TSTP Solution File: SYN001^4.004 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN001^4.004 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 02:00:48 EDT 2023
% Result : Theorem 0.18s 0.62s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN001^4.004 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : do_cvc5 %s %d
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 18:52:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.48 %----Proving TH0
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 % File : SYN001^4.004 : TPTP v8.1.2. Released v4.0.0.
% 0.18/0.48 % Domain : Logic Calculi (Intuitionistic logic)
% 0.18/0.48 % Problem : ILTP Problem SYJ212+1.004
% 0.18/0.48 % Version : [Goe33] axioms.
% 0.18/0.48 % English :
% 0.18/0.48
% 0.18/0.48 % Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% 0.18/0.48 % : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% 0.18/0.48 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 0.18/0.48 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.18/0.48 % : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% 0.18/0.48 % Source : [Ben09]
% 0.18/0.48 % Names : SYJ212+1.004 [ROK06]
% 0.18/0.48
% 0.18/0.48 % Status : CounterCounterSatisfiable
% 0.18/0.48 % Rating : 1.00 v8.1.0, 0.80 v7.5.0, 0.60 v7.4.0, 0.75 v7.2.0, 0.67 v5.4.0, 1.00 v4.0.0
% 0.18/0.48 % Syntax : Number of formulae : 46 ( 20 unt; 24 typ; 19 def)
% 0.18/0.48 % Number of atoms : 89 ( 19 equ; 0 cnn)
% 0.18/0.48 % Maximal formula atoms : 26 ( 4 avg)
% 0.18/0.48 % Number of connectives : 80 ( 3 ~; 1 |; 2 &; 72 @)
% 0.18/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.48 % Maximal formula depth : 13 ( 2 avg)
% 0.18/0.48 % Number of types : 2 ( 0 usr)
% 0.18/0.48 % Number of type conns : 99 ( 99 >; 0 *; 0 +; 0 <<)
% 0.18/0.48 % Number of symbols : 30 ( 28 usr; 5 con; 0-3 aty)
% 0.18/0.48 % Number of variables : 40 ( 31 ^; 7 !; 2 ?; 40 :)
% 0.18/0.48 % SPC : TH0_CSA_EQU_NAR
% 0.18/0.48
% 0.18/0.48 % Comments : This is an ILTP problem embedded in TH0
% 0.18/0.48 % : In classical logic this is a Theorem.
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 %------------------------------------------------------------------------------
% 0.18/0.48 %----Modal Logic S4 in HOL
% 0.18/0.48 %----We define an accessibility relation irel
% 0.18/0.48 thf(irel_type,type,
% 0.18/0.48 irel: $i > $i > $o ).
% 0.18/0.48
% 0.18/0.48 %----We require reflexivity and transitivity for irel
% 0.18/0.48 thf(refl_axiom,axiom,
% 0.18/0.48 ! [X: $i] : ( irel @ X @ X ) ).
% 0.18/0.48
% 0.18/0.48 thf(trans_axiom,axiom,
% 0.18/0.48 ! [X: $i,Y: $i,Z: $i] :
% 0.18/0.48 ( ( ( irel @ X @ Y )
% 0.18/0.48 & ( irel @ Y @ Z ) )
% 0.18/0.48 => ( irel @ X @ Z ) ) ).
% 0.18/0.48
% 0.18/0.48 %----We define S4 connective mnot (as set complement)
% 0.18/0.48 thf(mnot_decl_type,type,
% 0.18/0.48 mnot: ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(mnot,definition,
% 0.18/0.48 ( mnot
% 0.18/0.48 = ( ^ [X: $i > $o,U: $i] :
% 0.18/0.48 ~ ( X @ U ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %----We define S4 connective mor (as set union)
% 0.18/0.48 thf(mor_decl_type,type,
% 0.18/0.48 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(mor,definition,
% 0.18/0.48 ( mor
% 0.18/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.18/0.48 ( ( X @ U )
% 0.18/0.48 | ( Y @ U ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %----We define S4 connective mand (as set intersection)
% 0.18/0.48 thf(mand_decl_type,type,
% 0.18/0.48 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(mand,definition,
% 0.18/0.48 ( mand
% 0.18/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.18/0.48 ( ( X @ U )
% 0.18/0.48 & ( Y @ U ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %----We define S4 connective mimpl
% 0.18/0.48 thf(mimplies_decl_type,type,
% 0.18/0.48 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(mimplies,definition,
% 0.18/0.48 ( mimplies
% 0.18/0.48 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %----Definition of mbox_s4; since irel is reflexive and transitive,
% 0.18/0.48 %----it is easy to show that the K and the T axiom hold for mbox_s4
% 0.18/0.48 thf(mbox_s4_decl_type,type,
% 0.18/0.48 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(mbox_s4,definition,
% 0.18/0.48 ( mbox_s4
% 0.18/0.48 = ( ^ [P: $i > $o,X: $i] :
% 0.18/0.48 ! [Y: $i] :
% 0.18/0.48 ( ( irel @ X @ Y )
% 0.18/0.48 => ( P @ Y ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %----Intuitionistic Logic in Modal Logic S4
% 0.18/0.48 %----Definition of iatom: iatom P = P
% 0.18/0.48 %----Goedel maps atoms to atoms
% 0.18/0.48 thf(iatom_type,type,
% 0.18/0.48 iatom: ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(iatom,definition,
% 0.18/0.48 ( iatom
% 0.18/0.48 = ( ^ [P: $i > $o] : P ) ) ).
% 0.18/0.48
% 0.18/0.48 %----Definition of inot: inot P = mnot (mbox_s4 P)
% 0.18/0.48 thf(inot_type,type,
% 0.18/0.48 inot: ( $i > $o ) > $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(inot,definition,
% 0.18/0.48 ( inot
% 0.18/0.48 = ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ) ).
% 0.18/0.48
% 0.18/0.48 %----Definition of true and false
% 0.18/0.48 thf(itrue_type,type,
% 0.18/0.48 itrue: $i > $o ).
% 0.18/0.48
% 0.18/0.48 thf(itrue,definition,
% 0.18/0.48 ( itrue
% 0.18/0.48 = ( ^ [W: $i] : $true ) ) ).
% 0.18/0.48
% 0.18/0.48 thf(ifalse_type,type,
% 0.18/0.48 ifalse: $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(ifalse,definition,
% 0.18/0.49 ( ifalse
% 0.18/0.49 = ( inot @ itrue ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of iand: iand P Q = (mand P Q)
% 0.18/0.49 thf(iand_type,type,
% 0.18/0.49 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(iand,definition,
% 0.18/0.49 ( iand
% 0.18/0.49 = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of ior: ior P Q = (mor (mbox_s4 P) (mbox_s4 Q))
% 0.18/0.49 thf(ior_type,type,
% 0.18/0.49 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(ior,definition,
% 0.18/0.49 ( ior
% 0.18/0.49 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of iimplies: iimplies P Q =
% 0.18/0.49 %---- (mimplies (mbox_s4 P) (mbox_s4 Q))
% 0.18/0.49 thf(iimplies_type,type,
% 0.18/0.49 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(iimplies,definition,
% 0.18/0.49 ( iimplies
% 0.18/0.49 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of iimplied: iimplied P Q = (iimplies Q P)
% 0.18/0.49 thf(iimplied_type,type,
% 0.18/0.49 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(iimplied,definition,
% 0.18/0.49 ( iimplied
% 0.18/0.49 = ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of iequiv: iequiv P Q =
% 0.18/0.49 %---- (iand (iimplies P Q) (iimplies Q P))
% 0.18/0.49 thf(iequiv_type,type,
% 0.18/0.49 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(iequiv,definition,
% 0.18/0.49 ( iequiv
% 0.18/0.49 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of ixor: ixor P Q = (inot (iequiv P Q)
% 0.18/0.49 thf(ixor_type,type,
% 0.18/0.49 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(ixor,definition,
% 0.18/0.49 ( ixor
% 0.18/0.49 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of validity
% 0.18/0.49 thf(ivalid_type,type,
% 0.18/0.49 ivalid: ( $i > $o ) > $o ).
% 0.18/0.49
% 0.18/0.49 thf(ivalid,definition,
% 0.18/0.49 ( ivalid
% 0.18/0.49 = ( ^ [Phi: $i > $o] :
% 0.18/0.49 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of satisfiability
% 0.18/0.49 thf(isatisfiable_type,type,
% 0.18/0.49 isatisfiable: ( $i > $o ) > $o ).
% 0.18/0.49
% 0.18/0.49 thf(isatisfiable,definition,
% 0.18/0.49 ( isatisfiable
% 0.18/0.49 = ( ^ [Phi: $i > $o] :
% 0.18/0.49 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of countersatisfiability
% 0.18/0.49 thf(icountersatisfiable_type,type,
% 0.18/0.49 icountersatisfiable: ( $i > $o ) > $o ).
% 0.18/0.49
% 0.18/0.49 thf(icountersatisfiable,definition,
% 0.18/0.49 ( icountersatisfiable
% 0.18/0.49 = ( ^ [Phi: $i > $o] :
% 0.18/0.49 ? [W: $i] :
% 0.18/0.49 ~ ( Phi @ W ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %----Definition of invalidity
% 0.18/0.49 thf(iinvalid_type,type,
% 0.18/0.49 iinvalid: ( $i > $o ) > $o ).
% 0.18/0.49
% 0.18/0.49 thf(iinvalid,definition,
% 0.18/0.49 ( iinvalid
% 0.18/0.49 = ( ^ [Phi: $i > $o] :
% 0.18/0.49 ! [W: $i] :
% 0.18/0.49 ~ ( Phi @ W ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %------------------------------------------------------------------------------
% 0.18/0.49 %------------------------------------------------------------------------------
% 0.18/0.49 thf(a1_type,type,
% 0.18/0.49 a1: $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(a2_type,type,
% 0.18/0.49 a2: $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(a3_type,type,
% 0.18/0.49 a3: $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(a4_type,type,
% 0.18/0.49 a4: $i > $o ).
% 0.18/0.49
% 0.18/0.49 thf(con,conjecture,
% 0.18/0.49 ivalid @ ( iequiv @ ( iequiv @ ( iequiv @ ( iequiv @ ( inot @ ( inot @ ( iatom @ a1 ) ) ) @ ( iatom @ a2 ) ) @ ( iatom @ a3 ) ) @ ( iatom @ a4 ) ) @ ( iequiv @ ( iatom @ a4 ) @ ( iequiv @ ( iatom @ a3 ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ) ) ).
% 0.18/0.49
% 0.18/0.49 %------------------------------------------------------------------------------
% 0.18/0.49 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.AaL5mGzZLO/cvc5---1.0.5_16476.p...
% 0.18/0.49 (declare-sort $$unsorted 0)
% 0.18/0.49 (declare-fun tptp.irel ($$unsorted $$unsorted) Bool)
% 0.18/0.49 (assert (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))
% 0.18/0.49 (assert (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))))
% 0.18/0.49 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.49 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.18/0.49 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.49 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.18/0.49 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.49 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.18/0.49 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))
% 0.18/0.50 (declare-fun tptp.iatom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.inot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.itrue ($$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.itrue (lambda ((W $$unsorted)) true)))
% 0.18/0.50 (declare-fun tptp.ifalse ($$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.ifalse (@ tptp.inot tptp.itrue)))
% 0.18/0.50 (declare-fun tptp.iand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.ior ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.iimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.iimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.iequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.ixor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.18/0.50 (assert (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))
% 0.18/0.50 (declare-fun tptp.ivalid ((-> $$unsorted Bool)) Bool)
% 0.18/0.50 (assert (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.18/0.50 (declare-fun tptp.isatisfiable ((-> $$unsorted Bool)) Bool)
% 0.18/0.50 (assert (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.18/0.50 (declare-fun tptp.icountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.18/0.50 (assert (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.18/0.50 (declare-fun tptp.iinvalid ((-> $$unsorted Bool)) Bool)
% 0.18/0.50 (assert (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.18/0.50 (declare-fun tptp.a1 ($$unsorted) Bool)
% 0.18/0.50 (declare-fun tptp.a2 ($$unsorted) Bool)
% 0.18/0.50 (declare-fun tptp.a3 ($$unsorted) Bool)
% 0.18/0.50 (declare-fun tptp.a4 ($$unsorted) Bool)
% 0.18/0.50 (assert (let ((_let_1 (@ tptp.iatom tptp.a1))) (let ((_let_2 (@ tptp.iatom tptp.a2))) (let ((_let_3 (@ tptp.iatom tptp.a3))) (let ((_let_4 (@ tptp.iatom tptp.a4))) (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ tptp.inot (@ tptp.inot _let_1))) _let_2)) _let_3)) _let_4)) (@ (@ tptp.iequiv _let_4) (@ (@ tptp.iequiv _let_3) (@ (@ tptp.iequiv _let_2) _let_1)))))))))))
% 0.18/0.50 (set-info :filename cvc5---1.0.5_16476)
% 0.18/0.50 (check-sat-assuming ( true ))
% 0.18/0.50 ------- get file name : TPTP file name is SYN001^4.004
% 0.18/0.50 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16476.smt2...
% 0.18/0.50 --- Run --ho-elim --full-saturate-quant at 10...
% 0.18/0.62 % SZS status Theorem for SYN001^4.004
% 0.18/0.62 % SZS output start Proof for SYN001^4.004
% 0.18/0.62 (
% 0.18/0.62 (let ((_let_1 (@ tptp.iatom tptp.a1))) (let ((_let_2 (@ tptp.iatom tptp.a2))) (let ((_let_3 (@ tptp.iatom tptp.a3))) (let ((_let_4 (@ tptp.iatom tptp.a4))) (let ((_let_5 (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ (@ tptp.iequiv (@ tptp.inot (@ tptp.inot _let_1))) _let_2)) _let_3)) _let_4)) (@ (@ tptp.iequiv _let_4) (@ (@ tptp.iequiv _let_3) (@ (@ tptp.iequiv _let_2) _let_1)))))))) (let ((_let_6 (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_7 (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_8 (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_9 (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_10 (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))) (let ((_let_11 (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))) (let ((_let_12 (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))) (let ((_let_13 (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_14 (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_15 (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))) (let ((_let_16 (= tptp.ifalse (@ tptp.inot tptp.itrue)))) (let ((_let_17 (= tptp.itrue (lambda ((W $$unsorted)) true)))) (let ((_let_18 (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))) (let ((_let_19 (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_20 (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))) (let ((_let_21 (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_22 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_23 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_24 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_25 (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))) (let ((_let_26 (forall ((BOUND_VARIABLE_1875 $$unsorted) (BOUND_VARIABLE_2044 $$unsorted) (BOUND_VARIABLE_2035 $$unsorted) (BOUND_VARIABLE_2022 $$unsorted) (BOUND_VARIABLE_2009 $$unsorted) (BOUND_VARIABLE_2001 $$unsorted) (BOUND_VARIABLE_1994 $$unsorted) (BOUND_VARIABLE_1987 $$unsorted)) (let ((_let_1 (ho_4 k_6 BOUND_VARIABLE_1994))) (let ((_let_2 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1994) BOUND_VARIABLE_1994)))) (let ((_let_3 (not (forall ((BOUND_VARIABLE_1733 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1733) BOUND_VARIABLE_1733)))))) (let ((_let_4 (not (forall ((BOUND_VARIABLE_1663 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1663) BOUND_VARIABLE_1663)) (ho_4 k_7 BOUND_VARIABLE_1663)))))) (let ((_let_5 (ho_4 k_8 BOUND_VARIABLE_2009))) (let ((_let_6 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_2009) BOUND_VARIABLE_2009)))) (let ((_let_7 (not (forall ((BOUND_VARIABLE_1673 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1673) BOUND_VARIABLE_1673)) (ho_4 k_8 BOUND_VARIABLE_1673)))))) (let ((_let_8 (ho_4 k_7 BOUND_VARIABLE_2001))) (let ((_let_9 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_2001) BOUND_VARIABLE_2001)))) (let ((_let_10 (or (and (or _let_9 _let_8) _let_7) (and (or _let_6 _let_5) _let_4)))) (let ((_let_11 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_2022) BOUND_VARIABLE_2022)))) (let ((_let_12 (and (or _let_4 _let_6 _let_5) (or _let_7 _let_9 _let_8)))) (let ((_let_13 (not (forall ((BOUND_VARIABLE_1723 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1723) BOUND_VARIABLE_1723)) (ho_4 k_6 BOUND_VARIABLE_1723)))))) (or (and (or (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1987) BOUND_VARIABLE_1987)) (ho_4 k_5 BOUND_VARIABLE_1987)) (or (and (or _let_2 _let_1) _let_10 _let_3) (and (or _let_12 _let_11) _let_13)) (not (forall ((BOUND_VARIABLE_1797 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1797) BOUND_VARIABLE_1797))))) (and (or (and (or _let_13 _let_12 _let_11) (or (and _let_10 _let_3) _let_2 _let_1)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_2035) BOUND_VARIABLE_2035))) (not (forall ((BOUND_VARIABLE_1787 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1787) BOUND_VARIABLE_1787)) (ho_4 k_5 BOUND_VARIABLE_1787)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1875) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1875) BOUND_VARIABLE_2044))))))))))))))))))) (let ((_let_27 (forall ((BOUND_VARIABLE_1574 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1574) BOUND_VARIABLE_1574))))) (let ((_let_28 (forall ((BOUND_VARIABLE_1487 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1487) BOUND_VARIABLE_1487))))) (let ((_let_29 (forall ((BOUND_VARIABLE_1403 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1403) BOUND_VARIABLE_1403))))) (let ((_let_30 (forall ((BOUND_VARIABLE_1338 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1338) BOUND_VARIABLE_1338))))) (let ((_let_31 (not _let_30))) (let ((_let_32 (forall ((BOUND_VARIABLE_1305 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1305) BOUND_VARIABLE_1305)) (ho_4 k_8 BOUND_VARIABLE_1305))))) (let ((_let_33 (and _let_32 _let_31))) (let ((_let_34 (forall ((BOUND_VARIABLE_1412 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1412) BOUND_VARIABLE_1412)) (ho_4 k_7 BOUND_VARIABLE_1412))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_29))) (let ((_let_37 (not _let_29))) (let ((_let_38 (not _let_32))) (let ((_let_39 (or _let_38 _let_30))) (let ((_let_40 (and _let_39 _let_37))) (let ((_let_41 (or _let_40 _let_34))) (let ((_let_42 (and _let_41 _let_36))) (let ((_let_43 (forall ((BOUND_VARIABLE_1496 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1496) BOUND_VARIABLE_1496)) (ho_4 k_6 BOUND_VARIABLE_1496))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42 _let_28))) (let ((_let_46 (not _let_28))) (let ((_let_47 (and _let_34 _let_39 _let_37))) (let ((_let_48 (or _let_33 _let_29))) (let ((_let_49 (and _let_48 _let_35))) (let ((_let_50 (or _let_49 _let_47))) (let ((_let_51 (and _let_50 _let_46))) (let ((_let_52 (or _let_51 _let_43))) (let ((_let_53 (and _let_52 _let_45))) (let ((_let_54 (forall ((BOUND_VARIABLE_1583 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1583) BOUND_VARIABLE_1583)) (ho_4 k_5 BOUND_VARIABLE_1583))))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_27))) (let ((_let_57 (not _let_27))) (let ((_let_58 (and _let_43 _let_50 _let_46))) (let ((_let_59 (or _let_42 _let_28))) (let ((_let_60 (and _let_59 _let_44))) (let ((_let_61 (or _let_60 _let_58))) (let ((_let_62 (and _let_61 _let_57))) (let ((_let_63 (or _let_62 _let_54))) (let ((_let_64 (and _let_63 _let_56))) (let ((_let_65 (or _let_64 _let_26))) (let ((_let_66 (forall ((BOUND_VARIABLE_1864 $$unsorted) (BOUND_VARIABLE_1961 $$unsorted) (BOUND_VARIABLE_1940 $$unsorted) (BOUND_VARIABLE_1933 $$unsorted) (BOUND_VARIABLE_1947 $$unsorted) (BOUND_VARIABLE_1921 $$unsorted) (BOUND_VARIABLE_1912 $$unsorted) (BOUND_VARIABLE_1905 $$unsorted) (BOUND_VARIABLE_1898 $$unsorted) (BOUND_VARIABLE_1890 $$unsorted)) (let ((_let_1 (not (forall ((BOUND_VARIABLE_1487 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1487) BOUND_VARIABLE_1487)))))) (let ((_let_2 (not (forall ((BOUND_VARIABLE_1403 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1403) BOUND_VARIABLE_1403)))))) (let ((_let_3 (or (not (forall ((BOUND_VARIABLE_1305 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1305) BOUND_VARIABLE_1305)) (ho_4 k_8 BOUND_VARIABLE_1305)))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1912) BOUND_VARIABLE_1912))))) (let ((_let_4 (ho_4 k_7 BOUND_VARIABLE_1905))) (let ((_let_5 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1905) BOUND_VARIABLE_1905)))) (let ((_let_6 (not (forall ((BOUND_VARIABLE_1412 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1412) BOUND_VARIABLE_1412)) (ho_4 k_7 BOUND_VARIABLE_1412)))))) (let ((_let_7 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1898) BOUND_VARIABLE_1898)))) (let ((_let_8 (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1890) BOUND_VARIABLE_1890)) (ho_4 k_8 BOUND_VARIABLE_1890)) (not (forall ((BOUND_VARIABLE_1338 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1338) BOUND_VARIABLE_1338))))))) (let ((_let_9 (or (and (or _let_8 _let_7) _let_6) (and (or _let_5 _let_4) _let_3 _let_2)))) (let ((_let_10 (ho_4 k_6 BOUND_VARIABLE_1921))) (let ((_let_11 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1921) BOUND_VARIABLE_1921)))) (let ((_let_12 (not (forall ((BOUND_VARIABLE_1496 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1496) BOUND_VARIABLE_1496)) (ho_4 k_6 BOUND_VARIABLE_1496)))))) (let ((_let_13 (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1933) BOUND_VARIABLE_1933)))) (let ((_let_14 (and (or (and _let_3 _let_2) _let_5 _let_4) (or _let_6 _let_8 _let_7)))) (or (and (or (and (or (and (or (and _let_9 _let_1) _let_11 _let_10) (or _let_12 _let_14 _let_13)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1940) BOUND_VARIABLE_1940))) (not (forall ((BOUND_VARIABLE_1583 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1583) BOUND_VARIABLE_1583)) (ho_4 k_5 BOUND_VARIABLE_1583))))) (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1947) BOUND_VARIABLE_1947)) (ho_4 k_5 BOUND_VARIABLE_1947)) (or (and (or _let_14 _let_13) _let_12) (and (or _let_11 _let_10) _let_9 _let_1)) (not (forall ((BOUND_VARIABLE_1574 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1574) BOUND_VARIABLE_1574)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1864) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1864) BOUND_VARIABLE_1961)))))))))))))))))))) (let ((_let_67 (forall ((BOUND_VARIABLE_1787 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1787) BOUND_VARIABLE_1787)) (ho_4 k_5 BOUND_VARIABLE_1787))))) (let ((_let_68 (forall ((BOUND_VARIABLE_1797 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1797) BOUND_VARIABLE_1797))))) (let ((_let_69 (not _let_68))) (let ((_let_70 (forall ((BOUND_VARIABLE_1723 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1723) BOUND_VARIABLE_1723)) (ho_4 k_6 BOUND_VARIABLE_1723))))) (let ((_let_71 (not _let_70))) (let ((_let_72 (forall ((BOUND_VARIABLE_1733 $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1733) BOUND_VARIABLE_1733))))) (let ((_let_73 (forall ((BOUND_VARIABLE_1663 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1663) BOUND_VARIABLE_1663)) (ho_4 k_7 BOUND_VARIABLE_1663))))) (let ((_let_74 (forall ((BOUND_VARIABLE_1673 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1673) BOUND_VARIABLE_1673)) (ho_4 k_8 BOUND_VARIABLE_1673))))) (let ((_let_75 (not _let_74))) (let ((_let_76 (or _let_75 _let_73))) (let ((_let_77 (not _let_73))) (let ((_let_78 (or _let_77 _let_74))) (let ((_let_79 (and _let_78 _let_76))) (let ((_let_80 (or _let_79 _let_72))) (let ((_let_81 (and _let_80 _let_71))) (let ((_let_82 (not _let_72))) (let ((_let_83 (and _let_74 _let_77))) (let ((_let_84 (and _let_73 _let_75))) (let ((_let_85 (or _let_84 _let_83))) (let ((_let_86 (and _let_70 _let_85 _let_82))) (let ((_let_87 (or _let_86 _let_81))) (let ((_let_88 (and _let_87 _let_69))) (let ((_let_89 (or _let_88 _let_67))) (let ((_let_90 (and _let_85 _let_82))) (let ((_let_91 (or _let_90 _let_70))) (let ((_let_92 (or _let_71 _let_79 _let_72))) (let ((_let_93 (and _let_92 _let_91))) (let ((_let_94 (not _let_67))) (let ((_let_95 (or _let_94 _let_93 _let_68))) (let ((_let_96 (and _let_95 _let_89))) (let ((_let_97 (or _let_96 _let_66))) (let ((_let_98 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)) (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20)))) (let ((_let_99 (ho_4 k_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_100 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_101 (not _let_100))) (let ((_let_102 (or _let_101 _let_99))) (let ((_let_103 (and _let_98 _let_31))) (let ((_let_104 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)))) (let ((_let_105 (or _let_35 _let_103 _let_104))) (let ((_let_106 (ho_4 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_107 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_38 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))))) (let ((_let_110 (and _let_109 _let_37))) (let ((_let_111 (or _let_110 _let_108 _let_106))) (let ((_let_112 (and _let_111 _let_105))) (let ((_let_113 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_114 (or _let_44 _let_112 _let_113))) (let ((_let_115 (ho_4 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_116 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_108 _let_106))) (let ((_let_119 (and _let_118 _let_109 _let_37))) (let ((_let_120 (or _let_103 _let_104))) (let ((_let_121 (and _let_120 _let_35))) (let ((_let_122 (or _let_121 _let_119))) (let ((_let_123 (and _let_122 _let_46))) (let ((_let_124 (or _let_123 _let_117 _let_115))) (let ((_let_125 (and _let_124 _let_114))) (let ((_let_126 (or _let_125 (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_127 (and _let_126 _let_55))) (let ((_let_128 (or _let_117 _let_115))) (let ((_let_129 (and _let_128 _let_122 _let_46))) (let ((_let_130 (or _let_112 _let_113))) (let ((_let_131 (and _let_130 _let_44))) (let ((_let_132 (or _let_131 _let_129))) (let ((_let_133 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)))) (let ((_let_134 (and _let_133 _let_132 _let_57))) (let ((_let_135 (or _let_127 _let_134))) (let ((_let_136 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) 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Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1864) BOUND_VARIABLE_1961))))))))))))))))))) (or (and (or (and (or (and (or _let_285 _let_276) _let_287) (and _let_286 _let_289 _let_288)) (not _let_275)) _let_290) (or (not _let_290) (and (or (and _let_289 _let_288) _let_286) (or _let_287 _let_285 _let_276)) _let_275)) (forall ((BOUND_VARIABLE_1875 $$unsorted) (BOUND_VARIABLE_2044 $$unsorted) (BOUND_VARIABLE_2035 $$unsorted) (BOUND_VARIABLE_2022 $$unsorted) (BOUND_VARIABLE_2009 $$unsorted) (BOUND_VARIABLE_2001 $$unsorted) (BOUND_VARIABLE_1994 $$unsorted) (BOUND_VARIABLE_1987 $$unsorted)) (let ((_let_1 (@ tptp.a3 BOUND_VARIABLE_1994))) (let ((_let_2 (not (@ (@ tptp.irel BOUND_VARIABLE_1994) BOUND_VARIABLE_1994)))) (let ((_let_3 (not (forall ((BOUND_VARIABLE_1733 $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1733) BOUND_VARIABLE_1733)))))) (let ((_let_4 (not (forall ((BOUND_VARIABLE_1663 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1663) BOUND_VARIABLE_1663)) (@ tptp.a2 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_let_363) (CONG (REFL :args _let_363) (REFL :args (_let_362)) (MACRO_SR_PRED_INTRO :args ((= (not _let_145) _let_144))) :args _let_195)) :args ((or _let_144 _let_174 _let_362))))) (let ((_let_365 (_let_144))) (let ((_let_366 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_365) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_365)))) (let ((_let_367 (REORDERING (CNF_OR_NEG :args (_let_78 1)) :args ((or _let_75 _let_78))))) (let ((_let_368 (EQUIV_ELIM1 _let_209))) (let ((_let_369 (CNF_AND_NEG :args (_let_79)))) (let ((_let_370 (_let_33))) (let ((_let_371 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_370) (CONG (REFL :args _let_370) (REFL :args (_let_38)) _let_196 :args _let_195)) :args ((or _let_30 _let_33 _let_38))))) (let ((_let_372 (CNF_OR_NEG :args (_let_92 1)))) (let ((_let_373 (CNF_OR_NEG :args (_let_36 1)))) (let ((_let_374 (CNF_AND_NEG :args (_let_93)))) (let ((_let_375 (CNF_AND_NEG :args (_let_42)))) (let ((_let_376 (CNF_OR_NEG :args (_let_95 1)))) (let ((_let_377 (CNF_OR_NEG :args (_let_45 1)))) (let ((_let_378 (CNF_AND_NEG :args (_let_53)))) (let ((_let_379 (CNF_OR_NEG :args (_let_56 1)))) (let ((_let_380 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 0)) (CONG (REFL :args (_let_78)) _let_202 :args _let_195)) :args ((or _let_73 _let_78))))) (let ((_let_381 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG (REFL :args (_let_36)) _let_205 :args _let_195)) :args ((or _let_34 _let_36))))) (let ((_let_382 (CNF_OR_NEG :args (_let_120 0)))) (let ((_let_383 (not _let_120))) (let ((_let_384 (_let_121))) (let ((_let_385 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_384) (CONG (REFL :args _let_384) (REFL :args (_let_383)) _let_205 :args _let_195)) :args ((or _let_34 _let_121 _let_383))))) (let ((_let_386 (CNF_OR_NEG :args (_let_122 0)))) (let ((_let_387 (CNF_OR_NEG :args (_let_155 1)))) (let ((_let_388 (not _let_102))) (let ((_let_389 (_let_149))) (let ((_let_390 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args 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(MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST _let_366 _let_364 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_347 _let_346 _let_342 _let_341 _let_340 _let_338 _let_255 _let_334 _let_253 _let_333 _let_320 _let_247 _let_216 _let_319 :args ((or _let_72 _let_242 _let_218 _let_322 _let_331 _let_321 _let_330 _let_246) false _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_134 false _let_132 false _let_173 false _let_129 false _let_172 false _let_122 false _let_170 false _let_119 false _let_169 true _let_27 true _let_28 true _let_29 true _let_68)) _let_245 _let_214 _let_244 _let_210 :args ((or _let_72 _let_74 _let_242 _let_322 _let_331 _let_321 _let_330 _let_240) false _let_155 false _let_109 false _let_154 true _let_32)) _let_238 _let_237 _let_235 _let_232 _let_231 _let_192 _let_318 :args ((or _let_77 (not _let_91) _let_268 _let_267 (not _let_52) _let_322 _let_331 _let_321 _let_330) false _let_64 true _let_65 false _let_56 false _let_97 false _let_53 false _let_96 false _let_45 false _let_95 false _let_42 false _let_93 false _let_36 false _let_92 false _let_33 false _let_79 false _let_32 false _let_78 false _let_74 false _let_41 false _let_153 false _let_118 false _let_34 false _let_76 true _let_30 true _let_72)) (REORDERING (CNF_OR_NEG :args (_let_52 1)) :args ((or _let_44 _let_52))) _let_329 _let_327 _let_323 (REORDERING (CNF_OR_NEG :args (_let_91 1)) :args ((or _let_71 _let_91))) _let_216 _let_318 :args ((or _let_71 _let_268 _let_267 _let_322 _let_321) true _let_64 false _let_56 true _let_65 false _let_53 false _let_97 false _let_45 false _let_96 false _let_42 false _let_95 false _let_41 false _let_93 false _let_40 false _let_92 false _let_39 false _let_79 true _let_32 false _let_76 true _let_74 false _let_36 true _let_34 false _let_78 true _let_73 false _let_52 false _let_168 false _let_128 false _let_43 false _let_91 true _let_29 true _let_72)))) (let ((_let_399 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_92 0)) (CONG (REFL :args (_let_92)) _let_227 :args _let_195)) :args ((or _let_70 _let_92))))) (let ((_let_400 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) _let_229 :args _let_195)) :args ((or _let_43 _let_45))))) (let ((_let_401 (CNF_OR_NEG :args (_let_166 0)))) (let ((_let_402 (not _let_166))) (let ((_let_403 (_let_167))) (let ((_let_404 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_403) (CONG (REFL :args _let_403) (REFL :args (_let_402)) _let_227 :args _let_195)) :args ((or _let_70 _let_167 _let_402))))) (let ((_let_405 (CNF_AND_NEG :args (_let_112)))) (let ((_let_406 (CNF_OR_NEG :args (_let_170 1)))) (let ((_let_407 (CNF_OR_NEG :args (_let_130 0)))) (let ((_let_408 (not _let_130))) (let ((_let_409 (_let_131))) (let ((_let_410 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_409) (CONG (REFL :args _let_409) (REFL :args (_let_408)) _let_229 :args _let_195)) :args 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:args (_let_50 0)))) (let ((_let_425 (not _let_50))) (let ((_let_426 (REFL :args (_let_425)))) (let ((_let_427 (_let_51))) (let ((_let_428 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_427) (CONG (REFL :args _let_427) _let_426 _let_258 :args _let_195)) :args ((or _let_28 _let_51 _let_425))))) (let ((_let_429 (CNF_OR_NEG :args (_let_52 0)))) (let ((_let_430 (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_108 _let_106 _let_242))))) (let ((_let_431 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_185 :args _let_236) :args _let_187)) _let_186 :args (_let_151 false _let_180)))) (let ((_let_432 (REORDERING (CNF_OR_POS :args (_let_153)) :args ((or _let_152 _let_150 _let_240))))) (let ((_let_433 (CNF_OR_NEG :args (_let_111 2)))) (let ((_let_434 (CNF_OR_NEG :args (_let_159 2)))) (let ((_let_435 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_160 1)) (CONG _let_203 (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_100))) :args _let_195)) :args ((or _let_100 _let_160))))) (let ((_let_436 (CNF_OR_NEG :args (_let_160 2)))) (let ((_let_437 (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_101 _let_99 _let_388))))) (let ((_let_438 (_let_84))) (let ((_let_439 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_438) (CONG (REFL :args _let_438) (REFL :args (_let_77)) _let_211 :args _let_195)) :args ((or _let_77 _let_74 _let_84))))) (let ((_let_440 (CNF_OR_NEG :args (_let_85 0)))) (let ((_let_441 (_let_47))) (let ((_let_442 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_441) (CONG (REFL :args _let_441) (REFL :args (_let_35)) _let_394 _let_219 :args _let_195)) :args ((or _let_29 _let_35 _let_47 _let_393))))) (let ((_let_443 (CNF_OR_NEG :args (_let_50 1)))) (let ((_let_444 (MACRO_RESOLUTION_TRUST _let_274 _let_272 _let_317 _let_379 _let_273 _let_378 _let_271 _let_429 _let_376 _let_428 _let_374 _let_443 _let_420 _let_442 _let_418 _let_392 _let_440 _let_210 _let_439 (MACRO_RESOLUTION_TRUST _let_437 _let_436 _let_435 _let_215 _let_401 _let_404 _let_406 _let_338 _let_341 _let_364 _let_366 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_347 _let_346 _let_411 _let_410 _let_407 _let_405 _let_199 _let_198 _let_179 _let_178 _let_226 :args ((or _let_75 _let_70 _let_68 _let_27 _let_30 (not _let_111) _let_322 _let_321 (not _let_159)) true _let_99 false _let_100 true _let_160 true _let_161 true _let_166 true _let_167 true _let_170 true _let_172 true _let_173 true _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_134 false _let_132 false _let_131 false _let_130 false _let_112 false _let_105 false _let_103 false _let_102 false _let_98 true _let_43)) _let_434 _let_433 _let_432 _let_431 _let_430 _let_189 _let_237 _let_235 _let_232 (MACRO_RESOLUTION_TRUST _let_272 _let_274 _let_379 _let_317 _let_378 _let_273 _let_429 _let_271 _let_428 _let_376 _let_424 _let_374 _let_423 _let_420 _let_419 _let_418 _let_371 _let_414 _let_368 _let_413 (MACRO_RESOLUTION_TRUST _let_366 _let_364 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_347 _let_346 _let_411 _let_341 _let_410 _let_338 _let_407 _let_406 _let_405 _let_404 _let_224 _let_401 _let_222 _let_215 _let_214 _let_212 _let_210 _let_226 :args ((or _let_74 _let_70 _let_68 _let_27 _let_29 _let_208 _let_322 _let_321 _let_207) false _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_134 false _let_132 false _let_173 false _let_131 false _let_172 false _let_130 false _let_170 false _let_112 false _let_167 false _let_111 false _let_166 false _let_110 false _let_161 false _let_109 false _let_159 true _let_32 true _let_43)) _let_206 _let_204 _let_201 _let_216 _let_319 _let_320 _let_192 _let_399 _let_247 _let_318 _let_400 _let_226 _let_398 :args ((or _let_73 _let_268 _let_267 _let_322 _let_321) true _let_64 false _let_56 true _let_65 false 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1)))) (let ((_let_451 (CNF_OR_NEG :args (_let_126 0)))) (let ((_let_452 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_264) _let_444 :args (_let_55 true _let_67)))) (let ((_let_453 (not _let_126))) (let ((_let_454 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))))) (let ((_let_455 (_let_127))) (let ((_let_456 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_455) (CONG (REFL :args _let_455) (REFL :args (_let_453)) _let_454 :args _let_195)) :args ((or _let_54 _let_127 _let_453))))) (let ((_let_457 (CNF_OR_NEG :args (_let_135 0)))) (let ((_let_458 (CNF_OR_NEG :args (_let_80 0)))) (let ((_let_459 (not _let_80))) (let ((_let_460 (_let_81))) (let ((_let_461 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_460) (CONG (REFL :args _let_460) (REFL :args (_let_459)) _let_227 :args _let_195)) :args ((or _let_70 _let_81 _let_459))))) (let ((_let_462 (CNF_OR_NEG :args (_let_87 1)))) (let ((_let_463 (CNF_OR_NEG :args (_let_59 0)))) (let ((_let_464 (MACRO_RESOLUTION_TRUST _let_319 _let_191 :args (_let_69 true _let_72)))) (let ((_let_465 (not _let_87))) (let ((_let_466 (_let_88))) (let ((_let_467 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_466) (CONG (REFL :args _let_466) (REFL :args (_let_465)) _let_336 :args _let_195)) :args ((or _let_68 _let_88 _let_465))))) (let ((_let_468 (not _let_59))) (let ((_let_469 (_let_60))) (let ((_let_470 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_469) (CONG (REFL :args _let_469) (REFL :args (_let_468)) _let_229 :args _let_195)) :args ((or _let_43 _let_60 _let_468))))) (let ((_let_471 (CNF_OR_NEG :args (_let_89 0)))) (let ((_let_472 (CNF_OR_NEG :args (_let_61 0)))) (let ((_let_473 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_95 0)) (CONG (REFL :args (_let_95)) _let_446 :args _let_195)) :args ((or _let_67 _let_95))) _let_444 :args (_let_95 true _let_67)))) (let ((_let_474 (MACRO_RESOLUTION_TRUST _let_320 _let_191 :args (_let_57 true _let_72)))) (let ((_let_475 (not _let_61))) (let ((_let_476 (_let_62))) (let ((_let_477 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_476) (CONG (REFL :args _let_476) (REFL :args (_let_475)) _let_344 :args _let_195)) :args ((or _let_27 _let_62 _let_475))))) (let ((_let_478 (CNF_OR_NEG :args (_let_63 0)))) (let ((_let_479 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG (REFL :args (_let_56)) _let_454 :args _let_195)) :args ((or _let_54 _let_56))) _let_452 :args (_let_56 true _let_54)))) (let ((_let_480 (MACRO_RESOLUTION_TRUST _let_247 _let_191 :args (_let_46 true _let_72)))) (let ((_let_481 (MACRO_RESOLUTION_TRUST _let_272 _let_479 _let_274 _let_478 _let_317 _let_477 _let_474 _let_273 _let_472 _let_271 _let_473 _let_470 _let_471 _let_463 _let_467 _let_464 _let_375 _let_462 _let_397 _let_461 _let_396 _let_217 _let_458 _let_392 _let_369 _let_210 _let_391 (MACRO_RESOLUTION_TRUST _let_366 _let_364 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_457 _let_456 _let_452 _let_450 _let_451 _let_448 _let_444 _let_449 _let_262 _let_263 _let_256 _let_261 _let_480 _let_254 _let_386 _let_251 _let_191 _let_385 _let_387 _let_382 _let_390 _let_198 _let_193 _let_179 _let_178 _let_201 :args ((or _let_73 _let_75 _let_241 _let_239) false _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_127 true _let_54 false _let_173 false _let_126 false _let_165 true _let_67 false _let_125 false _let_164 false _let_124 false _let_163 false _let_123 true _let_28 false _let_157 false _let_122 false _let_156 true _let_72 false _let_121 false _let_155 false _let_120 false _let_149 false _let_103 true _let_30 false _let_102 false _let_98 true _let_34)) _let_381 _let_201 _let_380 (MACRO_RESOLUTION_TRUST _let_274 _let_272 _let_479 _let_317 _let_478 _let_273 _let_477 _let_474 _let_271 _let_473 _let_472 _let_471 _let_470 _let_467 _let_464 _let_463 _let_462 _let_375 _let_461 _let_373 _let_458 _let_371 _let_193 _let_369 _let_368 _let_367 (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST _let_366 _let_364 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_457 _let_456 _let_452 _let_451 _let_450 _let_449 _let_448 _let_444 _let_263 _let_262 _let_261 _let_256 _let_255 _let_254 _let_253 _let_251 _let_247 _let_216 :args ((or _let_72 _let_242 _let_218 _let_241 _let_246 _let_239) false _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_127 true _let_54 false _let_126 false _let_173 false _let_125 false _let_165 true _let_67 false _let_124 false _let_164 false _let_123 false _let_163 false _let_122 false _let_157 false _let_119 false _let_156 true _let_28 true _let_29)) _let_191 _let_245 _let_214 _let_244 _let_210 :args ((or _let_74 _let_242 _let_241 _let_240 _let_239) true _let_72 false _let_155 false _let_109 false _let_154 true _let_32)) _let_238 _let_237 _let_235 _let_232 _let_231 _let_230 _let_228 _let_226 :args ((or _let_77 _let_70) false _let_64 false _let_56 true _let_65 false _let_63 false _let_97 false _let_62 true _let_27 false _let_96 false _let_95 false _let_61 false _let_89 false _let_60 false _let_88 true _let_68 false _let_59 false _let_87 false _let_42 false _let_81 false _let_36 false _let_80 false _let_33 true _let_30 false _let_79 false _let_32 false _let_78 false _let_74 false _let_41 false _let_153 false _let_118 false _let_34 false _let_76 false _let_114 false _let_162 true _let_43)) _let_230 _let_228 _let_226 :args (_let_70 false _let_56 true _let_64 false _let_63 true _let_65 false _let_62 true _let_27 false _let_97 false _let_61 false _let_96 false _let_95 false _let_60 false _let_89 false _let_59 false _let_88 true _let_68 false _let_42 false _let_87 false _let_41 false _let_81 false _let_40 true _let_29 false _let_80 false _let_39 false _let_79 true _let_32 false _let_76 true _let_74 false _let_36 true _let_34 false _let_78 true _let_73 false _let_114 false _let_162 true _let_43)))) (let ((_let_482 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_157 2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_168)) :args ((or _let_148 _let_146 _let_330))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_185 :args _let_328) :args _let_187)) _let_186 :args (_let_147 false _let_180)) (MACRO_RESOLUTION_TRUST _let_329 _let_481 :args (_let_168 false _let_70)) :args (_let_146 false _let_147 false _let_168)) :args (_let_157 false _let_146)))) (let ((_let_483 (CNF_OR_NEG :args (_let_114 1)))) (let ((_let_484 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_124 2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_117 _let_115 _let_331))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_185 :args _let_325) :args _let_187)) _let_186 :args (_let_116 false _let_180)) (MACRO_RESOLUTION_TRUST _let_327 _let_481 :args (_let_128 false _let_70)) :args (_let_115 false _let_116 false _let_128)) :args (_let_124 false _let_115)))) (let ((_let_485 (_let_86))) (let ((_let_486 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_485) (CONG (REFL :args _let_485) (REFL :args (_let_71)) _let_416 _let_248 :args _let_195)) :args ((or _let_72 _let_71 _let_86 _let_415))))) (let ((_let_487 (CNF_OR_NEG :args (_let_87 0)))) (let ((_let_488 (MACRO_RESOLUTION_TRUST _let_323 _let_481 :args (_let_43 false _let_70)))) (let ((_let_489 (_let_58))) (let ((_let_490 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_489) (CONG (REFL :args _let_489) (REFL :args (_let_44)) _let_426 _let_258 :args _let_195)) :args ((or _let_28 _let_44 _let_58 _let_425))))) (let ((_let_491 (CNF_OR_NEG :args (_let_61 1)))) (let ((_let_492 (MACRO_RESOLUTION_TRUST _let_272 _let_479 _let_274 _let_478 _let_317 _let_477 _let_474 _let_273 _let_491 _let_271 _let_473 _let_490 _let_488 _let_480 _let_471 _let_424 _let_467 _let_464 _let_423 _let_487 _let_419 _let_486 _let_191 _let_481 _let_371 _let_193 _let_414 _let_368 _let_413 (MACRO_RESOLUTION_TRUST _let_366 _let_364 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_457 _let_456 _let_452 _let_451 _let_450 _let_449 _let_484 _let_448 _let_444 _let_483 _let_262 _let_405 _let_256 _let_482 _let_224 _let_223 _let_222 _let_217 _let_215 _let_214 _let_212 _let_210 :args ((or _let_74 _let_208 _let_207) false _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_127 true _let_54 false _let_126 false _let_173 false _let_125 false _let_124 false _let_165 true _let_67 false _let_114 false _let_164 false _let_112 false _let_163 false _let_157 false _let_111 false _let_162 false _let_110 true _let_29 false _let_161 false _let_109 false _let_159 true _let_32)) _let_206 _let_204 _let_201 :args (_let_73 false _let_56 true _let_64 false _let_63 true _let_65 false _let_62 true _let_27 false _let_97 false _let_61 false _let_96 false _let_95 false _let_58 false _let_43 true _let_28 false _let_89 false _let_50 false _let_88 true _let_68 false _let_49 false _let_87 false _let_48 false _let_86 true _let_72 false _let_70 false _let_33 true _let_30 false _let_85 false _let_32 false _let_83 false _let_74 false _let_105 false _let_160 true _let_34)))) (let ((_let_493 (MACRO_RESOLUTION_TRUST _let_437 _let_436 _let_435 _let_215 (MACRO_RESOLUTION_TRUST _let_434 (MACRO_RESOLUTION_TRUST _let_432 _let_431 (MACRO_RESOLUTION_TRUST _let_237 _let_492 :args (_let_153 false _let_73)) :args (_let_150 false _let_151 false _let_153)) :args (_let_159 false _let_150)) _let_223 _let_256 _let_482 _let_262 _let_448 _let_444 _let_450 _let_364 _let_366 _let_361 _let_360 _let_359 _let_356 _let_317 _let_355 _let_354 _let_351 _let_457 _let_456 _let_452 _let_451 _let_449 _let_484 _let_483 _let_405 (MACRO_RESOLUTION_TRUST _let_433 (MACRO_RESOLUTION_TRUST _let_430 _let_189 (MACRO_RESOLUTION_TRUST _let_235 _let_492 :args (_let_118 false _let_73)) :args (_let_106 false _let_107 false _let_118)) :args (_let_111 false _let_106)) _let_199 _let_198 _let_193 _let_179 _let_178 :args (_let_75 true _let_99 false _let_100 true _let_160 false _let_159 true _let_161 true _let_162 false _let_157 true _let_163 true _let_164 true _let_67 true _let_165 true _let_173 true _let_144 false _let_142 true _let_174 true _let_175 true _let_26 true _let_65 false _let_97 false _let_66 false _let_141 false _let_135 false _let_127 true _let_54 false _let_126 false _let_125 false _let_124 false _let_114 false _let_112 false _let_111 false _let_105 false _let_103 true _let_30 false _let_102 false _let_98)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_274 (MACRO_RESOLUTION_TRUST _let_272 (MACRO_RESOLUTION_TRUST _let_478 (MACRO_RESOLUTION_TRUST _let_477 _let_474 (MACRO_RESOLUTION_TRUST _let_491 (MACRO_RESOLUTION_TRUST _let_490 _let_480 _let_488 (MACRO_RESOLUTION_TRUST _let_443 (MACRO_RESOLUTION_TRUST _let_442 _let_217 (MACRO_RESOLUTION_TRUST _let_232 _let_492 :args (_let_34 false _let_73)) (MACRO_RESOLUTION_TRUST _let_392 (MACRO_RESOLUTION_TRUST _let_210 _let_493 :args (_let_38 true _let_74)) :args (_let_39 true _let_32)) :args (_let_47 true _let_29 false _let_34 false _let_39)) :args (_let_50 false _let_47)) :args (_let_58 true _let_28 false _let_43 false _let_50)) :args (_let_61 false _let_58)) :args (_let_62 true _let_27 false _let_61)) :args (_let_63 false _let_62)) _let_479 :args (_let_64 false _let_63 false _let_56)) (MACRO_RESOLUTION_TRUST _let_317 (MACRO_RESOLUTION_TRUST _let_273 (MACRO_RESOLUTION_TRUST _let_271 _let_473 (MACRO_RESOLUTION_TRUST _let_471 (MACRO_RESOLUTION_TRUST _let_467 _let_464 (MACRO_RESOLUTION_TRUST _let_487 (MACRO_RESOLUTION_TRUST _let_486 _let_191 _let_481 (MACRO_RESOLUTION_TRUST _let_440 (MACRO_RESOLUTION_TRUST _let_439 _let_492 _let_493 :args (_let_84 false _let_73 true _let_74)) :args (_let_85 false _let_84)) :args (_let_86 true _let_72 false _let_70 false _let_85)) :args (_let_87 false _let_86)) :args (_let_88 true _let_68 false _let_87)) :args (_let_89 false _let_88)) :args (_let_96 false _let_95 false _let_89)) :args (_let_97 false _let_96)) :args ((not _let_65) false _let_97)) :args (false false _let_64 true _let_65)) :args (_let_25 (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_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 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.62 )
% 0.18/0.62 % SZS output end Proof for SYN001^4.004
% 0.18/0.62 % cvc5---1.0.5 exiting
% 0.18/0.62 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------