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cocATP---0.2.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : PHI003^2 : TPTP v6.1.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n190.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 13:28:40 EDT 2014

% Result   : Theorem 0.52s
% Output   : Proof 0.52s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : PHI003^2 : TPTP v6.1.0. Released v6.1.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n190.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 07:24:16 CDT 2014
% % CPUTime  : 0.52 
% 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/LCL016^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0xff2368>, <kernel.Type object at 0xff25f0>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0xff2488>, <kernel.DependentProduct object at 0xff23b0>) of role type named meq_ind_type
% Using role type
% Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% FOF formula (<kernel.Constant object at 0xff23f8>, <kernel.DependentProduct object at 0xff27a0>) of role type named mtrue_type
% Using role type
% Declaring mtrue:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% Defined: mtrue:=(fun (W:fofType)=> True)
% FOF formula (<kernel.Constant object at 0xff27a0>, <kernel.DependentProduct object at 0xff2440>) of role type named mfalse_type
% Using role type
% Declaring mfalse:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mfalse) (fun (W:fofType)=> False)) of role definition named mfalse
% A new definition: (((eq (fofType->Prop)) mfalse) (fun (W:fofType)=> False))
% Defined: mfalse:=(fun (W:fofType)=> False)
% FOF formula (<kernel.Constant object at 0xff2440>, <kernel.DependentProduct object at 0xff2098>) of role type named mnot_type
% Using role type
% Declaring mnot:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% FOF formula (<kernel.Constant object at 0xff2098>, <kernel.DependentProduct object at 0xff25f0>) of role type named mor_type
% Using role type
% Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0xff25f0>, <kernel.DependentProduct object at 0xff24d0>) of role type named mand_type
% Using role type
% Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W)))) of role definition named mand
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W))))
% Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0xff24d0>, <kernel.DependentProduct object at 0xff2560>) of role type named mimplies_type
% Using role type
% Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W)))) of role definition named mimplies
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W))))
% Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W)))
% FOF formula (<kernel.Constant object at 0x10470e0>, <kernel.DependentProduct object at 0x1047830>) of role type named mimplied_type
% Using role type
% Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W)))) of role definition named mimplied
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W))))
% Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W)))
% FOF formula (<kernel.Constant object at 0x1047320>, <kernel.DependentProduct object at 0xff29e0>) of role type named mequiv_type
% Using role type
% Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W)))) of role definition named mequiv
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W))))
% Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0x1047320>, <kernel.DependentProduct object at 0xff27a0>) of role type named mxor_type
% Using role type
% Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W))))) of role definition named mxor
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W)))))
% Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W))))
% FOF formula (<kernel.Constant object at 0xff27a0>, <kernel.DependentProduct object at 0xff2368>) of role type named mforall_ind_type
% Using role type
% Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0xff2a28>, <kernel.DependentProduct object at 0xff2098>) of role type named mforall_indset_type
% Using role type
% Declaring mforall_indset:(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mforall_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W)))) of role definition named mforall_indset
% A new definition: (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mforall_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W))))
% Defined: mforall_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0xff27a0>, <kernel.DependentProduct object at 0xbfb5a8>) of role type named mforall_prop_type
% Using role type
% Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% FOF formula (<kernel.Constant object at 0xff2a28>, <kernel.DependentProduct object at 0xbfb6c8>) of role type named mexists_ind_type
% Using role type
% Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W))))) of role definition named mexists_ind
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W)))))
% Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W))))
% FOF formula (<kernel.Constant object at 0xff2098>, <kernel.DependentProduct object at 0xbfb5a8>) of role type named mexists_indset_type
% Using role type
% Declaring mexists_indset:(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mexists_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W))))) of role definition named mexists_indset
% A new definition: (((eq (((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop))) mexists_indset) (fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W)))))
% Defined: mexists_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W))))
% FOF formula (<kernel.Constant object at 0xbfb5a8>, <kernel.DependentProduct object at 0xbfb710>) of role type named mexists_prop_type
% Using role type
% Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W))))) of role definition named mexists_prop
% A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W)))))
% Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W))))
% FOF formula (<kernel.Constant object at 0xbfb680>, <kernel.DependentProduct object at 0xbfb878>) of role type named mbox_generic_type
% Using role type
% Declaring mbox_generic:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox_generic
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))))
% Defined: mbox_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% FOF formula (<kernel.Constant object at 0xbfb5a8>, <kernel.DependentProduct object at 0xbfba28>) of role type named mdia_generic_type
% Using role type
% Declaring mdia_generic:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V)))))) of role definition named mdia_generic
% A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia_generic) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V))))))
% Defined: mdia_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V)))))
% FOF formula (<kernel.Constant object at 0xbfb680>, <kernel.DependentProduct object at 0xbfb830>) of role type named rel_type
% Using role type
% Declaring rel:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xbfbd88>, <kernel.DependentProduct object at 0xbfb488>) of role type named mbox_type
% Using role type
% Declaring mbox:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox) (mbox_generic rel)) of role definition named mbox
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox) (mbox_generic rel))
% Defined: mbox:=(mbox_generic rel)
% FOF formula (<kernel.Constant object at 0xbfbd88>, <kernel.DependentProduct object at 0xbfb488>) of role type named mdia_type
% Using role type
% Declaring mdia:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia) (mdia_generic rel)) of role definition named mdia
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia) (mdia_generic rel))
% Defined: mdia:=(mdia_generic rel)
% FOF formula (<kernel.Constant object at 0xbfb9e0>, <kernel.DependentProduct object at 0xbfbcf8>) of role type named mvalid_type
% Using role type
% Declaring mvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% FOF formula (<kernel.Constant object at 0xbfbd88>, <kernel.DependentProduct object at 0xbfbb90>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% FOF formula (<kernel.Constant object at 0xc16c20>, <kernel.DependentProduct object at 0xc16560>) of role type named positive_tp
% Using role type
% Declaring positive:((mu->(fofType->Prop))->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xc16ea8>, <kernel.DependentProduct object at 0xc16bd8>) of role type named god_tp
% Using role type
% Declaring god:(mu->(fofType->Prop))
% FOF formula (((eq (mu->(fofType->Prop))) god) (fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X)))))) of role definition named defD1
% A new definition: (((eq (mu->(fofType->Prop))) god) (fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X))))))
% Defined: god:=(fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X)))))
% FOF formula (mvalid (positive god)) of role axiom named axA3
% A new axiom: (mvalid (positive god))
% FOF formula (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (mdia (mexists_ind (fun (X:mu)=> (Phi X)))))))) of role lemma named thmT1
% A new axiom: (mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (mdia (mexists_ind (fun (X:mu)=> (Phi X))))))))
% FOF formula (mvalid (mdia (mexists_ind (fun (X:mu)=> (god X))))) of role conjecture named corC
% Conjecture to prove = (mvalid (mdia (mexists_ind (fun (X:mu)=> (god X))))):Prop
% Parameter mu_DUMMY:mu.
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(mvalid (mdia (mexists_ind (fun (X:mu)=> (god X)))))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(fun (W:fofType)=> False):(fofType->Prop).
% Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((and (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Phi W)->(Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((Psi W)->(Phi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((iff (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or ((and (Phi W)) ((Psi W)->False))) ((and ((Phi W)->False)) (Psi W)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> (forall (X:(mu->(fofType->Prop))), ((Phi X) W))):(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> ((ex mu) (fun (X:mu)=> ((Phi X) W)))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_indset:=(fun (Phi:((mu->(fofType->Prop))->(fofType->Prop))) (W:fofType)=> ((ex (mu->(fofType->Prop))) (fun (X:(mu->(fofType->Prop)))=> ((Phi X) W)))):(((mu->(fofType->Prop))->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> ((ex (fofType->Prop)) (fun (P:(fofType->Prop))=> ((Phi P) W)))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mbox_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mdia_generic:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> ((ex fofType) (fun (V:fofType)=> ((and ((R W) V)) (Phi V))))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Parameter rel:(fofType->(fofType->Prop)).
% Definition mbox:=(mbox_generic rel):((fofType->Prop)->(fofType->Prop)).
% Definition mdia:=(mdia_generic rel):((fofType->Prop)->(fofType->Prop)).
% Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Parameter positive:((mu->(fofType->Prop))->(fofType->Prop)).
% Definition god:=(fun (X:mu)=> (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (Phi X))))):(mu->(fofType->Prop)).
% Axiom axA3:(mvalid (positive god)).
% Axiom thmT1:(mvalid (mforall_indset (fun (Phi:(mu->(fofType->Prop)))=> ((mimplies (positive Phi)) (mdia (mexists_ind (fun (X:mu)=> (Phi X)))))))).
% Trying to prove (mvalid (mdia (mexists_ind (fun (X:mu)=> (god X)))))
% Found axA30:=(axA3 W):((positive god) W)
% Found (axA3 W) as proof of ((positive (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) W)
% Found (axA3 W) as proof of ((positive (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) W)
% Found (thmT100 (axA3 W)) as proof of ((mdia (mexists_ind (fun (X:mu)=> (god X)))) W)
% Found ((thmT10 (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) (axA3 W)) as proof of ((mdia (mexists_ind (fun (X:mu)=> (god X)))) W)
% Found (((thmT1 W) (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) (axA3 W)) as proof of ((mdia (mexists_ind (fun (X:mu)=> (god X)))) W)
% Found (fun (W:fofType)=> (((thmT1 W) (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) (axA3 W))) as proof of ((mdia (mexists_ind (fun (X:mu)=> (god X)))) W)
% Found (fun (W:fofType)=> (((thmT1 W) (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) (axA3 W))) as proof of (mvalid (mdia (mexists_ind (fun (X:mu)=> (god X)))))
% Got proof (fun (W:fofType)=> (((thmT1 W) (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) (axA3 W)))
% Time elapsed = 0.138111s
% node=13 cost=256.000000 depth=6
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (W:fofType)=> (((thmT1 W) (fun (x3:mu) (x20:fofType)=> (forall (X1:(mu->(fofType->Prop))), (((mimplies (positive X1)) (X1 x3)) x20)))) (axA3 W)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------