TSTP Solution File: SYN045^4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN045^4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 : Fri Sep 1 02:01:00 EDT 2023
% Result : Theorem 0.23s 0.64s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.20 % Problem : SYN045^4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.21 % Command : do_cvc5 %s %d
% 0.16/0.43 % Computer : n022.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8042.1875MB
% 0.16/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Aug 26 21:32:40 EDT 2023
% 0.16/0.43 % CPUTime :
% 0.23/0.58 %----Proving TH0
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 % File : SYN045^4 : TPTP v8.1.2. Released v4.0.0.
% 0.23/0.59 % Domain : Logic Calculi (Intuitionistic logic)
% 0.23/0.59 % Problem : Pelletier Problem 13
% 0.23/0.59 % Version : [Goe33] axioms.
% 0.23/0.59 % English :
% 0.23/0.59
% 0.23/0.59 % Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% 0.23/0.59 % : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% 0.23/0.59 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 0.23/0.59 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.23/0.59 % : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% 0.23/0.59 % Source : [Ben09]
% 0.23/0.59 % Names :
% 0.23/0.59
% 0.23/0.59 % Status : Theorem
% 0.23/0.59 % Rating : 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.23/0.59 % Syntax : Number of formulae : 45 ( 20 unt; 23 typ; 19 def)
% 0.23/0.59 % Number of atoms : 84 ( 19 equ; 0 cnn)
% 0.23/0.59 % Maximal formula atoms : 21 ( 3 avg)
% 0.23/0.59 % Number of connectives : 75 ( 3 ~; 1 |; 2 &; 67 @)
% 0.23/0.59 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.23/0.59 % Maximal formula depth : 8 ( 2 avg)
% 0.23/0.59 % Number of types : 2 ( 0 usr)
% 0.23/0.59 % Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% 0.23/0.59 % Number of symbols : 30 ( 28 usr; 6 con; 0-3 aty)
% 0.23/0.59 % Number of variables : 40 ( 31 ^; 7 !; 2 ?; 40 :)
% 0.23/0.59 % SPC : TH0_THM_EQU_NAR
% 0.23/0.59
% 0.23/0.59 % Comments : This is an ILTP problem embedded in TH0
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 %----Modal Logic S4 in HOL
% 0.23/0.59 %----We define an accessibility relation irel
% 0.23/0.59 thf(irel_type,type,
% 0.23/0.59 irel: $i > $i > $o ).
% 0.23/0.59
% 0.23/0.59 %----We require reflexivity and transitivity for irel
% 0.23/0.59 thf(refl_axiom,axiom,
% 0.23/0.59 ! [X: $i] : ( irel @ X @ X ) ).
% 0.23/0.59
% 0.23/0.59 thf(trans_axiom,axiom,
% 0.23/0.59 ! [X: $i,Y: $i,Z: $i] :
% 0.23/0.59 ( ( ( irel @ X @ Y )
% 0.23/0.59 & ( irel @ Y @ Z ) )
% 0.23/0.59 => ( irel @ X @ Z ) ) ).
% 0.23/0.59
% 0.23/0.59 %----We define S4 connective mnot (as set complement)
% 0.23/0.59 thf(mnot_decl_type,type,
% 0.23/0.59 mnot: ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(mnot,definition,
% 0.23/0.59 ( mnot
% 0.23/0.59 = ( ^ [X: $i > $o,U: $i] :
% 0.23/0.59 ~ ( X @ U ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----We define S4 connective mor (as set union)
% 0.23/0.59 thf(mor_decl_type,type,
% 0.23/0.59 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(mor,definition,
% 0.23/0.59 ( mor
% 0.23/0.59 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.59 ( ( X @ U )
% 0.23/0.59 | ( Y @ U ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----We define S4 connective mand (as set intersection)
% 0.23/0.59 thf(mand_decl_type,type,
% 0.23/0.59 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(mand,definition,
% 0.23/0.59 ( mand
% 0.23/0.59 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.23/0.59 ( ( X @ U )
% 0.23/0.59 & ( Y @ U ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----We define S4 connective mimpl
% 0.23/0.59 thf(mimplies_decl_type,type,
% 0.23/0.59 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(mimplies,definition,
% 0.23/0.59 ( mimplies
% 0.23/0.59 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of mbox_s4; since irel is reflexive and transitive,
% 0.23/0.59 %----it is easy to show that the K and the T axiom hold for mbox_s4
% 0.23/0.59 thf(mbox_s4_decl_type,type,
% 0.23/0.59 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(mbox_s4,definition,
% 0.23/0.59 ( mbox_s4
% 0.23/0.59 = ( ^ [P: $i > $o,X: $i] :
% 0.23/0.59 ! [Y: $i] :
% 0.23/0.59 ( ( irel @ X @ Y )
% 0.23/0.59 => ( P @ Y ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Intuitionistic Logic in Modal Logic S4
% 0.23/0.59 %----Definition of iatom: iatom P = P
% 0.23/0.59 %----Goedel maps atoms to atoms
% 0.23/0.59 thf(iatom_type,type,
% 0.23/0.59 iatom: ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(iatom,definition,
% 0.23/0.59 ( iatom
% 0.23/0.59 = ( ^ [P: $i > $o] : P ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of inot: inot P = mnot (mbox_s4 P)
% 0.23/0.59 thf(inot_type,type,
% 0.23/0.59 inot: ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(inot,definition,
% 0.23/0.59 ( inot
% 0.23/0.59 = ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of true and false
% 0.23/0.59 thf(itrue_type,type,
% 0.23/0.59 itrue: $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(itrue,definition,
% 0.23/0.59 ( itrue
% 0.23/0.59 = ( ^ [W: $i] : $true ) ) ).
% 0.23/0.59
% 0.23/0.59 thf(ifalse_type,type,
% 0.23/0.59 ifalse: $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(ifalse,definition,
% 0.23/0.59 ( ifalse
% 0.23/0.59 = ( inot @ itrue ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of iand: iand P Q = (mand P Q)
% 0.23/0.59 thf(iand_type,type,
% 0.23/0.59 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(iand,definition,
% 0.23/0.59 ( iand
% 0.23/0.59 = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of ior: ior P Q = (mor (mbox_s4 P) (mbox_s4 Q))
% 0.23/0.59 thf(ior_type,type,
% 0.23/0.59 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(ior,definition,
% 0.23/0.59 ( ior
% 0.23/0.59 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of iimplies: iimplies P Q =
% 0.23/0.59 %---- (mimplies (mbox_s4 P) (mbox_s4 Q))
% 0.23/0.59 thf(iimplies_type,type,
% 0.23/0.59 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(iimplies,definition,
% 0.23/0.59 ( iimplies
% 0.23/0.59 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of iimplied: iimplied P Q = (iimplies Q P)
% 0.23/0.59 thf(iimplied_type,type,
% 0.23/0.59 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(iimplied,definition,
% 0.23/0.59 ( iimplied
% 0.23/0.59 = ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of iequiv: iequiv P Q =
% 0.23/0.59 %---- (iand (iimplies P Q) (iimplies Q P))
% 0.23/0.59 thf(iequiv_type,type,
% 0.23/0.59 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(iequiv,definition,
% 0.23/0.59 ( iequiv
% 0.23/0.59 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of ixor: ixor P Q = (inot (iequiv P Q)
% 0.23/0.59 thf(ixor_type,type,
% 0.23/0.59 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(ixor,definition,
% 0.23/0.59 ( ixor
% 0.23/0.59 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of validity
% 0.23/0.59 thf(ivalid_type,type,
% 0.23/0.59 ivalid: ( $i > $o ) > $o ).
% 0.23/0.59
% 0.23/0.59 thf(ivalid,definition,
% 0.23/0.59 ( ivalid
% 0.23/0.59 = ( ^ [Phi: $i > $o] :
% 0.23/0.59 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of satisfiability
% 0.23/0.59 thf(isatisfiable_type,type,
% 0.23/0.59 isatisfiable: ( $i > $o ) > $o ).
% 0.23/0.59
% 0.23/0.59 thf(isatisfiable,definition,
% 0.23/0.59 ( isatisfiable
% 0.23/0.59 = ( ^ [Phi: $i > $o] :
% 0.23/0.59 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of countersatisfiability
% 0.23/0.59 thf(icountersatisfiable_type,type,
% 0.23/0.59 icountersatisfiable: ( $i > $o ) > $o ).
% 0.23/0.59
% 0.23/0.59 thf(icountersatisfiable,definition,
% 0.23/0.59 ( icountersatisfiable
% 0.23/0.59 = ( ^ [Phi: $i > $o] :
% 0.23/0.59 ? [W: $i] :
% 0.23/0.59 ~ ( Phi @ W ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %----Definition of invalidity
% 0.23/0.59 thf(iinvalid_type,type,
% 0.23/0.59 iinvalid: ( $i > $o ) > $o ).
% 0.23/0.59
% 0.23/0.59 thf(iinvalid,definition,
% 0.23/0.59 ( iinvalid
% 0.23/0.59 = ( ^ [Phi: $i > $o] :
% 0.23/0.59 ! [W: $i] :
% 0.23/0.59 ~ ( Phi @ W ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 thf(p_type,type,
% 0.23/0.59 p: $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(q_type,type,
% 0.23/0.59 q: $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(r_type,type,
% 0.23/0.59 r: $i > $o ).
% 0.23/0.59
% 0.23/0.59 thf(pel13,conjecture,
% 0.23/0.59 ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) ).
% 0.23/0.59
% 0.23/0.59 %------------------------------------------------------------------------------
% 0.23/0.59 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.FMTKI1Rd0j/cvc5---1.0.5_8899.p...
% 0.23/0.59 (declare-sort $$unsorted 0)
% 0.23/0.59 (declare-fun tptp.irel ($$unsorted $$unsorted) Bool)
% 0.23/0.59 (assert (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))
% 0.23/0.59 (assert (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))))
% 0.23/0.59 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.23/0.59 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.23/0.59 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.59 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.23/0.59 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))
% 0.23/0.64 (declare-fun tptp.iatom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.inot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.itrue ($$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.itrue (lambda ((W $$unsorted)) true)))
% 0.23/0.64 (declare-fun tptp.ifalse ($$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.ifalse (@ tptp.inot tptp.itrue)))
% 0.23/0.64 (declare-fun tptp.iand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.ior ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.iimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.iimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.iequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.ixor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.23/0.64 (assert (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))
% 0.23/0.64 (declare-fun tptp.ivalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.64 (assert (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.64 (declare-fun tptp.isatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.64 (assert (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.23/0.64 (declare-fun tptp.icountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.23/0.64 (assert (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.64 (declare-fun tptp.iinvalid ((-> $$unsorted Bool)) Bool)
% 0.23/0.64 (assert (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.23/0.64 (declare-fun tptp.p ($$unsorted) Bool)
% 0.23/0.64 (declare-fun tptp.q ($$unsorted) Bool)
% 0.23/0.64 (declare-fun tptp.r ($$unsorted) Bool)
% 0.23/0.64 (assert (let ((_let_1 (@ tptp.iatom tptp.r))) (let ((_let_2 (@ tptp.ior (@ tptp.iatom tptp.p)))) (let ((_let_3 (@ tptp.iatom tptp.q))) (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ _let_2 (@ (@ tptp.iand _let_3) _let_1))) (@ (@ tptp.iand (@ _let_2 _let_3)) (@ _let_2 _let_1)))))))))
% 0.23/0.64 (set-info :filename cvc5---1.0.5_8899)
% 0.23/0.64 (check-sat-assuming ( true ))
% 0.23/0.64 ------- get file name : TPTP file name is SYN045^4
% 0.23/0.64 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_8899.smt2...
% 0.23/0.64 --- Run --ho-elim --full-saturate-quant at 10...
% 0.23/0.64 % SZS status Theorem for SYN045^4
% 0.23/0.64 % SZS output start Proof for SYN045^4
% 0.23/0.64 (
% 0.23/0.64 (let ((_let_1 (@ tptp.iatom tptp.r))) (let ((_let_2 (@ tptp.ior (@ tptp.iatom tptp.p)))) (let ((_let_3 (@ tptp.iatom tptp.q))) (let ((_let_4 (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ _let_2 (@ (@ tptp.iand _let_3) _let_1))) (@ (@ tptp.iand (@ _let_2 _let_3)) (@ _let_2 _let_1))))))) (let ((_let_5 (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_6 (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_7 (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_8 (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_9 (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))) (let ((_let_10 (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))) (let ((_let_11 (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))) (let ((_let_12 (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_13 (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_14 (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))) (let ((_let_15 (= tptp.ifalse (@ tptp.inot tptp.itrue)))) (let ((_let_16 (= tptp.itrue (lambda ((W $$unsorted)) true)))) (let ((_let_17 (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))) (let ((_let_18 (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_19 (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))) (let ((_let_20 (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_21 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_22 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_23 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_24 (forall ((BOUND_VARIABLE_1503 $$unsorted) (BOUND_VARIABLE_1529 $$unsorted)) (let ((_let_1 (not (forall ((BOUND_VARIABLE_1420 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1420) BOUND_VARIABLE_1420)) (ho_4 k_6 BOUND_VARIABLE_1420)))))) (or (and (or (and _let_1 (not (forall ((BOUND_VARIABLE_1429 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1429) BOUND_VARIABLE_1429)) (ho_4 k_7 BOUND_VARIABLE_1429))))) (and _let_1 (not (forall ((BOUND_VARIABLE_1439 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1439) BOUND_VARIABLE_1439)) (ho_4 k_5 BOUND_VARIABLE_1439)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1503) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1503) BOUND_VARIABLE_1529))))))) (let ((_let_25 (forall ((BOUND_VARIABLE_1339 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1339) BOUND_VARIABLE_1339)) (and (ho_4 k_7 BOUND_VARIABLE_1339) (ho_4 k_5 BOUND_VARIABLE_1339)))))) (let ((_let_26 (forall ((BOUND_VARIABLE_1330 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1330) BOUND_VARIABLE_1330)) (ho_4 k_6 BOUND_VARIABLE_1330))))) (let ((_let_27 (or _let_26 _let_25 _let_24))) (let ((_let_28 (forall ((BOUND_VARIABLE_1492 $$unsorted) (BOUND_VARIABLE_1518 $$unsorted)) (or (and (not (forall ((BOUND_VARIABLE_1330 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1330) BOUND_VARIABLE_1330)) (ho_4 k_6 BOUND_VARIABLE_1330)))) (not (forall ((BOUND_VARIABLE_1339 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1339) BOUND_VARIABLE_1339)) (and (ho_4 k_7 BOUND_VARIABLE_1339) (ho_4 k_5 BOUND_VARIABLE_1339))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1492) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1492) BOUND_VARIABLE_1518)))))) (let ((_let_29 (forall ((BOUND_VARIABLE_1439 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1439) BOUND_VARIABLE_1439)) (ho_4 k_5 BOUND_VARIABLE_1439))))) (let ((_let_30 (forall ((BOUND_VARIABLE_1420 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1420) BOUND_VARIABLE_1420)) (ho_4 k_6 BOUND_VARIABLE_1420))))) (let ((_let_31 (or _let_30 _let_29))) (let ((_let_32 (forall ((BOUND_VARIABLE_1429 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1429) BOUND_VARIABLE_1429)) (ho_4 k_7 BOUND_VARIABLE_1429))))) (let ((_let_33 (or _let_30 _let_32))) (let ((_let_34 (and _let_33 _let_31))) (let ((_let_35 (or _let_34 _let_28))) (let ((_let_36 (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_37 (ho_4 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_38 (and _let_37 _let_36))) (let ((_let_39 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (or _let_40 _let_37))) (let ((_let_43 (or _let_40 _let_36))) (let ((_let_44 (ho_4 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_45 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44))) (let ((_let_48 (and _let_44 (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_49 (or _let_46 _let_48))) (let ((_let_50 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_51 (not _let_50))) (let ((_let_52 (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Y))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (not _let_25))) (let ((_let_55 (not _let_26))) (let ((_let_56 (and _let_55 _let_54 _let_53))) (let ((_let_57 (or _let_56 _let_51))) (let ((_let_58 (not _let_32))) (let ((_let_59 (not _let_30))) (let ((_let_60 (and _let_59 _let_58))) (let ((_let_61 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_62 (not _let_61))) (let ((_let_63 (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) Y))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_29))) (let ((_let_66 (and _let_59 _let_65))) (let ((_let_67 (or _let_60 _let_66))) (let ((_let_68 (and _let_67 _let_64))) (let ((_let_69 (or _let_68 _let_62))) (let ((_let_70 (ALPHA_EQUIV :args (_let_30 (= BOUND_VARIABLE_1420 BOUND_VARIABLE_1330))))) (let ((_let_71 (EQUIV_ELIM2 _let_70))) (let ((_let_72 (or))) (let ((_let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_32))))) (let ((_let_74 (_let_58))) (let ((_let_75 (_let_25))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_25))))) (let ((_let_78 (_let_56))) (let ((_let_79 (_let_52))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_79) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_79)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_78) (CONG (REFL :args _let_78) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_26))) _let_77 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_72)) :args ((or _let_25 _let_26 _let_52 _let_56))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_57 1)) (CONG (REFL :args (_let_57)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_72)) :args ((or _let_50 _let_57))) (CNF_OR_NEG :args (_let_57 0)) :args ((or _let_25 _let_26 _let_57) false _let_52 false _let_50 true _let_56)))) (let ((_let_81 (not _let_28))) (let ((_let_82 (_let_81))) (let ((_let_83 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_82)) :args _let_82)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_81) _let_28))) (REFL :args ((not _let_57))) :args _let_72)))) (let ((_let_84 (CNF_OR_NEG :args (_let_35 1)))) (let ((_let_85 (forall ((BOUND_VARIABLE_1420 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1420) BOUND_VARIABLE_1420)) (@ tptp.p BOUND_VARIABLE_1420))))) (let ((_let_86 (ASSUME :args (_let_23)))) (let ((_let_87 (ASSUME :args (_let_22)))) (let ((_let_88 (ASSUME :args (_let_21)))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_88 _let_87 _let_86) :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (ASSUME :args (_let_18)))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_13)) (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) :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_12)) (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) :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_5)) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_8)) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86) :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (and (or (and (or _let_85 (forall ((BOUND_VARIABLE_1429 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1429) BOUND_VARIABLE_1429)) (@ tptp.q BOUND_VARIABLE_1429)))) (or _let_85 (forall ((BOUND_VARIABLE_1439 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1439) BOUND_VARIABLE_1439)) (@ tptp.r BOUND_VARIABLE_1439))))) (forall ((BOUND_VARIABLE_1492 $$unsorted) (BOUND_VARIABLE_1518 $$unsorted)) (or (and (not (forall ((BOUND_VARIABLE_1330 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1330) BOUND_VARIABLE_1330)) (@ tptp.p BOUND_VARIABLE_1330)))) (not (forall ((BOUND_VARIABLE_1339 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1339) BOUND_VARIABLE_1339)) (and (@ tptp.q BOUND_VARIABLE_1339) (@ tptp.r BOUND_VARIABLE_1339))))) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1492) Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1492) BOUND_VARIABLE_1518))))) (or (forall ((BOUND_VARIABLE_1330 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1330) BOUND_VARIABLE_1330)) (@ tptp.p BOUND_VARIABLE_1330))) (forall ((BOUND_VARIABLE_1339 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1339) BOUND_VARIABLE_1339)) (and (@ tptp.q BOUND_VARIABLE_1339) (@ tptp.r BOUND_VARIABLE_1339)))) (forall ((BOUND_VARIABLE_1503 $$unsorted) (BOUND_VARIABLE_1529 $$unsorted)) (let ((_let_1 (not (forall ((BOUND_VARIABLE_1420 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1420) BOUND_VARIABLE_1420)) (@ tptp.p BOUND_VARIABLE_1420)))))) (or (and (or (and _let_1 (not (forall ((BOUND_VARIABLE_1429 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1429) BOUND_VARIABLE_1429)) (@ tptp.q BOUND_VARIABLE_1429))))) (and _let_1 (not (forall ((BOUND_VARIABLE_1439 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1439) BOUND_VARIABLE_1439)) (@ tptp.r BOUND_VARIABLE_1439)))))) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1503) Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1503) BOUND_VARIABLE_1529)))))))) (not (and _let_35 _let_27)))))))))) (let ((_let_101 (CNF_OR_NEG :args (_let_27 2)))) (let ((_let_102 (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_30))))) (let ((_let_103 (_let_60))) (let ((_let_104 (not _let_24))) (let ((_let_105 (_let_104))) (let ((_let_106 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_105)) :args _let_105)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_24))) (REFL :args ((not _let_69))) :args _let_72)))) (let ((_let_107 (CNF_OR_NEG :args (_let_69 0)))) (let ((_let_108 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG (REFL :args (_let_69)) (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) :args _let_72)) :args ((or _let_61 _let_69))))) (let ((_let_109 (not _let_67))) (let ((_let_110 (_let_68))) (let ((_let_111 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_110) (CONG (REFL :args _let_110) (REFL :args (_let_109)) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_72)) :args ((or _let_63 _let_68 _let_109))))) (let ((_let_112 (_let_63))) (let ((_let_113 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_112) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_112)))) (let ((_let_114 (MACRO_RESOLUTION_TRUST _let_113 _let_111 _let_108 _let_107 (CNF_OR_NEG :args (_let_67 0)) _let_106 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_103) (CONG (REFL :args _let_103) _let_102 _let_73 :args _let_72)) :args ((or _let_30 _let_32 _let_60))) _let_101 _let_100 _let_84 _let_83 _let_80 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_75)) (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_46 _let_48 (not _let_49)))) (REORDERING (CNF_AND_POS :args (_let_48 0)) :args ((or _let_44 (not _let_48)))) (CNF_OR_NEG :args (_let_47 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 0)) (CONG (REFL :args (_let_47)) (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_72)) :args ((or _let_45 _let_47))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_74)) :args _let_74)) (CONG _let_73 (REFL :args ((not _let_47))) :args _let_72)) _let_71 :args (_let_33 false _let_63 false _let_61 true _let_68 false _let_67 true _let_69 false _let_60 true _let_24 true _let_27 false _let_35 false _let_28 false _let_57 true _let_25 true _let_49 true _let_48 true _let_44 false _let_45 true _let_47 true _let_26)))) (let ((_let_115 (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_116 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_117 _let_115))) (let ((_let_119 (and (ho_4 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) _let_115))) (let ((_let_120 (or _let_117 _let_119))) (let ((_let_121 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_29))))) (let ((_let_122 (_let_66))) (let ((_let_123 (_let_65))) (let ((_let_124 (CNF_AND_NEG :args (_let_34)))) (let ((_let_125 (CNF_OR_NEG :args (_let_35 0)))) (let ((_let_126 (_let_54))) (let ((_let_127 (_let_32))) (let ((_let_128 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_129 (_let_29))) (let ((_let_130 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_129) :args _let_128) :args _let_129)) (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_40 _let_36 (not _let_43)))) (CNF_AND_NEG :args (_let_38)) (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_40 _let_37 (not _let_42)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_127) :args _let_128) :args _let_127)) (CNF_OR_NEG :args (_let_41 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_72)) :args ((or _let_39 _let_41))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_126)) :args _let_126)) (CONG _let_77 (REFL :args ((not _let_41))) :args _let_72)) (CNF_OR_NEG :args (_let_27 1)) _let_100 _let_125 _let_124 (REORDERING (CNF_OR_NEG :args (_let_31 1)) :args ((or _let_65 _let_31))) (MACRO_RESOLUTION_TRUST _let_113 _let_111 _let_108 _let_107 _let_106 _let_101 _let_100 _let_84 _let_83 _let_80 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_75)) (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_117 _let_119 (not _let_120)))) (REORDERING (CNF_AND_POS :args (_let_119 1)) :args ((or _let_115 (not _let_119)))) (CNF_OR_NEG :args (_let_118 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_118 0)) (CONG (REFL :args (_let_118)) (MACRO_SR_PRED_INTRO :args ((= (not _let_117) _let_116))) :args _let_72)) :args ((or _let_116 _let_118))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_123)) :args _let_123)) (CONG _let_121 (REFL :args ((not _let_118))) :args _let_72)) (CNF_OR_NEG :args (_let_67 1)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_122) (CONG (REFL :args _let_122) _let_102 _let_121 :args _let_72)) :args ((or _let_29 _let_30 _let_66))) _let_71 :args ((or _let_29 _let_30) false _let_63 false _let_61 true _let_68 true _let_69 true _let_24 true _let_27 false _let_35 false _let_28 false _let_57 true _let_25 true _let_120 true _let_119 true _let_115 false _let_116 true _let_118 false _let_67 false _let_66 true _let_26)) (REORDERING (CNF_OR_NEG :args (_let_33 1)) :args ((or _let_58 _let_33))) _let_114 :args (_let_30 true _let_43 true _let_36 false _let_37 false _let_42 true _let_38 false _let_39 true _let_41 true _let_25 true _let_27 false _let_35 false _let_34 false _let_31 false _let_29 false _let_33 false _let_32)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_100 (MACRO_RESOLUTION_TRUST _let_125 (MACRO_RESOLUTION_TRUST _let_124 _let_114 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_31 0)) :args ((or _let_59 _let_31))) _let_130 :args (_let_31 false _let_30)) :args (_let_34 false _let_33 false _let_31)) :args (_let_35 false _let_34)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 0)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 _let_70) _let_130 :args (_let_26 false _let_30)) :args (_let_27 false _let_26)) :args (false false _let_35 false _let_27)) :args ((forall ((X $$unsorted)) (@ (@ tptp.irel X) X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))) _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.65 )
% 0.23/0.65 % SZS output end Proof for SYN045^4
% 0.23/0.65 % cvc5---1.0.5 exiting
% 0.23/0.65 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------