TSTP Solution File: SYN393^4.002 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SYN393^4.002 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 02:02:57 EDT 2023
% Result : Theorem 0.24s 0.59s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SYN393^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 19:05:23 EDT 2023
% 0.24/0.37 % CPUTime :
% 0.24/0.52 %----Proving TH0
% 0.24/0.53 %------------------------------------------------------------------------------
% 0.24/0.53 % File : SYN393^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.24/0.53 % Domain : Logic Calculi (Intuitionistic logic)
% 0.24/0.53 % Problem : ILTP Problem SYJ206+1.002
% 0.24/0.53 % Version : [Goe33] axioms.
% 0.24/0.53 % English :
% 0.24/0.53
% 0.24/0.53 % Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic
% 0.24/0.53 % : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of
% 0.24/0.53 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 0.24/0.53 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.24/0.53 % : [BP10] Benzmueller & Paulson (2009), Exploring Properties of
% 0.24/0.53 % Source : [Ben09]
% 0.24/0.53 % Names : SYJ206+1.002 [ROK06]
% 0.24/0.53
% 0.24/0.53 % Status : Theorem
% 0.24/0.53 % Rating : 0.31 v8.1.0, 0.18 v7.5.0, 0.29 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
% 0.24/0.53 % Syntax : Number of formulae : 44 ( 20 unt; 22 typ; 19 def)
% 0.24/0.53 % Number of atoms : 75 ( 19 equ; 0 cnn)
% 0.24/0.53 % Maximal formula atoms : 12 ( 3 avg)
% 0.24/0.53 % Number of connectives : 66 ( 3 ~; 1 |; 2 &; 58 @)
% 0.24/0.53 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.24/0.53 % Maximal formula depth : 8 ( 2 avg)
% 0.24/0.53 % Number of types : 2 ( 0 usr)
% 0.24/0.53 % Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% 0.24/0.53 % Number of symbols : 27 ( 25 usr; 4 con; 0-3 aty)
% 0.24/0.53 % Number of variables : 40 ( 31 ^; 7 !; 2 ?; 40 :)
% 0.24/0.53 % SPC : TH0_THM_EQU_NAR
% 0.24/0.53
% 0.24/0.53 % Comments : This is an ILTP problem embedded in TH0.
% 0.24/0.53 % : SYN390^4 is the size 1 instance.
% 0.24/0.53 %------------------------------------------------------------------------------
% 0.24/0.53 %------------------------------------------------------------------------------
% 0.24/0.53 %----Modal Logic S4 in HOL
% 0.24/0.53 %----We define an accessibility relation irel
% 0.24/0.53 thf(irel_type,type,
% 0.24/0.53 irel: $i > $i > $o ).
% 0.24/0.53
% 0.24/0.53 %----We require reflexivity and transitivity for irel
% 0.24/0.53 thf(refl_axiom,axiom,
% 0.24/0.53 ! [X: $i] : ( irel @ X @ X ) ).
% 0.24/0.53
% 0.24/0.53 thf(trans_axiom,axiom,
% 0.24/0.53 ! [X: $i,Y: $i,Z: $i] :
% 0.24/0.53 ( ( ( irel @ X @ Y )
% 0.24/0.53 & ( irel @ Y @ Z ) )
% 0.24/0.53 => ( irel @ X @ Z ) ) ).
% 0.24/0.53
% 0.24/0.53 %----We define S4 connective mnot (as set complement)
% 0.24/0.53 thf(mnot_decl_type,type,
% 0.24/0.53 mnot: ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(mnot,definition,
% 0.24/0.53 ( mnot
% 0.24/0.53 = ( ^ [X: $i > $o,U: $i] :
% 0.24/0.53 ~ ( X @ U ) ) ) ).
% 0.24/0.53
% 0.24/0.53 %----We define S4 connective mor (as set union)
% 0.24/0.53 thf(mor_decl_type,type,
% 0.24/0.53 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(mor,definition,
% 0.24/0.53 ( mor
% 0.24/0.53 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.24/0.53 ( ( X @ U )
% 0.24/0.53 | ( Y @ U ) ) ) ) ).
% 0.24/0.53
% 0.24/0.53 %----We define S4 connective mand (as set intersection)
% 0.24/0.53 thf(mand_decl_type,type,
% 0.24/0.53 mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(mand,definition,
% 0.24/0.53 ( mand
% 0.24/0.53 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.24/0.53 ( ( X @ U )
% 0.24/0.53 & ( Y @ U ) ) ) ) ).
% 0.24/0.53
% 0.24/0.53 %----We define S4 connective mimpl
% 0.24/0.53 thf(mimplies_decl_type,type,
% 0.24/0.53 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(mimplies,definition,
% 0.24/0.53 ( mimplies
% 0.24/0.53 = ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
% 0.24/0.53
% 0.24/0.53 %----Definition of mbox_s4; since irel is reflexive and transitive,
% 0.24/0.53 %----it is easy to show that the K and the T axiom hold for mbox_s4
% 0.24/0.53 thf(mbox_s4_decl_type,type,
% 0.24/0.53 mbox_s4: ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(mbox_s4,definition,
% 0.24/0.53 ( mbox_s4
% 0.24/0.53 = ( ^ [P: $i > $o,X: $i] :
% 0.24/0.53 ! [Y: $i] :
% 0.24/0.53 ( ( irel @ X @ Y )
% 0.24/0.53 => ( P @ Y ) ) ) ) ).
% 0.24/0.53
% 0.24/0.53 %----Intuitionistic Logic in Modal Logic S4
% 0.24/0.53 %----Definition of iatom: iatom P = P
% 0.24/0.53 %----Goedel maps atoms to atoms
% 0.24/0.53 thf(iatom_type,type,
% 0.24/0.53 iatom: ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(iatom,definition,
% 0.24/0.53 ( iatom
% 0.24/0.53 = ( ^ [P: $i > $o] : P ) ) ).
% 0.24/0.53
% 0.24/0.53 %----Definition of inot: inot P = mnot (mbox_s4 P)
% 0.24/0.53 thf(inot_type,type,
% 0.24/0.53 inot: ( $i > $o ) > $i > $o ).
% 0.24/0.53
% 0.24/0.53 thf(inot,definition,
% 0.24/0.53 ( inot
% 0.24/0.53 = ( ^ [P: $i > $o] : ( mnot @ ( mbox_s4 @ P ) ) ) ) ).
% 0.24/0.53
% 0.24/0.53 %----Definition of true and false
% 0.24/0.53 thf(itrue_type,type,
% 0.24/0.54 itrue: $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(itrue,definition,
% 0.24/0.54 ( itrue
% 0.24/0.54 = ( ^ [W: $i] : $true ) ) ).
% 0.24/0.54
% 0.24/0.54 thf(ifalse_type,type,
% 0.24/0.54 ifalse: $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(ifalse,definition,
% 0.24/0.54 ( ifalse
% 0.24/0.54 = ( inot @ itrue ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of iand: iand P Q = (mand P Q)
% 0.24/0.54 thf(iand_type,type,
% 0.24/0.54 iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(iand,definition,
% 0.24/0.54 ( iand
% 0.24/0.54 = ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of ior: ior P Q = (mor (mbox_s4 P) (mbox_s4 Q))
% 0.24/0.54 thf(ior_type,type,
% 0.24/0.54 ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(ior,definition,
% 0.24/0.54 ( ior
% 0.24/0.54 = ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of iimplies: iimplies P Q =
% 0.24/0.54 %---- (mimplies (mbox_s4 P) (mbox_s4 Q))
% 0.24/0.54 thf(iimplies_type,type,
% 0.24/0.54 iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(iimplies,definition,
% 0.24/0.54 ( iimplies
% 0.24/0.54 = ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of iimplied: iimplied P Q = (iimplies Q P)
% 0.24/0.54 thf(iimplied_type,type,
% 0.24/0.54 iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(iimplied,definition,
% 0.24/0.54 ( iimplied
% 0.24/0.54 = ( ^ [P: $i > $o,Q: $i > $o] : ( iimplies @ Q @ P ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of iequiv: iequiv P Q =
% 0.24/0.54 %---- (iand (iimplies P Q) (iimplies Q P))
% 0.24/0.54 thf(iequiv_type,type,
% 0.24/0.54 iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(iequiv,definition,
% 0.24/0.54 ( iequiv
% 0.24/0.54 = ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of ixor: ixor P Q = (inot (iequiv P Q)
% 0.24/0.54 thf(ixor_type,type,
% 0.24/0.54 ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(ixor,definition,
% 0.24/0.54 ( ixor
% 0.24/0.54 = ( ^ [P: $i > $o,Q: $i > $o] : ( inot @ ( iequiv @ P @ Q ) ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of validity
% 0.24/0.54 thf(ivalid_type,type,
% 0.24/0.54 ivalid: ( $i > $o ) > $o ).
% 0.24/0.54
% 0.24/0.54 thf(ivalid,definition,
% 0.24/0.54 ( ivalid
% 0.24/0.54 = ( ^ [Phi: $i > $o] :
% 0.24/0.54 ! [W: $i] : ( Phi @ W ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of satisfiability
% 0.24/0.54 thf(isatisfiable_type,type,
% 0.24/0.54 isatisfiable: ( $i > $o ) > $o ).
% 0.24/0.54
% 0.24/0.54 thf(isatisfiable,definition,
% 0.24/0.54 ( isatisfiable
% 0.24/0.54 = ( ^ [Phi: $i > $o] :
% 0.24/0.54 ? [W: $i] : ( Phi @ W ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of countersatisfiability
% 0.24/0.54 thf(icountersatisfiable_type,type,
% 0.24/0.54 icountersatisfiable: ( $i > $o ) > $o ).
% 0.24/0.54
% 0.24/0.54 thf(icountersatisfiable,definition,
% 0.24/0.54 ( icountersatisfiable
% 0.24/0.54 = ( ^ [Phi: $i > $o] :
% 0.24/0.54 ? [W: $i] :
% 0.24/0.54 ~ ( Phi @ W ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %----Definition of invalidity
% 0.24/0.54 thf(iinvalid_type,type,
% 0.24/0.54 iinvalid: ( $i > $o ) > $o ).
% 0.24/0.54
% 0.24/0.54 thf(iinvalid,definition,
% 0.24/0.54 ( iinvalid
% 0.24/0.54 = ( ^ [Phi: $i > $o] :
% 0.24/0.54 ! [W: $i] :
% 0.24/0.54 ~ ( Phi @ W ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %------------------------------------------------------------------------------
% 0.24/0.54 %------------------------------------------------------------------------------
% 0.24/0.54 thf(a1_type,type,
% 0.24/0.54 a1: $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(a2_type,type,
% 0.24/0.54 a2: $i > $o ).
% 0.24/0.54
% 0.24/0.54 thf(con,conjecture,
% 0.24/0.54 ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ).
% 0.24/0.54
% 0.24/0.54 %------------------------------------------------------------------------------
% 0.24/0.54 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.BAD52YCJUP/cvc5---1.0.5_21145.p...
% 0.24/0.54 (declare-sort $$unsorted 0)
% 0.24/0.54 (declare-fun tptp.irel ($$unsorted $$unsorted) Bool)
% 0.24/0.54 (assert (forall ((X $$unsorted)) (@ (@ tptp.irel X) X)))
% 0.24/0.54 (assert (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ tptp.irel X))) (=> (and (@ _let_1 Y) (@ (@ tptp.irel Y) Z)) (@ _let_1 Z)))))
% 0.24/0.54 (declare-fun tptp.mnot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.24/0.54 (declare-fun tptp.mor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.24/0.54 (declare-fun tptp.mand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.54 (assert (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.24/0.54 (declare-fun tptp.mimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.mbox_s4 ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))
% 0.24/0.59 (declare-fun tptp.iatom ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.inot ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.itrue ($$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.itrue (lambda ((W $$unsorted)) true)))
% 0.24/0.59 (declare-fun tptp.ifalse ($$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.ifalse (@ tptp.inot tptp.itrue)))
% 0.24/0.59 (declare-fun tptp.iand ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.ior ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.iimplies ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.iimplied ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.iequiv ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.ixor ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.24/0.59 (assert (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))
% 0.24/0.59 (declare-fun tptp.ivalid ((-> $$unsorted Bool)) Bool)
% 0.24/0.59 (assert (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))
% 0.24/0.59 (declare-fun tptp.isatisfiable ((-> $$unsorted Bool)) Bool)
% 0.24/0.59 (assert (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))
% 0.24/0.59 (declare-fun tptp.icountersatisfiable ((-> $$unsorted Bool)) Bool)
% 0.24/0.59 (assert (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))
% 0.24/0.59 (declare-fun tptp.iinvalid ((-> $$unsorted Bool)) Bool)
% 0.24/0.59 (assert (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))
% 0.24/0.59 (declare-fun tptp.a1 ($$unsorted) Bool)
% 0.24/0.59 (declare-fun tptp.a2 ($$unsorted) Bool)
% 0.24/0.59 (assert (let ((_let_1 (@ tptp.iatom tptp.a1))) (let ((_let_2 (@ tptp.iatom tptp.a2))) (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ (@ tptp.iequiv _let_1) _let_2)) (@ (@ tptp.iequiv _let_2) _let_1)))))))
% 0.24/0.59 (set-info :filename cvc5---1.0.5_21145)
% 0.24/0.59 (check-sat-assuming ( true ))
% 0.24/0.59 ------- get file name : TPTP file name is SYN393^4.002
% 0.24/0.59 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21145.smt2...
% 0.24/0.59 --- Run --ho-elim --full-saturate-quant at 10...
% 0.24/0.59 % SZS status Theorem for SYN393^4.002
% 0.24/0.59 % SZS output start Proof for SYN393^4.002
% 0.24/0.59 (
% 0.24/0.59 (let ((_let_1 (@ tptp.iatom tptp.a1))) (let ((_let_2 (@ tptp.iatom tptp.a2))) (let ((_let_3 (not (@ tptp.ivalid (@ (@ tptp.iequiv (@ (@ tptp.iequiv _let_1) _let_2)) (@ (@ tptp.iequiv _let_2) _let_1)))))) (let ((_let_4 (= tptp.iinvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_5 (= tptp.icountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (@ Phi W))))))) (let ((_let_6 (= tptp.isatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (@ Phi W)))))) (let ((_let_7 (= tptp.ivalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (@ Phi W)))))) (let ((_let_8 (= tptp.ixor (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.inot (@ (@ tptp.iequiv P) Q)) __flatten_var_0))))) (let ((_let_9 (= tptp.iequiv (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iand (@ (@ tptp.iimplies P) Q)) (@ (@ tptp.iimplies Q) P)) __flatten_var_0))))) (let ((_let_10 (= tptp.iimplied (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.iimplies Q) P) __flatten_var_0))))) (let ((_let_11 (= tptp.iimplies (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mimplies (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_12 (= tptp.ior (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mbox_s4 P)) (@ tptp.mbox_s4 Q)) __flatten_var_0))))) (let ((_let_13 (= tptp.iand (lambda ((P (-> $$unsorted Bool)) (Q (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mand P) Q) __flatten_var_0))))) (let ((_let_14 (= tptp.ifalse (@ tptp.inot tptp.itrue)))) (let ((_let_15 (= tptp.itrue (lambda ((W $$unsorted)) true)))) (let ((_let_16 (= tptp.inot (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ tptp.mnot (@ tptp.mbox_s4 P)) __flatten_var_0))))) (let ((_let_17 (= tptp.iatom (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ P __flatten_var_0))))) (let ((_let_18 (= tptp.mbox_s4 (lambda ((P (-> $$unsorted Bool)) (X $$unsorted)) (forall ((Y $$unsorted)) (=> (@ (@ tptp.irel X) Y) (@ P Y))))))) (let ((_let_19 (= tptp.mimplies (lambda ((U (-> $$unsorted Bool)) (V (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (@ (@ (@ tptp.mor (@ tptp.mnot U)) V) __flatten_var_0))))) (let ((_let_20 (= tptp.mand (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_21 (= tptp.mor (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_22 (= tptp.mnot (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_23 (forall ((BOUND_VARIABLE_1314 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1314) BOUND_VARIABLE_1314)) (ho_4 k_6 BOUND_VARIABLE_1314))))) (let ((_let_24 (forall ((BOUND_VARIABLE_1324 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1324) BOUND_VARIABLE_1324)) (ho_4 k_5 BOUND_VARIABLE_1324))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23))) (let ((_let_27 (not _let_23))) (let ((_let_28 (or _let_27 _let_24))) (let ((_let_29 (and _let_28 _let_26))) (let ((_let_30 (forall ((BOUND_VARIABLE_1454 $$unsorted) (BOUND_VARIABLE_1516 $$unsorted) (BOUND_VARIABLE_1506 $$unsorted) (BOUND_VARIABLE_1498 $$unsorted)) (or (and (or (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1498) BOUND_VARIABLE_1498)) (ho_4 k_5 BOUND_VARIABLE_1498)) (not (forall ((BOUND_VARIABLE_1387 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1387) BOUND_VARIABLE_1387)) (ho_4 k_6 BOUND_VARIABLE_1387))))) (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1506) BOUND_VARIABLE_1506)) (ho_4 k_6 BOUND_VARIABLE_1506)) (not (forall ((BOUND_VARIABLE_1377 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1377) BOUND_VARIABLE_1377)) (ho_4 k_5 BOUND_VARIABLE_1377)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1454) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1454) BOUND_VARIABLE_1516)))))) (let ((_let_31 (or _let_29 _let_30))) (let ((_let_32 (forall ((BOUND_VARIABLE_1377 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1377) BOUND_VARIABLE_1377)) (ho_4 k_5 BOUND_VARIABLE_1377))))) (let ((_let_33 (forall ((BOUND_VARIABLE_1387 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1387) BOUND_VARIABLE_1387)) (ho_4 k_6 BOUND_VARIABLE_1387))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32))) (let ((_let_36 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_37 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) (ho_4 k_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))) (let ((_let_38 (not _let_32))) (let ((_let_39 (or _let_38 _let_33))) (let ((_let_40 (and _let_39 _let_35))) (let ((_let_41 (forall ((BOUND_VARIABLE_1443 $$unsorted) (BOUND_VARIABLE_1487 $$unsorted) (BOUND_VARIABLE_1477 $$unsorted) (BOUND_VARIABLE_1469 $$unsorted)) (or (and (or (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1469) BOUND_VARIABLE_1469)) (ho_4 k_6 BOUND_VARIABLE_1469)) (not (forall ((BOUND_VARIABLE_1324 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1324) BOUND_VARIABLE_1324)) (ho_4 k_5 BOUND_VARIABLE_1324))))) (and (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1477) BOUND_VARIABLE_1477)) (ho_4 k_5 BOUND_VARIABLE_1477)) (not (forall ((BOUND_VARIABLE_1314 $$unsorted)) (or (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1314) BOUND_VARIABLE_1314)) (ho_4 k_6 BOUND_VARIABLE_1314)))))) (not (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1443) Y))))) (not (ho_4 (ho_3 k_2 BOUND_VARIABLE_1443) BOUND_VARIABLE_1487)))))) (let ((_let_42 (or _let_40 _let_41))) (let ((_let_43 (ALPHA_EQUIV :args (_let_32 (= BOUND_VARIABLE_1377 BOUND_VARIABLE_1324))))) (let ((_let_44 (_let_32))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (and _let_37 _let_34))) (let ((_let_47 (and _let_36 _let_27))) (let ((_let_48 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) (ho_4 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_49 (and _let_48 _let_38))) (let ((_let_50 (or _let_46 _let_49))) (let ((_let_51 (or (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)) (ho_4 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) (let ((_let_52 (and _let_51 _let_25))) (let ((_let_53 (or _let_52 _let_47))) (let ((_let_54 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_55 (not _let_54))) (let ((_let_56 (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) Y))))) (let ((_let_57 (not _let_56))) (let ((_let_58 (and _let_53 _let_57))) (let ((_let_59 (or _let_58 _let_55))) (let ((_let_60 (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_61 (not _let_60))) (let ((_let_62 (forall ((Y $$unsorted)) (not (ho_4 (ho_3 k_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Y))))) (let ((_let_63 (not _let_62))) (let ((_let_64 (and _let_50 _let_63))) (let ((_let_65 (or _let_64 _let_61))) (let ((_let_66 (not _let_37))) (let ((_let_67 (not _let_36))) (let ((_let_68 (ALPHA_EQUIV :args (_let_33 (= BOUND_VARIABLE_1387 BOUND_VARIABLE_1314))))) (let ((_let_69 (EQUIV_ELIM2 _let_68))) (let ((_let_70 (or))) (let ((_let_71 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))))) (let ((_let_72 (_let_46))) (let ((_let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_23))))) (let ((_let_74 (_let_47))) (let ((_let_75 (not _let_53))) (let ((_let_76 (_let_58))) (let ((_let_77 (_let_56))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_77) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_77)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_76) (CONG (REFL :args _let_76) (REFL :args (_let_75)) (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_70)) :args ((or _let_56 _let_58 _let_75))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 1)) (CONG (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_70)) :args ((or _let_54 _let_59))) (CNF_OR_NEG :args (_let_59 0)) :args ((or _let_59 _let_75) false _let_56 false _let_54 true _let_58)))) (let ((_let_79 (not _let_41))) (let ((_let_80 (_let_79))) (let ((_let_81 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_80)) :args _let_80)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_41))) (REFL :args ((not _let_59))) :args _let_70)))) (let ((_let_82 (CNF_OR_NEG :args (_let_42 1)))) (let ((_let_83 (forall ((BOUND_VARIABLE_1314 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1314) BOUND_VARIABLE_1314)) (@ tptp.a1 BOUND_VARIABLE_1314))))) (let ((_let_84 (forall ((BOUND_VARIABLE_1324 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1324) BOUND_VARIABLE_1324)) (@ tptp.a2 BOUND_VARIABLE_1324))))) (let ((_let_85 (forall ((BOUND_VARIABLE_1377 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1377) BOUND_VARIABLE_1377)) (@ tptp.a2 BOUND_VARIABLE_1377))))) (let ((_let_86 (forall ((BOUND_VARIABLE_1387 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1387) BOUND_VARIABLE_1387)) (@ tptp.a1 BOUND_VARIABLE_1387))))) (let ((_let_87 (ASSUME :args (_let_22)))) (let ((_let_88 (ASSUME :args (_let_21)))) (let ((_let_89 (ASSUME :args (_let_20)))) (let ((_let_90 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_89 _let_88 _let_87) :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (ASSUME :args (_let_17)))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_92 _let_91 _let_90 _let_89 _let_88 _let_87) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :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) :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) :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) :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) :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) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (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) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO (AND_INTRO (ASSUME :args (_let_4)) (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_7)) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_100 _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) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) _let_100 _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) :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (and (or (and (or (not _let_85) _let_86) (or (not _let_86) _let_85)) (forall ((BOUND_VARIABLE_1443 $$unsorted) (BOUND_VARIABLE_1487 $$unsorted) (BOUND_VARIABLE_1477 $$unsorted) (BOUND_VARIABLE_1469 $$unsorted)) (or (and (or (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1469) BOUND_VARIABLE_1469)) (@ tptp.a1 BOUND_VARIABLE_1469)) (not (forall ((BOUND_VARIABLE_1324 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1324) BOUND_VARIABLE_1324)) (@ tptp.a2 BOUND_VARIABLE_1324))))) (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1477) BOUND_VARIABLE_1477)) (@ tptp.a2 BOUND_VARIABLE_1477)) (not (forall ((BOUND_VARIABLE_1314 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1314) BOUND_VARIABLE_1314)) (@ tptp.a1 BOUND_VARIABLE_1314)))))) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1443) Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1443) BOUND_VARIABLE_1487))))) (or (and (or (not _let_83) _let_84) (or (not _let_84) _let_83)) (forall ((BOUND_VARIABLE_1454 $$unsorted) (BOUND_VARIABLE_1516 $$unsorted) (BOUND_VARIABLE_1506 $$unsorted) (BOUND_VARIABLE_1498 $$unsorted)) (or (and (or (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1498) BOUND_VARIABLE_1498)) (@ tptp.a2 BOUND_VARIABLE_1498)) (not (forall ((BOUND_VARIABLE_1387 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1387) BOUND_VARIABLE_1387)) (@ tptp.a1 BOUND_VARIABLE_1387))))) (and (or (not (@ (@ tptp.irel BOUND_VARIABLE_1506) BOUND_VARIABLE_1506)) (@ tptp.a1 BOUND_VARIABLE_1506)) (not (forall ((BOUND_VARIABLE_1377 $$unsorted)) (or (not (@ (@ tptp.irel BOUND_VARIABLE_1377) BOUND_VARIABLE_1377)) (@ tptp.a2 BOUND_VARIABLE_1377)))))) (not (forall ((Y $$unsorted)) (not (@ (@ tptp.irel BOUND_VARIABLE_1454) Y))))) (not (@ (@ tptp.irel BOUND_VARIABLE_1454) BOUND_VARIABLE_1516))))))) (not (and _let_42 _let_31)))))))))) (let ((_let_102 (CNF_OR_NEG :args (_let_31 1)))) (let ((_let_103 (not _let_30))) (let ((_let_104 (_let_103))) (let ((_let_105 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_104)) :args _let_104)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_30))) (REFL :args ((not _let_65))) :args _let_70)))) (let ((_let_106 (CNF_OR_NEG :args (_let_65 0)))) (let ((_let_107 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 1)) (CONG (REFL :args (_let_65)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_70)) :args ((or _let_60 _let_65))))) (let ((_let_108 (not _let_50))) (let ((_let_109 (_let_64))) (let ((_let_110 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_109) (CONG (REFL :args _let_109) (REFL :args (_let_108)) (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_70)) :args ((or _let_62 _let_64 _let_108))))) (let ((_let_111 (_let_62))) (let ((_let_112 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_111) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_111)))) (let ((_let_113 (CNF_AND_NEG :args (_let_40)))) (let ((_let_114 (CNF_OR_NEG :args (_let_42 0)))) (let ((_let_115 (CNF_AND_NEG :args (_let_29)))) (let ((_let_116 (CNF_OR_NEG :args (_let_31 0)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST _let_116 _let_101 _let_115 _let_114 (CNF_OR_NEG :args (_let_26 1)) _let_113 (EQUIV_ELIM1 _let_68) (REORDERING (CNF_OR_NEG :args (_let_39 1)) :args ((or _let_34 _let_39))) (MACRO_RESOLUTION_TRUST _let_112 _let_110 _let_107 _let_106 _let_105 _let_102 _let_101 _let_82 _let_81 _let_78 (CNF_OR_NEG :args (_let_53 1)) (CNF_OR_NEG :args (_let_50 0)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_74) (CONG (REFL :args _let_74) (REFL :args (_let_67)) _let_73 :args _let_70)) :args ((or _let_23 _let_47 _let_67))) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_72) (CONG (REFL :args _let_72) (REFL :args (_let_66)) _let_71 :args _let_70)) :args ((or _let_33 _let_46 _let_66))) _let_69 :args ((or _let_33 _let_67 _let_66) false _let_62 false _let_60 true _let_64 true _let_65 true _let_30 true _let_31 false _let_42 false _let_41 false _let_59 false _let_53 false _let_50 false _let_47 false _let_46 true _let_23)) (REORDERING (CNF_OR_NEG :args (_let_28 1)) :args ((or _let_25 _let_28))) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_44)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_45 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_44)) (EQUIV_ELIM1 _let_43) (REORDERING (CNF_OR_NEG :args (_let_35 1)) :args ((or _let_38 _let_35))) :args (_let_38 true _let_31 false _let_29 false _let_42 false _let_26 false _let_40 false _let_23 false _let_39 false _let_33 false _let_28 false _let_37 false _let_36 false _let_24 false _let_35)))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 _let_43) _let_117 :args (_let_25 true _let_32)))) (let ((_let_119 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))))) (let ((_let_120 (_let_33))) (let ((_let_121 (ASSUME :args _let_120))) (let ((_let_122 (not _let_51))) (let ((_let_123 (_let_52))) (let ((_let_124 (not _let_48))) (let ((_let_125 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_32))))) (let ((_let_126 (_let_49))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_120)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_126) (CONG (REFL :args _let_126) (REFL :args (_let_124)) _let_125 :args _let_70)) :args ((or _let_32 _let_49 _let_124))) _let_117 (CNF_OR_NEG :args (_let_50 1)) _let_110 _let_112 _let_107 _let_106 _let_105 _let_102 _let_101 _let_82 _let_81 _let_78 (CNF_OR_NEG :args (_let_53 0)) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_123) (CONG (REFL :args _let_123) (REFL :args (_let_122)) _let_119 :args _let_70)) :args ((or _let_24 _let_52 _let_122))) _let_118 (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_120)) :args (_let_34 true _let_48 true _let_32 true _let_49 true _let_50 true _let_62 false _let_60 true _let_64 true _let_65 true _let_30 true _let_31 false _let_42 false _let_41 false _let_59 false _let_53 false _let_52 true _let_24 false _let_51)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_116 (MACRO_RESOLUTION_TRUST _let_101 (MACRO_RESOLUTION_TRUST _let_114 (MACRO_RESOLUTION_TRUST _let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG (REFL :args (_let_39)) _let_125 :args _let_70)) :args ((or _let_32 _let_39))) _let_117 :args (_let_39 true _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG (REFL :args (_let_35)) _let_71 :args _let_70)) :args ((or _let_33 _let_35))) _let_127 :args (_let_35 true _let_33)) :args (_let_40 false _let_39 false _let_35)) :args (_let_42 false _let_40)) :args ((not _let_31) false _let_42)) (MACRO_RESOLUTION_TRUST _let_115 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 0)) (CONG (REFL :args (_let_28)) _let_73 :args _let_70)) :args ((or _let_23 _let_28))) (MACRO_RESOLUTION_TRUST _let_69 _let_127 :args (_let_27 true _let_33)) :args (_let_28 true _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) _let_119 :args _let_70)) :args ((or _let_24 _let_26))) _let_118 :args (_let_26 true _let_24)) :args (_let_29 false _let_28 false _let_26)) :args (false true _let_31 false _let_29)) :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_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 _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.24/0.59 )
% 0.24/0.59 % SZS output end Proof for SYN393^4.002
% 0.24/0.59 % cvc5---1.0.5 exiting
% 0.24/0.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------