TSTP Solution File: SWV442^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV442^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 21:51:32 EDT 2023
% Result : Theorem 0.11s 0.44s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SWV442^1 : TPTP v8.1.2. Released v3.7.0.
% 0.02/0.08 % Command : do_cvc5 %s %d
% 0.07/0.27 % Computer : n003.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Aug 29 06:05:55 EDT 2023
% 0.11/0.27 % CPUTime :
% 0.11/0.38 %----Proving TH0
% 0.11/0.39 %------------------------------------------------------------------------------
% 0.11/0.39 % File : SWV442^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.39 % Domain : Software Verification (Security)
% 0.11/0.39 % Problem : A => A in BL
% 0.11/0.39 % Version : [Gar08] axioms.
% 0.11/0.39 % English :
% 0.11/0.39
% 0.11/0.39 % Refs : [AM+01] Alechina et al. (2001), Categorical and Kripke Semanti
% 0.11/0.39 % : [Gar08] Garg (2008), Principal-Centric Reasoning in Constructi
% 0.11/0.39 % : [Gar09] Garg (2009), Email to Geoff Sutcliffe
% 0.11/0.39 % Source : [Gar09]
% 0.11/0.39 % Names :
% 0.11/0.39
% 0.11/0.39 % Status : Theorem
% 0.11/0.39 % Rating : 0.23 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% 0.11/0.39 % Syntax : Number of formulae : 84 ( 34 unt; 43 typ; 34 def)
% 0.11/0.39 % Number of atoms : 148 ( 34 equ; 0 cnn)
% 0.11/0.39 % Maximal formula atoms : 10 ( 3 avg)
% 0.11/0.39 % Number of connectives : 117 ( 3 ~; 1 |; 2 &; 110 @)
% 0.11/0.39 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.11/0.39 % Maximal formula depth : 8 ( 2 avg)
% 0.11/0.39 % Number of types : 3 ( 1 usr)
% 0.11/0.39 % Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% 0.11/0.39 % Number of symbols : 48 ( 45 usr; 7 con; 0-3 aty)
% 0.11/0.39 % Number of variables : 64 ( 50 ^; 10 !; 4 ?; 64 :)
% 0.11/0.39 % SPC : TH0_THM_EQU_NAR
% 0.11/0.39
% 0.11/0.39 % Comments :
% 0.11/0.39 %------------------------------------------------------------------------------
% 0.11/0.39 %----Include axioms of multi-modal logic
% 0.11/0.39 %------------------------------------------------------------------------------
% 0.11/0.39 %----Our possible worlds are are encoded as terms the type $i;
% 0.11/0.39 %----Here is a constant for the current world:
% 0.11/0.39 thf(current_world,type,
% 0.11/0.39 current_world: $i ).
% 0.11/0.39
% 0.11/0.39 %----Modal logic propositions are then becoming predicates of type ( $i> $o);
% 0.11/0.39 %----We introduce some atomic multi-modal logic propositions as constants of
% 0.11/0.39 %----type ( $i> $o):
% 0.11/0.39 thf(prop_a,type,
% 0.11/0.39 prop_a: $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(prop_b,type,
% 0.11/0.39 prop_b: $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(prop_c,type,
% 0.11/0.39 prop_c: $i > $o ).
% 0.11/0.39
% 0.11/0.39 %----The idea is that an atomic multi-modal logic proposition P (of type
% 0.11/0.39 %---- $i > $o) holds at a world W (of type $i) iff W is in P resp. (P @ W)
% 0.11/0.39 %----Now we define the multi-modal logic connectives by reducing them to set
% 0.11/0.39 %----operations
% 0.11/0.39 %----mfalse corresponds to emptyset (of type $i)
% 0.11/0.39 thf(mfalse_decl,type,
% 0.11/0.39 mfalse: $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mfalse,definition,
% 0.11/0.39 ( mfalse
% 0.11/0.39 = ( ^ [X: $i] : $false ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mtrue corresponds to the universal set (of type $i)
% 0.11/0.39 thf(mtrue_decl,type,
% 0.11/0.39 mtrue: $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mtrue,definition,
% 0.11/0.39 ( mtrue
% 0.11/0.39 = ( ^ [X: $i] : $true ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mnot corresponds to set complement
% 0.11/0.39 thf(mnot_decl,type,
% 0.11/0.39 mnot: ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mnot,definition,
% 0.11/0.39 ( mnot
% 0.11/0.39 = ( ^ [X: $i > $o,U: $i] :
% 0.11/0.39 ~ ( X @ U ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mor corresponds to set union
% 0.11/0.39 thf(mor_decl,type,
% 0.11/0.39 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mor,definition,
% 0.11/0.39 ( mor
% 0.11/0.39 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.11/0.39 ( ( X @ U )
% 0.11/0.39 | ( Y @ U ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mand corresponds to set intersection
% 0.11/0.39 thf(mand_decl,type,
% 0.11/0.39 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mand,definition,
% 0.11/0.39 ( mand
% 0.11/0.39 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.11/0.39 ( ( X @ U )
% 0.11/0.39 & ( Y @ U ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mimpl defined via mnot and mor
% 0.11/0.39 thf(mimpl_decl,type,
% 0.11/0.39 mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mimpl,definition,
% 0.11/0.39 ( mimpl
% 0.11/0.39 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----miff defined via mand and mimpl
% 0.11/0.39 thf(miff_decl,type,
% 0.11/0.39 miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(miff,definition,
% 0.11/0.39 ( miff
% 0.11/0.39 = ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mbox
% 0.11/0.39 thf(mbox_decl,type,
% 0.11/0.39 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mbox,definition,
% 0.11/0.39 ( mbox
% 0.11/0.39 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.11/0.39 ! [Y: $i] :
% 0.11/0.39 ( ( R @ X @ Y )
% 0.11/0.39 => ( P @ Y ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mdia
% 0.11/0.39 thf(mdia_decl,type,
% 0.11/0.39 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mdia,definition,
% 0.11/0.39 ( mdia
% 0.11/0.39 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.11/0.39 ? [Y: $i] :
% 0.11/0.39 ( ( R @ X @ Y )
% 0.11/0.39 & ( P @ Y ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----For mall and mexists, i.e., first order modal logic, we declare a new
% 0.11/0.39 %----base type individuals
% 0.11/0.39 thf(individuals_decl,type,
% 0.11/0.39 individuals: $tType ).
% 0.11/0.39
% 0.11/0.39 %----mall
% 0.11/0.39 thf(mall_decl,type,
% 0.11/0.39 mall: ( individuals > $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mall,definition,
% 0.11/0.39 ( mall
% 0.11/0.39 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.11/0.39 ! [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----mexists
% 0.11/0.39 thf(mexists_decl,type,
% 0.11/0.39 mexists: ( individuals > $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mexists,definition,
% 0.11/0.39 ( mexists
% 0.11/0.39 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.11/0.39 ? [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----Validity of a multi modal logic formula can now be encoded as
% 0.11/0.39 thf(mvalid_decl,type,
% 0.11/0.39 mvalid: ( $i > $o ) > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mvalid,definition,
% 0.11/0.39 ( mvalid
% 0.11/0.39 = ( ^ [P: $i > $o] :
% 0.11/0.39 ! [W: $i] : ( P @ W ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----Satisfiability of a multi modal logic formula can now be encoded as
% 0.11/0.39 thf(msatisfiable_decl,type,
% 0.11/0.39 msatisfiable: ( $i > $o ) > $o ).
% 0.11/0.39
% 0.11/0.39 thf(msatisfiable,definition,
% 0.11/0.39 ( msatisfiable
% 0.11/0.39 = ( ^ [P: $i > $o] :
% 0.11/0.39 ? [W: $i] : ( P @ W ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----Countersatisfiability of a multi modal logic formula can now be encoded as
% 0.11/0.39 thf(mcountersatisfiable_decl,type,
% 0.11/0.39 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.11/0.39
% 0.11/0.39 thf(mcountersatisfiable,definition,
% 0.11/0.39 ( mcountersatisfiable
% 0.11/0.39 = ( ^ [P: $i > $o] :
% 0.11/0.39 ? [W: $i] :
% 0.11/0.39 ~ ( P @ W ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----Invalidity of a multi modal logic formula can now be encoded as
% 0.11/0.39 thf(minvalid_decl,type,
% 0.11/0.39 minvalid: ( $i > $o ) > $o ).
% 0.11/0.39
% 0.11/0.39 thf(minvalid,definition,
% 0.11/0.39 ( minvalid
% 0.11/0.39 = ( ^ [P: $i > $o] :
% 0.11/0.39 ! [W: $i] :
% 0.11/0.39 ~ ( P @ W ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %------------------------------------------------------------------------------
% 0.11/0.39 %----Include axioms translating constructive S4 (CS4) to bimodal classical
% 0.11/0.39 %----S4 (BS4)
% 0.11/0.39 %------------------------------------------------------------------------------
% 0.11/0.39 %----To encode constructive S4 into bimodal classical S4, we need two relations
% 0.11/0.39 %----reli to encode intuitionistic accessibility, and relr to encode modal
% 0.11/0.39 %----accessibility.
% 0.11/0.39 thf(reli,type,
% 0.11/0.39 reli: $i > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(relr,type,
% 0.11/0.39 relr: $i > $i > $o ).
% 0.11/0.39
% 0.11/0.39 %----We now introduce one predicate for each connective of CS4, and define the
% 0.11/0.39 %----predicates following [AM+01].
% 0.11/0.39 thf(cs4_atom_decl,type,
% 0.11/0.39 cs4_atom: ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_and_decl,type,
% 0.11/0.39 cs4_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_or_decl,type,
% 0.11/0.39 cs4_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_impl_decl,type,
% 0.11/0.39 cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_true_decl,type,
% 0.11/0.39 cs4_true: $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_false_decl,type,
% 0.11/0.39 cs4_false: $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_all_decl,type,
% 0.11/0.39 cs4_all: ( individuals > $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_box_decl,type,
% 0.11/0.39 cs4_box: ( $i > $o ) > $i > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_atom,definition,
% 0.11/0.39 ( cs4_atom
% 0.11/0.39 = ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_and,definition,
% 0.11/0.39 ( cs4_and
% 0.11/0.39 = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_or,definition,
% 0.11/0.39 ( cs4_or
% 0.11/0.39 = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_impl,definition,
% 0.11/0.39 ( cs4_impl
% 0.11/0.39 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_true,definition,
% 0.11/0.39 cs4_true = mtrue ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_false,definition,
% 0.11/0.39 cs4_false = mfalse ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_all,definition,
% 0.11/0.39 ( cs4_all
% 0.11/0.39 = ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_box,definition,
% 0.11/0.39 ( cs4_box
% 0.11/0.39 = ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----Validity in CS4
% 0.11/0.39 thf(cs4_valid_decl,type,
% 0.11/0.39 cs4_valid: ( $i > $o ) > $o ).
% 0.11/0.39
% 0.11/0.39 thf(cs4_valid_def,definition,
% 0.11/0.39 ( cs4_valid
% 0.11/0.39 = ( ^ [A: $i > $o] : ( mvalid @ A ) ) ) ).
% 0.11/0.39
% 0.11/0.39 %----Axioms to make the bimodal logic S4xS4.
% 0.11/0.39 thf(refl_axiom_i,axiom,
% 0.11/0.39 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(refl_axiom_r,axiom,
% 0.11/0.39 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ) ).
% 0.11/0.39
% 0.11/0.39 thf(trans_axiom_i,axiom,
% 0.11/0.40 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(trans_axiom_r,axiom,
% 0.11/0.40 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ ( mbox @ relr @ ( mbox @ relr @ A ) ) ) ) ).
% 0.11/0.40
% 0.11/0.40 %----Finally, we need a commutativity axiom to recover the axiom 4 in the
% 0.11/0.40 %----translation. We need: [i][r] A --> [r][i] A.
% 0.11/0.40 thf(ax_i_r_commute,axiom,
% 0.11/0.40 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ ( mbox @ relr @ A ) ) @ ( mbox @ relr @ ( mbox @ reli @ A ) ) ) ) ).
% 0.11/0.40
% 0.11/0.40 %------------------------------------------------------------------------------
% 0.11/0.40 %----Include axioms for translation from Binder Logic (BL) to CS4
% 0.11/0.40 %------------------------------------------------------------------------------
% 0.11/0.40 %----We now introduce one predicate for each connective of BL, and define the
% 0.11/0.40 %----predicates.
% 0.11/0.40 %----An injection from principals to formulas. Has no definition, it's symbolic.
% 0.11/0.40 thf(princ_inj,type,
% 0.11/0.40 princ_inj: individuals > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_atom_decl,type,
% 0.11/0.40 bl_atom: ( $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_princ_decl,type,
% 0.11/0.40 bl_princ: ( $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_and_decl,type,
% 0.11/0.40 bl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_or_decl,type,
% 0.11/0.40 bl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_impl_decl,type,
% 0.11/0.40 bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_all_decl,type,
% 0.11/0.40 bl_all: ( individuals > $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_true_decl,type,
% 0.11/0.40 bl_true: $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_false_decl,type,
% 0.11/0.40 bl_false: $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_says_decl,type,
% 0.11/0.40 bl_says: individuals > ( $i > $o ) > $i > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_atom,definition,
% 0.11/0.40 ( bl_atom
% 0.11/0.40 = ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(bl_princ,definition,
% 0.11/0.40 ( bl_princ
% 0.11/0.40 = ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(bl_and,definition,
% 0.11/0.40 ( bl_and
% 0.11/0.40 = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_and @ A @ B ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(bl_or,definition,
% 0.11/0.40 ( bl_or
% 0.11/0.40 = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_or @ A @ B ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(bl_impl,definition,
% 0.11/0.40 ( bl_impl
% 0.11/0.40 = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_impl @ A @ B ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(bl_all,definition,
% 0.11/0.40 ( bl_all
% 0.11/0.40 = ( ^ [A: individuals > $i > $o] : ( cs4_all @ A ) ) ) ).
% 0.11/0.40
% 0.11/0.40 thf(bl_true,definition,
% 0.11/0.40 bl_true = cs4_true ).
% 0.11/0.40
% 0.11/0.40 thf(bl_false,definition,
% 0.11/0.40 bl_false = cs4_false ).
% 0.11/0.40
% 0.11/0.40 thf(bl_says,definition,
% 0.11/0.40 ( bl_says
% 0.11/0.40 = ( ^ [K: individuals,A: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) ) ) ) ).
% 0.11/0.40
% 0.11/0.40 %----Validity in BL
% 0.11/0.40 thf(bl_valid_decl,type,
% 0.11/0.40 bl_valid: ( $i > $o ) > $o ).
% 0.11/0.40
% 0.11/0.40 thf(bl_valid_def,definition,
% 0.11/0.40 bl_valid = mvalid ).
% 0.11/0.40
% 0.11/0.40 %----Local authority (loca) - the strongest principal.
% 0.11/0.40 thf(loca_decl,type,
% 0.11/0.40 loca: individuals ).
% 0.11/0.40
% 0.11/0.40 %----Every principal must entail loca, this makes loca the strongest principal.
% 0.11/0.40 %----This is done by adding the CS4 axiom: forall K. [] (K => loca).
% 0.11/0.40 thf(loca_strength,axiom,
% 0.11/0.40 ( cs4_valid
% 0.11/0.40 @ ( cs4_all
% 0.11/0.40 @ ^ [K: individuals] : ( cs4_impl @ ( princ_inj @ K ) @ ( princ_inj @ loca ) ) ) ) ).
% 0.11/0.40
% 0.11/0.40 %------------------------------------------------------------------------------
% 0.11/0.40 %------------------------------------------------------------------------------
% 0.11/0.40 thf(bl_id,conjecture,
% 0.11/0.40 ! [A: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ A ) @ ( bl_atom @ A ) ) ) ).
% 0.11/0.40
% 0.11/0.40 %------------------------------------------------------------------------------
% 0.11/0.40 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.QkpG8ncVOH/cvc5---1.0.5_10350.p...
% 0.11/0.40 (declare-sort $$unsorted 0)
% 0.11/0.40 (declare-fun tptp.current_world () $$unsorted)
% 0.11/0.40 (declare-fun tptp.prop_a ($$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.prop_b ($$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.prop_c ($$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mfalse (lambda ((X $$unsorted)) false)))
% 0.11/0.40 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mtrue (lambda ((X $$unsorted)) true)))
% 0.11/0.40 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.11/0.40 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.11/0.40 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.11/0.40 (declare-fun tptp.mimpl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.11/0.40 (declare-fun tptp.miff ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))
% 0.11/0.40 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))
% 0.11/0.40 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))
% 0.11/0.40 (declare-sort tptp.individuals 0)
% 0.11/0.40 (declare-fun tptp.mall ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.11/0.40 (declare-fun tptp.mexists ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.11/0.40 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.11/0.40 (assert (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))
% 0.11/0.40 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.11/0.40 (assert (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))
% 0.11/0.40 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.11/0.40 (assert (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))
% 0.11/0.40 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.11/0.40 (assert (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))
% 0.11/0.40 (declare-fun tptp.reli ($$unsorted $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.relr ($$unsorted $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_true ($$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_false ($$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_all ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (declare-fun tptp.cs4_box ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.40 (assert (= tptp.cs4_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) P) __flatten_var_0))))
% 0.11/0.40 (assert (= tptp.cs4_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))
% 0.11/0.40 (assert (= tptp.cs4_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))
% 0.11/0.40 (assert (= tptp.cs4_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.11/0.40 (assert (= tptp.cs4_true tptp.mtrue))
% 0.11/0.40 (assert (= tptp.cs4_false tptp.mfalse))
% 0.11/0.40 (assert (= tptp.cs4_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ tptp.mall A)) __flatten_var_0))))
% 0.11/0.40 (assert (= tptp.cs4_box (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mbox tptp.relr) A)) __flatten_var_0))))
% 0.11/0.44 (declare-fun tptp.cs4_valid ((-> $$unsorted Bool)) Bool)
% 0.11/0.44 (assert (= tptp.cs4_valid (lambda ((A (-> $$unsorted Bool))) (@ tptp.mvalid A))))
% 0.11/0.44 (assert (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.reli) A)) A))))
% 0.11/0.44 (assert (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.relr) A)) A))))
% 0.11/0.44 (assert (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.reli))) (let ((_let_2 (@ _let_1 A))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))))
% 0.11/0.44 (assert (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.relr))) (let ((_let_2 (@ _let_1 A))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))))
% 0.11/0.44 (assert (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.reli))) (let ((_let_2 (@ tptp.mbox tptp.relr))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ _let_1 (@ _let_2 A))) (@ _let_2 (@ _let_1 A))))))))
% 0.11/0.44 (declare-fun tptp.princ_inj (tptp.individuals $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_princ ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_all ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_true ($$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_false ($$unsorted) Bool)
% 0.11/0.44 (declare-fun tptp.bl_says (tptp.individuals (-> $$unsorted Bool) $$unsorted) Bool)
% 0.11/0.44 (assert (= tptp.bl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))
% 0.11/0.44 (assert (= tptp.bl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))
% 0.11/0.44 (assert (= tptp.bl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_and A) B) __flatten_var_0))))
% 0.11/0.44 (assert (= tptp.bl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_or A) B) __flatten_var_0))))
% 0.11/0.44 (assert (= tptp.bl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl A) B) __flatten_var_0))))
% 0.11/0.44 (assert (= tptp.bl_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_all A) __flatten_var_0))))
% 0.11/0.44 (assert (= tptp.bl_true tptp.cs4_true))
% 0.11/0.44 (assert (= tptp.bl_false tptp.cs4_false))
% 0.11/0.44 (assert (= tptp.bl_says (lambda ((K tptp.individuals) (A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_box (@ (@ tptp.cs4_impl (@ tptp.bl_princ (@ tptp.princ_inj K))) A)) __flatten_var_0))))
% 0.11/0.44 (declare-fun tptp.bl_valid ((-> $$unsorted Bool)) Bool)
% 0.11/0.44 (assert (= tptp.bl_valid tptp.mvalid))
% 0.11/0.44 (declare-fun tptp.loca () tptp.individuals)
% 0.11/0.44 (assert (@ tptp.cs4_valid (@ tptp.cs4_all (lambda ((K tptp.individuals) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl (@ tptp.princ_inj K)) (@ tptp.princ_inj tptp.loca)) __flatten_var_0)))))
% 0.11/0.44 (assert (not (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.bl_atom A))) (@ tptp.bl_valid (@ (@ tptp.bl_impl _let_1) _let_1))))))
% 0.11/0.44 (set-info :filename cvc5---1.0.5_10350)
% 0.11/0.44 (check-sat-assuming ( true ))
% 0.11/0.44 ------- get file name : TPTP file name is SWV442^1
% 0.11/0.44 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_10350.smt2...
% 0.11/0.44 --- Run --ho-elim --full-saturate-quant at 10...
% 0.11/0.44 % SZS status Theorem for SWV442^1
% 0.11/0.44 % SZS output start Proof for SWV442^1
% 0.11/0.44 (
% 0.11/0.44 (let ((_let_1 (not (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.bl_atom A))) (@ tptp.bl_valid (@ (@ tptp.bl_impl _let_1) _let_1))))))) (let ((_let_2 (= tptp.bl_valid tptp.mvalid))) (let ((_let_3 (= tptp.bl_says (lambda ((K tptp.individuals) (A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_box (@ (@ tptp.cs4_impl (@ tptp.bl_princ (@ tptp.princ_inj K))) A)) __flatten_var_0))))) (let ((_let_4 (= tptp.bl_false tptp.cs4_false))) (let ((_let_5 (= tptp.bl_true tptp.cs4_true))) (let ((_let_6 (= tptp.bl_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_all A) __flatten_var_0))))) (let ((_let_7 (= tptp.bl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl A) B) __flatten_var_0))))) (let ((_let_8 (= tptp.bl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_or A) B) __flatten_var_0))))) (let ((_let_9 (= tptp.bl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_and A) B) __flatten_var_0))))) (let ((_let_10 (= tptp.bl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))) (let ((_let_11 (= tptp.bl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))) (let ((_let_12 (= tptp.cs4_valid (lambda ((A (-> $$unsorted Bool))) (@ tptp.mvalid A))))) (let ((_let_13 (= tptp.cs4_box (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mbox tptp.relr) A)) __flatten_var_0))))) (let ((_let_14 (= tptp.cs4_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ tptp.mall A)) __flatten_var_0))))) (let ((_let_15 (= tptp.cs4_false tptp.mfalse))) (let ((_let_16 (= tptp.cs4_true tptp.mtrue))) (let ((_let_17 (= tptp.cs4_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_18 (= tptp.cs4_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))) (let ((_let_19 (= tptp.cs4_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))) (let ((_let_20 (= tptp.cs4_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) P) __flatten_var_0))))) (let ((_let_21 (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))) (let ((_let_22 (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))) (let ((_let_23 (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))) (let ((_let_24 (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))) (let ((_let_25 (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_26 (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_27 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))) (let ((_let_28 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))) (let ((_let_29 (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))) (let ((_let_30 (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_31 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_32 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_33 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_34 (= tptp.mtrue (lambda ((X $$unsorted)) true)))) (let ((_let_35 (= tptp.mfalse (lambda ((X $$unsorted)) false)))) (let ((_let_36 (forall ((BOUND_VARIABLE_2095 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2095) BOUND_VARIABLE_2095)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 BOUND_VARIABLE_2095))))) (let ((_let_37 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_38 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (not _let_36))) (let ((_let_42 (or _let_41 _let_39 _let_37))) (let ((_let_43 (forall ((BOUND_VARIABLE_2351 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2146 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_2095 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2095) BOUND_VARIABLE_2095)) (ho_2 BOUND_VARIABLE_2351 BOUND_VARIABLE_2095)))) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2146) BOUND_VARIABLE_2146)) (ho_2 BOUND_VARIABLE_2351 BOUND_VARIABLE_2146))))) (let ((_let_44 (not _let_42))) (let ((_let_45 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (ASSUME :args (_let_33)))) (let ((_let_48 (ASSUME :args (_let_32)))) (let ((_let_49 (ASSUME :args (_let_31)))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_27)) (MACRO_SR_EQ_INTRO :args (_let_27 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (ASSUME :args (_let_26)))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (ASSUME :args (_let_24)))) (let ((_let_57 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (ASSUME :args (_let_21)))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (EQ_RESOLVE (SYMM (ASSUME :args (_let_16))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.mtrue tptp.cs4_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (SYMM (ASSUME :args (_let_15))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.mfalse tptp.cs4_false) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (SYMM (ASSUME :args (_let_5))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.cs4_true tptp.bl_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (SYMM (ASSUME :args (_let_4))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.cs4_false tptp.bl_false) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (or))) (let ((_let_79 (not _let_43))) (let ((_let_80 (_let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_80)) :args _let_80)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_43))) (REFL :args (_let_44)) :args _let_78)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (SYMM (EQ_RESOLVE (SYMM (ASSUME :args (_let_2))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.mvalid tptp.bl_valid) SB_DEFAULT SBA_FIXPOINT)))) _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (forall ((W $$unsorted) (Y $$unsorted)) (not (@ (@ tptp.reli W) Y))) (forall ((A (-> $$unsorted Bool)) (BOUND_VARIABLE_2146 $$unsorted)) (or (not (forall ((BOUND_VARIABLE_2095 $$unsorted)) (or (not (@ (@ tptp.reli BOUND_VARIABLE_2095) BOUND_VARIABLE_2095)) (@ A BOUND_VARIABLE_2095)))) (not (@ (@ tptp.reli BOUND_VARIABLE_2146) BOUND_VARIABLE_2146)) (@ A BOUND_VARIABLE_2146))))) (not (or (forall ((W $$unsorted) (Y $$unsorted)) (not (ho_2 (ho_4 k_3 W) Y))) _let_43))))))) :args (1)) :args (_let_44 true _let_43)))) (let ((_let_82 (REFL :args (_let_42)))) (let ((_let_83 (not _let_40))) (let ((_let_84 (_let_36))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 _let_83))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_82 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_78)) :args ((or _let_38 _let_42))) _let_81 :args (_let_38 true _let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 2)) _let_81 :args ((not _let_37) true _let_42)) :args (_let_83 false _let_38 true _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_82 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_36))) :args _let_78)) :args ((or _let_36 _let_42))) _let_81 :args (_let_36 true _let_42)) :args (false true _let_40 false _let_36)) :args (_let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.reli) A)) A))) (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.relr) A)) A))) (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.reli))) (let ((_let_2 (@ _let_1 A))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))) (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.relr))) (let ((_let_2 (@ _let_1 A))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))) (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.reli))) (let ((_let_2 (@ tptp.mbox tptp.relr))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ _let_1 (@ _let_2 A))) (@ _let_2 (@ _let_1 A))))))) _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 (@ tptp.cs4_valid (@ tptp.cs4_all (lambda ((K tptp.individuals) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl (@ tptp.princ_inj K)) (@ tptp.princ_inj tptp.loca)) __flatten_var_0)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.11/0.44 )
% 0.11/0.44 % SZS output end Proof for SWV442^1
% 0.11/0.44 % cvc5---1.0.5 exiting
% 0.11/0.44 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------