TSTP Solution File: PRO029^16 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:06:30 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 18:59:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 % File : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% 0.20/0.50 % Domain : Processes
% 0.20/0.50 % Problem : Phone user and company (requirement 1)
% 0.20/0.50 % Version : [BP13] axioms.
% 0.20/0.50 % English : Phone user U and phone company C have following relationship:
% 0.20/0.50 % + U does not pay a call before he has dialled it.
% 0.20/0.50 % + Both U nd C are able to prove when U is being charged.
% 0.20/0.50 % + U is able to prove that C can prove that U has made a call,
% 0.20/0.50 % + C is able to prove that U can prove that U has paid his call,
% 0.20/0.50 % + U is able to prove that C cannot prove that U has made a call,
% 0.20/0.50 % + C is able to prove that U cannot prove that he has paid his
% 0.20/0.50 % call, whenever these facts are true.
% 0.20/0.50 % Then the following requirement is true: From U's point of view,
% 0.20/0.50 % C should charge U only if he has made a call that is not yet paid.
% 0.20/0.50
% 0.20/0.50 % Refs : [HA97] Huima & Aura (1997), Using Multimodal Logic to Express
% 0.20/0.50 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.20/0.50 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.20/0.50 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.20/0.50 % Source : [TPTP]
% 0.20/0.50 % Names : MML011+1 [QMLTP]
% 0.20/0.50 % : MML011^1.016_s4_cumulative_rigid.p [QMLTP/5_THF]
% 0.20/0.50
% 0.20/0.50 % Status : Theorem
% 0.20/0.50 % Rating : 0.31 v8.1.0
% 0.20/0.50 % Syntax : Number of formulae : 36 ( 10 unt; 17 typ; 8 def)
% 0.20/0.50 % Number of atoms : 85 ( 8 equ; 0 cnn)
% 0.20/0.50 % Maximal formula atoms : 17 ( 4 avg)
% 0.20/0.50 % Number of connectives : 118 ( 1 ~; 1 |; 4 &; 107 @)
% 0.20/0.50 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.50 % Maximal formula depth : 9 ( 4 avg)
% 0.20/0.50 % Number of types : 3 ( 2 usr)
% 0.20/0.50 % Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% 0.20/0.50 % Number of symbols : 16 ( 15 usr; 3 con; 0-3 aty)
% 0.20/0.50 % Number of variables : 31 ( 21 ^; 9 !; 1 ?; 31 :)
% 0.20/0.50 % SPC : TH0_THM_EQU_NAR
% 0.20/0.50
% 0.20/0.50 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.20/0.50 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.20/0.50 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.20/0.50 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.20/0.50 % $modalities == $modal_system_S4].
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 thf(mworld,type,
% 0.20/0.50 mworld: $tType ).
% 0.20/0.50
% 0.20/0.50 thf(mindex,type,
% 0.20/0.50 mindex: $tType ).
% 0.20/0.50
% 0.20/0.50 thf(mrel_type,type,
% 0.20/0.50 mrel: mindex > mworld > mworld > $o ).
% 0.20/0.50
% 0.20/0.50 thf('#c_type',type,
% 0.20/0.50 '#c': mindex ).
% 0.20/0.50
% 0.20/0.50 thf('#u_type',type,
% 0.20/0.50 '#u': mindex ).
% 0.20/0.50
% 0.20/0.50 thf(mactual_type,type,
% 0.20/0.50 mactual: mworld ).
% 0.20/0.50
% 0.20/0.50 thf(mlocal_type,type,
% 0.20/0.50 mlocal: ( mworld > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mlocal_def,definition,
% 0.20/0.50 ( mlocal
% 0.20/0.50 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mnot_type,type,
% 0.20/0.50 mnot: ( mworld > $o ) > mworld > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mand_type,type,
% 0.20/0.50 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mor_type,type,
% 0.20/0.50 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mimplies_type,type,
% 0.20/0.50 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mequiv_type,type,
% 0.20/0.50 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mnot_def,definition,
% 0.20/0.50 ( mnot
% 0.20/0.50 = ( ^ [A: mworld > $o,W: mworld] :
% 0.20/0.50 ~ ( A @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mand_def,definition,
% 0.20/0.50 ( mand
% 0.20/0.50 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.50 ( ( A @ W )
% 0.20/0.50 & ( B @ W ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mor_def,definition,
% 0.20/0.50 ( mor
% 0.20/0.50 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.50 ( ( A @ W )
% 0.20/0.50 | ( B @ W ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mimplies_def,definition,
% 0.20/0.50 ( mimplies
% 0.20/0.50 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.50 ( ( A @ W )
% 0.20/0.50 => ( B @ W ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mequiv_def,definition,
% 0.20/0.50 ( mequiv
% 0.20/0.50 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.20/0.50 ( ( A @ W )
% 0.20/0.50 <=> ( B @ W ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(mbox_type,type,
% 0.20/0.51 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.20/0.51
% 0.20/0.51 thf(mbox_def,definition,
% 0.20/0.51 ( mbox
% 0.20/0.51 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.20/0.51 ! [V: mworld] :
% 0.20/0.51 ( ( mrel @ R @ W @ V )
% 0.20/0.51 => ( Phi @ V ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(mdia_type,type,
% 0.20/0.51 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.20/0.51
% 0.20/0.51 thf(mdia_def,definition,
% 0.20/0.51 ( mdia
% 0.20/0.51 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.20/0.51 ? [V: mworld] :
% 0.20/0.51 ( ( mrel @ R @ W @ V )
% 0.20/0.51 & ( Phi @ V ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf('mrel_#c_reflexive',axiom,
% 0.20/0.51 ! [W: mworld] : ( mrel @ '#c' @ W @ W ) ).
% 0.20/0.51
% 0.20/0.51 thf('mrel_#c_transitive',axiom,
% 0.20/0.51 ! [W: mworld,V: mworld,U: mworld] :
% 0.20/0.51 ( ( ( mrel @ '#c' @ W @ V )
% 0.20/0.51 & ( mrel @ '#c' @ V @ U ) )
% 0.20/0.51 => ( mrel @ '#c' @ W @ U ) ) ).
% 0.20/0.51
% 0.20/0.51 thf('mrel_#u_reflexive',axiom,
% 0.20/0.51 ! [W: mworld] : ( mrel @ '#u' @ W @ W ) ).
% 0.20/0.51
% 0.20/0.51 thf('mrel_#u_transitive',axiom,
% 0.20/0.51 ! [W: mworld,V: mworld,U: mworld] :
% 0.20/0.51 ( ( ( mrel @ '#u' @ W @ V )
% 0.20/0.51 & ( mrel @ '#u' @ V @ U ) )
% 0.20/0.51 => ( mrel @ '#u' @ W @ U ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(charge_decl,type,
% 0.20/0.51 charge: mworld > $o ).
% 0.20/0.51
% 0.20/0.51 thf(called_decl,type,
% 0.20/0.51 called: mworld > $o ).
% 0.20/0.51
% 0.20/0.51 thf(paid_decl,type,
% 0.20/0.51 paid: mworld > $o ).
% 0.20/0.51
% 0.20/0.51 thf(aciom_paid_charge,axiom,
% 0.20/0.51 mlocal @ ( mimplies @ paid @ called ) ).
% 0.20/0.51
% 0.20/0.51 thf(axiom_charge_u,axiom,
% 0.20/0.51 mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(axiom_1,axiom,
% 0.20/0.51 mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(axiom_2,axiom,
% 0.20/0.51 mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(axiom_3,axiom,
% 0.20/0.51 mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(axiom_4,axiom,
% 0.20/0.51 mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#u' @ paid ) ) @ ( mbox @ '#c' @ ( mnot @ ( mbox @ '#u' @ paid ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(requirement_1,conjecture,
% 0.20/0.51 mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.2hun8j19ad/cvc5---1.0.5_2663.p...
% 0.20/0.51 (declare-sort $$unsorted 0)
% 0.20/0.51 (declare-sort tptp.mworld 0)
% 0.20/0.51 (declare-sort tptp.mindex 0)
% 0.20/0.51 (declare-fun tptp.mrel (tptp.mindex tptp.mworld tptp.mworld) Bool)
% 0.20/0.51 (declare-fun |tptp.'#c'| () tptp.mindex)
% 0.20/0.51 (declare-fun |tptp.'#u'| () tptp.mindex)
% 0.20/0.51 (declare-fun tptp.mactual () tptp.mworld)
% 0.20/0.51 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.20/0.51 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.20/0.51 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.20/0.51 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.20/0.51 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.20/0.51 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.20/0.51 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.20/0.51 (declare-fun tptp.mbox (tptp.mindex (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (assert (= tptp.mbox (lambda ((R tptp.mindex) (Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ (@ tptp.mrel R) W) V) (@ Phi V))))))
% 0.20/0.51 (declare-fun tptp.mdia (tptp.mindex (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.20/0.51 (assert (= tptp.mdia (lambda ((R tptp.mindex) (Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ (@ tptp.mrel R) W) V) (@ Phi V))))))
% 0.20/0.56 (assert (forall ((W tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#c'|) W) W)))
% 0.20/0.56 (assert (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel |tptp.'#c'|))) (let ((_let_2 (@ _let_1 W))) (=> (and (@ _let_2 V) (@ (@ _let_1 V) U)) (@ _let_2 U))))))
% 0.20/0.56 (assert (forall ((W tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#u'|) W) W)))
% 0.20/0.56 (assert (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel |tptp.'#u'|))) (let ((_let_2 (@ _let_1 W))) (=> (and (@ _let_2 V) (@ (@ _let_1 V) U)) (@ _let_2 U))))))
% 0.20/0.56 (declare-fun tptp.charge (tptp.mworld) Bool)
% 0.20/0.56 (declare-fun tptp.called (tptp.mworld) Bool)
% 0.20/0.56 (declare-fun tptp.paid (tptp.mworld) Bool)
% 0.20/0.56 (assert (@ tptp.mlocal (@ (@ tptp.mimplies tptp.paid) tptp.called)))
% 0.20/0.56 (assert (@ tptp.mlocal (@ (@ tptp.mimplies tptp.charge) (@ (@ tptp.mand (@ (@ tptp.mbox |tptp.'#u'|) tptp.charge)) (@ (@ tptp.mbox |tptp.'#c'|) tptp.charge)))))
% 0.20/0.56 (assert (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#u'|) (@ (@ tptp.mimplies tptp.called) (@ (@ tptp.mbox |tptp.'#c'|) tptp.called)))))
% 0.20/0.56 (assert (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#c'|) (@ (@ tptp.mimplies tptp.paid) (@ (@ tptp.mbox |tptp.'#u'|) tptp.paid)))))
% 0.20/0.56 (assert (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox |tptp.'#c'|) tptp.called)))) (@ tptp.mlocal (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox |tptp.'#u'|) _let_1)))))
% 0.20/0.56 (assert (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mbox |tptp.'#u'|) tptp.paid)))) (@ tptp.mlocal (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox |tptp.'#c'|) _let_1)))))
% 0.20/0.56 (assert (let ((_let_1 (@ tptp.mnot (@ (@ tptp.mimplies tptp.charge) (@ (@ tptp.mand tptp.called) (@ tptp.mnot tptp.paid)))))) (not (@ tptp.mlocal (@ (@ tptp.mimplies _let_1) (@ (@ tptp.mbox |tptp.'#u'|) _let_1))))))
% 0.20/0.56 (set-info :filename cvc5---1.0.5_2663)
% 0.20/0.56 (check-sat-assuming ( true ))
% 0.20/0.56 ------- get file name : TPTP file name is PRO029^16
% 0.20/0.56 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_2663.smt2...
% 0.20/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.56 % SZS status Theorem for PRO029^16
% 0.20/0.56 % SZS output start Proof for PRO029^16
% 0.20/0.56 (
% 0.20/0.56 (let ((_let_1 (@ tptp.mimplies tptp.charge))) (let ((_let_2 (@ tptp.mnot (@ _let_1 (@ (@ tptp.mand tptp.called) (@ tptp.mnot tptp.paid)))))) (let ((_let_3 (@ tptp.mbox |tptp.'#u'|))) (let ((_let_4 (not (@ tptp.mlocal (@ (@ tptp.mimplies _let_2) (@ _let_3 _let_2)))))) (let ((_let_5 (@ _let_3 tptp.paid))) (let ((_let_6 (@ tptp.mnot _let_5))) (let ((_let_7 (@ tptp.mbox |tptp.'#c'|))) (let ((_let_8 (@ _let_7 tptp.called))) (let ((_let_9 (@ tptp.mnot _let_8))) (let ((_let_10 (@ tptp.mimplies tptp.paid))) (let ((_let_11 (@ tptp.mlocal (@ _let_7 (@ _let_10 _let_5))))) (let ((_let_12 (@ tptp.mlocal (@ _let_3 (@ (@ tptp.mimplies tptp.called) _let_8))))) (let ((_let_13 (@ tptp.mlocal (@ _let_1 (@ (@ tptp.mand (@ _let_3 tptp.charge)) (@ _let_7 tptp.charge)))))) (let ((_let_14 (forall ((W tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#u'|) W) W)))) (let ((_let_15 (forall ((W tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#c'|) W) W)))) (let ((_let_16 (= tptp.mdia (lambda ((R tptp.mindex) (Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (exists ((V tptp.mworld)) (and (@ (@ (@ tptp.mrel R) W) V) (@ Phi V))))))) (let ((_let_17 (= tptp.mbox (lambda ((R tptp.mindex) (Phi (-> tptp.mworld Bool)) (W tptp.mworld)) (forall ((V tptp.mworld)) (=> (@ (@ (@ tptp.mrel R) W) V) (@ Phi V))))))) (let ((_let_18 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))) (let ((_let_19 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_20 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))) (let ((_let_21 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))) (let ((_let_22 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))) (let ((_let_23 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) (let ((_let_24 (forall ((V tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) tptp.mactual) V)) (not (ho_5 k_7 V)))))) (let ((_let_25 (ho_5 k_7 tptp.mactual))) (let ((_let_26 (not _let_25))) (let ((_let_27 (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) tptp.mactual) tptp.mactual))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_26))) (let ((_let_30 (forall ((BOUND_VARIABLE_1001 tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#u'|) BOUND_VARIABLE_1001) BOUND_VARIABLE_1001)) (ho_5 k_7 BOUND_VARIABLE_1001))))) (let ((_let_31 (ho_5 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_32 (ho_3 k_2 |tptp.'#u'|))) (let ((_let_33 (ho_5 (ho_4 _let_32 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_31))) (let ((_let_36 (not _let_35))) (let ((_let_37 (forall ((W tptp.mworld)) (ho_5 (ho_4 (ho_3 k_2 |tptp.'#u'|) W) W)))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_14)) (PREPROCESS :args ((= _let_14 _let_37)))))) (let ((_let_39 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_40 (ho_5 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_31))) (let ((_let_43 (ho_5 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_44 (and _let_43 _let_42))) (let ((_let_45 (ho_5 (ho_4 _let_32 tptp.mactual) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_43))) (let ((_let_48 (forall ((V tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#u'|) tptp.mactual) V)) (ho_5 k_8 V))))) (let ((_let_49 (and _let_48 (forall ((V tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) tptp.mactual) V)) (ho_5 k_8 V)))))) (let ((_let_50 (ho_5 k_8 tptp.mactual))) (let ((_let_51 (forall ((V tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#u'|) tptp.mactual) V)) (and (ho_5 k_8 V) (or (not (ho_5 k_6 V)) (ho_5 k_7 V))))))) (let ((_let_52 (ho_5 k_6 tptp.mactual))) (let ((_let_53 (@ tptp.charge tptp.mactual))) (let ((_let_54 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_18)) (ASSUME :args (_let_19)) (ASSUME :args (_let_20)) (ASSUME :args (_let_21)) (ASSUME :args (_let_22)) (ASSUME :args (_let_23))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_54 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (not (=> _let_53 (and (@ tptp.called tptp.mactual) (not (@ tptp.paid tptp.mactual))))) (forall ((V tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#u'|) tptp.mactual) V)) (and (@ tptp.charge V) (or (not (@ tptp.called V)) (@ tptp.paid V))))))) (not (=> (not (=> _let_50 (and _let_52 _let_26))) _let_51))))))))) (let ((_let_56 (NOT_IMPLIES_ELIM1 _let_55))) (let ((_let_57 (_let_48))) (let ((_let_58 (or _let_46 _let_44))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or))) (let ((_let_61 (not _let_51))) (let ((_let_62 (_let_61))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_62)) :args _let_62)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_51))) (REFL :args (_let_59)) :args _let_60)) (NOT_IMPLIES_ELIM2 _let_55) :args (_let_59 true _let_51)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG (REFL :args (_let_58)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_60)) :args ((or _let_45 _let_58))) _let_63 :args (_let_45 true _let_58)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_44)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_58 1)) _let_63 :args ((not _let_44) true _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_43 (not _let_47)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args _let_39) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_13)) (TRANS (MACRO_SR_EQ_INTRO _let_54 :args (_let_13 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> _let_53 (and (forall ((V tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#u'|) tptp.mactual) V)) (@ tptp.charge V))) (forall ((V tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#c'|) tptp.mactual) V)) (@ tptp.charge V))))) (=> _let_50 _let_49))))))) :args ((or _let_49 (not _let_50)))) (NOT_IMPLIES_ELIM1 _let_56) :args (_let_49 false _let_50)) :args (_let_48 false _let_49)) :args (_let_47 false _let_48)) :args (_let_43 false _let_45 false _let_47)) :args ((not _let_42) true _let_44 false _let_43)))) (let ((_let_66 (_let_30))) (let ((_let_67 (not _let_29))) (let ((_let_68 (forall ((W tptp.mworld)) (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) W) W)))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_15)) (PREPROCESS :args ((= _let_15 _let_68)))))) (let ((_let_70 (tptp.mactual QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args _let_70) :args (_let_68))) _let_69 :args (_let_27 false _let_68)))) (let ((_let_72 (or _let_28 _let_52))) (let ((_let_73 (forall ((BOUND_VARIABLE_946 tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) BOUND_VARIABLE_946) BOUND_VARIABLE_946)) (ho_5 k_6 BOUND_VARIABLE_946))))) (let ((_let_74 (forall ((V tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#u'|) tptp.mactual) V)) (not (ho_5 k_6 V)))))) (let ((_let_75 (or _let_46 _let_41))) (let ((_let_76 (not _let_75))) (let ((_let_77 (_let_74))) (let ((_let_78 (_let_73))) (let ((_let_79 (not _let_52))) (let ((_let_80 (_let_24))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args _let_70) :args _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_26 _let_28 _let_67))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (NOT_IMPLIES_ELIM2 _let_56)) (CONG (REFL :args (_let_79)) (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_60)) :args ((or _let_25 _let_79))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_52 _let_28 (not _let_72)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_78) :args (tptp.mactual QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_5 k_6 BOUND_VARIABLE_946) true))))) :args _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO _let_54 :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_946 tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#c'|) BOUND_VARIABLE_946) BOUND_VARIABLE_946)) (@ tptp.called BOUND_VARIABLE_946))) (forall ((V tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#u'|) tptp.mactual) V)) (not (@ tptp.called V))))) (or _let_73 _let_74)))))) :args ((or _let_74 _let_73))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_77) :args _let_39) :args _let_77)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_46 _let_41 _let_76))) _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_60)) :args ((or _let_40 _let_42))) _let_65 :args (_let_40 true _let_42)) :args (_let_76 false _let_45 false _let_40)) :args ((not _let_74) true _let_75)) :args (_let_73 true _let_74)) :args (_let_72 false _let_73)) :args (_let_52 false _let_27 false _let_72)) :args (_let_25 false _let_52)) _let_71 :args (_let_67 false _let_25 false _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO _let_54 :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_1001 tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#u'|) BOUND_VARIABLE_1001) BOUND_VARIABLE_1001)) (@ tptp.paid BOUND_VARIABLE_1001))) (forall ((V tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#c'|) tptp.mactual) V)) (not (@ tptp.paid V))))) (or _let_30 _let_24)))))) :args ((or _let_24 _let_30))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_66) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_5 k_7 BOUND_VARIABLE_1001) true))))) :args _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_31 _let_34 _let_36))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 1)) _let_65 :args ((not _let_31) true _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args _let_39) :args (_let_37))) _let_38 :args (_let_33 false _let_37)) :args (_let_36 true _let_31 false _let_33)) :args ((not _let_30) true _let_35)) :args (_let_24 true _let_30)) :args (false true _let_29 false _let_24)) :args (_let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel |tptp.'#c'|))) (let ((_let_2 (@ _let_1 W))) (=> (and (@ _let_2 V) (@ (@ _let_1 V) U)) (@ _let_2 U))))) _let_14 (forall ((W tptp.mworld) (V tptp.mworld) (U tptp.mworld)) (let ((_let_1 (@ tptp.mrel |tptp.'#u'|))) (let ((_let_2 (@ _let_1 W))) (=> (and (@ _let_2 V) (@ (@ _let_1 V) U)) (@ _let_2 U))))) (@ tptp.mlocal (@ _let_10 tptp.called)) _let_13 _let_12 _let_11 (@ tptp.mlocal (@ (@ tptp.mimplies _let_9) (@ _let_3 _let_9))) (@ tptp.mlocal (@ (@ tptp.mimplies _let_6) (@ _let_7 _let_6))) _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56 )
% 0.20/0.56 % SZS output end Proof for PRO029^16
% 0.20/0.56 % cvc5---1.0.5 exiting
% 0.20/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------