TSTP Solution File: PUZ150^18 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : PUZ150^18 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 13:13:37 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ150^18 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 22:34:57 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.19/0.48 %----Proving TH0
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : PUZ150^18 : TPTP v8.1.2. Released v8.1.0.
% 0.19/0.48 % Domain : Puzzles
% 0.19/0.48 % Problem : Russian card problem (very simple variant)
% 0.19/0.48 % Version : [BP13] axioms.
% 0.19/0.48 % English : Anne, Bill and Cath draw 0, 1, and 2. Anne knows that Bill knows
% 0.19/0.48 % that Cath knows her own card, etc. Anne has card 0. Then Bill
% 0.19/0.48 % knows that Anne does not consider it possible that Bill considers
% 0.19/0.48 % it possible that Cath knows that Anne does not have card 0.
% 0.19/0.48
% 0.19/0.48 % Refs : [vDK06] van Ditmarsch & Kooi (2006), The Secret of My Success
% 0.19/0.48 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.19/0.48 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.19/0.48 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.19/0.48 % Source : [TPTP]
% 0.19/0.48 % Names : MML007+1 [QMLTP]
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.31 v8.1.0
% 0.19/0.48 % Syntax : Number of formulae : 45 ( 11 unt; 25 typ; 8 def)
% 0.19/0.48 % Number of atoms : 108 ( 8 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 11 ( 5 avg)
% 0.19/0.48 % Number of connectives : 151 ( 1 ~; 1 |; 2 &; 144 @)
% 0.19/0.48 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 9 ( 5 avg)
% 0.19/0.48 % Number of types : 3 ( 2 usr)
% 0.19/0.48 % Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 24 ( 23 usr; 4 con; 0-3 aty)
% 0.19/0.48 % Number of variables : 29 ( 21 ^; 7 !; 1 ?; 29 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.19/0.48 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.19/0.48 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.19/0.48 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.19/0.48 % $modalities == $modal_system_S5U].
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(mworld,type,
% 0.19/0.48 mworld: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(mindex,type,
% 0.19/0.48 mindex: $tType ).
% 0.19/0.48
% 0.19/0.48 thf(mrel_type,type,
% 0.19/0.48 mrel: mindex > mworld > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf('#c_type',type,
% 0.19/0.48 '#c': mindex ).
% 0.19/0.48
% 0.19/0.48 thf('#b_type',type,
% 0.19/0.48 '#b': mindex ).
% 0.19/0.48
% 0.19/0.48 thf('#a_type',type,
% 0.19/0.48 '#a': mindex ).
% 0.19/0.48
% 0.19/0.48 thf(mactual_type,type,
% 0.19/0.48 mactual: mworld ).
% 0.19/0.48
% 0.19/0.48 thf(mlocal_type,type,
% 0.19/0.48 mlocal: ( mworld > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mlocal_def,definition,
% 0.19/0.48 ( mlocal
% 0.19/0.48 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mnot_type,type,
% 0.19/0.48 mnot: ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mand_type,type,
% 0.19/0.48 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mor_type,type,
% 0.19/0.48 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mimplies_type,type,
% 0.19/0.48 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mequiv_type,type,
% 0.19/0.48 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mnot_def,definition,
% 0.19/0.48 ( mnot
% 0.19/0.48 = ( ^ [A: mworld > $o,W: mworld] :
% 0.19/0.48 ~ ( A @ W ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mand_def,definition,
% 0.19/0.48 ( mand
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 & ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mor_def,definition,
% 0.19/0.48 ( mor
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 | ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mimplies_def,definition,
% 0.19/0.48 ( mimplies
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 => ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mequiv_def,definition,
% 0.19/0.48 ( mequiv
% 0.19/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.48 ( ( A @ W )
% 0.19/0.48 <=> ( B @ W ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mbox_type,type,
% 0.19/0.48 mbox: mindex > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mbox_def,definition,
% 0.19/0.48 ( mbox
% 0.19/0.48 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.19/0.48 ! [V: mworld] :
% 0.19/0.48 ( ( mrel @ R @ W @ V )
% 0.19/0.48 => ( Phi @ V ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(mdia_type,type,
% 0.19/0.48 mdia: mindex > ( mworld > $o ) > mworld > $o ).
% 0.19/0.48
% 0.19/0.48 thf(mdia_def,definition,
% 0.19/0.48 ( mdia
% 0.19/0.48 = ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
% 0.19/0.48 ? [V: mworld] :
% 0.19/0.48 ( ( mrel @ R @ W @ V )
% 0.19/0.49 & ( Phi @ V ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf('mrel_#c_universal',axiom,
% 0.19/0.49 ! [W: mworld,V: mworld] : ( mrel @ '#c' @ W @ V ) ).
% 0.19/0.49
% 0.19/0.49 thf('mrel_#b_universal',axiom,
% 0.19/0.49 ! [W: mworld,V: mworld] : ( mrel @ '#b' @ W @ V ) ).
% 0.19/0.49
% 0.19/0.49 thf('mrel_#a_universal',axiom,
% 0.19/0.49 ! [W: mworld,V: mworld] : ( mrel @ '#a' @ W @ V ) ).
% 0.19/0.49
% 0.19/0.49 %%% This output was generated by tptputils, version 1.2.
% 0.19/0.49 %%% Generated on Wed Apr 27 15:49:37 CEST 2022 using command 'downgrade(tff)'.
% 0.19/0.49 thf(c0_decl,type,
% 0.19/0.49 c0: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(c1_decl,type,
% 0.19/0.49 c1: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(b0_decl,type,
% 0.19/0.49 b0: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(c2_decl,type,
% 0.19/0.49 c2: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(b1_decl,type,
% 0.19/0.49 b1: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(a0_decl,type,
% 0.19/0.49 a0: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(b2_decl,type,
% 0.19/0.49 b2: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(a1_decl,type,
% 0.19/0.49 a1: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(a2_decl,type,
% 0.19/0.49 a2: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(cb_decl,type,
% 0.19/0.49 cb: mworld > $o ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_a_b_c,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#a' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_b_a_c,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#b' @ ( mbox @ '#a' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_a_b_c_0,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#a' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_a_c_b,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#a' @ ( mbox @ '#c' @ ( mor @ ( mbox @ '#b' @ b0 ) @ ( mor @ ( mbox @ '#b' @ b1 ) @ ( mbox @ '#b' @ b2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_c_a_b,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#c' @ ( mbox @ '#a' @ ( mor @ ( mbox @ '#b' @ cb ) @ ( mor @ ( mbox @ '#b' @ b1 ) @ ( mbox @ '#b' @ b2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_c_b_a,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#c' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#a' @ a0 ) @ ( mor @ ( mbox @ '#a' @ a1 ) @ ( mbox @ '#a' @ a2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_knows_b_c_a,axiom,
% 0.19/0.49 mlocal @ ( mbox @ '#b' @ ( mbox @ '#c' @ ( mor @ ( mbox @ '#a' @ a0 ) @ ( mor @ ( mbox @ '#a' @ a1 ) @ ( mbox @ '#a' @ a2 ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 thf(axiom_a0,axiom,
% 0.19/0.49 mlocal @ a0 ).
% 0.19/0.49
% 0.19/0.49 thf(con,conjecture,
% 0.19/0.49 mlocal @ ( mbox @ '#b' @ ( mnot @ ( mdia @ '#a' @ ( mdia @ '#b' @ ( mbox @ '#c' @ ( mnot @ a0 ) ) ) ) ) ) ).
% 0.19/0.49
% 0.19/0.49 %------------------------------------------------------------------------------
% 0.19/0.49 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.M0QheyBLUe/cvc5---1.0.5_28620.p...
% 0.19/0.49 (declare-sort $$unsorted 0)
% 0.19/0.49 (declare-sort tptp.mworld 0)
% 0.19/0.49 (declare-sort tptp.mindex 0)
% 0.19/0.49 (declare-fun tptp.mrel (tptp.mindex tptp.mworld tptp.mworld) Bool)
% 0.19/0.49 (declare-fun |tptp.'#c'| () tptp.mindex)
% 0.19/0.49 (declare-fun |tptp.'#b'| () tptp.mindex)
% 0.19/0.49 (declare-fun |tptp.'#a'| () tptp.mindex)
% 0.19/0.49 (declare-fun tptp.mactual () tptp.mworld)
% 0.19/0.49 (declare-fun tptp.mlocal ((-> tptp.mworld Bool)) Bool)
% 0.19/0.49 (assert (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))
% 0.19/0.49 (declare-fun tptp.mnot ((-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.49 (declare-fun tptp.mand ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.49 (declare-fun tptp.mor ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.49 (declare-fun tptp.mimplies ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.49 (declare-fun tptp.mequiv ((-> tptp.mworld Bool) (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.49 (assert (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))
% 0.19/0.49 (assert (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))
% 0.19/0.49 (assert (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))
% 0.19/0.49 (assert (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))
% 0.19/0.49 (assert (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))
% 0.19/0.49 (declare-fun tptp.mbox (tptp.mindex (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.49 (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))))))
% 0.19/0.57 (declare-fun tptp.mdia (tptp.mindex (-> tptp.mworld Bool) tptp.mworld) Bool)
% 0.19/0.57 (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))))))
% 0.19/0.57 (assert (forall ((W tptp.mworld) (V tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#c'|) W) V)))
% 0.19/0.57 (assert (forall ((W tptp.mworld) (V tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#b'|) W) V)))
% 0.19/0.57 (assert (forall ((W tptp.mworld) (V tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#a'|) W) V)))
% 0.19/0.57 (declare-fun tptp.c0 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.c1 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.b0 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.c2 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.b1 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.a0 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.b2 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.a1 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.a2 (tptp.mworld) Bool)
% 0.19/0.57 (declare-fun tptp.cb (tptp.mworld) Bool)
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#c'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#a'|) (@ (@ tptp.mbox |tptp.'#b'|) (@ (@ tptp.mor (@ _let_1 tptp.c0)) (@ (@ tptp.mor (@ _let_1 tptp.c1)) (@ _let_1 tptp.c2))))))))
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#c'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#b'|) (@ (@ tptp.mbox |tptp.'#a'|) (@ (@ tptp.mor (@ _let_1 tptp.c0)) (@ (@ tptp.mor (@ _let_1 tptp.c1)) (@ _let_1 tptp.c2))))))))
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#c'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#a'|) (@ (@ tptp.mbox |tptp.'#b'|) (@ (@ tptp.mor (@ _let_1 tptp.c0)) (@ (@ tptp.mor (@ _let_1 tptp.c1)) (@ _let_1 tptp.c2))))))))
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#b'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#a'|) (@ (@ tptp.mbox |tptp.'#c'|) (@ (@ tptp.mor (@ _let_1 tptp.b0)) (@ (@ tptp.mor (@ _let_1 tptp.b1)) (@ _let_1 tptp.b2))))))))
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#b'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#c'|) (@ (@ tptp.mbox |tptp.'#a'|) (@ (@ tptp.mor (@ _let_1 tptp.cb)) (@ (@ tptp.mor (@ _let_1 tptp.b1)) (@ _let_1 tptp.b2))))))))
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#a'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#c'|) (@ (@ tptp.mbox |tptp.'#b'|) (@ (@ tptp.mor (@ _let_1 tptp.a0)) (@ (@ tptp.mor (@ _let_1 tptp.a1)) (@ _let_1 tptp.a2))))))))
% 0.19/0.57 (assert (let ((_let_1 (@ tptp.mbox |tptp.'#a'|))) (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#b'|) (@ (@ tptp.mbox |tptp.'#c'|) (@ (@ tptp.mor (@ _let_1 tptp.a0)) (@ (@ tptp.mor (@ _let_1 tptp.a1)) (@ _let_1 tptp.a2))))))))
% 0.19/0.57 (assert (@ tptp.mlocal tptp.a0))
% 0.19/0.57 (assert (not (@ tptp.mlocal (@ (@ tptp.mbox |tptp.'#b'|) (@ tptp.mnot (@ (@ tptp.mdia |tptp.'#a'|) (@ (@ tptp.mdia |tptp.'#b'|) (@ (@ tptp.mbox |tptp.'#c'|) (@ tptp.mnot tptp.a0)))))))))
% 0.19/0.57 (set-info :filename cvc5---1.0.5_28620)
% 0.19/0.57 (check-sat-assuming ( true ))
% 0.19/0.57 ------- get file name : TPTP file name is PUZ150^18
% 0.19/0.57 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28620.smt2...
% 0.19/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.57 % SZS status Theorem for PUZ150^18
% 0.19/0.57 % SZS output start Proof for PUZ150^18
% 0.19/0.57 (
% 0.19/0.57 (let ((_let_1 (@ tptp.mbox |tptp.'#c'|))) (let ((_let_2 (@ tptp.mbox |tptp.'#b'|))) (let ((_let_3 (not (@ tptp.mlocal (@ _let_2 (@ tptp.mnot (@ (@ tptp.mdia |tptp.'#a'|) (@ (@ tptp.mdia |tptp.'#b'|) (@ _let_1 (@ tptp.mnot tptp.a0)))))))))) (let ((_let_4 (@ tptp.mlocal tptp.a0))) (let ((_let_5 (@ tptp.mbox |tptp.'#a'|))) (let ((_let_6 (@ (@ tptp.mor (@ _let_5 tptp.a0)) (@ (@ tptp.mor (@ _let_5 tptp.a1)) (@ _let_5 tptp.a2))))) (let ((_let_7 (@ (@ tptp.mor (@ _let_2 tptp.b1)) (@ _let_2 tptp.b2)))) (let ((_let_8 (@ (@ tptp.mor (@ _let_1 tptp.c0)) (@ (@ tptp.mor (@ _let_1 tptp.c1)) (@ _let_1 tptp.c2))))) (let ((_let_9 (@ tptp.mlocal (@ _let_5 (@ _let_2 _let_8))))) (let ((_let_10 (forall ((W tptp.mworld) (V tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#c'|) W) V)))) (let ((_let_11 (= 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_12 (= 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_13 (= tptp.mequiv (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (= (@ A W) (@ B W)))))) (let ((_let_14 (= tptp.mimplies (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (=> (@ A W) (@ B W)))))) (let ((_let_15 (= tptp.mor (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (or (@ A W) (@ B W)))))) (let ((_let_16 (= tptp.mand (lambda ((A (-> tptp.mworld Bool)) (B (-> tptp.mworld Bool)) (W tptp.mworld)) (and (@ A W) (@ B W)))))) (let ((_let_17 (= tptp.mnot (lambda ((A (-> tptp.mworld Bool)) (W tptp.mworld)) (not (@ A W)))))) (let ((_let_18 (= tptp.mlocal (lambda ((Phi (-> tptp.mworld Bool))) (@ Phi tptp.mactual))))) (let ((_let_19 (forall ((W tptp.mworld) (V tptp.mworld)) (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) W) V)))) (let ((_let_20 (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) tptp.mactual))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_19)))))) (let ((_let_22 (ho_5 k_15 tptp.mactual))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_20))) (let ((_let_25 (or _let_24 _let_23))) (let ((_let_26 (forall ((BOUND_VARIABLE_1622 tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) BOUND_VARIABLE_1622)) (not (ho_5 k_15 BOUND_VARIABLE_1622)))))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#b'|) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) _let_27))) (let ((_let_29 (forall ((BOUND_VARIABLE_1578 tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#b'|) BOUND_VARIABLE_1578) BOUND_VARIABLE_1578)) (not (forall ((BOUND_VARIABLE_1622 tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#c'|) BOUND_VARIABLE_1578) BOUND_VARIABLE_1622)) (not (ho_5 k_15 BOUND_VARIABLE_1622))))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_13)) (ASSUME :args (_let_14)) (ASSUME :args (_let_15)) (ASSUME :args (_let_16)) (ASSUME :args (_let_17)) (ASSUME :args (_let_18))))) (let ((_let_32 (or))) (let ((_let_33 (not _let_29))) (let ((_let_34 (_let_33))) (let ((_let_35 (_let_26))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 tptp.mactual QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_19))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_23 _let_24 (not _let_25)))) (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_31 :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ tptp.a0 tptp.mactual) _let_22))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_35) :args (tptp.mactual QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_5 k_15 BOUND_VARIABLE_1622) false))))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG (REFL :args (_let_28)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_32)) :args ((or _let_26 _let_28))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_34)) :args _let_34)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_29))) (REFL :args (_let_30)) :args _let_32)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_31 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (forall ((BOUND_VARIABLE_1578 tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#b'|) BOUND_VARIABLE_1578) BOUND_VARIABLE_1578)) (not (forall ((BOUND_VARIABLE_1622 tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#c'|) BOUND_VARIABLE_1578) BOUND_VARIABLE_1622)) (not (@ tptp.a0 BOUND_VARIABLE_1622))))))) (forall ((V tptp.mworld) (BOUND_VARIABLE_1639 tptp.mworld)) (or (not (@ (@ (@ tptp.mrel |tptp.'#b'|) tptp.mactual) V)) (not (@ (@ (@ tptp.mrel |tptp.'#a'|) V) BOUND_VARIABLE_1639)))))) (not (or _let_29 (forall ((V tptp.mworld) (BOUND_VARIABLE_1639 tptp.mworld)) (or (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#b'|) tptp.mactual) V)) (not (ho_5 (ho_4 (ho_3 k_2 |tptp.'#a'|) V) BOUND_VARIABLE_1639))))))))))) :args (0)) :args (_let_30 true _let_29)) :args (_let_26 true _let_28)) :args (_let_25 false _let_26)) :args (_let_24 false _let_22 false _let_25)) _let_21 :args (false true _let_20 false _let_19)) :args (_let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 (forall ((W tptp.mworld) (V tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#b'|) W) V)) (forall ((W tptp.mworld) (V tptp.mworld)) (@ (@ (@ tptp.mrel |tptp.'#a'|) W) V)) _let_9 (@ tptp.mlocal (@ _let_2 (@ _let_5 _let_8))) _let_9 (@ tptp.mlocal (@ _let_5 (@ _let_1 (@ (@ tptp.mor (@ _let_2 tptp.b0)) _let_7)))) (@ tptp.mlocal (@ _let_1 (@ _let_5 (@ (@ tptp.mor (@ _let_2 tptp.cb)) _let_7)))) (@ tptp.mlocal (@ _let_1 (@ _let_2 _let_6))) (@ tptp.mlocal (@ _let_2 (@ _let_1 _let_6))) _let_4 _let_3 true))))))))))))))))))))))))))))))))))))))
% 0.19/0.58 )
% 0.19/0.58 % SZS output end Proof for PUZ150^18
% 0.19/0.58 % cvc5---1.0.5 exiting
% 0.19/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------