0.00/0.10	% Problem    : Vampire---4.8_1266 : TPTP v0.0.0. Released v0.0.0.
0.00/0.10	% Command    : do_cvc5 %s %d
0.10/0.30	% Computer : n007.cluster.edu
0.10/0.30	% Model    : x86_64 x86_64
0.10/0.30	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	% Memory   : 8042.1875MB
0.10/0.30	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.30	% CPULimit   : 1440
0.10/0.30	% WCLimit    : 180
0.10/0.30	% DateTime   : Mon Jul  3 12:55:58 EDT 2023
0.10/0.30	% CPUTime    : 
0.15/0.41	%----Proving TH0
0.15/0.42	thf(mu_type,type,
0.15/0.42	    mu: $tType ).
0.15/0.42	
0.15/0.42	thf(meq_ind_type,type,
0.15/0.42	    meq_ind: mu > mu > $i > $o ).
0.15/0.42	
0.15/0.42	thf(meq_ind,definition,
0.15/0.42	    ( meq_ind
0.15/0.42	    = ( ^ [X: mu,Y: mu,W: $i] : ( X = Y ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mtrue_type,type,
0.15/0.42	    mtrue: $i > $o ).
0.15/0.42	
0.15/0.42	thf(mtrue,definition,
0.15/0.42	    ( mtrue
0.15/0.42	    = ( ^ [W: $i] : $true ) ) ).
0.15/0.42	
0.15/0.42	thf(mfalse_type,type,
0.15/0.42	    mfalse: $i > $o ).
0.15/0.42	
0.15/0.42	thf(mfalse,definition,
0.15/0.42	    ( mfalse
0.15/0.42	    = ( ^ [W: $i] : $false ) ) ).
0.15/0.42	
0.15/0.42	thf(mnot_type,type,
0.15/0.42	    mnot: ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mnot,definition,
0.15/0.42	    ( mnot
0.15/0.42	    = ( ^ [Phi: $i > $o,W: $i] :
0.15/0.42	          ~ ( Phi @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mor_type,type,
0.15/0.42	    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mor,definition,
0.15/0.42	    ( mor
0.15/0.42	    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
0.15/0.42	          ( ( Phi @ W )
0.15/0.42	          | ( Psi @ W ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mand_type,type,
0.15/0.42	    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mand,definition,
0.15/0.42	    ( mand
0.15/0.42	    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
0.15/0.42	          ( ( Phi @ W )
0.15/0.42	          & ( Psi @ W ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mimplies_type,type,
0.15/0.42	    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mimplies,definition,
0.15/0.42	    ( mimplies
0.15/0.42	    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
0.15/0.42	          ( ( Phi @ W )
0.15/0.42	         => ( Psi @ W ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mimplied_type,type,
0.15/0.42	    mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mimplied,definition,
0.15/0.42	    ( mimplied
0.15/0.42	    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
0.15/0.42	          ( ( Psi @ W )
0.15/0.42	         => ( Phi @ W ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mequiv_type,type,
0.15/0.42	    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mequiv,definition,
0.15/0.42	    ( mequiv
0.15/0.42	    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
0.15/0.42	          ( ( Phi @ W )
0.15/0.42	        <=> ( Psi @ W ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mxor_type,type,
0.15/0.42	    mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mxor,definition,
0.15/0.42	    ( mxor
0.15/0.42	    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
0.15/0.42	          ( ( ( Phi @ W )
0.15/0.42	            & ~ ( Psi @ W ) )
0.15/0.42	          | ( ~ ( Phi @ W )
0.15/0.42	            & ( Psi @ W ) ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mforall_ind_type,type,
0.15/0.42	    mforall_ind: ( mu > $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mforall_ind,definition,
0.15/0.42	    ( mforall_ind
0.15/0.42	    = ( ^ [Phi: mu > $i > $o,W: $i] :
0.15/0.42	        ! [X: mu] : ( Phi @ X @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mforall_indset_type,type,
0.15/0.42	    mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mforall_indset,definition,
0.15/0.42	    ( mforall_indset
0.15/0.42	    = ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
0.15/0.42	        ! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mforall_prop_type,type,
0.15/0.42	    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mforall_prop,definition,
0.15/0.42	    ( mforall_prop
0.15/0.42	    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
0.15/0.42	        ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mexists_ind_type,type,
0.15/0.42	    mexists_ind: ( mu > $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mexists_ind,definition,
0.15/0.42	    ( mexists_ind
0.15/0.42	    = ( ^ [Phi: mu > $i > $o,W: $i] :
0.15/0.42	        ? [X: mu] : ( Phi @ X @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mexists_indset_type,type,
0.15/0.42	    mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mexists_indset,definition,
0.15/0.42	    ( mexists_indset
0.15/0.42	    = ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
0.15/0.42	        ? [X: mu > $i > $o] : ( Phi @ X @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mexists_prop_type,type,
0.15/0.42	    mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mexists_prop,definition,
0.15/0.42	    ( mexists_prop
0.15/0.42	    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
0.15/0.42	        ? [P: $i > $o] : ( Phi @ P @ W ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mbox_generic_type,type,
0.15/0.42	    mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mbox_generic,definition,
0.15/0.42	    ( mbox_generic
0.15/0.42	    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
0.15/0.42	        ! [V: $i] :
0.15/0.42	          ( ~ ( R @ W @ V )
0.15/0.42	          | ( Phi @ V ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(mdia_generic_type,type,
0.15/0.42	    mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mdia_generic,definition,
0.15/0.42	    ( mdia_generic
0.15/0.42	    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
0.15/0.42	        ? [V: $i] :
0.15/0.42	          ( ( R @ W @ V )
0.15/0.42	          & ( Phi @ V ) ) ) ) ).
0.15/0.42	
0.15/0.42	thf(rel_type,type,
0.15/0.42	    rel: $i > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mbox_type,type,
0.15/0.42	    mbox: ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mbox,definition,
0.15/0.42	    ( mbox
0.15/0.42	    = ( mbox_generic @ rel ) ) ).
0.15/0.42	
0.15/0.42	thf(mdia_type,type,
0.15/0.42	    mdia: ( $i > $o ) > $i > $o ).
0.15/0.42	
0.15/0.42	thf(mdia,definition,
0.15/0.42	    ( mdia
0.15/0.42	    = ( mdia_generic @ rel ) ) ).
0.15/0.43	
0.15/0.43	thf(mvalid_type,type,
0.15/0.43	    mvalid: ( $i > $o ) > $o ).
0.15/0.43	
0.15/0.43	thf(mvalid,definition,
0.15/0.43	    ( mvalid
0.15/0.43	    = ( ^ [Phi: $i > $o] :
0.15/0.43	        ! [W: $i] : ( Phi @ W ) ) ) ).
0.15/0.43	
0.15/0.43	thf(minvalid_type,type,
0.15/0.43	    minvalid: ( $i > $o ) > $o ).
0.15/0.43	
0.15/0.43	thf(minvalid,definition,
0.15/0.43	    ( minvalid
0.15/0.43	    = ( ^ [Phi: $i > $o] :
0.15/0.43	        ! [W: $i] :
0.15/0.43	          ~ ( Phi @ W ) ) ) ).
0.15/0.43	
0.15/0.43	thf(positive_tp,type,
0.15/0.43	    positive: ( mu > $i > $o ) > $i > $o ).
0.15/0.43	
0.15/0.43	thf(god_tp,type,
0.15/0.43	    god: mu > $i > $o ).
0.15/0.43	
0.15/0.43	thf(defD1,definition,
0.15/0.43	    ( god
0.15/0.43	    = ( ^ [X: mu] :
0.15/0.43	          ( mforall_indset
0.15/0.43	          @ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ) ).
0.15/0.43	
0.15/0.43	thf(axA3,axiom,
0.15/0.43	    mvalid @ ( positive @ god ) ).
0.15/0.43	
0.15/0.43	thf(thmT1,lemma,
0.15/0.43	    ( mvalid
0.15/0.43	    @ ( mforall_indset
0.15/0.43	      @ ^ [Phi: mu > $i > $o] :
0.15/0.43	          ( mimplies @ ( positive @ Phi )
0.15/0.43	          @ ( mdia
0.15/0.43	            @ ( mexists_ind
0.15/0.43	              @ ^ [X: mu] : ( Phi @ X ) ) ) ) ) ) ).
0.15/0.43	
0.15/0.43	thf(corC,conjecture,
0.15/0.43	    ( mvalid
0.15/0.43	    @ ( mdia
0.15/0.43	      @ ( mexists_ind
0.15/0.43	        @ ^ [X: mu] : ( god @ X ) ) ) ) ).
0.15/0.43	
0.15/0.43	------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XY4rEy6D7s/cvc5---1.0.5_1369.p...
0.15/0.43	(declare-sort $$unsorted 0)
0.15/0.43	(declare-sort tptp.mu 0)
0.15/0.43	(declare-fun tptp.meq_ind (tptp.mu tptp.mu $$unsorted) Bool)
0.15/0.43	(assert (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))
0.15/0.43	(declare-fun tptp.mtrue ($$unsorted) Bool)
0.15/0.43	(assert (= tptp.mtrue (lambda ((W $$unsorted)) true)))
0.15/0.43	(declare-fun tptp.mfalse ($$unsorted) Bool)
0.15/0.43	(assert (= tptp.mfalse (lambda ((W $$unsorted)) false)))
0.15/0.43	(declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))
0.15/0.43	(declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))
0.15/0.43	(declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (and (@ Phi W) (@ Psi W)))))
0.15/0.43	(declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (=> (@ Phi W) (@ Psi W)))))
0.15/0.43	(declare-fun tptp.mimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (=> (@ Psi W) (@ Phi W)))))
0.15/0.43	(declare-fun tptp.mequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (= (@ Phi W) (@ Psi W)))))
0.15/0.43	(declare-fun tptp.mxor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (let ((_let_1 (@ Psi W))) (let ((_let_2 (@ Phi W))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))
0.15/0.43	(declare-fun tptp.mforall_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))
0.15/0.43	(declare-fun tptp.mforall_indset ((-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mforall_indset (lambda ((Phi (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((X (-> tptp.mu $$unsorted Bool))) (@ (@ Phi X) W)))))
0.15/0.43	(declare-fun tptp.mforall_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
0.15/0.43	(declare-fun tptp.mexists_ind ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.mu)) (@ (@ Phi X) W)))))
0.15/0.43	(declare-fun tptp.mexists_indset ((-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
0.15/0.43	(assert (= tptp.mexists_indset (lambda ((Phi (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (exists ((X (-> tptp.mu $$unsorted Bool))) (@ (@ Phi X) W)))))
51.77/52.16	(declare-fun tptp.mexists_prop ((-> (-> $$unsorted Bool) $$unsorted Bool) $$unsorted) Bool)
51.77/52.16	(assert (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (exists ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))
51.77/52.16	(declare-fun tptp.mbox_generic ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
51.77/52.16	(assert (= tptp.mbox_generic (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))
51.77/52.16	(declare-fun tptp.mdia_generic ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
51.77/52.16	(assert (= tptp.mdia_generic (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (exists ((V $$unsorted)) (and (@ (@ R W) V) (@ Phi V))))))
51.77/52.16	(declare-fun tptp.rel ($$unsorted $$unsorted) Bool)
51.77/52.16	(declare-fun tptp.mbox ((-> $$unsorted Bool) $$unsorted) Bool)
51.77/52.16	(assert (= tptp.mbox (@ tptp.mbox_generic tptp.rel)))
51.77/52.16	(declare-fun tptp.mdia ((-> $$unsorted Bool) $$unsorted) Bool)
51.77/52.16	(assert (= tptp.mdia (@ tptp.mdia_generic tptp.rel)))
51.77/52.16	(declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
51.77/52.16	(assert (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
51.77/52.16	(declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
51.77/52.16	(assert (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
51.77/52.16	(declare-fun tptp.positive ((-> tptp.mu $$unsorted Bool) $$unsorted) Bool)
51.77/52.16	(declare-fun tptp.god (tptp.mu $$unsorted) Bool)
51.77/52.16	(assert (= tptp.god (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_indset (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.positive Phi)) (@ Phi X)) __flatten_var_0))) __flatten_var_0))))
51.77/52.16	(assert (@ tptp.mvalid (@ tptp.positive tptp.god)))
51.77/52.16	(assert (@ tptp.mvalid (@ tptp.mforall_indset (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.positive Phi)) (@ tptp.mdia (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ Phi X) __flatten_var_0))))) __flatten_var_0)))))
51.77/52.16	(assert (not (@ tptp.mvalid (@ tptp.mdia (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.god X) __flatten_var_0)))))))
51.77/52.16	(set-info :filename cvc5---1.0.5_1369)
51.77/52.16	(check-sat-assuming ( true ))
51.77/52.16	------- get file name : TPTP file name is 
51.77/52.16	------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1369.smt2...
51.77/52.16	--- Run --ho-elim --full-saturate-quant at 10...
51.77/52.16	--- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
51.77/52.16	--- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
51.77/52.16	--- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
51.77/52.16	--- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
51.77/52.16	--- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
51.77/52.16	--- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
51.77/52.16	% SZS status Theorem for 
51.77/52.16	% SZS output start Proof for 
51.77/52.16	(
51.77/52.16	(let ((_let_1 (not (@ tptp.mvalid (@ tptp.mdia (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.god X) __flatten_var_0)))))))) (let ((_let_2 (@ tptp.mvalid (@ tptp.mforall_indset (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.positive Phi)) (@ tptp.mdia (@ tptp.mexists_ind (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ Phi X) __flatten_var_0))))) __flatten_var_0)))))) (let ((_let_3 (@ tptp.mvalid (@ tptp.positive tptp.god)))) (let ((_let_4 (= tptp.god (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mforall_indset (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.positive Phi)) (@ Phi X)) __flatten_var_0))) __flatten_var_0))))) (let ((_let_5 (= tptp.minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_6 (= tptp.mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_7 (= tptp.mdia (@ tptp.mdia_generic tptp.rel)))) (let ((_let_8 (= tptp.mbox (@ tptp.mbox_generic tptp.rel)))) (let ((_let_9 (= tptp.mdia_generic (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (exists ((V $$unsorted)) (and (@ (@ R W) V) (@ Phi V))))))) (let ((_let_10 (= tptp.mbox_generic (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not (@ (@ R W) V)) (@ Phi V))))))) (let ((_let_11 (= tptp.mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (exists ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_12 (= tptp.mexists_indset (lambda ((Phi (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (exists ((X (-> tptp.mu $$unsorted Bool))) (@ (@ Phi X) W)))))) (let ((_let_13 (= tptp.mexists_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.mu)) (@ (@ Phi X) W)))))) (let ((_let_14 (= tptp.mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) (@ (@ Phi P) W)))))) (let ((_let_15 (= tptp.mforall_indset (lambda ((Phi (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((X (-> tptp.mu $$unsorted Bool))) (@ (@ Phi X) W)))))) (let ((_let_16 (= tptp.mforall_ind (lambda ((Phi (-> tptp.mu $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.mu)) (@ (@ Phi X) W)))))) (let ((_let_17 (= tptp.mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (let ((_let_1 (@ Psi W))) (let ((_let_2 (@ Phi W))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))) (let ((_let_18 (= tptp.mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (= (@ Phi W) (@ Psi W)))))) (let ((_let_19 (= tptp.mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (=> (@ Psi W) (@ Phi W)))))) (let ((_let_20 (= tptp.mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (=> (@ Phi W) (@ Psi W)))))) (let ((_let_21 (= tptp.mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (and (@ Phi W) (@ Psi W)))))) (let ((_let_22 (= tptp.mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (@ Phi W) (@ Psi W)))))) (let ((_let_23 (= tptp.mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (@ Phi W)))))) (let ((_let_24 (= tptp.mfalse (lambda ((W $$unsorted)) false)))) (let ((_let_25 (= tptp.mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_26 (= tptp.meq_ind (lambda ((X tptp.mu) (Y tptp.mu) (W $$unsorted)) (= X Y))))) (let ((_let_27 (forall ((V $$unsorted) (BOUND_VARIABLE_1188 tptp.mu)) (or (not (@ (@ tptp.rel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) V)) (not (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) V)) (@ (@ X BOUND_VARIABLE_1188) V)))))))) (let ((_let_28 (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32)) (@ (@ X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (tptp.rel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29))) (let ((_let_33 (forall ((W $$unsorted)) (not (forall ((V $$unsorted) (BOUND_VARIABLE_1188 tptp.mu)) (or (not (@ (@ tptp.rel W) V)) (not (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) V)) (@ (@ X BOUND_VARIABLE_1188) V)))))))))) (let ((_let_34 (ASSUME :args (_let_26)))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (ASSUME :args (_let_23)))) (let ((_let_38 (ASSUME :args (_let_22)))) (let ((_let_39 (ASSUME :args (_let_21)))) (let ((_let_40 (ASSUME :args (_let_20)))) (let ((_let_41 (ASSUME :args (_let_19)))) (let ((_let_42 (ASSUME :args (_let_18)))) (let ((_let_43 (ASSUME :args (_let_17)))) (let ((_let_44 (ASSUME :args (_let_16)))) (let ((_let_45 (ASSUME :args (_let_15)))) (let ((_let_46 (ASSUME :args (_let_14)))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (ASSUME :args (_let_10)))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (ASSUME :args (_let_6)))) (let ((_let_55 (ASSUME :args (_let_5)))) (let ((_let_56 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36 _let_35 _let_34))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO _let_56 :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (or))) (let ((_let_59 (_let_27))) (let ((_let_60 (REFL :args _let_59))) (let ((_let_61 (not _let_33))) (let ((_let_62 (not _let_32))) (let ((_let_63 (lambdaF_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32))) (let ((_let_64 (= _let_63 _let_28))) (let ((_let_65 (forall ((X tptp.mu) (__flatten_var_0 $$unsorted)) (= (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) __flatten_var_0)) (@ (@ X X) __flatten_var_0))) (lambdaF_5 X __flatten_var_0))))) (let ((_let_66 ((forall ((X tptp.mu) (__flatten_var_0 $$unsorted)) (= (lambdaF_5 X __flatten_var_0) (@ (@ (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) __flatten_var_0)) (@ (@ X X) __flatten_var_0)))) X) __flatten_var_0)))))) (let ((_let_67 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_66) (REWRITE :args _let_66)))) (let ((_let_68 (not _let_63))) (let ((_let_69 (or _let_31 _let_68))) (let ((_let_70 (forall ((V $$unsorted) (BOUND_VARIABLE_1052 tptp.mu)) (or (not (@ (@ tptp.rel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) V)) (not (@ (@ lambdaF_5 BOUND_VARIABLE_1052) V)))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (not _let_70))) (let ((_let_73 (tptp.positive lambdaF_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_74 (not _let_73))) (let ((_let_75 (or _let_74 _let_72))) (let ((_let_76 (forall ((W $$unsorted) (X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) W)) (not (forall ((V $$unsorted) (BOUND_VARIABLE_1052 tptp.mu)) (or (not (@ (@ tptp.rel W) V)) (not (@ (@ X BOUND_VARIABLE_1052) V))))))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_56 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (=>))) (let ((_let_79 (_let_72))) (let ((_let_80 (REFL :args _let_79))) (let ((_let_81 (not))) (let ((_let_82 (THEORY_PREPROCESS :args ((= (@ (@ tptp.positive lambdaF_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_73))))) (let ((_let_83 (_let_76))) (let ((_let_84 (forall ((W $$unsorted)) (@ (@ tptp.positive (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) __flatten_var_0)) (@ (@ X X) __flatten_var_0))))) W)))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO _let_56 :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (@))) (let ((_let_87 (_let_84))) (let ((_let_88 (CONG (THEORY_PREPROCESS :args ((= (@ (@ tptp.rel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32) _let_30))) :args _let_81))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79) (CONG _let_80 (CONG (CONG _let_88 (CONG (THEORY_PREPROCESS :args ((= (@ (@ lambdaF_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32) _let_63))) :args _let_81) :args _let_58) :args _let_81) :args _let_78))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_70))) (REFL :args (_let_71)) :args _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_72 _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args _let_87) (CONG (REFL :args _let_87) (TRANS (CONG (CONG (REFL :args (tptp.positive)) (MACRO_SR_PRED_INTRO :args ((= (lambda ((X tptp.mu) (__flatten_var_0 $$unsorted)) (forall ((X (-> tptp.mu $$unsorted Bool))) (or (not (@ (@ tptp.positive X) __flatten_var_0)) (@ (@ X X) __flatten_var_0)))) lambdaF_5))) :args _let_86) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) :args _let_86) _let_82) :args _let_78))) _let_85 :args (_let_73 false _let_84)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_77 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 lambdaF_5 QUANTIFIERS_INST_ENUM)) :args _let_83) (CONG (REFL :args _let_83) (CONG (CONG _let_82 :args _let_81) _let_80 :args _let_58) :args _let_78))) _let_77 :args (_let_75 false _let_76)) :args (_let_72 false _let_73 false _let_75)) :args (_let_71 true _let_70)))) (let ((_let_90 (REFL :args (_let_69)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 QUANTIFIERS_INST_ENUM)) :args _let_59) (CONG _let_60 (CONG _let_88 (REFL :args (_let_29)) :args _let_58) :args _let_78))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_29 _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_58)) :args ((or _let_30 _let_69))) _let_89 :args (_let_30 true _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or _let_68 _let_28 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_63))) :args _let_58)) :args ((or _let_63 _let_69))) _let_89 :args (_let_63 true _let_69)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_33 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_5 X __flatten_var_0)))) :args (_let_65)))) _let_67 :args (_let_64 false _let_65)) :args (_let_28 false _let_63 false _let_64)) :args (_let_62 false _let_30 false _let_28)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_57) :args (_let_61)) (REWRITE :args ((=> _let_61 (not (not _let_27))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_33))) _let_60 :args _let_58)) _let_57 :args (_let_27 true _let_33)) :args (false true _let_32 false _let_27)) :args (_let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
51.77/52.17	)
51.77/52.17	% SZS output end Proof for 
51.77/52.17	% cvc5---1.0.5 exiting
51.77/52.17	% cvc5---1.0.5 exiting
51.77/52.17	EOF