TSTP Solution File: SEV000^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV000^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:21:16 EDT 2023
% Result : Theorem 0.22s 0.56s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV000^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 03:00:01 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.50 %----Proving TH0
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 % File : SEV000^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.51 % Domain : Set Theory (Relations)
% 0.22/0.51 % Problem : TPS problem MODULAR-EQUIV-THM
% 0.22/0.51 % Version : Especial.
% 0.22/0.51 % English : The equivalence of two definitions of modularity.
% 0.22/0.51
% 0.22/0.51 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.51 % Source : [Bro09]
% 0.22/0.51 % Names : tps_0562 [Bro09]
% 0.22/0.51 % : MODULAR-EQUIV-THM [TPS]
% 0.22/0.51
% 0.22/0.51 % Status : Theorem
% 0.22/0.51 % Rating : 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 1.00 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% 0.22/0.51 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.22/0.51 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.22/0.51 % Maximal formula atoms : 11 ( 11 avg)
% 0.22/0.51 % Number of connectives : 68 ( 0 ~; 0 |; 7 &; 58 @)
% 0.22/0.51 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.22/0.51 % Maximal formula depth : 13 ( 13 avg)
% 0.22/0.51 % Number of types : 1 ( 1 usr)
% 0.22/0.51 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.22/0.51 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.22/0.51 % Number of variables : 24 ( 0 ^; 24 !; 0 ?; 24 :)
% 0.22/0.51 % SPC : TH0_THM_EQU_NAR
% 0.22/0.51
% 0.22/0.51 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.51 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.51 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.51 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.51 % : Polymorphic definitions expanded.
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 thf(a_type,type,
% 0.22/0.51 a: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(cMODULAR_EQUIV_THM_pme,conjecture,
% 0.22/0.51 ! [JOIN: a > a > a,MEET: a > a > a] :
% 0.22/0.51 ( ( ! [Xx: a] :
% 0.22/0.51 ( ( JOIN @ Xx @ Xx )
% 0.22/0.51 = Xx )
% 0.22/0.51 & ! [Xx: a] :
% 0.22/0.51 ( ( MEET @ Xx @ Xx )
% 0.22/0.51 = Xx )
% 0.22/0.51 & ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.51 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 0.22/0.51 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 0.22/0.51 & ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.51 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 0.22/0.51 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 0.22/0.51 & ! [Xx: a,Xy: a] :
% 0.22/0.51 ( ( JOIN @ Xx @ Xy )
% 0.22/0.51 = ( JOIN @ Xy @ Xx ) )
% 0.22/0.51 & ! [Xx: a,Xy: a] :
% 0.22/0.51 ( ( MEET @ Xx @ Xy )
% 0.22/0.51 = ( MEET @ Xy @ Xx ) )
% 0.22/0.51 & ! [Xx: a,Xy: a] :
% 0.22/0.51 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 0.22/0.51 = Xy )
% 0.22/0.51 & ! [Xx: a,Xy: a] :
% 0.22/0.51 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 0.22/0.51 = Xy ) )
% 0.22/0.51 => ( ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.51 ( ( ( JOIN @ Xx @ Xz )
% 0.22/0.51 = Xz )
% 0.22/0.51 => ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 0.22/0.51 = ( MEET @ ( JOIN @ Xx @ Xy ) @ Xz ) ) )
% 0.22/0.51 <=> ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.51 ( ( JOIN @ Xx @ ( MEET @ Xy @ ( JOIN @ Xx @ Xz ) ) )
% 0.22/0.51 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.I4J3kDEHCW/cvc5---1.0.5_22554.p...
% 0.22/0.51 (declare-sort $$unsorted 0)
% 0.22/0.51 (declare-sort tptp.a 0)
% 0.22/0.51 (assert (not (forall ((JOIN (-> tptp.a tptp.a tptp.a)) (MEET (-> tptp.a tptp.a tptp.a))) (=> (and (forall ((Xx tptp.a)) (= (@ (@ JOIN Xx) Xx) Xx)) (forall ((Xx tptp.a)) (= (@ (@ MEET Xx) Xx) Xx)) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (= (@ (@ JOIN (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ JOIN Xy) Xz))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ MEET Xx))) (= (@ (@ MEET (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ MEET Xy) Xz))))) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ JOIN Xx) Xy) (@ (@ JOIN Xy) Xx))) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ MEET Xx) Xy) (@ (@ MEET Xy) Xx))) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ JOIN (@ (@ MEET Xx) Xy)) Xy) Xy)) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ MEET (@ (@ JOIN Xx) Xy)) Xy) Xy))) (= (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (=> (= (@ _let_1 Xz) Xz) (= (@ _let_1 (@ (@ MEET Xy) Xz)) (@ (@ MEET (@ _let_1 Xy)) Xz))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (let ((_let_2 (@ _let_1 Xz))) (= (@ _let_1 (@ (@ MEET Xy) _let_2)) (@ (@ MEET (@ _let_1 Xy)) _let_2))))))))))
% 0.22/0.56 (set-info :filename cvc5---1.0.5_22554)
% 0.22/0.56 (check-sat-assuming ( true ))
% 0.22/0.56 ------- get file name : TPTP file name is SEV000^5
% 0.22/0.56 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22554.smt2...
% 0.22/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.56 % SZS status Theorem for SEV000^5
% 0.22/0.56 % SZS output start Proof for SEV000^5
% 0.22/0.56 (
% 0.22/0.56 (let ((_let_1 (not (forall ((JOIN (-> tptp.a tptp.a tptp.a)) (MEET (-> tptp.a tptp.a tptp.a))) (=> (and (forall ((Xx tptp.a)) (= (@ (@ JOIN Xx) Xx) Xx)) (forall ((Xx tptp.a)) (= (@ (@ MEET Xx) Xx) Xx)) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (= (@ (@ JOIN (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ JOIN Xy) Xz))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ MEET Xx))) (= (@ (@ MEET (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ MEET Xy) Xz))))) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ JOIN Xx) Xy) (@ (@ JOIN Xy) Xx))) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ MEET Xx) Xy) (@ (@ MEET Xy) Xx))) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ JOIN (@ (@ MEET Xx) Xy)) Xy) Xy)) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ MEET (@ (@ JOIN Xx) Xy)) Xy) Xy))) (= (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (=> (= (@ _let_1 Xz) Xz) (= (@ _let_1 (@ (@ MEET Xy) Xz)) (@ (@ MEET (@ _let_1 Xy)) Xz))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (let ((_let_2 (@ _let_1 Xz))) (= (@ _let_1 (@ (@ MEET Xy) _let_2)) (@ (@ MEET (@ _let_1 Xy)) _let_2))))))))))) (let ((_let_2 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx))) (let ((_let_2 (ho_3 _let_1 Xz))) (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_1 Xy)) _let_2) (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy) _let_2)))))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_4 (ho_3 _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_5 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_6 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_7 (= (ho_3 _let_6 _let_4) (ho_3 _let_3 (ho_3 _let_5 _let_4))))) (let ((_let_8 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx))) (or (not (= Xz (ho_3 _let_1 Xz))) (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_1 Xy)) Xz) (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy) Xz)))))))) (let ((_let_9 (= _let_8 _let_2))) (let ((_let_10 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx))) (= (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy) Xz)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_3 _let_1 Xy)) Xz)))))) (let ((_let_11 (not _let_10))) (let ((_let_12 (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) Xx))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 (not (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) Xx)))) _let_11 (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))) (= (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy) Xz)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_1 Xy)) Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy) Xx) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy) Xx) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) Xy)) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) Xy)) Xy)))) _let_9))) (let ((_let_15 (forall ((BOUND_VARIABLE_721 |u_(-> tptp.a tptp.a tptp.a)|) (BOUND_VARIABLE_729 |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 BOUND_VARIABLE_721 Xx) Xx)))) (not (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 BOUND_VARIABLE_729 Xx) Xx)))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_721 Xx))) (= (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_721 Xy) Xz)) (ho_3 (ho_2 BOUND_VARIABLE_721 (ho_3 _let_1 Xy)) Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_729 Xx))) (= (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_729 Xy) Xz)) (ho_3 (ho_2 BOUND_VARIABLE_729 (ho_3 _let_1 Xy)) Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (ho_3 (ho_2 BOUND_VARIABLE_721 Xy) Xx) (ho_3 (ho_2 BOUND_VARIABLE_721 Xx) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (ho_3 (ho_2 BOUND_VARIABLE_729 Xy) Xx) (ho_3 (ho_2 BOUND_VARIABLE_729 Xx) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_3 (ho_2 BOUND_VARIABLE_721 (ho_3 (ho_2 BOUND_VARIABLE_729 Xx) Xy)) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_3 (ho_2 BOUND_VARIABLE_729 (ho_3 (ho_2 BOUND_VARIABLE_721 Xx) Xy)) Xy)))) (= (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_721 Xx))) (or (not (= Xz (ho_3 _let_1 Xz))) (= (ho_3 (ho_2 BOUND_VARIABLE_729 (ho_3 _let_1 Xy)) Xz) (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_729 Xy) Xz)))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_721 Xx))) (let ((_let_2 (ho_3 _let_1 Xz))) (= (ho_3 (ho_2 BOUND_VARIABLE_729 (ho_3 _let_1 Xy)) _let_2) (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_729 Xy) _let_2))))))))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_18 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_19 (forall ((u |u_(-> tptp.a tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_20 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_21 (not _let_15))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((JOIN (-> tptp.a tptp.a tptp.a)) (MEET (-> tptp.a tptp.a tptp.a))) (or (not (forall ((Xx tptp.a)) (= Xx (@ (@ JOIN Xx) Xx)))) (not (forall ((Xx tptp.a)) (= Xx (@ (@ MEET Xx) Xx)))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (= (@ (@ JOIN (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ JOIN Xy) Xz)))))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ MEET Xx))) (= (@ (@ MEET (@ _let_1 Xy)) Xz) (@ _let_1 (@ (@ MEET Xy) Xz)))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ JOIN Xx) Xy) (@ (@ JOIN Xy) Xx)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ (@ MEET Xx) Xy) (@ (@ MEET Xy) Xx)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (@ (@ JOIN (@ (@ MEET Xx) Xy)) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (@ (@ MEET (@ (@ JOIN Xx) Xy)) Xy)))) (= (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (let ((_let_2 (@ _let_1 Xz))) (= (@ _let_1 (@ (@ MEET Xy) _let_2)) (@ (@ MEET (@ _let_1 Xy)) _let_2))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (or (not (= Xz (@ _let_1 Xz))) (= (@ _let_1 (@ (@ MEET Xy) Xz)) (@ (@ MEET (@ _let_1 Xy)) Xz))))))))) _let_21))))))) (let ((_let_23 (or))) (let ((_let_24 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_22) :args (_let_21))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_15))) (REFL :args (_let_16)) :args _let_23)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_22 (PREPROCESS :args ((and _let_20 _let_19 _let_18 _let_17)))) :args ((and _let_21 _let_20 _let_19 _let_18 _let_17))) :args (0)) :args (_let_16 true _let_15)))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 8)) _let_24 :args ((not _let_9) true _let_14)))) (let ((_let_26 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_27 (ho_3 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_28 (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) _let_27) (ho_3 _let_26 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_27))))) (let ((_let_29 (ho_3 _let_26 _let_27))) (let ((_let_30 (= _let_27 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_28))) (let ((_let_33 (not _let_8))) (let ((_let_34 (_let_9))) (let ((_let_35 (_let_8))) (let ((_let_36 (not _let_2))) (let ((_let_37 (_let_36))) (let ((_let_38 (ho_3 _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_39 (= _let_29 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_38) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)))) (let ((_let_40 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_38))) (let ((_let_41 (REFL :args (_let_14)))) (let ((_let_42 (_let_10))) (let ((_let_43 (_let_12))) (let ((_let_44 (and _let_40 _let_39))) (let ((_let_45 (ASSUME :args (_let_39)))) (let ((_let_46 (APPLY_UF ho_3))) (let ((_let_47 (ASSUME :args (_let_40)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_28 _let_31 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_44)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_45 _let_47) (SCOPE (TRANS (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (SYMM (SYMM _let_47)) :args (APPLY_UF ho_2)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) :args _let_46) (SYMM _let_45)) :args (_let_39 _let_40))) :args (_let_40 _let_39))) :args (true _let_44)) :args ((or _let_30 (not _let_40) (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 0)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_23)) :args ((or _let_12 _let_14))) _let_24 :args (_let_12 true _let_14)) :args (_let_40 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 2)) (CONG _let_41 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_10))) :args _let_23)) :args ((or _let_10 _let_14))) _let_24 :args (_let_10 true _let_14)) :args (_let_39 false _let_10)) :args (_let_30 false _let_40 false _let_39)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_37)) :args _let_37)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_2))) (REFL :args ((not _let_28))) :args _let_23)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_35) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_27 QUANTIFIERS_INST_E_MATCHING ((ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) Xy)) Xz)))) :args _let_35)) (CNF_EQUIV_NEG2 :args _let_34) _let_25 :args (_let_33 false _let_30 true _let_28 false _let_32 true _let_2 true _let_9)))) (let ((_let_49 (= (ho_3 _let_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) (ho_3 _let_3 (ho_3 _let_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_50 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_4))) (let ((_let_51 (not _let_7))) (let ((_let_52 (not _let_50))) (let ((_let_53 (or _let_52 _let_49))) (let ((_let_54 (not _let_49))) (let ((_let_55 (not _let_53))) (let ((_let_56 (_let_33))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_56)) :args _let_56)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_8))) (REFL :args (_let_55)) :args _let_23)) _let_48 :args (_let_55 true _let_8)))) (let ((_let_58 (and _let_50 _let_54))) (let ((_let_59 (_let_50 _let_54))) (let ((_let_60 (ASSUME :args (_let_54)))) (let ((_let_61 (ASSUME :args (_let_50)))) (let ((_let_62 (SYMM _let_61))) (let ((_let_63 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_63) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_61 _let_60) (SCOPE (FALSE_ELIM (TRANS (CONG (CONG (REFL :args (_let_6)) _let_62 :args _let_46) (CONG (REFL :args (_let_3)) (CONG (REFL :args (_let_5)) _let_62 :args _let_46) :args _let_46) :args (=)) (FALSE_INTRO _let_60))) :args _let_59)) :args _let_59)) :args (true _let_58)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_49))) (REFL :args (_let_51)) :args _let_23)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_53 0)) (CONG (REFL :args (_let_53)) (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_50))) :args _let_23)) :args ((or _let_50 _let_53))) _let_57 :args (_let_50 true _let_53)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_53 1)) _let_57 :args (_let_54 true _let_53)) :args (_let_51 false _let_50 true _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_34) :args ((or _let_8 _let_2 _let_9))) _let_48 _let_25 :args (_let_2 true _let_8 true _let_9)) :args (false true _let_7 false _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.57 )
% 0.22/0.57 % SZS output end Proof for SEV000^5
% 0.22/0.57 % cvc5---1.0.5 exiting
% 0.22/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------