TSTP Solution File: SWV444^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWV444^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n011.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 21:51:33 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV444^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n011.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 : Tue Aug 29 06:27:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : SWV444^1 : TPTP v8.1.2. Released v3.7.0.
% 0.20/0.49 % Domain : Software Verification (Security)
% 0.20/0.49 % Problem : (loca says A) => (K says A) in BL
% 0.20/0.49 % Version : [Gar08] axioms.
% 0.20/0.49 % English :
% 0.20/0.49
% 0.20/0.49 % Refs : [AM+01] Alechina et al. (2001), Categorical and Kripke Semanti
% 0.20/0.49 % : [Gar08] Garg (2008), Principal-Centric Reasoning in Constructi
% 0.20/0.49 % : [Gar09] Garg (2009), Email to Geoff Sutcliffe
% 0.20/0.49 % Source : [Gar09]
% 0.20/0.49 % Names :
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % Rating : 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.71 v6.1.0, 0.57 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.20/0.49 % Syntax : Number of formulae : 84 ( 34 unt; 43 typ; 34 def)
% 0.20/0.49 % Number of atoms : 152 ( 34 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 10 ( 3 avg)
% 0.20/0.49 % Number of connectives : 121 ( 3 ~; 1 |; 2 &; 114 @)
% 0.20/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 8 ( 2 avg)
% 0.20/0.49 % Number of types : 3 ( 1 usr)
% 0.20/0.49 % Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 50 ( 47 usr; 9 con; 0-3 aty)
% 0.20/0.49 % Number of variables : 65 ( 50 ^; 11 !; 4 ?; 65 :)
% 0.20/0.49 % SPC : TH0_THM_EQU_NAR
% 0.20/0.49
% 0.20/0.49 % Comments :
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 %----Include axioms of multi-modal logic
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 %----Our possible worlds are are encoded as terms the type $i;
% 0.20/0.49 %----Here is a constant for the current world:
% 0.20/0.49 thf(current_world,type,
% 0.20/0.49 current_world: $i ).
% 0.20/0.49
% 0.20/0.49 %----Modal logic propositions are then becoming predicates of type ( $i> $o);
% 0.20/0.49 %----We introduce some atomic multi-modal logic propositions as constants of
% 0.20/0.49 %----type ( $i> $o):
% 0.20/0.49 thf(prop_a,type,
% 0.20/0.49 prop_a: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(prop_b,type,
% 0.20/0.49 prop_b: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(prop_c,type,
% 0.20/0.49 prop_c: $i > $o ).
% 0.20/0.49
% 0.20/0.49 %----The idea is that an atomic multi-modal logic proposition P (of type
% 0.20/0.49 %---- $i > $o) holds at a world W (of type $i) iff W is in P resp. (P @ W)
% 0.20/0.49 %----Now we define the multi-modal logic connectives by reducing them to set
% 0.20/0.49 %----operations
% 0.20/0.49 %----mfalse corresponds to emptyset (of type $i)
% 0.20/0.49 thf(mfalse_decl,type,
% 0.20/0.49 mfalse: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mfalse,definition,
% 0.20/0.49 ( mfalse
% 0.20/0.49 = ( ^ [X: $i] : $false ) ) ).
% 0.20/0.49
% 0.20/0.49 %----mtrue corresponds to the universal set (of type $i)
% 0.20/0.49 thf(mtrue_decl,type,
% 0.20/0.49 mtrue: $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mtrue,definition,
% 0.20/0.49 ( mtrue
% 0.20/0.49 = ( ^ [X: $i] : $true ) ) ).
% 0.20/0.49
% 0.20/0.49 %----mnot corresponds to set complement
% 0.20/0.49 thf(mnot_decl,type,
% 0.20/0.49 mnot: ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mnot,definition,
% 0.20/0.49 ( mnot
% 0.20/0.49 = ( ^ [X: $i > $o,U: $i] :
% 0.20/0.49 ~ ( X @ U ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----mor corresponds to set union
% 0.20/0.49 thf(mor_decl,type,
% 0.20/0.49 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mor,definition,
% 0.20/0.49 ( mor
% 0.20/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.20/0.49 ( ( X @ U )
% 0.20/0.49 | ( Y @ U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----mand corresponds to set intersection
% 0.20/0.49 thf(mand_decl,type,
% 0.20/0.49 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mand,definition,
% 0.20/0.49 ( mand
% 0.20/0.49 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.20/0.49 ( ( X @ U )
% 0.20/0.49 & ( Y @ U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----mimpl defined via mnot and mor
% 0.20/0.49 thf(mimpl_decl,type,
% 0.20/0.49 mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mimpl,definition,
% 0.20/0.49 ( mimpl
% 0.20/0.49 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----miff defined via mand and mimpl
% 0.20/0.49 thf(miff_decl,type,
% 0.20/0.49 miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(miff,definition,
% 0.20/0.49 ( miff
% 0.20/0.49 = ( ^ [U: $i > $o,V: $i > $o] : ( mand @ ( mimpl @ U @ V ) @ ( mimpl @ V @ U ) ) ) ) ).
% 0.20/0.49
% 0.20/0.49 %----mbox
% 0.20/0.49 thf(mbox_decl,type,
% 0.20/0.49 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.49
% 0.20/0.49 thf(mbox,definition,
% 0.20/0.49 ( mbox
% 0.20/0.49 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.20/0.49 ! [Y: $i] :
% 0.20/0.49 ( ( R @ X @ Y )
% 0.20/0.49 => ( P @ Y ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----mdia
% 0.20/0.50 thf(mdia_decl,type,
% 0.20/0.50 mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mdia,definition,
% 0.20/0.50 ( mdia
% 0.20/0.50 = ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
% 0.20/0.50 ? [Y: $i] :
% 0.20/0.50 ( ( R @ X @ Y )
% 0.20/0.50 & ( P @ Y ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----For mall and mexists, i.e., first order modal logic, we declare a new
% 0.20/0.50 %----base type individuals
% 0.20/0.50 thf(individuals_decl,type,
% 0.20/0.50 individuals: $tType ).
% 0.20/0.50
% 0.20/0.50 %----mall
% 0.20/0.50 thf(mall_decl,type,
% 0.20/0.50 mall: ( individuals > $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mall,definition,
% 0.20/0.50 ( mall
% 0.20/0.50 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.20/0.50 ! [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----mexists
% 0.20/0.50 thf(mexists_decl,type,
% 0.20/0.50 mexists: ( individuals > $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mexists,definition,
% 0.20/0.50 ( mexists
% 0.20/0.50 = ( ^ [P: individuals > $i > $o,W: $i] :
% 0.20/0.50 ? [X: individuals] : ( P @ X @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Validity of a multi modal logic formula can now be encoded as
% 0.20/0.50 thf(mvalid_decl,type,
% 0.20/0.50 mvalid: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mvalid,definition,
% 0.20/0.50 ( mvalid
% 0.20/0.50 = ( ^ [P: $i > $o] :
% 0.20/0.50 ! [W: $i] : ( P @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Satisfiability of a multi modal logic formula can now be encoded as
% 0.20/0.50 thf(msatisfiable_decl,type,
% 0.20/0.50 msatisfiable: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(msatisfiable,definition,
% 0.20/0.50 ( msatisfiable
% 0.20/0.50 = ( ^ [P: $i > $o] :
% 0.20/0.50 ? [W: $i] : ( P @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Countersatisfiability of a multi modal logic formula can now be encoded as
% 0.20/0.50 thf(mcountersatisfiable_decl,type,
% 0.20/0.50 mcountersatisfiable: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(mcountersatisfiable,definition,
% 0.20/0.50 ( mcountersatisfiable
% 0.20/0.50 = ( ^ [P: $i > $o] :
% 0.20/0.50 ? [W: $i] :
% 0.20/0.50 ~ ( P @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Invalidity of a multi modal logic formula can now be encoded as
% 0.20/0.50 thf(minvalid_decl,type,
% 0.20/0.50 minvalid: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(minvalid,definition,
% 0.20/0.50 ( minvalid
% 0.20/0.50 = ( ^ [P: $i > $o] :
% 0.20/0.50 ! [W: $i] :
% 0.20/0.50 ~ ( P @ W ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %----Include axioms translating constructive S4 (CS4) to bimodal classical
% 0.20/0.50 %----S4 (BS4)
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 %----To encode constructive S4 into bimodal classical S4, we need two relations
% 0.20/0.50 %----reli to encode intuitionistic accessibility, and relr to encode modal
% 0.20/0.50 %----accessibility.
% 0.20/0.50 thf(reli,type,
% 0.20/0.50 reli: $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(relr,type,
% 0.20/0.50 relr: $i > $i > $o ).
% 0.20/0.50
% 0.20/0.50 %----We now introduce one predicate for each connective of CS4, and define the
% 0.20/0.50 %----predicates following [AM+01].
% 0.20/0.50 thf(cs4_atom_decl,type,
% 0.20/0.50 cs4_atom: ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_and_decl,type,
% 0.20/0.50 cs4_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_or_decl,type,
% 0.20/0.50 cs4_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_impl_decl,type,
% 0.20/0.50 cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_true_decl,type,
% 0.20/0.50 cs4_true: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_false_decl,type,
% 0.20/0.50 cs4_false: $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_all_decl,type,
% 0.20/0.50 cs4_all: ( individuals > $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_box_decl,type,
% 0.20/0.50 cs4_box: ( $i > $o ) > $i > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_atom,definition,
% 0.20/0.50 ( cs4_atom
% 0.20/0.50 = ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_and,definition,
% 0.20/0.50 ( cs4_and
% 0.20/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mand @ A @ B ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_or,definition,
% 0.20/0.50 ( cs4_or
% 0.20/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mor @ A @ B ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_impl,definition,
% 0.20/0.50 ( cs4_impl
% 0.20/0.50 = ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_true,definition,
% 0.20/0.50 cs4_true = mtrue ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_false,definition,
% 0.20/0.50 cs4_false = mfalse ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_all,definition,
% 0.20/0.50 ( cs4_all
% 0.20/0.50 = ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_box,definition,
% 0.20/0.50 ( cs4_box
% 0.20/0.50 = ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Validity in CS4
% 0.20/0.50 thf(cs4_valid_decl,type,
% 0.20/0.50 cs4_valid: ( $i > $o ) > $o ).
% 0.20/0.50
% 0.20/0.50 thf(cs4_valid_def,definition,
% 0.20/0.50 ( cs4_valid
% 0.20/0.50 = ( ^ [A: $i > $o] : ( mvalid @ A ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %----Axioms to make the bimodal logic S4xS4.
% 0.20/0.50 thf(refl_axiom_i,axiom,
% 0.20/0.50 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ) ).
% 0.20/0.50
% 0.20/0.50 thf(refl_axiom_r,axiom,
% 0.20/0.50 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(trans_axiom_i,axiom,
% 0.20/0.51 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(trans_axiom_r,axiom,
% 0.20/0.51 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ ( mbox @ relr @ ( mbox @ relr @ A ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %----Finally, we need a commutativity axiom to recover the axiom 4 in the
% 0.20/0.51 %----translation. We need: [i][r] A --> [r][i] A.
% 0.20/0.51 thf(ax_i_r_commute,axiom,
% 0.20/0.51 ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ ( mbox @ relr @ A ) ) @ ( mbox @ relr @ ( mbox @ reli @ A ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 %----Include axioms for translation from Binder Logic (BL) to CS4
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 %----We now introduce one predicate for each connective of BL, and define the
% 0.20/0.51 %----predicates.
% 0.20/0.51 %----An injection from principals to formulas. Has no definition, it's symbolic.
% 0.20/0.51 thf(princ_inj,type,
% 0.20/0.51 princ_inj: individuals > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_atom_decl,type,
% 0.20/0.51 bl_atom: ( $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_princ_decl,type,
% 0.20/0.51 bl_princ: ( $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_and_decl,type,
% 0.20/0.51 bl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_or_decl,type,
% 0.20/0.51 bl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_impl_decl,type,
% 0.20/0.51 bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_all_decl,type,
% 0.20/0.51 bl_all: ( individuals > $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_true_decl,type,
% 0.20/0.51 bl_true: $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_false_decl,type,
% 0.20/0.51 bl_false: $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_says_decl,type,
% 0.20/0.51 bl_says: individuals > ( $i > $o ) > $i > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_atom,definition,
% 0.20/0.51 ( bl_atom
% 0.20/0.51 = ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(bl_princ,definition,
% 0.20/0.51 ( bl_princ
% 0.20/0.51 = ( ^ [P: $i > $o] : ( cs4_atom @ P ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(bl_and,definition,
% 0.20/0.51 ( bl_and
% 0.20/0.51 = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_and @ A @ B ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(bl_or,definition,
% 0.20/0.51 ( bl_or
% 0.20/0.51 = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_or @ A @ B ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(bl_impl,definition,
% 0.20/0.51 ( bl_impl
% 0.20/0.51 = ( ^ [A: $i > $o,B: $i > $o] : ( cs4_impl @ A @ B ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(bl_all,definition,
% 0.20/0.51 ( bl_all
% 0.20/0.51 = ( ^ [A: individuals > $i > $o] : ( cs4_all @ A ) ) ) ).
% 0.20/0.51
% 0.20/0.51 thf(bl_true,definition,
% 0.20/0.51 bl_true = cs4_true ).
% 0.20/0.51
% 0.20/0.51 thf(bl_false,definition,
% 0.20/0.51 bl_false = cs4_false ).
% 0.20/0.51
% 0.20/0.51 thf(bl_says,definition,
% 0.20/0.51 ( bl_says
% 0.20/0.51 = ( ^ [K: individuals,A: $i > $o] : ( cs4_box @ ( cs4_impl @ ( bl_princ @ ( princ_inj @ K ) ) @ A ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %----Validity in BL
% 0.20/0.51 thf(bl_valid_decl,type,
% 0.20/0.51 bl_valid: ( $i > $o ) > $o ).
% 0.20/0.51
% 0.20/0.51 thf(bl_valid_def,definition,
% 0.20/0.51 bl_valid = mvalid ).
% 0.20/0.51
% 0.20/0.51 %----Local authority (loca) - the strongest principal.
% 0.20/0.51 thf(loca_decl,type,
% 0.20/0.51 loca: individuals ).
% 0.20/0.51
% 0.20/0.51 %----Every principal must entail loca, this makes loca the strongest principal.
% 0.20/0.51 %----This is done by adding the CS4 axiom: forall K. [] (K => loca).
% 0.20/0.51 thf(loca_strength,axiom,
% 0.20/0.51 ( cs4_valid
% 0.20/0.51 @ ( cs4_all
% 0.20/0.51 @ ^ [K: individuals] : ( cs4_impl @ ( princ_inj @ K ) @ ( princ_inj @ loca ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 thf(bl_strength,conjecture,
% 0.20/0.51 ! [K: individuals,A: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_says @ loca @ ( bl_atom @ A ) ) @ ( bl_says @ K @ ( bl_atom @ A ) ) ) ) ).
% 0.20/0.51
% 0.20/0.51 %------------------------------------------------------------------------------
% 0.20/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.LZsROZ81rT/cvc5---1.0.5_13074.p...
% 0.20/0.51 (declare-sort $$unsorted 0)
% 0.20/0.51 (declare-fun tptp.current_world () $$unsorted)
% 0.20/0.51 (declare-fun tptp.prop_a ($$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.prop_b ($$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.prop_c ($$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.mfalse ($$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mfalse (lambda ((X $$unsorted)) false)))
% 0.20/0.51 (declare-fun tptp.mtrue ($$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mtrue (lambda ((X $$unsorted)) true)))
% 0.20/0.51 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.20/0.51 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.20/0.51 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.20/0.51 (declare-fun tptp.mimpl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.20/0.51 (declare-fun tptp.miff ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))
% 0.20/0.51 (declare-fun tptp.mbox ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))
% 0.20/0.51 (declare-fun tptp.mdia ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))
% 0.20/0.51 (declare-sort tptp.individuals 0)
% 0.20/0.51 (declare-fun tptp.mall ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.20/0.51 (declare-fun tptp.mexists ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))
% 0.20/0.51 (declare-fun tptp.mvalid ((-> $$unsorted Bool)) Bool)
% 0.20/0.51 (assert (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))
% 0.20/0.51 (declare-fun tptp.msatisfiable ((-> $$unsorted Bool)) Bool)
% 0.20/0.51 (assert (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))
% 0.20/0.51 (declare-fun tptp.mcountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.20/0.51 (assert (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))
% 0.20/0.51 (declare-fun tptp.minvalid ((-> $$unsorted Bool)) Bool)
% 0.20/0.51 (assert (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))
% 0.20/0.51 (declare-fun tptp.reli ($$unsorted $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.relr ($$unsorted $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_true ($$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_false ($$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_all ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (declare-fun tptp.cs4_box ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.51 (assert (= tptp.cs4_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) P) __flatten_var_0))))
% 0.20/0.51 (assert (= tptp.cs4_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))
% 0.20/0.51 (assert (= tptp.cs4_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))
% 0.20/0.51 (assert (= tptp.cs4_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))
% 0.20/0.51 (assert (= tptp.cs4_true tptp.mtrue))
% 0.20/0.51 (assert (= tptp.cs4_false tptp.mfalse))
% 0.20/0.51 (assert (= tptp.cs4_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ tptp.mall A)) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.cs4_box (lambda ((A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mbox tptp.relr) A)) __flatten_var_0))))
% 0.20/0.58 (declare-fun tptp.cs4_valid ((-> $$unsorted Bool)) Bool)
% 0.20/0.58 (assert (= tptp.cs4_valid (lambda ((A (-> $$unsorted Bool))) (@ tptp.mvalid A))))
% 0.20/0.58 (assert (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.reli) A)) A))))
% 0.20/0.58 (assert (forall ((A (-> $$unsorted Bool))) (@ tptp.mvalid (@ (@ tptp.mimpl (@ (@ tptp.mbox tptp.relr) A)) A))))
% 0.20/0.58 (assert (forall ((A (-> $$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)))))))
% 0.20/0.58 (assert (forall ((A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.mbox tptp.relr))) (let ((_let_2 (@ _let_1 A))) (@ tptp.mvalid (@ (@ tptp.mimpl _let_2) (@ _let_1 _let_2)))))))
% 0.20/0.58 (assert (forall ((A (-> $$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))))))))
% 0.20/0.58 (declare-fun tptp.princ_inj (tptp.individuals $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_atom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_princ ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_and ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_or ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_impl ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_all ((-> tptp.individuals $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_true ($$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_false ($$unsorted) Bool)
% 0.20/0.58 (declare-fun tptp.bl_says (tptp.individuals (-> $$unsorted Bool) $$unsorted) Bool)
% 0.20/0.58 (assert (= tptp.bl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.bl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.bl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_and A) B) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.bl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_or A) B) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.bl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl A) B) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.bl_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_all A) __flatten_var_0))))
% 0.20/0.58 (assert (= tptp.bl_true tptp.cs4_true))
% 0.20/0.58 (assert (= tptp.bl_false tptp.cs4_false))
% 0.20/0.58 (assert (= tptp.bl_says (lambda ((K tptp.individuals) (A (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_box (@ (@ tptp.cs4_impl (@ tptp.bl_princ (@ tptp.princ_inj K))) A)) __flatten_var_0))))
% 0.20/0.58 (declare-fun tptp.bl_valid ((-> $$unsorted Bool)) Bool)
% 0.20/0.58 (assert (= tptp.bl_valid tptp.mvalid))
% 0.20/0.58 (declare-fun tptp.loca () tptp.individuals)
% 0.20/0.58 (assert (@ tptp.cs4_valid (@ tptp.cs4_all (lambda ((K tptp.individuals) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl (@ tptp.princ_inj K)) (@ tptp.princ_inj tptp.loca)) __flatten_var_0)))))
% 0.20/0.58 (assert (not (forall ((K tptp.individuals) (A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.bl_atom A))) (@ tptp.bl_valid (@ (@ tptp.bl_impl (@ (@ tptp.bl_says tptp.loca) _let_1)) (@ (@ tptp.bl_says K) _let_1)))))))
% 0.20/0.58 (set-info :filename cvc5---1.0.5_13074)
% 0.20/0.58 (check-sat-assuming ( true ))
% 0.20/0.58 ------- get file name : TPTP file name is SWV444^1
% 0.20/0.58 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_13074.smt2...
% 0.20/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.58 % SZS status Theorem for SWV444^1
% 0.20/0.58 % SZS output start Proof for SWV444^1
% 0.20/0.58 (
% 0.20/0.58 (let ((_let_1 (not (forall ((K tptp.individuals) (A (-> $$unsorted Bool))) (let ((_let_1 (@ tptp.bl_atom A))) (@ tptp.bl_valid (@ (@ tptp.bl_impl (@ (@ tptp.bl_says tptp.loca) _let_1)) (@ (@ tptp.bl_says K) _let_1)))))))) (let ((_let_2 (@ tptp.cs4_valid (@ tptp.cs4_all (lambda ((K tptp.individuals) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl (@ tptp.princ_inj K)) (@ tptp.princ_inj tptp.loca)) __flatten_var_0)))))) (let ((_let_3 (= tptp.bl_valid tptp.mvalid))) (let ((_let_4 (= 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_5 (= tptp.bl_false tptp.cs4_false))) (let ((_let_6 (= tptp.bl_true tptp.cs4_true))) (let ((_let_7 (= tptp.bl_all (lambda ((A (-> tptp.individuals $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_all A) __flatten_var_0))))) (let ((_let_8 (= tptp.bl_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_impl A) B) __flatten_var_0))))) (let ((_let_9 (= tptp.bl_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_or A) B) __flatten_var_0))))) (let ((_let_10 (= tptp.bl_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.cs4_and A) B) __flatten_var_0))))) (let ((_let_11 (= tptp.bl_princ (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))) (let ((_let_12 (= tptp.bl_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.cs4_atom P) __flatten_var_0))))) (let ((_let_13 (= tptp.cs4_valid (lambda ((A (-> $$unsorted Bool))) (@ tptp.mvalid A))))) (let ((_let_14 (= 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_15 (= 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_16 (= tptp.cs4_false tptp.mfalse))) (let ((_let_17 (= tptp.cs4_true tptp.mtrue))) (let ((_let_18 (= tptp.cs4_impl (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) (@ (@ tptp.mimpl A) B)) __flatten_var_0))))) (let ((_let_19 (= tptp.cs4_or (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor A) B) __flatten_var_0))))) (let ((_let_20 (= tptp.cs4_and (lambda ((A (-> $$unsorted Bool)) (B (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand A) B) __flatten_var_0))))) (let ((_let_21 (= tptp.cs4_atom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mbox tptp.reli) P) __flatten_var_0))))) (let ((_let_22 (= tptp.minvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ P W))))))) (let ((_let_23 (= tptp.mcountersatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ P W))))))) (let ((_let_24 (= tptp.msatisfiable (lambda ((P (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ P W)))))) (let ((_let_25 (= tptp.mvalid (lambda ((P (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ P W)))))) (let ((_let_26 (= tptp.mexists (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (exists ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_27 (= tptp.mall (lambda ((P (-> tptp.individuals $$unsorted Bool)) (W $$unsorted)) (forall ((X tptp.individuals)) (@ (@ P X) W)))))) (let ((_let_28 (= tptp.mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R X) Y) (@ P Y))))))) (let ((_let_29 (= tptp.mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ R X) Y) (@ P Y))))))) (let ((_let_30 (= tptp.miff (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand (@ (@ tptp.mimpl U) V)) (@ (@ tptp.mimpl V) U)) __flatten_var_0))))) (let ((_let_31 (= tptp.mimpl (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_32 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_33 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_34 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_35 (= tptp.mtrue (lambda ((X $$unsorted)) true)))) (let ((_let_36 (= tptp.mfalse (lambda ((X $$unsorted)) false)))) (let ((_let_37 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_38 (ho_2 (ho_7 k_6 tptp.loca) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_39 (ho_2 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_40 (not _let_39))) (let ((_let_41 (not _let_37))) (let ((_let_42 (or _let_41 _let_40 _let_38))) (let ((_let_43 (or _let_41 _let_38))) (let ((_let_44 (forall ((BOUND_VARIABLE_1331 $$unsorted) (BOUND_VARIABLE_1978 $$unsorted) (BOUND_VARIABLE_2115 $$unsorted)) (or (not (ho_2 (ho_4 k_5 BOUND_VARIABLE_1331) BOUND_VARIABLE_1331)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1331) BOUND_VARIABLE_1978)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1978) BOUND_VARIABLE_2115)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 BOUND_VARIABLE_2115))))) (let ((_let_45 (not _let_44))) (let ((_let_46 (forall ((BOUND_VARIABLE_2145 $$unsorted)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2145) BOUND_VARIABLE_2145))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (and _let_47 _let_43 _let_45))) (let ((_let_49 (not _let_43))) (let ((_let_50 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_51 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_52 (not _let_51))) (let ((_let_53 (ho_2 (ho_4 k_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_54 (not _let_53))) (let ((_let_55 (ho_2 (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_48 _let_56 _let_54 _let_52 _let_50))) (let ((_let_58 (forall ((BOUND_VARIABLE_2451 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_2231 $$unsorted) (BOUND_VARIABLE_2229 $$unsorted) (BOUND_VARIABLE_2227 $$unsorted) (BOUND_VARIABLE_2219 $$unsorted)) (or (and (not (forall ((BOUND_VARIABLE_2145 $$unsorted)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2145) BOUND_VARIABLE_2145)))) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2219) BOUND_VARIABLE_2219)) (ho_2 (ho_7 k_6 tptp.loca) BOUND_VARIABLE_2219)) (not (forall ((BOUND_VARIABLE_1331 $$unsorted) (BOUND_VARIABLE_1978 $$unsorted) (BOUND_VARIABLE_2115 $$unsorted)) (or (not (ho_2 (ho_4 k_5 BOUND_VARIABLE_1331) BOUND_VARIABLE_1331)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1331) BOUND_VARIABLE_1978)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1978) BOUND_VARIABLE_2115)) (ho_2 BOUND_VARIABLE_2451 BOUND_VARIABLE_2115))))) (not (ho_2 (ho_4 k_5 BOUND_VARIABLE_2227) BOUND_VARIABLE_2227)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2227) BOUND_VARIABLE_2229)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2229) BOUND_VARIABLE_2231)) (ho_2 BOUND_VARIABLE_2451 BOUND_VARIABLE_2231))))) (let ((_let_59 (not _let_57))) (let ((_let_60 (forall ((K tptp.individuals)) (not (forall ((BOUND_VARIABLE_1936 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1936) BOUND_VARIABLE_1936)) (ho_2 (ho_7 k_6 K) BOUND_VARIABLE_1936))))))) (let ((_let_61 (forall ((W $$unsorted) (Y $$unsorted)) (not (ho_2 (ho_4 k_3 W) Y))))) (let ((_let_62 (forall ((BOUND_VARIABLE_2189 $$unsorted)) (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2189) BOUND_VARIABLE_2189))))) (let ((_let_63 (forall ((W $$unsorted) (Y $$unsorted)) (not (@ (@ tptp.reli W) Y))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_36)) (MACRO_SR_EQ_INTRO :args (_let_36 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_35)) (MACRO_SR_EQ_INTRO :args (_let_35 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (ASSUME :args (_let_34)))) (let ((_let_67 (ASSUME :args (_let_33)))) (let ((_let_68 (ASSUME :args (_let_32)))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_68 _let_67 _let_66 _let_65 _let_64) :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_69 _let_68 _let_67 _let_66 _let_65 _let_64) :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_28)) (MACRO_SR_EQ_INTRO :args (_let_28 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (ASSUME :args (_let_27)))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (ASSUME :args (_let_25)))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (ASSUME :args (_let_22)))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_78 _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) :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_79 _let_78 _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) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_80 _let_79 _let_78 _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) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_81 _let_80 _let_79 _let_78 _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) :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (EQ_RESOLVE (SYMM (ASSUME :args (_let_17))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args ((= tptp.mtrue tptp.cs4_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (EQ_RESOLVE (SYMM (ASSUME :args (_let_16))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args ((= tptp.mfalse tptp.cs4_false) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (EQ_RESOLVE (SYMM (ASSUME :args (_let_6))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args ((= tptp.cs4_true tptp.bl_true) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (SYMM (ASSUME :args (_let_5))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args ((= tptp.cs4_false tptp.bl_false) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (AND_INTRO (SYMM (EQ_RESOLVE (SYMM (ASSUME :args (_let_3))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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) :args ((= tptp.mvalid tptp.bl_valid) SB_DEFAULT SBA_FIXPOINT)))) _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _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 ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_97 :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or (forall ((BOUND_VARIABLE_2189 $$unsorted)) (not (@ (@ tptp.reli BOUND_VARIABLE_2189) BOUND_VARIABLE_2189))) _let_63 (forall ((A (-> $$unsorted Bool)) (BOUND_VARIABLE_2231 $$unsorted) (BOUND_VARIABLE_2229 $$unsorted) (BOUND_VARIABLE_2227 $$unsorted) (BOUND_VARIABLE_2219 $$unsorted)) (or (and (not (forall ((BOUND_VARIABLE_2145 $$unsorted)) (not (@ (@ tptp.reli BOUND_VARIABLE_2145) BOUND_VARIABLE_2145)))) (or (not (@ (@ tptp.reli BOUND_VARIABLE_2219) BOUND_VARIABLE_2219)) (@ (@ tptp.princ_inj tptp.loca) BOUND_VARIABLE_2219)) (not (forall ((BOUND_VARIABLE_1331 $$unsorted) (BOUND_VARIABLE_1978 $$unsorted) (BOUND_VARIABLE_2115 $$unsorted)) (or (not (@ (@ tptp.relr BOUND_VARIABLE_1331) BOUND_VARIABLE_1331)) (not (@ (@ tptp.reli BOUND_VARIABLE_1331) BOUND_VARIABLE_1978)) (not (@ (@ tptp.reli BOUND_VARIABLE_1978) BOUND_VARIABLE_2115)) (@ A BOUND_VARIABLE_2115))))) (not (@ (@ tptp.relr BOUND_VARIABLE_2227) BOUND_VARIABLE_2227)) (not (@ (@ tptp.reli BOUND_VARIABLE_2227) BOUND_VARIABLE_2229)) (not (@ (@ tptp.reli BOUND_VARIABLE_2229) BOUND_VARIABLE_2231)) (@ A BOUND_VARIABLE_2231))) (forall ((K tptp.individuals)) (not (forall ((BOUND_VARIABLE_1936 $$unsorted)) (or (not (@ (@ tptp.reli BOUND_VARIABLE_1936) BOUND_VARIABLE_1936)) (@ (@ tptp.princ_inj K) BOUND_VARIABLE_1936))))))) (not (or _let_62 _let_61 _let_58 _let_60))))))))) (let ((_let_99 (or))) (let ((_let_100 (not _let_58))) (let ((_let_101 (_let_100))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_101)) :args _let_101)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_58))) (REFL :args (_let_59)) :args _let_99)) (NOT_OR_ELIM _let_98 :args (2)) :args (_let_59 true _let_58)))) (let ((_let_103 (or _let_56 _let_54 _let_52 _let_50))) (let ((_let_104 (not _let_103))) (let ((_let_105 (REFL :args (_let_57)))) (let ((_let_106 (_let_44))) (let ((_let_107 (_let_48))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_107) (CONG (REFL :args _let_107) (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) (REFL :args (_let_49)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_99)) :args ((or _let_46 _let_44 _let_48 _let_49))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (SYMM (ALPHA_EQUIV :args (_let_62 (= BOUND_VARIABLE_2189 BOUND_VARIABLE_2145))))) (NOT_OR_ELIM _let_98 :args (0)) :args (_let_47 true _let_62)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_106) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_106)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_56 _let_54 _let_52 _let_50 _let_104))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_99)) :args ((or _let_55 _let_57))) _let_102 :args (_let_55 true _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 2)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_99)) :args ((or _let_53 _let_57))) _let_102 :args (_let_53 true _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 3)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_99)) :args ((or _let_51 _let_57))) _let_102 :args (_let_51 true _let_57)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 4)) _let_102 :args ((not _let_50) true _let_57)) :args (_let_104 false _let_55 false _let_53 false _let_51 true _let_50)) :args (_let_45 true _let_103)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 0)) _let_102 :args ((not _let_48) true _let_57)) :args (_let_49 true _let_46 true _let_44 true _let_48)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) :args _let_99)) :args ((or _let_37 _let_43))) _let_108 :args (_let_37 true _let_43)))) (let ((_let_110 (forall ((BOUND_VARIABLE_1283 tptp.individuals) (BOUND_VARIABLE_2047 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_2047) BOUND_VARIABLE_2047)) (not (ho_2 (ho_7 k_6 BOUND_VARIABLE_1283) BOUND_VARIABLE_2047)) (ho_2 (ho_7 k_6 tptp.loca) BOUND_VARIABLE_2047))))) (let ((_let_111 (_let_110))) (let ((_let_112 (or _let_41 _let_39))) (let ((_let_113 (forall ((BOUND_VARIABLE_1936 $$unsorted)) (or (not (ho_2 (ho_4 k_3 BOUND_VARIABLE_1936) BOUND_VARIABLE_1936)) (ho_2 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) BOUND_VARIABLE_1936))))) (let ((_let_114 (_let_113))) (let ((_let_115 (not _let_60))) (let ((_let_116 (_let_115))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_38 _let_40 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_41 _let_39 (not _let_112)))) _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_114) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_4 k_3 BOUND_VARIABLE_1936)))) :args _let_114)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_116)) :args _let_116) (REWRITE :args ((=> _let_115 (not (not _let_113))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_60))) (REFL :args _let_114) :args _let_99)) (NOT_OR_ELIM _let_98 :args (3)) :args (_let_113 true _let_60)) :args (_let_112 false _let_113)) :args (_let_39 false _let_37 false _let_112)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 1)) _let_108 :args ((not _let_38) true _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_111) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_111)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_97 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or (forall ((BOUND_VARIABLE_1283 tptp.individuals) (BOUND_VARIABLE_2047 $$unsorted)) (or (not (@ (@ tptp.reli BOUND_VARIABLE_2047) BOUND_VARIABLE_2047)) (not (@ (@ tptp.princ_inj BOUND_VARIABLE_1283) BOUND_VARIABLE_2047)) (@ (@ tptp.princ_inj tptp.loca) BOUND_VARIABLE_2047))) _let_63) (or _let_110 _let_61)))))) :args ((or _let_61 _let_110))) (NOT_OR_ELIM _let_98 :args (1)) :args (_let_110 true _let_61)) :args (_let_42 false _let_110)) _let_109 :args (false false _let_39 true _let_38 false _let_42 false _let_37)) :args (_let_36 _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 (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_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.58 )
% 0.20/0.58 % SZS output end Proof for SWV444^1
% 0.20/0.58 % cvc5---1.0.5 exiting
% 0.20/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------