TSTP Solution File: SEU470^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU470^1 : TPTP v6.1.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n106.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:32:15 EDT 2014
% Result : Timeout 300.04s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU470^1 : TPTP v6.1.0. Released v3.6.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:18:06 CDT 2014
% % CPUTime : 300.04
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/SET009^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0xfae0e0>, <kernel.DependentProduct object at 0xfae248>) of role type named subrel_type
% Using role type
% Declaring subrel:((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) subrel) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((S X) Y))))) of role definition named subrel
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop))) subrel) (fun (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((S X) Y)))))
% Defined: subrel:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((S X) Y))))
% FOF formula (<kernel.Constant object at 0xfaed88>, <kernel.DependentProduct object at 0xfae248>) of role type named inv_type
% Using role type
% Declaring inv:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) inv) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X))) of role definition named inverse
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) inv) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X)))
% Defined: inv:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X))
% FOF formula (<kernel.Constant object at 0xfaed88>, <kernel.DependentProduct object at 0xfae3f8>) of role type named idem_type
% Using role type
% Declaring idem:(((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)
% FOF formula (((eq (((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)) idem) (fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), (((eq (fofType->(fofType->Prop))) (F (F R))) (F R))))) of role definition named idempotent
% A new definition: (((eq (((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)) idem) (fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), (((eq (fofType->(fofType->Prop))) (F (F R))) (F R)))))
% Defined: idem:=(fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), (((eq (fofType->(fofType->Prop))) (F (F R))) (F R))))
% FOF formula (<kernel.Constant object at 0xfaed40>, <kernel.DependentProduct object at 0xfaeab8>) of role type named infl_type
% Using role type
% Declaring infl:(((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)
% FOF formula (((eq (((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)) infl) (fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), ((subrel R) (F R))))) of role definition named inflationary
% A new definition: (((eq (((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)) infl) (fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), ((subrel R) (F R)))))
% Defined: infl:=(fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), ((subrel R) (F R))))
% FOF formula (<kernel.Constant object at 0xfaed88>, <kernel.DependentProduct object at 0xfae368>) of role type named mono_type
% Using role type
% Declaring mono:(((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)
% FOF formula (((eq (((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)) mono) (fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop))), (((subrel R) S)->((subrel (F R)) (F S)))))) of role definition named monotonic
% A new definition: (((eq (((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop)) mono) (fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop))), (((subrel R) S)->((subrel (F R)) (F S))))))
% Defined: mono:=(fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop))), (((subrel R) S)->((subrel (F R)) (F S)))))
% FOF formula (<kernel.Constant object at 0xfaed88>, <kernel.DependentProduct object at 0xfaeea8>) of role type named refl_type
% Using role type
% Declaring refl:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) refl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X)))) of role definition named reflexive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) refl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X))))
% Defined: refl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X)))
% FOF formula (<kernel.Constant object at 0xfae518>, <kernel.DependentProduct object at 0x1206050>) of role type named irrefl_type
% Using role type
% Declaring irrefl:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) irrefl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False)))) of role definition named irreflexive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) irrefl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False))))
% Defined: irrefl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False)))
% FOF formula (<kernel.Constant object at 0xfaed88>, <kernel.DependentProduct object at 0x1206878>) of role type named rc_type
% Using role type
% Declaring rc:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) rc) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or (((eq fofType) X) Y)) ((R X) Y)))) of role definition named reflexive_closure
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) rc) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or (((eq fofType) X) Y)) ((R X) Y))))
% Defined: rc:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or (((eq fofType) X) Y)) ((R X) Y)))
% FOF formula (<kernel.Constant object at 0x1206878>, <kernel.DependentProduct object at 0x12069e0>) of role type named symm_type
% Using role type
% Declaring symm:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) symm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X))))) of role definition named symmetric
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) symm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X)))))
% Defined: symm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X))))
% FOF formula (<kernel.Constant object at 0x1206cf8>, <kernel.DependentProduct object at 0x1206998>) of role type named antisymm_type
% Using role type
% Declaring antisymm:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) antisymm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((and ((R X) Y)) ((R Y) X))->(((eq fofType) X) Y))))) of role definition named antisymmetric
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) antisymm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((and ((R X) Y)) ((R Y) X))->(((eq fofType) X) Y)))))
% Defined: antisymm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((and ((R X) Y)) ((R Y) X))->(((eq fofType) X) Y))))
% FOF formula (<kernel.Constant object at 0x1206878>, <kernel.DependentProduct object at 0x1206488>) of role type named asymm_type
% Using role type
% Declaring asymm:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) asymm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->(((R Y) X)->False))))) of role definition named asymmetric
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) asymm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->(((R Y) X)->False)))))
% Defined: asymm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->(((R Y) X)->False))))
% FOF formula (<kernel.Constant object at 0x1206cf8>, <kernel.DependentProduct object at 0xfb09e0>) of role type named sc_type
% Using role type
% Declaring sc:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) sc) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or ((R Y) X)) ((R X) Y)))) of role definition named symmetric_closure
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) sc) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or ((R Y) X)) ((R X) Y))))
% Defined: sc:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or ((R Y) X)) ((R X) Y)))
% FOF formula (<kernel.Constant object at 0x1206290>, <kernel.DependentProduct object at 0xfb04d0>) of role type named trans_type
% Using role type
% Declaring trans:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) trans) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z))))) of role definition named transitive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) trans) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))))
% Defined: trans:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z))))
% FOF formula (<kernel.Constant object at 0xfb09e0>, <kernel.DependentProduct object at 0xfb0c68>) of role type named tc_type
% Using role type
% Declaring tc:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) tc) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> (forall (S:(fofType->(fofType->Prop))), (((and (trans S)) ((subrel R) S))->((S X) Y))))) of role definition named transitive_closure
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) tc) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> (forall (S:(fofType->(fofType->Prop))), (((and (trans S)) ((subrel R) S))->((S X) Y)))))
% Defined: tc:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> (forall (S:(fofType->(fofType->Prop))), (((and (trans S)) ((subrel R) S))->((S X) Y))))
% FOF formula (<kernel.Constant object at 0xdb1680>, <kernel.DependentProduct object at 0xdb1758>) of role type named trc_type
% Using role type
% Declaring trc:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) trc) (fun (R:(fofType->(fofType->Prop)))=> (rc (tc R)))) of role definition named transitive_reflexive_closure
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) trc) (fun (R:(fofType->(fofType->Prop)))=> (rc (tc R))))
% Defined: trc:=(fun (R:(fofType->(fofType->Prop)))=> (rc (tc R)))
% FOF formula (<kernel.Constant object at 0xdb17e8>, <kernel.DependentProduct object at 0xdb1a28>) of role type named trsc_type
% Using role type
% Declaring trsc:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) trsc) (fun (R:(fofType->(fofType->Prop)))=> (sc (rc (tc R))))) of role definition named transitive_reflexive_symmetric_closure
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) trsc) (fun (R:(fofType->(fofType->Prop)))=> (sc (rc (tc R)))))
% Defined: trsc:=(fun (R:(fofType->(fofType->Prop)))=> (sc (rc (tc R))))
% FOF formula (<kernel.Constant object at 0xdb17e8>, <kernel.DependentProduct object at 0xdb1878>) of role type named po_type
% Using role type
% Declaring po:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) po) (fun (R:(fofType->(fofType->Prop)))=> ((and ((and (refl R)) (antisymm R))) (trans R)))) of role definition named partial_order
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) po) (fun (R:(fofType->(fofType->Prop)))=> ((and ((and (refl R)) (antisymm R))) (trans R))))
% Defined: po:=(fun (R:(fofType->(fofType->Prop)))=> ((and ((and (refl R)) (antisymm R))) (trans R)))
% FOF formula (<kernel.Constant object at 0xdb1830>, <kernel.DependentProduct object at 0xdb1710>) of role type named so_type
% Using role type
% Declaring so:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) so) (fun (R:(fofType->(fofType->Prop)))=> ((and (asymm R)) (trans R)))) of role definition named strict_order
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) so) (fun (R:(fofType->(fofType->Prop)))=> ((and (asymm R)) (trans R))))
% Defined: so:=(fun (R:(fofType->(fofType->Prop)))=> ((and (asymm R)) (trans R)))
% FOF formula (<kernel.Constant object at 0xdb1878>, <kernel.DependentProduct object at 0xdb16c8>) of role type named total_type
% Using role type
% Declaring total:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) total) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((or ((or (((eq fofType) X) Y)) ((R X) Y))) ((R Y) X))))) of role definition named total
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) total) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((or ((or (((eq fofType) X) Y)) ((R X) Y))) ((R Y) X)))))
% Defined: total:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((or ((or (((eq fofType) X) Y)) ((R X) Y))) ((R Y) X))))
% FOF formula (<kernel.Constant object at 0xdb16c8>, <kernel.DependentProduct object at 0xdb1b90>) of role type named term_type
% Using role type
% Declaring term:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) term) (fun (R:(fofType->(fofType->Prop)))=> (forall (A:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (A X)))->((ex fofType) (fun (X:fofType)=> ((and (A X)) (forall (Y:fofType), ((A Y)->(((R X) Y)->False)))))))))) of role definition named terminating
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) term) (fun (R:(fofType->(fofType->Prop)))=> (forall (A:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (A X)))->((ex fofType) (fun (X:fofType)=> ((and (A X)) (forall (Y:fofType), ((A Y)->(((R X) Y)->False))))))))))
% Defined: term:=(fun (R:(fofType->(fofType->Prop)))=> (forall (A:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (A X)))->((ex fofType) (fun (X:fofType)=> ((and (A X)) (forall (Y:fofType), ((A Y)->(((R X) Y)->False)))))))))
% FOF formula (<kernel.Constant object at 0xdb1c20>, <kernel.DependentProduct object at 0xdb1fc8>) of role type named ind_type
% Using role type
% Declaring ind:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) ind) (fun (R:(fofType->(fofType->Prop)))=> (forall (P:(fofType->Prop)), ((forall (X:fofType), ((forall (Y:fofType), ((((tc R) X) Y)->(P Y)))->(P X)))->(forall (X:fofType), (P X)))))) of role definition named satisfying_the_induction_principle
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) ind) (fun (R:(fofType->(fofType->Prop)))=> (forall (P:(fofType->Prop)), ((forall (X:fofType), ((forall (Y:fofType), ((((tc R) X) Y)->(P Y)))->(P X)))->(forall (X:fofType), (P X))))))
% Defined: ind:=(fun (R:(fofType->(fofType->Prop)))=> (forall (P:(fofType->Prop)), ((forall (X:fofType), ((forall (Y:fofType), ((((tc R) X) Y)->(P Y)))->(P X)))->(forall (X:fofType), (P X)))))
% FOF formula (<kernel.Constant object at 0xdb1518>, <kernel.DependentProduct object at 0xdb1c20>) of role type named innf_type
% Using role type
% Declaring innf:((fofType->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) innf) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> (((ex fofType) (fun (Y:fofType)=> ((R X) Y)))->False))) of role definition named in_normal_form
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->Prop))) innf) (fun (R:(fofType->(fofType->Prop))) (X:fofType)=> (((ex fofType) (fun (Y:fofType)=> ((R X) Y)))->False)))
% Defined: innf:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> (((ex fofType) (fun (Y:fofType)=> ((R X) Y)))->False))
% FOF formula (<kernel.Constant object at 0xdb1fc8>, <kernel.DependentProduct object at 0xdb17e8>) of role type named nfof_type
% Using role type
% Declaring nfof:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) nfof) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((and (((trc R) Y) X)) ((innf R) X)))) of role definition named normal_form_of
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) nfof) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((and (((trc R) Y) X)) ((innf R) X))))
% Defined: nfof:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((and (((trc R) Y) X)) ((innf R) X)))
% FOF formula (<kernel.Constant object at 0xdb1518>, <kernel.DependentProduct object at 0xdb1d40>) of role type named norm_type
% Using role type
% Declaring norm:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) norm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((nfof R) Y) X)))))) of role definition named normalizing
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) norm) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((nfof R) Y) X))))))
% Defined: norm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((nfof R) Y) X)))))
% FOF formula (<kernel.Constant object at 0xdb1518>, <kernel.DependentProduct object at 0xdb1a70>) of role type named join_type
% Using role type
% Declaring join:((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) join) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((ex fofType) (fun (Z:fofType)=> ((and (((trc R) X) Z)) (((trc R) Y) Z)))))) of role definition named joinable
% A new definition: (((eq ((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))) join) (fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((ex fofType) (fun (Z:fofType)=> ((and (((trc R) X) Z)) (((trc R) Y) Z))))))
% Defined: join:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((ex fofType) (fun (Z:fofType)=> ((and (((trc R) X) Z)) (((trc R) Y) Z)))))
% FOF formula (<kernel.Constant object at 0xdb15a8>, <kernel.DependentProduct object at 0xf9d290>) of role type named lconfl_type
% Using role type
% Declaring lconfl:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) lconfl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) ((R X) Y))->(((join R) Z) Y))))) of role definition named locally_confluent
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) lconfl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) ((R X) Y))->(((join R) Z) Y)))))
% Defined: lconfl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) ((R X) Y))->(((join R) Z) Y))))
% FOF formula (<kernel.Constant object at 0xdb18c0>, <kernel.DependentProduct object at 0xf9d3b0>) of role type named sconfl_type
% Using role type
% Declaring sconfl:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) sconfl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) (((trc R) X) Y))->(((join R) Z) Y))))) of role definition named semi_confluent
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) sconfl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) (((trc R) X) Y))->(((join R) Z) Y)))))
% Defined: sconfl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) (((trc R) X) Y))->(((join R) Z) Y))))
% FOF formula (<kernel.Constant object at 0xf9d3b0>, <kernel.DependentProduct object at 0xf9d488>) of role type named confl_type
% Using role type
% Declaring confl:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) confl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and (((trc R) X) Z)) (((trc R) X) Y))->(((join R) Z) Y))))) of role definition named confluent
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) confl) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and (((trc R) X) Z)) (((trc R) X) Y))->(((join R) Z) Y)))))
% Defined: confl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and (((trc R) X) Z)) (((trc R) X) Y))->(((join R) Z) Y))))
% FOF formula (<kernel.Constant object at 0xf9d5a8>, <kernel.DependentProduct object at 0xf9d2d8>) of role type named cr_type
% Using role type
% Declaring cr:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) cr) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((((trsc R) X) Y)->(((join R) X) Y))))) of role definition named church_rosser
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) cr) (fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((((trsc R) X) Y)->(((join R) X) Y)))))
% Defined: cr:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((((trsc R) X) Y)->(((join R) X) Y))))
% FOF formula (forall (R:(fofType->(fofType->Prop))), ((and ((and (trans (trsc R))) (refl (trsc R)))) (symm (trsc R)))) of role conjecture named transitive_reflexive_symmetric_closure_is_transitive_reflexive_symmetric
% Conjecture to prove = (forall (R:(fofType->(fofType->Prop))), ((and ((and (trans (trsc R))) (refl (trsc R)))) (symm (trsc R)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (R:(fofType->(fofType->Prop))), ((and ((and (trans (trsc R))) (refl (trsc R)))) (symm (trsc R))))']
% Parameter fofType:Type.
% Definition subrel:=(fun (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((S X) Y)))):((fofType->(fofType->Prop))->((fofType->(fofType->Prop))->Prop)).
% Definition inv:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((R Y) X)):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition idem:=(fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), (((eq (fofType->(fofType->Prop))) (F (F R))) (F R)))):(((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop).
% Definition infl:=(fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))), ((subrel R) (F R)))):(((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop).
% Definition mono:=(fun (F:((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))=> (forall (R:(fofType->(fofType->Prop))) (S:(fofType->(fofType->Prop))), (((subrel R) S)->((subrel (F R)) (F S))))):(((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))->Prop).
% Definition refl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((R X) X))):((fofType->(fofType->Prop))->Prop).
% Definition irrefl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), (((R X) X)->False))):((fofType->(fofType->Prop))->Prop).
% Definition rc:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or (((eq fofType) X) Y)) ((R X) Y))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition symm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->((R Y) X)))):((fofType->(fofType->Prop))->Prop).
% Definition antisymm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((and ((R X) Y)) ((R Y) X))->(((eq fofType) X) Y)))):((fofType->(fofType->Prop))->Prop).
% Definition asymm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), (((R X) Y)->(((R Y) X)->False)))):((fofType->(fofType->Prop))->Prop).
% Definition sc:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((or ((R Y) X)) ((R X) Y))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition trans:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Y)) ((R Y) Z))->((R X) Z)))):((fofType->(fofType->Prop))->Prop).
% Definition tc:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> (forall (S:(fofType->(fofType->Prop))), (((and (trans S)) ((subrel R) S))->((S X) Y)))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition trc:=(fun (R:(fofType->(fofType->Prop)))=> (rc (tc R))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition trsc:=(fun (R:(fofType->(fofType->Prop)))=> (sc (rc (tc R)))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition po:=(fun (R:(fofType->(fofType->Prop)))=> ((and ((and (refl R)) (antisymm R))) (trans R))):((fofType->(fofType->Prop))->Prop).
% Definition so:=(fun (R:(fofType->(fofType->Prop)))=> ((and (asymm R)) (trans R))):((fofType->(fofType->Prop))->Prop).
% Definition total:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((or ((or (((eq fofType) X) Y)) ((R X) Y))) ((R Y) X)))):((fofType->(fofType->Prop))->Prop).
% Definition term:=(fun (R:(fofType->(fofType->Prop)))=> (forall (A:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (A X)))->((ex fofType) (fun (X:fofType)=> ((and (A X)) (forall (Y:fofType), ((A Y)->(((R X) Y)->False))))))))):((fofType->(fofType->Prop))->Prop).
% Definition ind:=(fun (R:(fofType->(fofType->Prop)))=> (forall (P:(fofType->Prop)), ((forall (X:fofType), ((forall (Y:fofType), ((((tc R) X) Y)->(P Y)))->(P X)))->(forall (X:fofType), (P X))))):((fofType->(fofType->Prop))->Prop).
% Definition innf:=(fun (R:(fofType->(fofType->Prop))) (X:fofType)=> (((ex fofType) (fun (Y:fofType)=> ((R X) Y)))->False)):((fofType->(fofType->Prop))->(fofType->Prop)).
% Definition nfof:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((and (((trc R) Y) X)) ((innf R) X))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition norm:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType), ((ex fofType) (fun (Y:fofType)=> (((nfof R) Y) X))))):((fofType->(fofType->Prop))->Prop).
% Definition join:=(fun (R:(fofType->(fofType->Prop))) (X:fofType) (Y:fofType)=> ((ex fofType) (fun (Z:fofType)=> ((and (((trc R) X) Z)) (((trc R) Y) Z))))):((fofType->(fofType->Prop))->(fofType->(fofType->Prop))).
% Definition lconfl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) ((R X) Y))->(((join R) Z) Y)))):((fofType->(fofType->Prop))->Prop).
% Definition sconfl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and ((R X) Z)) (((trc R) X) Y))->(((join R) Z) Y)))):((fofType->(fofType->Prop))->Prop).
% Definition confl:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType) (Z:fofType), (((and (((trc R) X) Z)) (((trc R) X) Y))->(((join R) Z) Y)))):((fofType->(fofType->Prop))->Prop).
% Definition cr:=(fun (R:(fofType->(fofType->Prop)))=> (forall (X:fofType) (Y:fofType), ((((trsc R) X) Y)->(((join R) X) Y)))):((fofType->(fofType->Prop))->Prop).
% Trying to prove (forall (R:(fofType->(fofType->Prop))), ((and ((and (trans (trsc R))) (refl (trsc R)))) (symm (trsc R))))
% Found or_comm_i000:=(or_comm_i00 x):((or (((rc (tc R)) X) Y)) (((rc (tc R)) Y) X))
% Found (or_comm_i00 x) as proof of ((or (((rc (tc R)) X) Y)) (((rc (tc R)) Y) X))
% Found ((or_comm_i0 (((rc (tc R)) X) Y)) x) as proof of ((or (((rc (tc R)) X) Y)) (((rc (tc R)) Y) X))
% Found (((or_comm_i (((rc (tc R)) Y) X)) (((rc (tc R)) X) Y)) x) as proof of ((or (((rc (tc R)) X) Y)) (((rc (tc R)) Y) X))
% Found (((or_comm_i (((rc (tc R)) Y) X)) (((rc (tc R)) X) Y)) x) as proof of ((or (((rc (tc R)) X) Y)) (((rc (tc R)) Y) X))
% Found (fun (x:(((trsc R) X) Y))=> (((or_comm_i (((rc (tc R)) Y) X)) (((rc (tc R)) X) Y)) x)) as proof of (((trsc R) Y) X)
% Found (fun (Y:fofType) (x:(((trsc R) X) Y))=> (((or_comm_i (((rc (tc R)) Y) X)) (((rc (tc R)) X) Y)) x)) as proof of ((((trsc R) X) Y)->(((trsc R) Y) X))
% Found (fun (X:fofType) (Y:fofType) (x:(((trsc R) X) Y))=> (((or_comm_i (((rc (tc R)) Y) X)) (((rc (tc R)) X) Y)) x)) as proof of (forall (Y:fofType), ((((trsc R) X) Y)->(((trsc R) Y) X)))
% Found (fun (X:fofType) (Y:fofType) (x:(((trsc R) X) Y))=> (((or_comm_i (((rc (tc R)) Y) X)) (((rc (tc R)) X) Y)) x)) as proof of (symm (trsc R))
% Found x300:=(x30 x0):(((trsc R) X) Z)
% Found (x30 x0) as proof of (((trsc R) X) Z)
% Found ((x3 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x300:=(x30 x1):(((trsc R) X) Z)
% Found (x30 x1) as proof of (((trsc R) X) Z)
% Found ((x3 (fun (x5:fofType)=> (((trsc R) x5) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> (((trsc R) x5) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> (((trsc R) x5) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found or_comm_i000:=(or_comm_i00 x):((or (((trc R) X) Y)) (((trc R) Y) X))
% Found (or_comm_i00 x) as proof of ((or (((trc R) X) Y)) (((trc R) Y) X))
% Found ((or_comm_i0 (((trc R) X) Y)) x) as proof of ((or (((trc R) X) Y)) (((trc R) Y) X))
% Found (((or_comm_i (((trc R) Y) X)) (((trc R) X) Y)) x) as proof of ((or (((trc R) X) Y)) (((trc R) Y) X))
% Found (((or_comm_i (((trc R) Y) X)) (((trc R) X) Y)) x) as proof of ((or (((trc R) X) Y)) (((trc R) Y) X))
% Found (fun (x:(((sc (trc R)) X) Y))=> (((or_comm_i (((trc R) Y) X)) (((trc R) X) Y)) x)) as proof of (((fun (x4:fofType) (x30:fofType)=> (((sc (trc R)) x30) x4)) X) Y)
% Found (fun (Y:fofType) (x:(((sc (trc R)) X) Y))=> (((or_comm_i (((trc R) Y) X)) (((trc R) X) Y)) x)) as proof of ((((sc (trc R)) X) Y)->(((fun (x4:fofType) (x30:fofType)=> (((sc (trc R)) x30) x4)) X) Y))
% Found (fun (X:fofType) (Y:fofType) (x:(((sc (trc R)) X) Y))=> (((or_comm_i (((trc R) Y) X)) (((trc R) X) Y)) x)) as proof of (forall (Y:fofType), ((((sc (trc R)) X) Y)->(((fun (x4:fofType) (x30:fofType)=> (((sc (trc R)) x30) x4)) X) Y)))
% Found (fun (X:fofType) (Y:fofType) (x:(((sc (trc R)) X) Y))=> (((or_comm_i (((trc R) Y) X)) (((trc R) X) Y)) x)) as proof of ((subrel (sc (trc R))) (fun (x4:fofType) (x30:fofType)=> (((sc (trc R)) x30) x4)))
% Found x400:=(x40 x1):(((trsc R) X) Z)
% Found (x40 x1) as proof of (((trsc R) X) Z)
% Found ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found x400:=(x40 x1):(((trsc R) X) Z)
% Found (x40 x1) as proof of (((trsc R) X) Z)
% Found ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found x400:=(x40 x0):(((trsc R) X) Z)
% Found (x40 x0) as proof of (((trsc R) X) Z)
% Found ((x4 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x400:=(x40 x0):(((trsc R) X) Z)
% Found (x40 x0) as proof of (((trsc R) X) Z)
% Found ((x4 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x400:=(x40 x0):(((trsc R) X) Z)
% Found (x40 x0) as proof of (((trsc R) X) Z)
% Found ((x4 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x400:=(x40 x1):(((trsc R) X) Z)
% Found (x40 x1) as proof of (((trsc R) X) Z)
% Found ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found x400:=(x40 x1):(((trsc R) X) Z)
% Found (x40 x1) as proof of (((trsc R) X) Z)
% Found ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) X))=> ((x4 (fun (x6:fofType)=> (((trsc R) x6) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found x400:=(x40 x0):(((trsc R) X) Z)
% Found (x40 x0) as proof of (((trsc R) X) Z)
% Found ((x4 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x4:(((eq fofType) Y) Z))=> ((x4 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x300:=(x30 x0):(((sc (trc R)) X) Z)
% Found (x30 x0) as proof of (((sc (trc R)) X) Z)
% Found ((x3 ((sc (trc R)) X)) x0) as proof of (((sc (trc R)) X) Z)
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 ((sc (trc R)) X)) x0)) as proof of (((sc (trc R)) X) Z)
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 ((sc (trc R)) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((sc (trc R)) X) Z))
% Found x300:=(x30 x1):(((sc (trc R)) X) Z)
% Found (x30 x1) as proof of (((sc (trc R)) X) Z)
% Found ((x3 (fun (x5:fofType)=> (((sc (trc R)) x5) Z))) x1) as proof of (((sc (trc R)) X) Z)
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> (((sc (trc R)) x5) Z))) x1)) as proof of (((sc (trc R)) X) Z)
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> (((sc (trc R)) x5) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((sc (trc R)) X) Z))
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) X)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) X)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) X)
% Found (or_introl00 ((eq_ref fofType) X)) as proof of ((or (((eq fofType) X) X)) (((tc R) X) X))
% Found ((or_introl0 (((tc R) X) X)) ((eq_ref fofType) X)) as proof of ((or (((eq fofType) X) X)) (((tc R) X) X))
% Found (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X)) as proof of ((or (((eq fofType) X) X)) (((tc R) X) X))
% Found (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X)) as proof of ((or (((eq fofType) X) X)) (((tc R) X) X))
% Found (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X)) as proof of (((rc (tc R)) X) X)
% Found (or_intror00 (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X))) as proof of ((or (((rc (tc R)) X) X)) (((rc (tc R)) X) X))
% Found ((or_intror0 (((rc (tc R)) X) X)) (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X))) as proof of ((or (((rc (tc R)) X) X)) (((rc (tc R)) X) X))
% Found (((or_intror (((rc (tc R)) X) X)) (((rc (tc R)) X) X)) (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X))) as proof of ((or (((rc (tc R)) X) X)) (((rc (tc R)) X) X))
% Found (((or_intror (((rc (tc R)) X) X)) (((rc (tc R)) X) X)) (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X))) as proof of ((or (((rc (tc R)) X) X)) (((rc (tc R)) X) X))
% Found (fun (X:fofType)=> (((or_intror (((rc (tc R)) X) X)) (((rc (tc R)) X) X)) (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X)))) as proof of (((trsc R) X) X)
% Found (fun (X:fofType)=> (((or_intror (((rc (tc R)) X) X)) (((rc (tc R)) X) X)) (((or_introl (((eq fofType) X) X)) (((tc R) X) X)) ((eq_ref fofType) X)))) as proof of (refl (trsc R))
% Found x300:=(x30 x0):(((trsc R) X) Z)
% Found (x30 x0) as proof of (((trsc R) X) Z)
% Found ((x3 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x300:=(x30 x1):(((trsc R) X) Z)
% Found (x30 x1) as proof of (((trsc R) X) Z)
% Found ((x3 (fun (x5:fofType)=> (((trsc R) x5) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> (((trsc R) x5) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> (((trsc R) x5) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found x500:=(x50 x0):(((trsc R) X) Z)
% Found (x50 x0) as proof of (((trsc R) X) Z)
% Found ((x5 ((trsc R) X)) x0) as proof of (((trsc R) X) Z)
% Found (fun (x5:(((eq fofType) Y) Z))=> ((x5 ((trsc R) X)) x0)) as proof of (((trsc R) X) Z)
% Found (fun (x5:(((eq fofType) Y) Z))=> ((x5 ((trsc R) X)) x0)) as proof of ((((eq fofType) Y) Z)->(((trsc R) X) Z))
% Found x500:=(x50 x1):(((trsc R) X) Z)
% Found (x50 x1) as proof of (((trsc R) X) Z)
% Found ((x5 (fun (x7:fofType)=> (((trsc R) x7) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x5:(((eq fofType) Y) X))=> ((x5 (fun (x7:fofType)=> (((trsc R) x7) Z))) x1)) as proof of (((trsc R) X) Z)
% Found (fun (x5:(((eq fofType) Y) X))=> ((x5 (fun (x7:fofType)=> (((trsc R) x7) Z))) x1)) as proof of ((((eq fofType) Y) X)->(((trsc R) X) Z))
% Found x300:=(x30 x0):((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (x30 x0) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0)) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0)) as proof of ((((eq fofType) Y) Z)->((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z)))
% Found x300:=(x30 x0):((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (x30 x0) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0)) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0)) as proof of ((((eq fofType) Y) Z)->((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z)))
% Found x300:=(x30 x1):((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (x30 x1) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1)) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1)) as proof of ((((eq fofType) Y) X)->((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z)))
% Found x300:=(x30 x1):((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (x30 x1) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1)) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1)) as proof of ((((eq fofType) Y) X)->((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z)))
% Found x300:=(x30 x0):((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (x30 x0) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0)) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) Z))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) x5) X)) (((rc (tc R)) X) x5)))) x0)) as proof of ((((eq fofType) Y) Z)->((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z)))
% Found x300:=(x30 x1):((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (x30 x1) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1)) as proof of ((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z))
% Found (fun (x3:(((eq fofType) Y) X))=> ((x3 (fun (x5:fofType)=> ((or (((rc (tc R)) Z) x5)) (((rc (tc R)) x5) Z)))) x1)) as proof of ((((eq fofType) Y) X)->((or (((rc (tc R)) Z) X)) (((rc (tc R)) X) Z)))
% Found eq_ref000:=(eq_ref00 (fun (x6:Prop)=> (((trsc R) X) Z0))):((((trsc R) X) Z0)->(((trsc R) X) Z0))
% Found (eq_ref00 (fun (x6:Prop)=> (((trsc R) X) Z0))) as proof of ((((trsc R) X) Z0)->(((trsc R) X) Z0))
% Found ((eq_ref0 (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0))) as proof of ((((trsc R) X) Z0)->(((trsc R) X) Z0))
% Found (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0))) as proof of ((((trsc R) X) Z0)->(((trsc R) X) Z0))
% Found (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))) as proof of ((((trsc R) X) Z0)->(((trsc R) X) Z0))
% Found (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))) as proof of ((((trsc R) X) Y0)->((((trsc R) X) Z0)->(((trsc R) X) Z0)))
% Found (and_rect10 (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0))))) as proof of (((fun (x6:fofType)=> ((trsc R) X)) X0) Z0)
% Found ((and_rect1 (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0))))) as proof of (((fun (x6:fofType)=> ((trsc R) X)) X0) Z0)
% Found (((fun (P:Type) (x5:((((trsc R) X) Y0)->((((trsc R) X) Z0)->P)))=> (((((and_rect (((trsc R) X) Y0)) (((trsc R) X) Z0)) P) x5) x4)) (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0))))) as proof of (((fun (x6:fofType)=> ((trsc R) X)) X0) Z0)
% Found (fun (x4:((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) X) Y0)->((((trsc R) X) Z0)->P)))=> (((((and_rect (((trsc R) X) Y0)) (((trsc R) X) Z0)) P) x5) x4)) (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))))) as proof of (((fun (x6:fofType)=> ((trsc R) X)) X0) Z0)
% Found (fun (Z0:fofType) (x4:((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) X) Y0)->((((trsc R) X) Z0)->P)))=> (((((and_rect (((trsc R) X) Y0)) (((trsc R) X) Z0)) P) x5) x4)) (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))))) as proof of (((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z0))->(((fun (x6:fofType)=> ((trsc R) X)) X0) Z0))
% Found (fun (Y0:fofType) (Z0:fofType) (x4:((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) X) Y0)->((((trsc R) X) Z0)->P)))=> (((((and_rect (((trsc R) X) Y0)) (((trsc R) X) Z0)) P) x5) x4)) (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))))) as proof of (forall (Z:fofType), (((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z))->(((fun (x6:fofType)=> ((trsc R) X)) X0) Z)))
% Found (fun (X0:fofType) (Y0:fofType) (Z0:fofType) (x4:((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) X) Y0)->((((trsc R) X) Z0)->P)))=> (((((and_rect (((trsc R) X) Y0)) (((trsc R) X) Z0)) P) x5) x4)) (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))))) as proof of (forall (Y:fofType) (Z:fofType), (((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y)) (((fun (x6:fofType)=> ((trsc R) X)) Y) Z))->(((fun (x6:fofType)=> ((trsc R) X)) X0) Z)))
% Found (fun (X0:fofType) (Y0:fofType) (Z0:fofType) (x4:((and (((fun (x6:fofType)=> ((trsc R) X)) X0) Y0)) (((fun (x6:fofType)=> ((trsc R) X)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) X) Y0)->((((trsc R) X) Z0)->P)))=> (((((and_rect (((trsc R) X) Y0)) (((trsc R) X) Z0)) P) x5) x4)) (((trsc R) X) Z0)) (fun (x5:(((trsc R) X) Y0))=> (((eq_ref Prop) (((rc (tc R)) X) Z0)) (fun (x6:Prop)=> (((trsc R) X) Z0)))))) as proof of (trans (fun (x6:fofType)=> ((trsc R) X)))
% Found eq_ref000:=(eq_ref00 (fun (x6:Prop)=> (((trsc R) Z0) Z))):((((trsc R) Z0) Z)->(((trsc R) Z0) Z))
% Found (eq_ref00 (fun (x6:Prop)=> (((trsc R) Z0) Z))) as proof of ((((trsc R) Z0) Z)->(((trsc R) Z0) Z))
% Found ((eq_ref0 (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z))) as proof of ((((trsc R) Z0) Z)->(((trsc R) Z0) Z))
% Found (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z))) as proof of ((((trsc R) Z0) Z)->(((trsc R) Z0) Z))
% Found (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))) as proof of ((((trsc R) Z0) Z)->(((trsc R) Z0) Z))
% Found (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))) as proof of ((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->(((trsc R) Z0) Z)))
% Found (and_rect10 (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z))))) as proof of (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0)
% Found ((and_rect1 (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z))))) as proof of (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0)
% Found (((fun (P:Type) (x5:((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->P)))=> (((((and_rect (((trsc R) Y0) Z)) (((trsc R) Z0) Z)) P) x5) x4)) (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z))))) as proof of (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0)
% Found (fun (x4:((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->P)))=> (((((and_rect (((trsc R) Y0) Z)) (((trsc R) Z0) Z)) P) x5) x4)) (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))))) as proof of (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0)
% Found (fun (Z0:fofType) (x4:((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->P)))=> (((((and_rect (((trsc R) Y0) Z)) (((trsc R) Z0) Z)) P) x5) x4)) (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))))) as proof of (((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0))->(((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0))
% Found (fun (Y0:fofType) (Z0:fofType) (x4:((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->P)))=> (((((and_rect (((trsc R) Y0) Z)) (((trsc R) Z0) Z)) P) x5) x4)) (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))))) as proof of (forall (Z0:fofType), (((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0))->(((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0)))
% Found (fun (X0:fofType) (Y0:fofType) (Z0:fofType) (x4:((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->P)))=> (((((and_rect (((trsc R) Y0) Z)) (((trsc R) Z0) Z)) P) x5) x4)) (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))))) as proof of (forall (Y:fofType) (Z0:fofType), (((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y) Z0))->(((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Z0)))
% Found (fun (X0:fofType) (Y0:fofType) (Z0:fofType) (x4:((and (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) X0) Y0)) (((fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)) Y0) Z0)))=> (((fun (P:Type) (x5:((((trsc R) Y0) Z)->((((trsc R) Z0) Z)->P)))=> (((((and_rect (((trsc R) Y0) Z)) (((trsc R) Z0) Z)) P) x5) x4)) (((trsc R) Z0) Z)) (fun (x5:(((trsc R) Y0) Z))=> (((eq_ref Prop) (((rc (tc R)) Z0) Z)) (fun (x6:Prop)=> (((trsc R) Z0) Z)))))) as proof of (trans (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))
% Found eq_ref00:=(eq_ref0 ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))):(((eq Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) ((subrel R) (fun (x6:fofType)=> ((trsc R) X))))
% Found (eq_ref0 ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) b)
% Found ((eq_ref Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) b)
% Found ((eq_ref Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) b)
% Found ((eq_ref Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType)=> ((trsc R) X)))) b)
% Found eq_ref00:=(eq_ref0 ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))):(((eq Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z))))
% Found (eq_ref0 ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) b)
% Found ((eq_ref Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) b)
% Found ((eq_ref Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) b)
% Found ((eq_ref Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) as proof of (((eq Prop) ((subrel R) (fun (x6:fofType) (x50:fofType)=> (((trsc R) x50) Z)))) b)
% Found x500:=(x50 x1):(((trsc R) X) Z)
% Found (x50 x1) as proof of (((trsc R) X) Z)
% Found ((x5 (fun (x7:fofType)=> (((trsc R) x7) Z))) x1) as proof of (((trsc R) X) Z)
% Found (fun (x5:(((eq fofType) Y) X))=> ((x5 (fun (x7:fofType)=>
% EOF
%------------------------------------------------------------------------------