TSTP Solution File: SEV002^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV002^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 0.55s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV002^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 03:40:30 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 % File : SEV002^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.50 % Domain : Set Theory (Relations)
% 0.22/0.50 % Problem : TPS problem from LATTICES-THMS
% 0.22/0.50 % Version : Especial.
% 0.22/0.50 % English :
% 0.22/0.50
% 0.22/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.50 % Source : [Bro09]
% 0.22/0.50 % Names : tps_1180 [Bro09]
% 0.22/0.50
% 0.22/0.50 % Status : Theorem
% 0.22/0.50 % Rating : 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.22/0.50 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.22/0.50 % Number of atoms : 11 ( 11 equ; 0 cnn)
% 0.22/0.50 % Maximal formula atoms : 11 ( 11 avg)
% 0.22/0.50 % Number of connectives : 78 ( 0 ~; 0 |; 9 &; 68 @)
% 0.22/0.50 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.22/0.50 % Maximal formula depth : 16 ( 16 avg)
% 0.22/0.50 % Number of types : 1 ( 1 usr)
% 0.22/0.50 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.22/0.50 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.22/0.50 % Number of variables : 27 ( 0 ^; 27 !; 0 ?; 27 :)
% 0.22/0.50 % SPC : TH0_THM_EQU_NAR
% 0.22/0.50
% 0.22/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 thf(a_type,type,
% 0.22/0.50 a: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(cMODULAR_THM_DEF2_pme,conjecture,
% 0.22/0.50 ! [JOIN: a > a > a,MEET: a > a > a] :
% 0.22/0.50 ( ( ! [Xx: a] :
% 0.22/0.50 ( ( JOIN @ Xx @ Xx )
% 0.22/0.50 = Xx )
% 0.22/0.50 & ! [Xx: a] :
% 0.22/0.50 ( ( MEET @ Xx @ Xx )
% 0.22/0.50 = Xx )
% 0.22/0.50 & ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.50 ( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
% 0.22/0.50 = ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
% 0.22/0.50 & ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.50 ( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
% 0.22/0.50 = ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
% 0.22/0.50 & ! [Xx: a,Xy: a] :
% 0.22/0.50 ( ( JOIN @ Xx @ Xy )
% 0.22/0.50 = ( JOIN @ Xy @ Xx ) )
% 0.22/0.50 & ! [Xx: a,Xy: a] :
% 0.22/0.50 ( ( MEET @ Xx @ Xy )
% 0.22/0.50 = ( MEET @ Xy @ Xx ) )
% 0.22/0.50 & ! [Xx: a,Xy: a] :
% 0.22/0.50 ( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
% 0.22/0.50 = Xy )
% 0.22/0.50 & ! [Xx: a,Xy: a] :
% 0.22/0.50 ( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
% 0.22/0.50 = Xy )
% 0.22/0.50 & ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.50 ( ( JOIN @ Xx @ ( MEET @ Xy @ Xz ) )
% 0.22/0.50 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) )
% 0.22/0.50 & ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.50 ( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
% 0.22/0.50 = ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) )
% 0.22/0.50 => ! [Xx: a,Xy: a,Xz: a] :
% 0.22/0.50 ( ( JOIN @ Xx @ ( MEET @ Xy @ ( JOIN @ Xx @ Xz ) ) )
% 0.22/0.50 = ( MEET @ ( JOIN @ Xx @ Xy ) @ ( JOIN @ Xx @ Xz ) ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.tx60Z6GdSB/cvc5---1.0.5_22472.p...
% 0.22/0.50 (declare-sort $$unsorted 0)
% 0.22/0.50 (declare-sort tptp.a 0)
% 0.22/0.50 (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 (@ (@ MEET Xy) Xz)) (@ (@ MEET (@ _let_1 Xy)) (@ _let_1 Xz))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ MEET Xx))) (= (@ _let_1 (@ (@ JOIN Xy) Xz)) (@ (@ JOIN (@ _let_1 Xy)) (@ _let_1 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)))))))))
% 0.22/0.55 (set-info :filename cvc5---1.0.5_22472)
% 0.22/0.55 (check-sat-assuming ( true ))
% 0.22/0.55 ------- get file name : TPTP file name is SEV002^5
% 0.22/0.55 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22472.smt2...
% 0.22/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.55 % SZS status Theorem for SEV002^5
% 0.22/0.55 % SZS output start Proof for SEV002^5
% 0.22/0.55 (
% 0.22/0.55 (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 (@ (@ MEET Xy) Xz)) (@ (@ MEET (@ _let_1 Xy)) (@ _let_1 Xz))))) (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ MEET Xx))) (= (@ _let_1 (@ (@ JOIN Xy) Xz)) (@ (@ JOIN (@ _let_1 Xy)) (@ _let_1 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 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_3 (ho_3 _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_4 (ho_3 _let_2 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) _let_3)))) (let ((_let_5 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)))) (let ((_let_6 (= (ho_3 _let_5 _let_3) _let_4))) (let ((_let_7 (ho_3 _let_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_7))) (let ((_let_9 (ho_3 _let_2 _let_3))) (let ((_let_10 (= _let_4 (ho_3 _let_5 _let_9)))) (let ((_let_11 (= _let_9 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) (let ((_let_12 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx))) (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (ho_3 _let_1 Xy)) (ho_3 _let_1 Xz)) (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy) Xz))))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (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_15 (not _let_14))) (let ((_let_16 (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) Xx))))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 (not (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx) Xx)))) _let_15 (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_13 (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx))) (= (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (ho_3 _let_1 Xy)) (ho_3 _let_1 Xz)) (ho_3 _let_1 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xy) Xz)))))) _let_6))) (let ((_let_19 (forall ((BOUND_VARIABLE_744 |u_(-> tptp.a tptp.a tptp.a)|) (BOUND_VARIABLE_753 |u_(-> tptp.a tptp.a tptp.a)|) (BOUND_VARIABLE_728 tptp.a) (BOUND_VARIABLE_726 tptp.a) (BOUND_VARIABLE_724 tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_744 BOUND_VARIABLE_724))) (let ((_let_2 (ho_3 _let_1 BOUND_VARIABLE_728))) (or (not (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 BOUND_VARIABLE_744 Xx) Xx)))) (not (forall ((Xx tptp.a)) (= Xx (ho_3 (ho_2 BOUND_VARIABLE_753 Xx) Xx)))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_744 Xx))) (= (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_744 Xy) Xz)) (ho_3 (ho_2 BOUND_VARIABLE_744 (ho_3 _let_1 Xy)) Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_753 Xx))) (= (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_753 Xy) Xz)) (ho_3 (ho_2 BOUND_VARIABLE_753 (ho_3 _let_1 Xy)) Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (ho_3 (ho_2 BOUND_VARIABLE_744 Xy) Xx) (ho_3 (ho_2 BOUND_VARIABLE_744 Xx) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= (ho_3 (ho_2 BOUND_VARIABLE_753 Xy) Xx) (ho_3 (ho_2 BOUND_VARIABLE_753 Xx) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_3 (ho_2 BOUND_VARIABLE_744 (ho_3 (ho_2 BOUND_VARIABLE_753 Xx) Xy)) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_3 (ho_2 BOUND_VARIABLE_753 (ho_3 (ho_2 BOUND_VARIABLE_744 Xx) Xy)) Xy)))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_744 Xx))) (= (ho_3 (ho_2 BOUND_VARIABLE_753 (ho_3 _let_1 Xy)) (ho_3 _let_1 Xz)) (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_753 Xy) Xz)))))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_753 Xx))) (= (ho_3 (ho_2 BOUND_VARIABLE_744 (ho_3 _let_1 Xy)) (ho_3 _let_1 Xz)) (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_744 Xy) Xz)))))) (= (ho_3 (ho_2 BOUND_VARIABLE_753 (ho_3 _let_1 BOUND_VARIABLE_726)) _let_2) (ho_3 _let_1 (ho_3 (ho_2 BOUND_VARIABLE_753 BOUND_VARIABLE_726) _let_2))))))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (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_22 (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_23 (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_24 (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_25 (not _let_19))) (let ((_let_26 (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)) (BOUND_VARIABLE_728 tptp.a) (BOUND_VARIABLE_726 tptp.a) (BOUND_VARIABLE_724 tptp.a)) (let ((_let_1 (@ JOIN BOUND_VARIABLE_724))) (let ((_let_2 (@ _let_1 BOUND_VARIABLE_728))) (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)))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ JOIN Xx))) (= (@ _let_1 (@ (@ MEET Xy) Xz)) (@ (@ MEET (@ _let_1 Xy)) (@ _let_1 Xz)))))) (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ MEET Xx))) (= (@ _let_1 (@ (@ JOIN Xy) Xz)) (@ (@ JOIN (@ _let_1 Xy)) (@ _let_1 Xz)))))) (= (@ _let_1 (@ (@ MEET BOUND_VARIABLE_726) _let_2)) (@ (@ MEET (@ _let_1 BOUND_VARIABLE_726)) _let_2))))))) _let_25))))))) (let ((_let_27 (or))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_26) :args (_let_25))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_19))) (REFL :args (_let_20)) :args _let_27)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_26 (PREPROCESS :args ((and _let_24 _let_23 _let_22 _let_21)))) :args ((and _let_25 _let_24 _let_23 _let_22 _let_21))) :args (0)) :args (_let_20 true _let_19)))) (let ((_let_29 (REFL :args (_let_18)))) (let ((_let_30 (_let_16))) (let ((_let_31 (_let_12))) (let ((_let_32 (_let_14))) (let ((_let_33 (and _let_8 _let_10 _let_11))) (let ((_let_34 (ASSUME :args (_let_10)))) (let ((_let_35 (APPLY_UF ho_3))) (let ((_let_36 (ASSUME :args (_let_11)))) (let ((_let_37 (ASSUME :args (_let_8)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_33)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_34 _let_36 _let_37) (SCOPE (TRANS (CONG (REFL :args (_let_5)) (TRANS (CONG (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (SYMM (SYMM _let_37)) :args (APPLY_UF ho_2)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) :args _let_35) (SYMM _let_36)) :args _let_35) (SYMM _let_34)) :args (_let_10 _let_11 _let_8))) :args (_let_8 _let_10 _let_11))) :args (true _let_33)) :args ((or _let_6 (not _let_8) (not _let_10) (not _let_11)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_32) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_PROP)) :args _let_32)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 2)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_27)) :args ((or _let_14 _let_18))) _let_28 :args (_let_14 true _let_18)) :args (_let_11 false _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_31) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_3 QUANTIFIERS_INST_E_MATCHING ((ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xy) Xz))))) :args _let_31))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 8)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_27)) :args ((or _let_12 _let_18))) _let_28 :args (_let_12 true _let_18)) :args (_let_10 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_30) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx)))) :args _let_30)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG _let_29 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_27)) :args ((or _let_16 _let_18))) _let_28 :args (_let_16 true _let_18)) :args (_let_8 false _let_16)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_18 10)) _let_28 :args ((not _let_6) true _let_18)) :args (false false _let_11 false _let_10 false _let_8 true _let_6)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))
% 0.22/0.55 )
% 0.22/0.55 % SZS output end Proof for SEV002^5
% 0.22/0.55 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------