))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f179])).
% 3.11/0.79 fof(f185,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_1(X0,X1)|~d(X1)|~d(X0)|bool(X1)|~bool(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f179])).
% 3.11/0.79 fof(f186,plain,(
% 3.11/0.79 ![X]: (~pd0_2(X)|(d(X)&phi(X)=X))),
% 3.11/0.79 inference(pre_NNF_transformation,[status(esa)],[f74])).
% 3.11/0.79 fof(f188,plain,(
% 3.11/0.79 ![X0]: (~pd0_2(X0)|phi(X0)=X0)),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f186])).
% 3.11/0.79 fof(f189,plain,(
% 3.11/0.79 ![X,Y]: ((~pd0_3(Y,X)|(~d(X)&d(Y)))&(pd0_3(Y,X)|(d(X)|~d(Y))))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f166])).
% 3.11/0.79 fof(f190,plain,(
% 3.11/0.79 (![X,Y]: (~pd0_3(Y,X)|(~d(X)&d(Y))))&(![X,Y]: (pd0_3(Y,X)|(d(X)|~d(Y))))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f189])).
% 3.11/0.79 fof(f191,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_3(X0,X1)|~d(X1))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f190])).
% 3.11/0.79 fof(f192,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_3(X0,X1)|d(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f190])).
% 3.11/0.79 fof(f193,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_3(X0,X1)|d(X1)|~d(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f190])).
% 3.11/0.79 fof(f194,plain,(
% 3.11/0.79 ![X,Y]: ((~pd0_4(Y,X)|(~d(X)&d(Y)))&(pd0_4(Y,X)|(d(X)|~d(Y))))),
% 3.11/0.79 inference(NNF_transformation,[status(esa)],[f176])).
% 3.11/0.79 fof(f195,plain,(
% 3.11/0.79 (![X,Y]: (~pd0_4(Y,X)|(~d(X)&d(Y))))&(![X,Y]: (pd0_4(Y,X)|(d(X)|~d(Y))))),
% 3.11/0.79 inference(miniscoping,[status(esa)],[f194])).
% 3.11/0.79 fof(f196,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_4(X0,X1)|~d(X1))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f195])).
% 3.11/0.79 fof(f197,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_4(X0,X1)|d(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f195])).
% 3.11/0.79 fof(f198,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_4(X0,X1)|d(X1)|~d(X0))),
% 3.11/0.79 inference(cnf_transformation,[status(esa)],[f195])).
% 3.11/0.79 fof(f199,plain,(
% 3.11/0.79 bool(false)),
% 3.11/0.79 inference(destructive_equality_resolution,[status(esa)],[f50])).
% 3.11/0.79 fof(f200,plain,(
% 3.11/0.79 bool(true)),
% 3.11/0.79 inference(destructive_equality_resolution,[status(esa)],[f51])).
% 3.11/0.79 fof(f201,plain,(
% 3.11/0.79 forallprefers(false,true)),
% 3.11/0.79 inference(destructive_equality_resolution,[status(esa)],[f65])).
% 3.11/0.79 fof(f204,plain,(
% 3.11/0.79 ![X0,X1]: (~pd0_1(X0,X1)|d(X0))),
% 3.11/0.79 inference(backward_subsumption_resolution,[status(thm)],[f181,f197])).
% 3.11/0.79 fof(f205,plain,(
% 3.11/0.79 spl0_0 <=> bool(true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f208,plain,(
% 3.11/0.79 spl0_1 <=> false=phi(true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f209,plain,(
% 3.11/0.79 false=phi(true)|~spl0_1),
% 3.11/0.79 inference(component_clause,[status(thm)],[f208])).
% 3.11/0.79 fof(f213,plain,(
% 3.11/0.79 spl0_2 <=> bool(false)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f216,plain,(
% 3.11/0.79 spl0_3 <=> true=phi(false)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f217,plain,(
% 3.11/0.79 true=phi(false)|~spl0_3),
% 3.11/0.79 inference(component_clause,[status(thm)],[f216])).
% 3.11/0.79 fof(f225,plain,(
% 3.11/0.79 spl0_4 <=> false=false),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f228,plain,(
% 3.11/0.79 spl0_5 <=> false=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f229,plain,(
% 3.11/0.79 false=true|~spl0_5),
% 3.11/0.79 inference(component_clause,[status(thm)],[f228])).
% 3.11/0.79 fof(f231,plain,(
% 3.11/0.79 false=false|false=true),
% 3.11/0.79 inference(resolution,[status(thm)],[f199,f49])).
% 3.11/0.79 fof(f232,plain,(
% 3.11/0.79 spl0_4|spl0_5),
% 3.11/0.79 inference(split_clause,[status(thm)],[f231,f225,f228])).
% 3.11/0.79 fof(f233,plain,(
% 3.11/0.79 spl0_6 <=> true=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f236,plain,(
% 3.11/0.79 true=false|true=true),
% 3.11/0.79 inference(resolution,[status(thm)],[f200,f49])).
% 3.11/0.79 fof(f237,plain,(
% 3.11/0.79 spl0_5|spl0_6),
% 3.11/0.79 inference(split_clause,[status(thm)],[f236,f228,f233])).
% 3.11/0.79 fof(f238,plain,(
% 3.11/0.79 $false|~spl0_5),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f229,f52])).
% 3.11/0.79 fof(f239,plain,(
% 3.11/0.79 ~spl0_5),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f238])).
% 3.11/0.79 fof(f247,plain,(
% 3.11/0.79 pd0_2(err)),
% 3.11/0.79 inference(resolution,[status(thm)],[f76,f57])).
% 3.11/0.79 fof(f248,plain,(
% 3.11/0.79 pd0_2(false)),
% 3.11/0.79 inference(resolution,[status(thm)],[f76,f56])).
% 3.11/0.79 fof(f249,plain,(
% 3.11/0.79 pd0_2(true)),
% 3.11/0.79 inference(resolution,[status(thm)],[f76,f55])).
% 3.11/0.79 fof(f253,plain,(
% 3.11/0.79 spl0_8 <=> pd0_1(false,true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f254,plain,(
% 3.11/0.79 pd0_1(false,true)|~spl0_8),
% 3.11/0.79 inference(component_clause,[status(thm)],[f253])).
% 3.11/0.79 fof(f260,plain,(
% 3.11/0.79 spl0_9 <=> ~bool(X0)|bool(X0)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f263,plain,(
% 3.11/0.79 ![X0]: (~false=false|~bool(X0)|bool(X0))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f84])).
% 3.11/0.79 fof(f264,plain,(
% 3.11/0.79 ~spl0_4|spl0_9),
% 3.11/0.79 inference(split_clause,[status(thm)],[f263,f225,f260])).
% 3.11/0.79 fof(f272,plain,(
% 3.11/0.79 spl0_11 <=> false2=err),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f273,plain,(
% 3.11/0.79 false2=err|~spl0_11),
% 3.11/0.79 inference(component_clause,[status(thm)],[f272])).
% 3.11/0.79 fof(f275,plain,(
% 3.11/0.79 spl0_12 <=> pd0_2(f7(sk0_6))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f277,plain,(
% 3.11/0.79 ~pd0_2(f7(sk0_6))|spl0_12),
% 3.11/0.79 inference(component_clause,[status(thm)],[f275])).
% 3.11/0.79 fof(f278,plain,(
% 3.11/0.79 false2=err|pd0_2(f7(sk0_6))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f77,f156])).
% 3.11/0.79 fof(f279,plain,(
% 3.11/0.79 spl0_11|spl0_12),
% 3.11/0.79 inference(split_clause,[status(thm)],[f278,f272,f275])).
% 3.11/0.79 fof(f282,plain,(
% 3.11/0.79 spl0_13 <=> false2=f7(sk0_6)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f283,plain,(
% 3.11/0.79 false2=f7(sk0_6)|~spl0_13),
% 3.11/0.79 inference(component_clause,[status(thm)],[f282])).
% 3.11/0.79 fof(f285,plain,(
% 3.11/0.79 ~pd0_2(f7(sk0_6))|false2=f7(sk0_6)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f156,f188])).
% 3.11/0.79 fof(f286,plain,(
% 3.11/0.79 ~spl0_12|spl0_13),
% 3.11/0.79 inference(split_clause,[status(thm)],[f285,f275,f282])).
% 3.11/0.79 fof(f287,plain,(
% 3.11/0.79 false2=phi(false2)|~spl0_13),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f283,f156])).
% 3.11/0.79 fof(f290,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(f7(X0),false2)|~spl0_13)),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f283,f157])).
% 3.11/0.79 fof(f291,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(f7(X0),err)|~spl0_11|~spl0_13)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f273,f290])).
% 3.11/0.79 fof(f292,plain,(
% 3.11/0.79 ![X0]: (not2(X0)=impl(X0,err)|~spl0_11)),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f273,f162])).
% 3.11/0.79 fof(f307,plain,(
% 3.11/0.79 spl0_16 <=> bool(err)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f308,plain,(
% 3.11/0.79 bool(err)|~spl0_16),
% 3.11/0.79 inference(component_clause,[status(thm)],[f307])).
% 3.11/0.79 fof(f315,plain,(
% 3.11/0.79 ![X0]: (bool(X0)|not2(X0)=phi(X0)|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f292,f88])).
% 3.11/0.79 fof(f322,plain,(
% 3.11/0.79 spl0_19 <=> not1(sk0_7)=phi(sk0_7)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f323,plain,(
% 3.11/0.79 not1(sk0_7)=phi(sk0_7)|~spl0_19),
% 3.11/0.79 inference(component_clause,[status(thm)],[f322])).
% 3.11/0.79 fof(f324,plain,(
% 3.11/0.79 ~not1(sk0_7)=phi(sk0_7)|spl0_19),
% 3.11/0.79 inference(component_clause,[status(thm)],[f322])).
% 3.11/0.79 fof(f325,plain,(
% 3.11/0.79 spl0_20 <=> bool(sk0_7)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f326,plain,(
% 3.11/0.79 bool(sk0_7)|~spl0_20),
% 3.11/0.79 inference(component_clause,[status(thm)],[f325])).
% 3.11/0.79 fof(f327,plain,(
% 3.11/0.79 ~bool(sk0_7)|spl0_20),
% 3.11/0.79 inference(component_clause,[status(thm)],[f325])).
% 3.11/0.79 fof(f328,plain,(
% 3.11/0.79 ~not1(sk0_7)=phi(sk0_7)|bool(sk0_7)|~spl0_11),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f315,f165])).
% 3.11/0.79 fof(f329,plain,(
% 3.11/0.79 ~spl0_19|spl0_20|~spl0_11),
% 3.11/0.79 inference(split_clause,[status(thm)],[f328,f322,f325,f272])).
% 3.11/0.79 fof(f331,plain,(
% 3.11/0.79 spl0_21 <=> phi(sk0_7)=phi(sk0_7)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f333,plain,(
% 3.11/0.79 ~phi(sk0_7)=phi(sk0_7)|spl0_21),
% 3.11/0.79 inference(component_clause,[status(thm)],[f331])).
% 3.11/0.79 fof(f334,plain,(
% 3.11/0.79 ~phi(sk0_7)=phi(sk0_7)|bool(sk0_7)|spl0_19),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f159,f324])).
% 3.11/0.79 fof(f335,plain,(
% 3.11/0.79 ~spl0_21|spl0_20|spl0_19),
% 3.11/0.79 inference(split_clause,[status(thm)],[f334,f331,f325,f322])).
% 3.11/0.79 fof(f336,plain,(
% 3.11/0.79 spl0_22 <=> sk0_7=false),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f337,plain,(
% 3.11/0.79 sk0_7=false|~spl0_22),
% 3.11/0.79 inference(component_clause,[status(thm)],[f336])).
% 3.11/0.79 fof(f339,plain,(
% 3.11/0.79 spl0_23 <=> sk0_7=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f340,plain,(
% 3.11/0.79 sk0_7=true|~spl0_23),
% 3.11/0.79 inference(component_clause,[status(thm)],[f339])).
% 3.11/0.79 fof(f342,plain,(
% 3.11/0.79 sk0_7=false|sk0_7=true|~spl0_20),
% 3.11/0.79 inference(resolution,[status(thm)],[f326,f49])).
% 3.11/0.79 fof(f343,plain,(
% 3.11/0.79 spl0_22|spl0_23|~spl0_20),
% 3.11/0.79 inference(split_clause,[status(thm)],[f342,f336,f339,f325])).
% 3.11/0.79 fof(f345,plain,(
% 3.11/0.79 ~not1(sk0_7)=not2(false)|~spl0_22),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f337,f165])).
% 3.11/0.79 fof(f346,plain,(
% 3.11/0.79 ~not1(false)=not2(false)|~spl0_22),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f337,f345])).
% 3.11/0.79 fof(f347,plain,(
% 3.11/0.79 ~true=not2(false)|~spl0_22),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f160,f346])).
% 3.11/0.79 fof(f362,plain,(
% 3.11/0.79 ![X0]: (f7(X0)=lazy_impl(false,X0)|bool(X0))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f153])).
% 3.11/0.79 fof(f363,plain,(
% 3.11/0.79 ![X0]: (f7(X0)=true|bool(X0))),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f362])).
% 3.11/0.79 fof(f364,plain,(
% 3.11/0.79 spl0_24 <=> forallprefers(true,err)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f367,plain,(
% 3.11/0.79 spl0_25 <=> bool(X0)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f368,plain,(
% 3.11/0.79 ![X0]: (bool(X0)|~spl0_25)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f367])).
% 3.11/0.79 fof(f370,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(true,err)|bool(X0)|~spl0_11|~spl0_13)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f363,f291])).
% 3.11/0.79 fof(f371,plain,(
% 3.11/0.79 ~spl0_24|spl0_25|~spl0_11|~spl0_13),
% 3.11/0.79 inference(split_clause,[status(thm)],[f370,f364,f367,f272,f282])).
% 3.11/0.79 fof(f372,plain,(
% 3.11/0.79 spl0_26 <=> not2(false)=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f373,plain,(
% 3.11/0.79 not2(false)=true|~spl0_26),
% 3.11/0.79 inference(component_clause,[status(thm)],[f372])).
% 3.11/0.79 fof(f377,plain,(
% 3.11/0.79 spl0_27 <=> ~bool(X0)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f378,plain,(
% 3.11/0.79 ![X0]: (~bool(X0)|~spl0_27)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f377])).
% 3.11/0.79 fof(f382,plain,(
% 3.11/0.79 spl0_28 <=> ~bool(X0)|not2(X0)=phi(err)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f385,plain,(
% 3.11/0.79 ![X0]: (~bool(X0)|bool(err)|not2(X0)=phi(err)|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f292,f90])).
% 3.11/0.79 fof(f386,plain,(
% 3.11/0.79 spl0_28|spl0_16|~spl0_11),
% 3.11/0.79 inference(split_clause,[status(thm)],[f385,f382,f307,f272])).
% 3.11/0.79 fof(f388,plain,(
% 3.11/0.79 ![X0]: (bool(prop(X0))|f7(X0)=phi(prop(X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f153,f97])).
% 3.11/0.79 fof(f389,plain,(
% 3.11/0.79 spl0_29 <=> phi(X0)=phi(true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f390,plain,(
% 3.11/0.79 ![X0]: (phi(X0)=phi(true)|~spl0_29)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f389])).
% 3.11/0.79 fof(f392,plain,(
% 3.11/0.79 ![X0]: (bool(true)|phi(X0)=phi(true))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f99,f97])).
% 3.11/0.79 fof(f393,plain,(
% 3.11/0.79 spl0_0|spl0_29),
% 3.11/0.79 inference(split_clause,[status(thm)],[f392,f205,f389])).
% 3.11/0.79 fof(f403,plain,(
% 3.11/0.79 spl0_30 <=> phi(false)=false),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f404,plain,(
% 3.11/0.79 phi(false)=false|~spl0_30),
% 3.11/0.79 inference(component_clause,[status(thm)],[f403])).
% 3.11/0.79 fof(f405,plain,(
% 3.11/0.79 ~phi(false)=false|spl0_30),
% 3.11/0.79 inference(component_clause,[status(thm)],[f403])).
% 3.11/0.79 fof(f421,plain,(
% 3.11/0.79 spl0_32 <=> phi(true)=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f422,plain,(
% 3.11/0.79 phi(true)=true|~spl0_32),
% 3.11/0.79 inference(component_clause,[status(thm)],[f421])).
% 3.11/0.79 fof(f423,plain,(
% 3.11/0.79 ~phi(true)=true|spl0_32),
% 3.11/0.79 inference(component_clause,[status(thm)],[f421])).
% 3.11/0.79 fof(f426,plain,(
% 3.11/0.79 ![X0,X1]: (d(X0)|~d(X1)|pd0_0(X1,X0))),
% 3.11/0.79 inference(resolution,[status(thm)],[f193,f174])).
% 3.11/0.79 fof(f427,plain,(
% 3.11/0.79 spl0_33 <=> d(X0)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f428,plain,(
% 3.11/0.79 ![X0]: (d(X0)|~spl0_33)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f427])).
% 3.11/0.79 fof(f430,plain,(
% 3.11/0.79 spl0_34 <=> ~d(X1)|d(X1)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f433,plain,(
% 3.11/0.79 ![X0,X1]: (d(X0)|~d(X1)|d(X1))),
% 3.11/0.79 inference(resolution,[status(thm)],[f193,f192])).
% 3.11/0.79 fof(f434,plain,(
% 3.11/0.79 spl0_33|spl0_34),
% 3.11/0.79 inference(split_clause,[status(thm)],[f433,f427,f430])).
% 3.11/0.79 fof(f440,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_0(X0,X1)|~d(X0)|bool(X1)|~bool(X0))),
% 3.11/0.79 inference(backward_subsumption_resolution,[status(thm)],[f175,f426])).
% 3.11/0.79 fof(f441,plain,(
% 3.11/0.79 ![X0,X1]: (d(X0)|~d(X1)|pd0_1(X1,X0))),
% 3.11/0.79 inference(resolution,[status(thm)],[f198,f184])).
% 3.11/0.79 fof(f446,plain,(
% 3.11/0.79 ![X0,X1]: (pd0_1(X0,X1)|~d(X0)|bool(X1)|~bool(X0))),
% 3.11/0.79 inference(backward_subsumption_resolution,[status(thm)],[f185,f441])).
% 3.11/0.79 fof(f447,plain,(
% 3.11/0.79 ![X0,X1]: (d(X0)|~d(X1)|forallprefers(X0,X1))),
% 3.11/0.79 inference(resolution,[status(thm)],[f426,f64])).
% 3.11/0.79 fof(f453,plain,(
% 3.11/0.79 spl0_36 <=> d(true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f455,plain,(
% 3.11/0.79 ~d(true)|spl0_36),
% 3.11/0.79 inference(component_clause,[status(thm)],[f453])).
% 3.11/0.79 fof(f456,plain,(
% 3.11/0.79 spl0_37 <=> d(err)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f458,plain,(
% 3.11/0.79 ~d(err)|spl0_37),
% 3.11/0.79 inference(component_clause,[status(thm)],[f456])).
% 3.11/0.79 fof(f468,plain,(
% 3.11/0.79 $false|spl0_37),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f458,f57])).
% 3.11/0.79 fof(f469,plain,(
% 3.11/0.79 spl0_37),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f468])).
% 3.11/0.79 fof(f475,plain,(
% 3.11/0.79 $false|spl0_21),
% 3.11/0.79 inference(trivial_equality_resolution,[status(esa)],[f333])).
% 3.11/0.79 fof(f476,plain,(
% 3.11/0.79 spl0_21),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f475])).
% 3.11/0.79 fof(f495,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f1(X0,X1,X2)=lazy_impl(false,impl(impl(X0,impl(X1,X2)),X2))|bool(X2))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f109])).
% 3.11/0.79 fof(f496,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f1(X0,X1,X2)=true|bool(X2))),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f495])).
% 3.11/0.79 fof(f515,plain,(
% 3.11/0.79 spl0_40 <=> forallprefers(true,f7(sk0_6))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f517,plain,(
% 3.11/0.79 ~forallprefers(true,f7(sk0_6))|spl0_40),
% 3.11/0.79 inference(component_clause,[status(thm)],[f515])).
% 3.11/0.79 fof(f518,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(true,f7(sk0_6))|bool(X0))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f363,f157])).
% 3.11/0.79 fof(f519,plain,(
% 3.11/0.79 ~spl0_40|spl0_25),
% 3.11/0.79 inference(split_clause,[status(thm)],[f518,f515,f367])).
% 3.11/0.79 fof(f520,plain,(
% 3.11/0.79 spl0_41 <=> ~forallprefers(f7(X0),true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f521,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(f7(X0),true)|~spl0_41)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f520])).
% 3.11/0.79 fof(f523,plain,(
% 3.11/0.79 spl0_42 <=> bool(sk0_6)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f524,plain,(
% 3.11/0.79 bool(sk0_6)|~spl0_42),
% 3.11/0.79 inference(component_clause,[status(thm)],[f523])).
% 3.11/0.79 fof(f525,plain,(
% 3.11/0.79 ~bool(sk0_6)|spl0_42),
% 3.11/0.79 inference(component_clause,[status(thm)],[f523])).
% 3.11/0.79 fof(f563,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f2(X0,X1,X2)=lazy_impl(false,impl(lazy_impl(X0,impl(X1,X2)),X2))|bool(X2))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f119])).
% 3.11/0.79 fof(f564,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f2(X0,X1,X2)=true|bool(X2))),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f563])).
% 3.11/0.79 fof(f570,plain,(
% 3.11/0.79 ![X0,X1]: (f2(false,X0,X1)=lazy_impl(prop(X1),impl(true,X1)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f98,f119])).
% 3.11/0.79 fof(f578,plain,(
% 3.11/0.79 ![X0,X1]: (f2(X0,X1,err)=lazy_impl(prop(err),not2(lazy_impl(X0,impl(X1,err))))|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f292,f119])).
% 3.11/0.79 fof(f579,plain,(
% 3.11/0.79 ![X0,X1]: (f2(X0,X1,err)=lazy_impl(prop(err),not2(lazy_impl(X0,not2(X1))))|~spl0_11)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f292,f578])).
% 3.11/0.79 fof(f582,plain,(
% 3.11/0.79 ![X0,X1]: (f1(X0,X1,err)=lazy_impl(prop(err),not2(impl(X0,impl(X1,err))))|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f292,f109])).
% 3.11/0.79 fof(f583,plain,(
% 3.11/0.79 ![X0,X1]: (f1(X0,X1,err)=lazy_impl(prop(err),not2(impl(X0,not2(X1))))|~spl0_11)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f292,f582])).
% 3.11/0.79 fof(f594,plain,(
% 3.11/0.79 spl0_44 <=> bool(prop(err))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f599,plain,(
% 3.11/0.79 spl0_45 <=> f2(X0,X1,err)=lazy_impl(false,not2(lazy_impl(X0,not2(X1))))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f600,plain,(
% 3.11/0.79 ![X0,X1]: (f2(X0,X1,err)=lazy_impl(false,not2(lazy_impl(X0,not2(X1))))|~spl0_45)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f599])).
% 3.11/0.79 fof(f602,plain,(
% 3.11/0.79 ![X0,X1]: (f2(X0,X1,err)=lazy_impl(false,not2(lazy_impl(X0,not2(X1))))|bool(err)|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f579])).
% 3.11/0.79 fof(f603,plain,(
% 3.11/0.79 spl0_45|spl0_16|~spl0_11),
% 3.11/0.79 inference(split_clause,[status(thm)],[f602,f599,f307,f272])).
% 3.11/0.79 fof(f605,plain,(
% 3.11/0.79 ![X0,X1]: (f2(prop(err),lazy_impl(X0,not2(X1)),err)=lazy_impl(prop(err),not2(f2(X0,X1,err)))|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f579,f579])).
% 3.11/0.79 fof(f613,plain,(
% 3.11/0.79 $false|~spl0_22|~spl0_26),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f373,f347])).
% 3.11/0.79 fof(f614,plain,(
% 3.11/0.79 ~spl0_22|~spl0_26),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f613])).
% 3.11/0.79 fof(f628,plain,(
% 3.11/0.79 spl0_46 <=> pd0_2(true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f635,plain,(
% 3.11/0.79 ![X0]: (impl(false,X0)=true|~spl0_25)),
% 3.11/0.79 inference(backward_subsumption_resolution,[status(thm)],[f92,f368])).
% 3.11/0.79 fof(f680,plain,(
% 3.11/0.79 spl0_47 <=> f2(X0,X1,X2)=phi(prop(X2))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f681,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f2(X0,X1,X2)=phi(prop(X2))|~spl0_47)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f680])).
% 3.11/0.79 fof(f826,plain,(
% 3.11/0.79 $false|~spl0_27),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f200,f378])).
% 3.11/0.79 fof(f827,plain,(
% 3.11/0.79 ~spl0_27),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f826])).
% 3.11/0.79 fof(f880,plain,(
% 3.11/0.79 spl0_52 <=> false2=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f881,plain,(
% 3.11/0.79 false2=true|~spl0_52),
% 3.11/0.79 inference(component_clause,[status(thm)],[f880])).
% 3.11/0.79 fof(f882,plain,(
% 3.11/0.79 ~false2=true|spl0_52),
% 3.11/0.79 inference(component_clause,[status(thm)],[f880])).
% 3.11/0.79 fof(f883,plain,(
% 3.11/0.79 false2=true|bool(sk0_6)|~spl0_13),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f283,f363])).
% 3.11/0.79 fof(f884,plain,(
% 3.11/0.79 spl0_52|spl0_42|~spl0_13),
% 3.11/0.79 inference(split_clause,[status(thm)],[f883,f880,f523,f282])).
% 3.11/0.79 fof(f892,plain,(
% 3.11/0.79 spl0_54 <=> forallprefers(true,true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f895,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(true,true)|bool(X0)|~spl0_41)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f363,f521])).
% 3.11/0.79 fof(f896,plain,(
% 3.11/0.79 ~spl0_54|spl0_25|~spl0_41),
% 3.11/0.79 inference(split_clause,[status(thm)],[f895,f892,f367,f520])).
% 3.11/0.79 fof(f1005,plain,(
% 3.11/0.79 not2(false)=true|~spl0_25),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f162,f635])).
% 3.11/0.79 fof(f1006,plain,(
% 3.11/0.79 spl0_26|~spl0_25),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1005,f372,f367])).
% 3.11/0.79 fof(f1009,plain,(
% 3.11/0.79 ![X0,X1]: (f2(X0,X1,err)=true|~spl0_45)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f600])).
% 3.11/0.79 fof(f1011,plain,(
% 3.11/0.79 ![X0,X1]: (true=lazy_impl(prop(err),not2(lazy_impl(X0,not2(X1))))|~spl0_45|~spl0_11)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f1009,f579])).
% 3.11/0.79 fof(f1013,plain,(
% 3.11/0.79 ![X0,X1]: (true=lazy_impl(prop(err),not2(f2(X0,X1,err)))|~spl0_45|~spl0_11)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f1009,f605])).
% 3.11/0.79 fof(f1014,plain,(
% 3.11/0.79 true=lazy_impl(prop(err),not2(true))|~spl0_45|~spl0_11),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f1009,f1013])).
% 3.11/0.79 fof(f1020,plain,(
% 3.11/0.79 err=phi(f7(sk0_6))|~spl0_11),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f273,f156])).
% 3.11/0.79 fof(f1029,plain,(
% 3.11/0.79 spl0_55 <=> true=err),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1030,plain,(
% 3.11/0.79 true=err|~spl0_55),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1029])).
% 3.11/0.79 fof(f1039,plain,(
% 3.11/0.79 spl0_57 <=> true=prop(err)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1040,plain,(
% 3.11/0.79 true=prop(err)|~spl0_57),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1039])).
% 3.11/0.79 fof(f1041,plain,(
% 3.11/0.79 ~true=prop(err)|spl0_57),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1039])).
% 3.11/0.79 fof(f1044,plain,(
% 3.11/0.79 $false|~spl0_55),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1030,f53])).
% 3.11/0.79 fof(f1045,plain,(
% 3.11/0.79 ~spl0_55),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1044])).
% 3.11/0.79 fof(f1092,plain,(
% 3.11/0.79 ~forallprefers(true,true)|bool(sk0_6)|spl0_40),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f363,f517])).
% 3.11/0.79 fof(f1093,plain,(
% 3.11/0.79 ~spl0_54|spl0_42|spl0_40),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1092,f892,f523,f515])).
% 3.11/0.79 fof(f1098,plain,(
% 3.11/0.79 ~pd0_2(true)|bool(sk0_6)|spl0_12),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f363,f277])).
% 3.11/0.79 fof(f1099,plain,(
% 3.11/0.79 ~spl0_46|spl0_42|spl0_12),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1098,f628,f523,f275])).
% 3.11/0.79 fof(f1101,plain,(
% 3.11/0.79 spl0_61 <=> true=lazy_impl(false,not2(lazy_impl(X0,not2(X1))))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1104,plain,(
% 3.11/0.79 ![X0,X1]: (true=lazy_impl(false,not2(lazy_impl(X0,not2(X1))))|bool(err)|~spl0_45|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f1011])).
% 3.11/0.79 fof(f1105,plain,(
% 3.11/0.79 spl0_61|spl0_16|~spl0_45|~spl0_11),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1104,f1101,f307,f599,f272])).
% 3.11/0.79 fof(f1106,plain,(
% 3.11/0.79 spl0_62 <=> f1(X0,X1,err)=lazy_impl(false,not2(impl(X0,not2(X1))))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1109,plain,(
% 3.11/0.79 ![X0,X1]: (f1(X0,X1,err)=lazy_impl(false,not2(impl(X0,not2(X1))))|bool(err)|~spl0_11)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f583])).
% 3.11/0.79 fof(f1110,plain,(
% 3.11/0.79 spl0_62|spl0_16|~spl0_11),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1109,f1106,f307,f272])).
% 3.11/0.79 fof(f1111,plain,(
% 3.11/0.79 spl0_63 <=> true=lazy_impl(false,not2(true))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1114,plain,(
% 3.11/0.79 true=lazy_impl(false,not2(true))|bool(err)|~spl0_45|~spl0_11),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f1014])).
% 3.11/0.79 fof(f1115,plain,(
% 3.11/0.79 spl0_63|spl0_16|~spl0_45|~spl0_11),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1114,f1111,f307,f599,f272])).
% 3.11/0.79 fof(f1146,plain,(
% 3.11/0.79 spl0_64 <=> prop(err)=false),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1147,plain,(
% 3.11/0.79 prop(err)=false|~spl0_64),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1146])).
% 3.11/0.79 fof(f1148,plain,(
% 3.11/0.79 ~prop(err)=false|spl0_64),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1146])).
% 3.11/0.79 fof(f1151,plain,(
% 3.11/0.79 spl0_65 <=> sk0_6=false),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1152,plain,(
% 3.11/0.79 sk0_6=false|~spl0_65),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1151])).
% 3.11/0.79 fof(f1154,plain,(
% 3.11/0.79 spl0_66 <=> sk0_6=true),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1155,plain,(
% 3.11/0.79 sk0_6=true|~spl0_66),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1154])).
% 3.11/0.79 fof(f1157,plain,(
% 3.11/0.79 sk0_6=false|sk0_6=true|~spl0_42),
% 3.11/0.79 inference(resolution,[status(thm)],[f49,f524])).
% 3.11/0.79 fof(f1158,plain,(
% 3.11/0.79 spl0_65|spl0_66|~spl0_42),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1157,f1151,f1154,f523])).
% 3.11/0.79 fof(f1242,plain,(
% 3.11/0.79 spl0_67 <=> ~forallprefers(true,f2(X0,X1,sk0_1(X1,X0)))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1243,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,f2(X0,X1,sk0_1(X1,X0)))|~spl0_67)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1242])).
% 3.11/0.79 fof(f1245,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(true,f2(X0,X1,sk0_1(X1,X0)))|bool(X2))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f564,f123])).
% 3.11/0.79 fof(f1246,plain,(
% 3.11/0.79 spl0_67|spl0_25),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1245,f1242,f367])).
% 3.11/0.79 fof(f1247,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(f2(X0,X1,X2),true)|bool(sk0_1(X1,X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f564,f123])).
% 3.11/0.79 fof(f1252,plain,(
% 3.11/0.79 bool(err)|~spl0_57),
% 3.11/0.79 inference(resolution,[status(thm)],[f1040,f80])).
% 3.11/0.79 fof(f1269,plain,(
% 3.11/0.79 f7(err)=lazy_impl(false,err)|~spl0_64),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1147,f153])).
% 3.11/0.79 fof(f1270,plain,(
% 3.11/0.79 f7(err)=true|~spl0_64),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f1269])).
% 3.11/0.79 fof(f1282,plain,(
% 3.11/0.79 false2=phi(f7(false))|~spl0_65),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f1152,f156])).
% 3.11/0.79 fof(f1284,plain,(
% 3.11/0.79 $false|~spl0_25|spl0_20),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f327,f368])).
% 3.11/0.79 fof(f1285,plain,(
% 3.11/0.79 ~spl0_25|spl0_20),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1284])).
% 3.11/0.79 fof(f1328,plain,(
% 3.11/0.79 ![X0]: (phi(X0)=true|~spl0_32|~spl0_29)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f422,f390])).
% 3.11/0.79 fof(f1393,plain,(
% 3.11/0.79 ![X0]: (pd0_2(X0)|true=err|~spl0_32|~spl0_29)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f1328,f77])).
% 3.11/0.79 fof(f1394,plain,(
% 3.11/0.79 ![X0]: (pd0_2(X0)|~spl0_32|~spl0_29)),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1393,f53])).
% 3.11/0.79 fof(f1395,plain,(
% 3.11/0.79 ![X0]: (~pd0_2(X0)|true=X0|~spl0_32|~spl0_29)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f1328,f188])).
% 3.11/0.79 fof(f1396,plain,(
% 3.11/0.79 ![X0]: (true=X0|~spl0_32|~spl0_29)),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1395,f1394])).
% 3.11/0.79 fof(f1412,plain,(
% 3.11/0.79 $false|~spl0_32|~spl0_29|spl0_57),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1041,f1396])).
% 3.11/0.79 fof(f1413,plain,(
% 3.11/0.79 ~spl0_32|~spl0_29|spl0_57),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1412])).
% 3.11/0.79 fof(f1414,plain,(
% 3.11/0.79 ~bool(err)|~spl0_64),
% 3.11/0.79 inference(resolution,[status(thm)],[f1147,f84])).
% 3.11/0.79 fof(f1422,plain,(
% 3.11/0.79 ![X0]: (pd0_2(X0)|~spl0_33)),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f76,f428])).
% 3.11/0.79 fof(f1453,plain,(
% 3.11/0.79 ![X0]: (phi(prop(X0))=true|bool(X0)|~spl0_47)),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f681,f564])).
% 3.11/0.79 fof(f1456,plain,(
% 3.11/0.79 spl0_68 <=> ~forallprefers(phi(prop(X0)),true)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1457,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(phi(prop(X0)),true)|~spl0_68)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1456])).
% 3.11/0.79 fof(f1459,plain,(
% 3.11/0.79 spl0_69 <=> bool(sk0_1(X1,X2))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1462,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(phi(prop(X0)),true)|bool(sk0_1(X1,X2))|~spl0_47)),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f681,f1247])).
% 3.11/0.79 fof(f1463,plain,(
% 3.11/0.79 spl0_68|spl0_69|~spl0_47),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1462,f1456,f1459,f680])).
% 3.11/0.79 fof(f1466,plain,(
% 3.11/0.79 ![X0]: (phi(X0)=X0|~spl0_33)),
% 3.11/0.79 inference(backward_subsumption_resolution,[status(thm)],[f188,f1422])).
% 3.11/0.79 fof(f1484,plain,(
% 3.11/0.79 ![X0]: (prop(X0)=true|bool(X0)|~spl0_33|~spl0_47)),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f1466,f1453])).
% 3.11/0.79 fof(f1485,plain,(
% 3.11/0.79 ![X0]: (bool(X0)|~spl0_33|~spl0_47)),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1484,f80])).
% 3.11/0.79 fof(f1505,plain,(
% 3.11/0.79 $false|~spl0_33|~spl0_47|~spl0_64),
% 3.11/0.79 inference(backward_subsumption_resolution,[status(thm)],[f1414,f1485])).
% 3.11/0.79 fof(f1506,plain,(
% 3.11/0.79 ~spl0_33|~spl0_47|~spl0_64),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1505])).
% 3.11/0.79 fof(f1508,plain,(
% 3.11/0.79 spl0_70 <=> err=phi(err)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1510,plain,(
% 3.11/0.79 ~err=phi(err)|spl0_70),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1508])).
% 3.11/0.79 fof(f1530,plain,(
% 3.11/0.79 ~forallprefers(phi(false),true)|~spl0_68|~spl0_64),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1147,f1457])).
% 3.11/0.79 fof(f1531,plain,(
% 3.11/0.79 ~forallprefers(false,true)|~spl0_30|~spl0_68|~spl0_64),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f404,f1530])).
% 3.11/0.79 fof(f1532,plain,(
% 3.11/0.79 $false|~spl0_30|~spl0_68|~spl0_64),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1531,f201])).
% 3.11/0.79 fof(f1533,plain,(
% 3.11/0.79 ~spl0_30|~spl0_68|~spl0_64),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1532])).
% 3.11/0.79 fof(f1554,plain,(
% 3.11/0.79 ![X0,X1]: (f3(X0,X1,err)=lazy_impl(false,impl(impl(X0,err),impl(impl(X1,err),err)))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1147,f133])).
% 3.11/0.79 fof(f1555,plain,(
% 3.11/0.79 ![X0,X1]: (f3(X0,X1,err)=true|~spl0_64)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f1554])).
% 3.11/0.79 fof(f1574,plain,(
% 3.11/0.79 ~pd0_2(false)|spl0_30),
% 3.11/0.79 inference(resolution,[status(thm)],[f188,f405])).
% 3.11/0.79 fof(f1575,plain,(
% 3.11/0.79 $false|spl0_30),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1574,f248])).
% 3.11/0.79 fof(f1576,plain,(
% 3.11/0.79 spl0_30),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1575])).
% 3.11/0.79 fof(f1577,plain,(
% 3.11/0.79 ~pd0_2(true)|spl0_32),
% 3.11/0.79 inference(resolution,[status(thm)],[f188,f423])).
% 3.11/0.79 fof(f1578,plain,(
% 3.11/0.79 $false|spl0_32),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1577,f249])).
% 3.11/0.79 fof(f1579,plain,(
% 3.11/0.79 spl0_32),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1578])).
% 3.11/0.79 fof(f1584,plain,(
% 3.11/0.79 true=false|~spl0_30|~spl0_3),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f404,f217])).
% 3.11/0.79 fof(f1585,plain,(
% 3.11/0.79 $false|~spl0_30|~spl0_3),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1584,f52])).
% 3.11/0.79 fof(f1586,plain,(
% 3.11/0.79 ~spl0_30|~spl0_3),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1585])).
% 3.11/0.79 fof(f1614,plain,(
% 3.11/0.79 false2=phi(true)|~spl0_52|~spl0_13),
% 3.11/0.79 inference(backward_demodulation,[status(thm)],[f881,f287])).
% 3.11/0.79 fof(f1615,plain,(
% 3.11/0.79 false2=true|~spl0_32|~spl0_52|~spl0_13),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f422,f1614])).
% 3.11/0.79 fof(f1644,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f3(X0,X1,X2)=lazy_impl(false,impl(impl(X0,X2),impl(impl(X1,X2),X2)))|bool(X2))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f133])).
% 3.11/0.79 fof(f1645,plain,(
% 3.11/0.79 ![X0,X1,X2]: (f3(X0,X1,X2)=true|bool(X2))),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f1644])).
% 3.11/0.79 fof(f1658,plain,(
% 3.11/0.79 ![X0]: (f6(X0,err)=lazy_impl(false,impl(f5(X0,err),err))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1147,f147])).
% 3.11/0.79 fof(f1659,plain,(
% 3.11/0.79 ![X0]: (f6(X0,err)=true|~spl0_64)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f1658])).
% 3.11/0.79 fof(f1660,plain,(
% 3.11/0.79 ![X0,X1]: (f6(X0,X1)=lazy_impl(false,impl(f5(X0,X1),X1))|bool(X1))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f147])).
% 3.11/0.79 fof(f1661,plain,(
% 3.11/0.79 ![X0,X1]: (f6(X0,X1)=true|bool(X1))),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f98,f1660])).
% 3.11/0.79 fof(f1716,plain,(
% 3.11/0.79 spl0_74 <=> pd0_2(false)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1718,plain,(
% 3.11/0.79 ~pd0_2(false)|spl0_74),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1716])).
% 3.11/0.79 fof(f1721,plain,(
% 3.11/0.79 $false|spl0_74),
% 3.11/0.79 inference(forward_subsumption_resolution,[status(thm)],[f1718,f248])).
% 3.11/0.79 fof(f1722,plain,(
% 3.11/0.79 spl0_74),
% 3.11/0.79 inference(contradiction_clause,[status(thm)],[f1721])).
% 3.11/0.79 fof(f1732,plain,(
% 3.11/0.79 pd0_2(true)|true=err|~spl0_32),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f422,f77])).
% 3.11/0.79 fof(f1733,plain,(
% 3.11/0.79 spl0_46|spl0_55|~spl0_32),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1732,f628,f1029,f421])).
% 3.11/0.79 fof(f1734,plain,(
% 3.11/0.79 spl0_75 <=> false=err),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1735,plain,(
% 3.11/0.79 false=err|~spl0_75),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1734])).
% 3.11/0.79 fof(f1852,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,f3(X0,X1,sk0_2(X1,X0)))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1555,f137])).
% 3.11/0.79 fof(f1852,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,f3(X0,X1,sk0_2(X1,X0)))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1555,f137])).
% 3.11/0.79 fof(f1875,plain,(
% 3.11/0.79 ![X0,X1]: (bool(prop(X0))|f6(X1,X0)=phi(prop(X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f147,f97])).
% 3.11/0.79 fof(f1961,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,true)|bool(sk0_1(X0,X1))|~spl0_67)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f564,f1243])).
% 3.11/0.79 fof(f1962,plain,(
% 3.11/0.79 ~spl0_54|spl0_69|~spl0_67),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1961,f892,f1459,f1242])).
% 3.11/0.79 fof(f1965,plain,(
% 3.11/0.79 spl0_78 <=> bool(sk0_2(X0,X1))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1968,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,true)|bool(sk0_2(X0,X1))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1645,f1852])).
% 3.11/0.79 fof(f1969,plain,(
% 3.11/0.79 ~spl0_54|spl0_78|~spl0_64),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1968,f892,f1965,f1146])).
% 3.11/0.79 fof(f1970,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(f3(X0,X1,X2),true)|bool(sk0_2(X1,X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1645,f137])).
% 3.11/0.79 fof(f1973,plain,(
% 3.11/0.79 spl0_79 <=> ~forallprefers(true,f3(X0,X1,sk0_2(X1,X0)))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1990,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(true,f6(X0,sk0_5(X0)))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1659,f151])).
% 3.11/0.79 fof(f1991,plain,(
% 3.11/0.79 spl0_80 <=> ~forallprefers(true,f6(X0,sk0_5(X0)))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f1992,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(true,f6(X0,sk0_5(X0)))|~spl0_80)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f1991])).
% 3.11/0.79 fof(f1994,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,f6(X0,sk0_5(X0)))|bool(X1))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1661,f151])).
% 3.11/0.79 fof(f1995,plain,(
% 3.11/0.79 spl0_80|spl0_25),
% 3.11/0.79 inference(split_clause,[status(thm)],[f1994,f1991,f367])).
% 3.11/0.79 fof(f1996,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(f6(X0,X1),true)|bool(sk0_5(X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1661,f151])).
% 3.11/0.79 fof(f2003,plain,(
% 3.11/0.79 ![X0]: (bool(prop(X0))|f7(X0)=err|pd0_2(prop(X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f77,f388])).
% 3.11/0.79 fof(f2004,plain,(
% 3.11/0.79 spl0_82 <=> f7(err)=phi(false)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2005,plain,(
% 3.11/0.79 f7(err)=phi(false)|~spl0_82),
% 3.11/0.79 inference(component_clause,[status(thm)],[f2004])).
% 3.11/0.79 fof(f2009,plain,(
% 3.11/0.79 ![X0]: (bool(prop(X0))|f7(X0)=phi(false)|bool(X0))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f85,f388])).
% 3.11/0.79 fof(f2010,plain,(
% 3.11/0.79 ![X0]: (bool(prop(X0))|f7(X0)=false|bool(X0)|~spl0_30)),
% 3.11/0.79 inference(forward_demodulation,[status(thm)],[f404,f2009])).
% 3.11/0.79 fof(f2023,plain,(
% 3.11/0.79 spl0_83 <=> ~forallprefers(true,f1(X0,X1,sk0_0(X1,X0)))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2024,plain,(
% 3.11/0.79 ![X0,X1]: (~forallprefers(true,f1(X0,X1,sk0_0(X1,X0)))|~spl0_83)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f2023])).
% 3.11/0.79 fof(f2026,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(true,f1(X0,X1,sk0_0(X1,X0)))|bool(X2))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f496,f113])).
% 3.11/0.79 fof(f2027,plain,(
% 3.11/0.79 spl0_83|spl0_25),
% 3.11/0.79 inference(split_clause,[status(thm)],[f2026,f2023,f367])).
% 3.11/0.79 fof(f2028,plain,(
% 3.11/0.79 ![X0,X1,X2]: (~forallprefers(f1(X0,X1,X2),true)|bool(sk0_0(X1,X0)))),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f496,f113])).
% 3.11/0.79 fof(f2034,plain,(
% 3.11/0.79 spl0_85 <=> bool(sk0_5(X0))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2035,plain,(
% 3.11/0.79 ![X0]: (bool(sk0_5(X0))|~spl0_85)),
% 3.11/0.79 inference(component_clause,[status(thm)],[f2034])).
% 3.11/0.79 fof(f2037,plain,(
% 3.11/0.79 ![X0]: (~forallprefers(true,true)|bool(sk0_5(X0))|~spl0_64)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1661,f1990])).
% 3.11/0.79 fof(f2038,plain,(
% 3.11/0.79 ~spl0_54|spl0_85|~spl0_64),
% 3.11/0.79 inference(split_clause,[status(thm)],[f2037,f892,f2034,f1146])).
% 3.11/0.79 fof(f2044,plain,(
% 3.11/0.79 spl0_87 <=> bool(sk0_0(X0,X1))),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2049,plain,(
% 3.11/0.79 bool(prop(err))|true=false|bool(err)|~spl0_30|~spl0_64),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f1270,f2010])).
% 3.11/0.79 fof(f2050,plain,(
% 3.11/0.79 spl0_44|spl0_5|spl0_16|~spl0_30|~spl0_64),
% 3.11/0.79 inference(split_clause,[status(thm)],[f2049,f594,f228,f307,f403,f1146])).
% 3.11/0.79 fof(f2051,plain,(
% 3.11/0.79 spl0_88 <=> bool(prop(X0))|bool(X0)|bool(X0)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2054,plain,(
% 3.11/0.79 ![X0]: (bool(prop(X0))|true=false|bool(X0)|bool(X0)|~spl0_30)),
% 3.11/0.79 inference(paramodulation,[status(thm)],[f363,f2010])).
% 3.11/0.79 fof(f2055,plain,(
% 3.11/0.79 spl0_88|spl0_5|~spl0_30),
% 3.11/0.79 inference(split_clause,[status(thm)],[f2054,f2051,f228,f403])).
% 3.11/0.79 fof(f2068,plain,(
% 3.11/0.79 spl0_91 <=> d(false)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2090,plain,(
% 3.11/0.79 spl0_92 <=> ~d(X0)|~bool(X0)|d(X0)),
% 3.11/0.79 introduced(split_symbol_definition)).
% 3.11/0.79 fof(f2093,plain,(
% 3.11/0.79 ![X0,X1]: (~d(X0)|bool(X1)|~bool(X0)|d(X0))),
% 3.11/0.80 inference(resolution,[status(thm)],[f446,f204])).
% 3.11/0.80 fof(f2094,plain,(
% 3.11/0.80 spl0_92|spl0_25),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2093,f2090,f367])).
% 3.11/0.80 fof(f2099,plain,(
% 3.11/0.80 ![X0,X1]: (~d(X0)|bool(X1)|~bool(X0)|forallprefers(X1,X0))),
% 3.11/0.80 inference(resolution,[status(thm)],[f440,f64])).
% 3.11/0.80 fof(f2100,plain,(
% 3.11/0.80 spl0_93 <=> bool(sk0_5(X0))|d(f6(X0,X1))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2101,plain,(
% 3.11/0.80 ![X0,X1]: (bool(sk0_5(X0))|d(f6(X0,X1))|~spl0_93)),
% 3.11/0.80 inference(component_clause,[status(thm)],[f2100])).
% 3.11/0.80 fof(f2103,plain,(
% 3.11/0.80 ![X0,X1]: (bool(sk0_5(X0))|d(f6(X0,X1))|~d(true))),
% 3.11/0.80 inference(resolution,[status(thm)],[f1996,f447])).
% 3.11/0.80 fof(f2104,plain,(
% 3.11/0.80 spl0_93|~spl0_36),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2103,f2100,f453])).
% 3.11/0.80 fof(f2109,plain,(
% 3.11/0.80 ![X0,X1]: (bool(sk0_5(X0))|pd0_2(f6(X0,X1))|~spl0_93)),
% 3.11/0.80 inference(resolution,[status(thm)],[f2101,f76])).
% 3.11/0.80 fof(f2137,plain,(
% 3.11/0.80 spl0_94 <=> bool(f6(X0,X1))|bool(sk0_5(X0))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2138,plain,(
% 3.11/0.80 ![X0,X1]: (bool(f6(X0,X1))|bool(sk0_5(X0))|~spl0_94)),
% 3.11/0.80 inference(component_clause,[status(thm)],[f2137])).
% 3.11/0.80 fof(f2140,plain,(
% 3.11/0.80 ![X0,X1]: (~d(true)|bool(f6(X0,X1))|~bool(true)|bool(sk0_5(X0)))),
% 3.11/0.80 inference(resolution,[status(thm)],[f2099,f1996])).
% 3.11/0.80 fof(f2141,plain,(
% 3.11/0.80 ~spl0_36|spl0_94|~spl0_0),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2140,f453,f2137,f205])).
% 3.11/0.80 fof(f2183,plain,(
% 3.11/0.80 f7(err)=false|~spl0_30|~spl0_82),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f404,f2005])).
% 3.11/0.80 fof(f2184,plain,(
% 3.11/0.80 $false|~spl0_75),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f1735,f54])).
% 3.11/0.80 fof(f2185,plain,(
% 3.11/0.80 ~spl0_75),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f2184])).
% 3.11/0.80 fof(f2232,plain,(
% 3.11/0.80 false=true|~spl0_32|~spl0_1),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f422,f209])).
% 3.11/0.80 fof(f2233,plain,(
% 3.11/0.80 $false|~spl0_32|~spl0_1),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f2232,f52])).
% 3.11/0.80 fof(f2234,plain,(
% 3.11/0.80 ~spl0_32|~spl0_1),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f2233])).
% 3.11/0.80 fof(f2273,plain,(
% 3.11/0.80 $false|spl0_36),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f455,f55])).
% 3.11/0.80 fof(f2274,plain,(
% 3.11/0.80 spl0_36),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f2273])).
% 3.11/0.80 fof(f2517,plain,(
% 3.11/0.80 ![X0,X1]: (bool(sk0_5(X0))|f6(X0,X1)=false|f6(X0,X1)=true|~spl0_94)),
% 3.11/0.80 inference(resolution,[status(thm)],[f2138,f49])).
% 3.11/0.80 fof(f2534,plain,(
% 3.11/0.80 ![X0,X1]: (~forallprefers(true,true)|bool(sk0_0(X0,X1))|~spl0_83)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f496,f2024])).
% 3.11/0.80 fof(f2535,plain,(
% 3.11/0.80 ~spl0_54|spl0_87|~spl0_83),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2534,f892,f2044,f2023])).
% 3.11/0.80 fof(f2556,plain,(
% 3.11/0.80 spl0_102 <=> bool(sk0_5(X0))|f6(X0,sk0_5(X0))=false),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2559,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,true)|bool(sk0_5(X0))|f6(X0,sk0_5(X0))=false|~spl0_80|~spl0_94)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f2517,f1992])).
% 3.11/0.80 fof(f2560,plain,(
% 3.11/0.80 ~spl0_54|spl0_102|~spl0_80|~spl0_94),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2559,f892,f2556,f1991,f2137])).
% 3.11/0.80 fof(f2569,plain,(
% 3.11/0.80 spl0_104 <=> bool(sk0_5(X0))|bool(sk0_5(X0))|f6(X0,X1)=false),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2628,plain,(
% 3.11/0.80 ![X0,X1]: (~forallprefers(true,true)|bool(sk0_5(X0))|bool(sk0_5(X0))|f6(X0,X1)=false|~spl0_94)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f2517,f1996])).
% 3.11/0.80 fof(f2629,plain,(
% 3.11/0.80 ~spl0_54|spl0_104|~spl0_94),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2628,f892,f2569,f2137])).
% 3.11/0.80 fof(f2641,plain,(
% 3.11/0.80 spl0_106 <=> true=phi(prop(err))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2642,plain,(
% 3.11/0.80 true=phi(prop(err))|~spl0_106),
% 3.11/0.80 inference(component_clause,[status(thm)],[f2641])).
% 3.11/0.80 fof(f2650,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,phi(prop(sk0_5(X0))))|bool(prop(sk0_5(X0)))|~spl0_80)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f1875,f1992])).
% 3.11/0.80 fof(f2654,plain,(
% 3.11/0.80 spl0_107 <=> ~forallprefers(phi(prop(X0)),true)|bool(prop(X0))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2657,plain,(
% 3.11/0.80 ![X0,X1]: (~forallprefers(phi(prop(X0)),true)|bool(sk0_5(X1))|bool(prop(X0)))),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f1875,f1996])).
% 3.11/0.80 fof(f2658,plain,(
% 3.11/0.80 spl0_107|spl0_85),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2657,f2654,f2034])).
% 3.11/0.80 fof(f2660,plain,(
% 3.11/0.80 spl0_108 <=> d(phi(prop(X1)))|bool(prop(X1))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2663,plain,(
% 3.11/0.80 ![X0,X1]: (bool(sk0_5(X0))|d(phi(prop(X1)))|bool(prop(X1))|~spl0_93)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f1875,f2101])).
% 3.11/0.80 fof(f2664,plain,(
% 3.11/0.80 spl0_85|spl0_108|~spl0_93),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2663,f2034,f2660,f2100])).
% 3.11/0.80 fof(f2665,plain,(
% 3.11/0.80 spl0_109 <=> pd0_2(phi(prop(X1)))|bool(prop(X1))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2668,plain,(
% 3.11/0.80 ![X0,X1]: (bool(sk0_5(X0))|pd0_2(phi(prop(X1)))|bool(prop(X1))|~spl0_93)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f1875,f2109])).
% 3.11/0.80 fof(f2669,plain,(
% 3.11/0.80 spl0_85|spl0_109|~spl0_93),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2668,f2034,f2665,f2100])).
% 3.11/0.80 fof(f2670,plain,(
% 3.11/0.80 spl0_110 <=> bool(phi(prop(X0)))|bool(prop(X0))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2673,plain,(
% 3.11/0.80 ![X0,X1]: (bool(phi(prop(X0)))|bool(sk0_5(X1))|bool(prop(X0))|~spl0_94)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f1875,f2138])).
% 3.11/0.80 fof(f2674,plain,(
% 3.11/0.80 spl0_110|spl0_85|~spl0_94),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2673,f2670,f2034,f2137])).
% 3.11/0.80 fof(f2676,plain,(
% 3.11/0.80 ![X0]: (sk0_5(X0)=false|sk0_5(X0)=true|~spl0_85)),
% 3.11/0.80 inference(resolution,[status(thm)],[f2035,f49])).
% 3.11/0.80 fof(f2699,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,f7(sk0_5(X0)))|bool(prop(sk0_5(X0)))|bool(prop(sk0_5(X0)))|~spl0_80)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f388,f2650])).
% 3.11/0.80 fof(f2700,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,f7(sk0_5(X0)))|bool(prop(sk0_5(X0)))|~spl0_80)),
% 3.11/0.80 inference(duplicate_literals_removal,[status(esa)],[f2699])).
% 3.11/0.80 fof(f2701,plain,(
% 3.11/0.80 spl0_114 <=> bool(prop(sk0_5(X0)))|pd0_2(prop(sk0_5(X0)))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2704,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,err)|bool(prop(sk0_5(X0)))|pd0_2(prop(sk0_5(X0)))|~spl0_80)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f77,f2650])).
% 3.11/0.80 fof(f2705,plain,(
% 3.11/0.80 ~spl0_24|spl0_114|~spl0_80),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2704,f364,f2701,f1991])).
% 3.11/0.80 fof(f2706,plain,(
% 3.11/0.80 spl0_115 <=> forallprefers(true,phi(false))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2709,plain,(
% 3.11/0.80 spl0_116 <=> bool(prop(sk0_5(X0)))|bool(sk0_5(X0))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2712,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,phi(false))|bool(prop(sk0_5(X0)))|bool(sk0_5(X0))|~spl0_80)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f85,f2650])).
% 3.11/0.80 fof(f2713,plain,(
% 3.11/0.80 ~spl0_115|spl0_116|~spl0_80),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2712,f2706,f2709,f1991])).
% 3.11/0.80 fof(f2714,plain,(
% 3.11/0.80 spl0_117 <=> forallprefers(true,phi(prop(true)))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2717,plain,(
% 3.11/0.80 spl0_118 <=> bool(prop(sk0_5(X0)))|sk0_5(X0)=false),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2720,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,phi(prop(true)))|bool(prop(sk0_5(X0)))|sk0_5(X0)=false|~spl0_80|~spl0_85)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f2676,f2650])).
% 3.11/0.80 fof(f2721,plain,(
% 3.11/0.80 ~spl0_117|spl0_118|~spl0_80|~spl0_85),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2720,f2714,f2717,f1991,f2034])).
% 3.11/0.80 fof(f2733,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,true)|bool(prop(sk0_5(X0)))|bool(sk0_5(X0))|~spl0_80)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f363,f2700])).
% 3.11/0.80 fof(f2734,plain,(
% 3.11/0.80 ~spl0_54|spl0_116|~spl0_80),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2733,f892,f2709,f1991])).
% 3.11/0.80 fof(f2735,plain,(
% 3.11/0.80 spl0_121 <=> forallprefers(true,f7(true))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2738,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,f7(true))|bool(prop(sk0_5(X0)))|sk0_5(X0)=false|~spl0_80|~spl0_85)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f2676,f2700])).
% 3.11/0.80 fof(f2739,plain,(
% 3.11/0.80 ~spl0_121|spl0_118|~spl0_80|~spl0_85),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2738,f2735,f2717,f1991,f2034])).
% 3.11/0.80 fof(f2835,plain,(
% 3.11/0.80 spl0_126 <=> bool(sk0_0(X0,X1))|bool(f1(X1,X0,X2))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2838,plain,(
% 3.11/0.80 ![X0,X1,X2]: (bool(sk0_0(X0,X1))|~d(true)|bool(f1(X1,X0,X2))|~bool(true))),
% 3.11/0.80 inference(resolution,[status(thm)],[f2028,f2099])).
% 3.11/0.80 fof(f2839,plain,(
% 3.11/0.80 spl0_126|~spl0_36|~spl0_0),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2838,f2835,f453,f205])).
% 3.11/0.80 fof(f2840,plain,(
% 3.11/0.80 spl0_127 <=> bool(sk0_0(X0,X1))|d(f1(X1,X0,X2))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2843,plain,(
% 3.11/0.80 ![X0,X1,X2]: (bool(sk0_0(X0,X1))|d(f1(X1,X0,X2))|~d(true))),
% 3.11/0.80 inference(resolution,[status(thm)],[f2028,f447])).
% 3.11/0.80 fof(f2844,plain,(
% 3.11/0.80 spl0_127|~spl0_36),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2843,f2840,f453])).
% 3.11/0.80 fof(f2849,plain,(
% 3.11/0.80 spl0_128 <=> bool(sk0_2(X0,X1))|bool(f3(X1,X0,X2))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2852,plain,(
% 3.11/0.80 ![X0,X1,X2]: (bool(sk0_2(X0,X1))|~d(true)|bool(f3(X1,X0,X2))|~bool(true))),
% 3.11/0.80 inference(resolution,[status(thm)],[f1970,f2099])).
% 3.11/0.80 fof(f2853,plain,(
% 3.11/0.80 spl0_128|~spl0_36|~spl0_0),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2852,f2849,f453,f205])).
% 3.11/0.80 fof(f2854,plain,(
% 3.11/0.80 spl0_129 <=> bool(sk0_2(X0,X1))|d(f3(X1,X0,X2))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2857,plain,(
% 3.11/0.80 ![X0,X1,X2]: (bool(sk0_2(X0,X1))|d(f3(X1,X0,X2))|~d(true))),
% 3.11/0.80 inference(resolution,[status(thm)],[f1970,f447])).
% 3.11/0.80 fof(f2858,plain,(
% 3.11/0.80 spl0_129|~spl0_36),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2857,f2854,f453])).
% 3.11/0.80 fof(f2863,plain,(
% 3.11/0.80 spl0_130 <=> bool(prop(false))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2865,plain,(
% 3.11/0.80 ~bool(prop(false))|spl0_130),
% 3.11/0.80 inference(component_clause,[status(thm)],[f2863])).
% 3.11/0.80 fof(f2873,plain,(
% 3.11/0.80 spl0_132 <=> bool(prop(X0))|pd0_2(prop(X0))|bool(X0)),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2876,plain,(
% 3.11/0.80 ![X0]: (bool(prop(X0))|true=err|pd0_2(prop(X0))|bool(X0))),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f363,f2003])).
% 3.11/0.80 fof(f2877,plain,(
% 3.11/0.80 spl0_132|spl0_55),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2876,f2873,f1029])).
% 3.11/0.80 fof(f2878,plain,(
% 3.11/0.80 spl0_133 <=> bool(prop(sk0_5(X0)))|bool(prop(sk0_5(X0)))|pd0_2(prop(sk0_5(X0)))),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f2881,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,err)|bool(prop(sk0_5(X0)))|bool(prop(sk0_5(X0)))|pd0_2(prop(sk0_5(X0)))|~spl0_80)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f2003,f2700])).
% 3.11/0.80 fof(f2882,plain,(
% 3.11/0.80 ~spl0_24|spl0_133|~spl0_80),
% 3.11/0.80 inference(split_clause,[status(thm)],[f2881,f364,f2878,f1991])).
% 3.11/0.80 fof(f3146,plain,(
% 3.11/0.80 true=f7(sk0_6)|~spl0_32|~spl0_52|~spl0_13),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f1615,f283])).
% 3.11/0.80 fof(f3154,plain,(
% 3.11/0.80 $false|~spl0_25|spl0_42),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f525,f368])).
% 3.11/0.80 fof(f3155,plain,(
% 3.11/0.80 ~spl0_25|spl0_42),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f3154])).
% 3.11/0.80 fof(f3163,plain,(
% 3.11/0.80 true=false|~spl0_64|~spl0_30|~spl0_82),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f1270,f2183])).
% 3.11/0.80 fof(f3164,plain,(
% 3.11/0.80 $false|~spl0_64|~spl0_30|~spl0_82),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f3163,f52])).
% 3.11/0.80 fof(f3165,plain,(
% 3.11/0.80 ~spl0_64|~spl0_30|~spl0_82),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f3164])).
% 3.11/0.80 fof(f3172,plain,(
% 3.11/0.80 true=phi(false)|~spl0_64|~spl0_106),
% 3.11/0.80 inference(backward_demodulation,[status(thm)],[f1147,f2642])).
% 3.11/0.80 fof(f3173,plain,(
% 3.11/0.80 spl0_3|~spl0_64|~spl0_106),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3172,f216,f1146,f2641])).
% 3.11/0.80 fof(f3239,plain,(
% 3.11/0.80 err=false|err=true|~spl0_57),
% 3.11/0.80 inference(resolution,[status(thm)],[f1252,f49])).
% 3.11/0.80 fof(f3240,plain,(
% 3.11/0.80 spl0_75|spl0_55|~spl0_57),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3239,f1734,f1029,f1039])).
% 3.11/0.80 fof(f3272,plain,(
% 3.11/0.80 err=false2|~spl0_11),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f156,f1020])).
% 3.11/0.80 fof(f3329,plain,(
% 3.11/0.80 err=false|err=true|~spl0_16),
% 3.11/0.80 inference(resolution,[status(thm)],[f308,f49])).
% 3.11/0.80 fof(f3330,plain,(
% 3.11/0.80 spl0_75|spl0_55|~spl0_16),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3329,f1734,f1029,f307])).
% 3.11/0.80 fof(f3332,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(f7(X0),true)|~spl0_32|~spl0_52|~spl0_13)),
% 3.11/0.80 inference(backward_demodulation,[status(thm)],[f3146,f157])).
% 3.11/0.80 fof(f3392,plain,(
% 3.11/0.80 bool(err)|spl0_64),
% 3.11/0.80 inference(resolution,[status(thm)],[f1148,f85])).
% 3.11/0.80 fof(f3393,plain,(
% 3.11/0.80 spl0_16|spl0_64),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3392,f307,f1146])).
% 3.11/0.80 fof(f3408,plain,(
% 3.11/0.80 ~pd0_2(err)|spl0_70),
% 3.11/0.80 inference(resolution,[status(thm)],[f1510,f188])).
% 3.11/0.80 fof(f3409,plain,(
% 3.11/0.80 $false|spl0_70),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f3408,f247])).
% 3.11/0.80 fof(f3410,plain,(
% 3.11/0.80 spl0_70),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f3409])).
% 3.11/0.80 fof(f3456,plain,(
% 3.11/0.80 spl0_137 <=> pd0_4(false,true)),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f3457,plain,(
% 3.11/0.80 pd0_4(false,true)|~spl0_137),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3456])).
% 3.11/0.80 fof(f3461,plain,(
% 3.11/0.80 pd0_4(false,true)|~bool(true)|~spl0_8),
% 3.11/0.80 inference(resolution,[status(thm)],[f254,f182])).
% 3.11/0.80 fof(f3462,plain,(
% 3.11/0.80 spl0_137|~spl0_0|~spl0_8),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3461,f3456,f205,f253])).
% 3.11/0.80 fof(f3472,plain,(
% 3.11/0.80 spl0_138 <=> prop(false)=false),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f3473,plain,(
% 3.11/0.80 prop(false)=false|~spl0_138),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3472])).
% 3.11/0.80 fof(f3475,plain,(
% 3.11/0.80 spl0_139 <=> prop(false)=true),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f3476,plain,(
% 3.11/0.80 prop(false)=true|~spl0_139),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3475])).
% 3.11/0.80 fof(f3477,plain,(
% 3.11/0.80 ~prop(false)=true|spl0_139),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3475])).
% 3.11/0.80 fof(f3482,plain,(
% 3.11/0.80 true=false|~spl0_139|~spl0_138),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f3476,f3473])).
% 3.11/0.80 fof(f3483,plain,(
% 3.11/0.80 $false|~spl0_139|~spl0_138),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f3482,f52])).
% 3.11/0.80 fof(f3484,plain,(
% 3.11/0.80 ~spl0_139|~spl0_138),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f3483])).
% 3.11/0.80 fof(f3494,plain,(
% 3.11/0.80 ~d(true)|~spl0_137),
% 3.11/0.80 inference(resolution,[status(thm)],[f3457,f196])).
% 3.11/0.80 fof(f3495,plain,(
% 3.11/0.80 ~spl0_36|~spl0_137),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3494,f453,f3456])).
% 3.11/0.80 fof(f3498,plain,(
% 3.11/0.80 ![X0]: (~forallprefers(true,true)|bool(X0)|~spl0_32|~spl0_52|~spl0_13)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f363,f3332])).
% 3.11/0.80 fof(f3499,plain,(
% 3.11/0.80 ~spl0_54|spl0_25|~spl0_32|~spl0_52|~spl0_13),
% 3.11/0.80 inference(split_clause,[status(thm)],[f3498,f892,f367,f421,f880,f282])).
% 3.11/0.80 fof(f3562,plain,(
% 3.11/0.80 ~phi(sk0_7)=not2(sk0_7)|~spl0_19),
% 3.11/0.80 inference(backward_demodulation,[status(thm)],[f323,f165])).
% 3.11/0.80 fof(f3563,plain,(
% 3.11/0.80 spl0_144 <=> pd0_3(true,false)),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f3564,plain,(
% 3.11/0.80 pd0_3(true,false)|~spl0_144),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3563])).
% 3.11/0.80 fof(f3565,plain,(
% 3.11/0.80 ~pd0_3(true,false)|spl0_144),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3563])).
% 3.11/0.80 fof(f3730,plain,(
% 3.11/0.80 ![X0]: (true=lazy_impl(prop(X0),impl(true,X0))|bool(X0))),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f564,f570])).
% 3.11/0.80 fof(f3821,plain,(
% 3.11/0.80 spl0_153 <=> prop(true)=false),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f3822,plain,(
% 3.11/0.80 prop(true)=false|~spl0_153),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3821])).
% 3.11/0.80 fof(f3824,plain,(
% 3.11/0.80 spl0_154 <=> prop(true)=true),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f3825,plain,(
% 3.11/0.80 prop(true)=true|~spl0_154),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3824])).
% 3.11/0.80 fof(f3826,plain,(
% 3.11/0.80 ~prop(true)=true|spl0_154),
% 3.11/0.80 inference(component_clause,[status(thm)],[f3824])).
% 3.11/0.80 fof(f3831,plain,(
% 3.11/0.80 true=false|~spl0_154|~spl0_153),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f3825,f3822])).
% 3.11/0.80 fof(f3832,plain,(
% 3.11/0.80 $false|~spl0_154|~spl0_153),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f3831,f52])).
% 3.11/0.80 fof(f3833,plain,(
% 3.11/0.80 ~spl0_154|~spl0_153),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f3832])).
% 3.11/0.80 fof(f3920,plain,(
% 3.11/0.80 f7(true)=lazy_impl(true,true)|~spl0_154),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f3825,f153])).
% 3.11/0.80 fof(f3921,plain,(
% 3.11/0.80 f7(true)=phi(true)|~spl0_154),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f99,f3920])).
% 3.11/0.80 fof(f3922,plain,(
% 3.11/0.80 f7(true)=true|~spl0_32|~spl0_154),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f422,f3921])).
% 3.11/0.80 fof(f4003,plain,(
% 3.11/0.80 ~not1(sk0_7)=not2(true)|~spl0_23),
% 3.11/0.80 inference(backward_demodulation,[status(thm)],[f340,f165])).
% 3.11/0.80 fof(f4004,plain,(
% 3.11/0.80 ~not1(true)=not2(true)|~spl0_23),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f340,f4003])).
% 3.11/0.80 fof(f4005,plain,(
% 3.11/0.80 ~false=not2(true)|~spl0_23),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f161,f4004])).
% 3.11/0.80 fof(f4027,plain,(
% 3.11/0.80 ~bool(false)|spl0_139),
% 3.11/0.80 inference(resolution,[status(thm)],[f3477,f81])).
% 3.11/0.80 fof(f4028,plain,(
% 3.11/0.80 $false|spl0_139),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f4027,f199])).
% 3.11/0.80 fof(f4029,plain,(
% 3.11/0.80 spl0_139),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f4028])).
% 3.11/0.80 fof(f4033,plain,(
% 3.11/0.80 ~bool(true)|~spl0_139|spl0_130),
% 3.11/0.80 inference(backward_demodulation,[status(thm)],[f3476,f2865])).
% 3.11/0.80 fof(f4034,plain,(
% 3.11/0.80 ~spl0_0|~spl0_139|spl0_130),
% 3.11/0.80 inference(split_clause,[status(thm)],[f4033,f205,f3475,f2863])).
% 3.11/0.80 fof(f4041,plain,(
% 3.11/0.80 ~d(false)|~spl0_144),
% 3.11/0.80 inference(resolution,[status(thm)],[f3564,f191])).
% 3.11/0.80 fof(f4042,plain,(
% 3.11/0.80 $false|~spl0_144),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f4041,f56])).
% 3.11/0.80 fof(f4043,plain,(
% 3.11/0.80 ~spl0_144),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f4042])).
% 3.11/0.80 fof(f4058,plain,(
% 3.11/0.80 spl0_157 <=> f7(false)=phi(true)),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f4059,plain,(
% 3.11/0.80 f7(false)=phi(true)|~spl0_157),
% 3.11/0.80 inference(component_clause,[status(thm)],[f4058])).
% 3.11/0.80 fof(f4063,plain,(
% 3.11/0.80 f7(false)=lazy_impl(true,false)|~spl0_139),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f3476,f153])).
% 3.11/0.80 fof(f4064,plain,(
% 3.11/0.80 f7(false)=phi(false)|~spl0_139),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f99,f4063])).
% 3.11/0.80 fof(f4065,plain,(
% 3.11/0.80 f7(false)=false|~spl0_30|~spl0_139),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f404,f4064])).
% 3.11/0.80 fof(f4072,plain,(
% 3.11/0.80 ~true=true|bool(false)|~spl0_139),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f3476,f80])).
% 3.11/0.80 fof(f4073,plain,(
% 3.11/0.80 ~spl0_6|spl0_2|~spl0_139),
% 3.11/0.80 inference(split_clause,[status(thm)],[f4072,f233,f213,f3475])).
% 3.11/0.80 fof(f4074,plain,(
% 3.11/0.80 false=phi(true)|~spl0_30|~spl0_139|~spl0_157),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f4065,f4059])).
% 3.11/0.80 fof(f4075,plain,(
% 3.11/0.80 false=true|~spl0_32|~spl0_30|~spl0_139|~spl0_157),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f422,f4074])).
% 3.11/0.80 fof(f4076,plain,(
% 3.11/0.80 $false|~spl0_32|~spl0_30|~spl0_139|~spl0_157),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f4075,f52])).
% 3.11/0.80 fof(f4077,plain,(
% 3.11/0.80 ~spl0_32|~spl0_30|~spl0_139|~spl0_157),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f4076])).
% 3.11/0.80 fof(f4080,plain,(
% 3.11/0.80 d(false)|~d(true)|spl0_144),
% 3.11/0.80 inference(resolution,[status(thm)],[f3565,f193])).
% 3.11/0.80 fof(f4081,plain,(
% 3.11/0.80 spl0_91|~spl0_36|spl0_144),
% 3.11/0.80 inference(split_clause,[status(thm)],[f4080,f2068,f453,f3563])).
% 3.11/0.80 fof(f4086,plain,(
% 3.11/0.80 ~forallprefers(false,true)|~spl0_32|~spl0_52|~spl0_13|~spl0_30|~spl0_139),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f4065,f3332])).
% 3.11/0.80 fof(f4087,plain,(
% 3.11/0.80 $false|~spl0_32|~spl0_52|~spl0_13|~spl0_30|~spl0_139),
% 3.11/0.80 inference(forward_subsumption_resolution,[status(thm)],[f4086,f201])).
% 3.11/0.80 fof(f4088,plain,(
% 3.11/0.80 ~spl0_32|~spl0_52|~spl0_13|~spl0_30|~spl0_139),
% 3.11/0.80 inference(contradiction_clause,[status(thm)],[f4087])).
% 3.11/0.80 fof(f4093,plain,(
% 3.11/0.80 spl0_79|~spl0_64),
% 3.11/0.80 inference(split_clause,[status(thm)],[f1852,f1973,f1146])).
% 3.11/0.80 fof(f4185,plain,(
% 3.11/0.80 false2=phi(false)|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f4065,f1282])).
% 3.11/0.80 fof(f4186,plain,(
% 3.11/0.80 false2=false|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.80 inference(forward_demodulation,[status(thm)],[f404,f4185])).
% 3.11/0.80 fof(f4228,plain,(
% 3.11/0.80 ![X0]: (not2(X0)=impl(X0,false)|~spl0_30|~spl0_139|~spl0_65)),
% 3.11/0.80 inference(backward_demodulation,[status(thm)],[f4186,f162])).
% 3.11/0.80 fof(f4329,plain,(
% 3.11/0.80 ![X0]: (not2(X0)=phi(X0)|bool(X0)|~spl0_30|~spl0_139|~spl0_65)),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f88,f4228])).
% 3.11/0.80 fof(f4330,plain,(
% 3.11/0.80 ~bool(false)|not2(false)=true|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f4228,f92])).
% 3.11/0.80 fof(f4331,plain,(
% 3.11/0.80 ~spl0_2|spl0_26|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.80 inference(split_clause,[status(thm)],[f4330,f213,f372,f403,f3475,f1151])).
% 3.11/0.80 fof(f4332,plain,(
% 3.11/0.80 spl0_159 <=> not2(true)=false),
% 3.11/0.80 introduced(split_symbol_definition)).
% 3.11/0.80 fof(f4333,plain,(
% 3.11/0.80 not2(true)=false|~spl0_159),
% 3.11/0.80 inference(component_clause,[status(thm)],[f4332])).
% 3.11/0.80 fof(f4335,plain,(
% 3.11/0.80 ~bool(false)|not2(true)=false|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.80 inference(paramodulation,[status(thm)],[f4228,f94])).
% 3.11/0.80 fof(f4336,plain,(
% 3.11/0.80 ~spl0_2|spl0_159|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.80 inference(split_clause,[status(thm)],[f4335,f213,f4332,f403,f3475,f1151])).
% 3.11/0.81 fof(f4490,plain,(
% 3.11/0.81 ~phi(sk0_7)=phi(sk0_7)|bool(sk0_7)|~spl0_19|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.81 inference(paramodulation,[status(thm)],[f4329,f3562])).
% 3.11/0.81 fof(f4491,plain,(
% 3.11/0.81 ~spl0_21|spl0_20|~spl0_19|~spl0_30|~spl0_139|~spl0_65),
% 3.11/0.81 inference(split_clause,[status(thm)],[f4490,f331,f325,f322,f403,f3475,f1151])).
% 3.11/0.81 fof(f4494,plain,(
% 3.11/0.81 ~false=false|~spl0_159|~spl0_23),
% 3.11/0.81 inference(forward_demodulation,[status(thm)],[f4333,f4005])).
% 3.11/0.81 fof(f4495,plain,(
% 3.11/0.81 $false|~spl0_159|~spl0_23),
% 3.11/0.81 inference(trivial_equality_resolution,[status(esa)],[f4494])).
% 3.11/0.81 fof(f4496,plain,(
% 3.11/0.81 ~spl0_159|~spl0_23),
% 3.11/0.81 inference(contradiction_clause,[status(thm)],[f4495])).
% 3.11/0.81 fof(f4521,plain,(
% 3.11/0.81 false2=f7(true)|~spl0_66|~spl0_13),
% 3.11/0.81 inference(backward_demodulation,[status(thm)],[f1155,f283])).
% 3.11/0.81 fof(f4522,plain,(
% 3.11/0.81 false2=true|~spl0_32|~spl0_154|~spl0_66|~spl0_13),
% 3.11/0.81 inference(forward_demodulation,[status(thm)],[f3922,f4521])).
% 3.11/0.81 fof(f4523,plain,(
% 3.11/0.81 $false|spl0_52|~spl0_32|~spl0_154|~spl0_66|~spl0_13),
% 3.11/0.81 inference(forward_subsumption_resolution,[status(thm)],[f4522,f882])).
% 3.11/0.81 fof(f4524,plain,(
% 3.11/0.81 spl0_52|~spl0_32|~spl0_154|~spl0_66|~spl0_13),
% 3.11/0.81 inference(contradiction_clause,[status(thm)],[f4523])).
% 3.11/0.81 fof(f4598,plain,(
% 3.11/0.81 err=phi(f7(sk0_6))|~spl0_11),
% 3.11/0.81 inference(forward_demodulation,[status(thm)],[f3272,f156])).
% 3.11/0.81 fof(f4599,plain,(
% 3.11/0.81 err=phi(f7(true))|~spl0_66|~spl0_11),
% 3.11/0.81 inference(forward_demodulation,[status(thm)],[f1155,f4598])).
% 3.11/0.81 fof(f4600,plain,(
% 3.11/0.81 err=phi(true)|~spl0_32|~spl0_154|~spl0_66|~spl0_11),
% 3.11/0.81 inference(forward_demodulation,[status(thm)],[f3922,f4599])).
% 3.11/0.81 fof(f4601,plain,(
% 3.11/0.81 err=true|~spl0_32|~spl0_154|~spl0_66|~spl0_11),
% 3.11/0.81 inference(forward_demodulation,[status(thm)],[f422,f4600])).
% 3.11/0.81 fof(f4602,plain,(
% 3.11/0.81 $false|~spl0_32|~spl0_154|~spl0_66|~spl0_11),
% 3.11/0.81 inference(forward_subsumption_resolution,[status(thm)],[f4601,f53])).
% 3.11/0.81 fof(f4603,plain,(
% 3.11/0.81 ~spl0_32|~spl0_154|~spl0_66|~spl0_11),
% 3.11/0.81 inference(contradiction_clause,[status(thm)],[f4602])).
% 3.11/0.81 fof(f4768,plain,(
% 3.11/0.81 spl0_162 <=> true=lazy_impl(false,impl(true,err))),
% 3.11/0.81 introduced(split_symbol_definition)).
% 3.11/0.81 fof(f4771,plain,(
% 3.11/0.81 true=lazy_impl(false,impl(true,err))|bool(err)|~spl0_64),
% 3.11/0.81 inference(paramodulation,[status(thm)],[f1147,f3730])).
% 3.11/0.81 fof(f4772,plain,(
% 3.11/0.81 spl0_162|spl0_16|~spl0_64),
% 3.11/0.81 inference(split_clause,[status(thm)],[f4771,f4768,f307,f1146])).
% 3.11/0.81 fof(f4774,plain,(
% 3.11/0.81 spl0_163 <=> true=lazy_impl(prop(err),not2(true))),
% 3.11/0.81 introduced(split_symbol_definition)).
% 3.11/0.81 fof(f4777,plain,(
% 3.11/0.81 true=lazy_impl(prop(err),not2(true))|bool(err)|~spl0_11),
% 3.11/0.81 inference(paramodulation,[status(thm)],[f292,f3730])).
% 3.11/0.81 fof(f4778,plain,(
% 3.11/0.81 spl0_163|spl0_16|~spl0_11),
% 3.11/0.81 inference(split_clause,[status(thm)],[f4777,f4774,f307,f272])).
% 3.11/0.81 fof(f4934,plain,(
% 3.11/0.81 ~bool(true)|spl0_154),
% 3.11/0.81 inference(resolution,[status(thm)],[f3826,f81])).
% 3.11/0.81 fof(f4935,plain,(
% 3.11/0.81 ~spl0_0|spl0_154),
% 3.11/0.81 inference(split_clause,[status(thm)],[f4934,f205,f3824])).
% 3.11/0.81 fof(f4938,plain,(
% 3.11/0.81 $false),
% 3.11/0.81 inference(sat_refutation,[status(thm)],[f232,f237,f239,f264,f279,f286,f329,f335,f343,f371,f386,f393,f434,f469,f476,f519,f603,f614,f827,f884,f896,f1006,f1045,f1093,f1099,f1105,f1110,f1115,f1158,f1246,f1285,f1413,f1463,f1506,f1533,f1576,f1579,f1586,f1722,f1733,f1962,f1969,f1995,f2027,f2038,f2050,f2055,f2094,f2104,f2141,f2185,f2234,f2274,f2535,f2560,f2629,f2658,f2664,f2669,f2674,f2705,f2713,f2721,f2734,f2739,f2839,f2844,f2853,f2858,f2877,f2882,f3155,f3165,f3173,f3240,f3330,f3393,f3410,f3462,f3484,f3495,f3499,f3833,f4029,f4034,f4043,f4073,f4077,f4081,f4088,f4093,f4331,f4336,f4491,f4496,f4524,f4603,f4772,f4778,f4935])).
% 3.11/0.81 % SZS output end CNFRefutation for theBenchmark.p
% 3.11/0.82 % Elapsed time: 0.454287 seconds
% 3.11/0.82 % CPU time: 3.415107 seconds
% 3.11/0.82 % Total memory used: 114.922 MB
% 3.11/0.82 % Net memory used: 111.996 MB
%------------------------------------------------------------------------------