TSTP Solution File: ALG290^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ALG290^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 : Wed Aug 30 16:09:12 EDT 2023
% Result : Theorem 0.20s 0.66s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG290^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:55:49 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 %----Proving TH0
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : ALG290^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.48 % Domain : General Algebra (Domain theory)
% 0.20/0.48 % Problem : TPS problem from PU-LAMBDA-MODEL-THMS
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_1190 [Bro09]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.62 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% 0.20/0.48 % Number of atoms : 17 ( 10 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 7 ( 17 avg)
% 0.20/0.48 % Number of connectives : 81 ( 1 ~; 2 |; 15 &; 50 @)
% 0.20/0.48 % ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 15 ( 15 avg)
% 0.20/0.48 % Number of types : 2 ( 1 usr)
% 0.20/0.48 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 8 ( 7 usr; 1 con; 0-2 aty)
% 0.20/0.48 % Number of variables : 25 ( 2 ^; 16 !; 7 ?; 25 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(a_type,type,
% 0.20/0.48 a: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(cP,type,
% 0.20/0.48 cP: a > a > a ).
% 0.20/0.48
% 0.20/0.48 thf(cG,type,
% 0.20/0.48 cG: a > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cX,type,
% 0.20/0.48 cX: a > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cR,type,
% 0.20/0.48 cR: a > a ).
% 0.20/0.48
% 0.20/0.48 thf(cL,type,
% 0.20/0.48 cL: a > a ).
% 0.20/0.48
% 0.20/0.48 thf(cF,type,
% 0.20/0.48 cF: a > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cZ,type,
% 0.20/0.48 cZ: a ).
% 0.20/0.48
% 0.20/0.48 thf(cPU_X2310A_pme,conjecture,
% 0.20/0.48 ( ( ( ( cL @ cZ )
% 0.20/0.48 = cZ )
% 0.20/0.48 & ( ( cR @ cZ )
% 0.20/0.48 = cZ )
% 0.20/0.48 & ! [Xx: a,Xy: a] :
% 0.20/0.48 ( ( cL @ ( cP @ Xx @ Xy ) )
% 0.20/0.48 = Xx )
% 0.20/0.48 & ! [Xx: a,Xy: a] :
% 0.20/0.48 ( ( cR @ ( cP @ Xx @ Xy ) )
% 0.20/0.48 = Xy )
% 0.20/0.48 & ! [Xt: a] :
% 0.20/0.48 ( ( Xt != cZ )
% 0.20/0.48 <=> ( Xt
% 0.20/0.48 = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) )
% 0.20/0.48 & ! [X0: a > $o] :
% 0.20/0.48 ( ? [Xt: a] :
% 0.20/0.48 ( ( X0 @ Xt )
% 0.20/0.48 & ! [Xu: a] :
% 0.20/0.48 ( ( X0 @ Xu )
% 0.20/0.48 => ( X0 @ ( cL @ Xu ) ) ) )
% 0.20/0.48 => ( X0 @ cZ ) ) )
% 0.20/0.48 => ( ( ^ [Xy: a] :
% 0.20/0.48 ? [Xx: a] :
% 0.20/0.48 ( ! [Xx_17: a] :
% 0.20/0.48 ( ! [X0: a > $o] :
% 0.20/0.48 ( ( ( X0 @ Xx )
% 0.20/0.48 & ! [Xz: a] :
% 0.20/0.48 ( ( X0 @ Xz )
% 0.20/0.48 => ( X0 @ ( cL @ Xz ) ) ) )
% 0.20/0.48 => ? [Xv: a] :
% 0.20/0.48 ( ( X0 @ Xv )
% 0.20/0.48 & ( ( cR @ Xv )
% 0.20/0.48 = Xx_17 ) ) )
% 0.20/0.48 => ( cX @ Xx_17 ) )
% 0.20/0.48 & ( ( cF @ ( cP @ Xx @ Xy ) )
% 0.20/0.48 | ( cG @ ( cP @ Xx @ Xy ) ) ) ) )
% 0.20/0.48 = ( ^ [Xz: a] :
% 0.20/0.48 ( ? [Xx: a] :
% 0.20/0.48 ( ! [Xx_18: a] :
% 0.20/0.48 ( ! [X0: a > $o] :
% 0.20/0.48 ( ( ( X0 @ Xx )
% 0.20/0.48 & ! [Xz0: a] :
% 0.20/0.48 ( ( X0 @ Xz0 )
% 0.20/0.48 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 0.20/0.48 => ? [Xv: a] :
% 0.20/0.48 ( ( X0 @ Xv )
% 0.20/0.48 & ( ( cR @ Xv )
% 0.20/0.48 = Xx_18 ) ) )
% 0.20/0.48 => ( cX @ Xx_18 ) )
% 0.20/0.48 & ( cF @ ( cP @ Xx @ Xz ) ) )
% 0.20/0.48 | ? [Xx: a] :
% 0.20/0.48 ( ! [Xx_19: a] :
% 0.20/0.48 ( ! [X0: a > $o] :
% 0.20/0.48 ( ( ( X0 @ Xx )
% 0.20/0.48 & ! [Xz0: a] :
% 0.20/0.48 ( ( X0 @ Xz0 )
% 0.20/0.48 => ( X0 @ ( cL @ Xz0 ) ) ) )
% 0.20/0.48 => ? [Xv: a] :
% 0.20/0.48 ( ( X0 @ Xv )
% 0.20/0.48 & ( ( cR @ Xv )
% 0.20/0.48 = Xx_19 ) ) )
% 0.20/0.48 => ( cX @ Xx_19 ) )
% 0.20/0.66 & ( cG @ ( cP @ Xx @ Xz ) ) ) ) ) ) ) ).
% 0.20/0.66
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XGjpxIgKXT/cvc5---1.0.5_21940.p...
% 0.20/0.66 (declare-sort $$unsorted 0)
% 0.20/0.66 (declare-sort tptp.a 0)
% 0.20/0.66 (declare-fun tptp.cP (tptp.a tptp.a) tptp.a)
% 0.20/0.66 (declare-fun tptp.cG (tptp.a) Bool)
% 0.20/0.66 (declare-fun tptp.cX (tptp.a) Bool)
% 0.20/0.66 (declare-fun tptp.cR (tptp.a) tptp.a)
% 0.20/0.66 (declare-fun tptp.cL (tptp.a) tptp.a)
% 0.20/0.66 (declare-fun tptp.cF (tptp.a) Bool)
% 0.20/0.66 (declare-fun tptp.cZ () tptp.a)
% 0.20/0.66 (assert (not (=> (and (= (@ tptp.cL tptp.cZ) tptp.cZ) (= (@ tptp.cR tptp.cZ) tptp.cZ) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ tptp.cL (@ (@ tptp.cP Xx) Xy)) Xx)) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ tptp.cR (@ (@ tptp.cP Xx) Xy)) Xy)) (forall ((Xt tptp.a)) (= (not (= Xt tptp.cZ)) (= Xt (@ (@ tptp.cP (@ tptp.cL Xt)) (@ tptp.cR Xt))))) (forall ((X0 (-> tptp.a Bool))) (=> (exists ((Xt tptp.a)) (and (@ X0 Xt) (forall ((Xu tptp.a)) (=> (@ X0 Xu) (@ X0 (@ tptp.cL Xu)))))) (@ X0 tptp.cZ)))) (= (lambda ((Xy tptp.a)) (exists ((Xx tptp.a)) (let ((_let_1 (@ (@ tptp.cP Xx) Xy))) (and (forall ((Xx_17 tptp.a)) (=> (forall ((X0 (-> tptp.a Bool))) (=> (and (@ X0 Xx) (forall ((Xz tptp.a)) (=> (@ X0 Xz) (@ X0 (@ tptp.cL Xz))))) (exists ((Xv tptp.a)) (and (@ X0 Xv) (= (@ tptp.cR Xv) Xx_17))))) (@ tptp.cX Xx_17))) (or (@ tptp.cF _let_1) (@ tptp.cG _let_1)))))) (lambda ((Xz tptp.a)) (or (exists ((Xx tptp.a)) (and (forall ((Xx_18 tptp.a)) (=> (forall ((X0 (-> tptp.a Bool))) (=> (and (@ X0 Xx) (forall ((Xz0 tptp.a)) (=> (@ X0 Xz0) (@ X0 (@ tptp.cL Xz0))))) (exists ((Xv tptp.a)) (and (@ X0 Xv) (= (@ tptp.cR Xv) Xx_18))))) (@ tptp.cX Xx_18))) (@ tptp.cF (@ (@ tptp.cP Xx) Xz)))) (exists ((Xx tptp.a)) (and (forall ((Xx_19 tptp.a)) (=> (forall ((X0 (-> tptp.a Bool))) (=> (and (@ X0 Xx) (forall ((Xz0 tptp.a)) (=> (@ X0 Xz0) (@ X0 (@ tptp.cL Xz0))))) (exists ((Xv tptp.a)) (and (@ X0 Xv) (= (@ tptp.cR Xv) Xx_19))))) (@ tptp.cX Xx_19))) (@ tptp.cG (@ (@ tptp.cP Xx) Xz))))))))))
% 0.20/0.66 (set-info :filename cvc5---1.0.5_21940)
% 0.20/0.66 (check-sat-assuming ( true ))
% 0.20/0.66 ------- get file name : TPTP file name is ALG290^5
% 0.20/0.66 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21940.smt2...
% 0.20/0.66 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.66 % SZS status Theorem for ALG290^5
% 0.20/0.66 % SZS output start Proof for ALG290^5
% 0.20/0.66 (
% 0.20/0.66 (let ((_let_1 (@ tptp.cR tptp.cZ))) (let ((_let_2 (@ tptp.cL tptp.cZ))) (let ((_let_3 (not (=> (and (= _let_2 tptp.cZ) (= _let_1 tptp.cZ) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ tptp.cL (@ (@ tptp.cP Xx) Xy)) Xx)) (forall ((Xx tptp.a) (Xy tptp.a)) (= (@ tptp.cR (@ (@ tptp.cP Xx) Xy)) Xy)) (forall ((Xt tptp.a)) (= (not (= Xt tptp.cZ)) (= Xt (@ (@ tptp.cP (@ tptp.cL Xt)) (@ tptp.cR Xt))))) (forall ((X0 (-> tptp.a Bool))) (=> (exists ((Xt tptp.a)) (and (@ X0 Xt) (forall ((Xu tptp.a)) (=> (@ X0 Xu) (@ X0 (@ tptp.cL Xu)))))) (@ X0 tptp.cZ)))) (= (lambda ((Xy tptp.a)) (exists ((Xx tptp.a)) (let ((_let_1 (@ (@ tptp.cP Xx) Xy))) (and (forall ((Xx_17 tptp.a)) (=> (forall ((X0 (-> tptp.a Bool))) (=> (and (@ X0 Xx) (forall ((Xz tptp.a)) (=> (@ X0 Xz) (@ X0 (@ tptp.cL Xz))))) (exists ((Xv tptp.a)) (and (@ X0 Xv) (= (@ tptp.cR Xv) Xx_17))))) (@ tptp.cX Xx_17))) (or (@ tptp.cF _let_1) (@ tptp.cG _let_1)))))) (lambda ((Xz tptp.a)) (or (exists ((Xx tptp.a)) (and (forall ((Xx_18 tptp.a)) (=> (forall ((X0 (-> tptp.a Bool))) (=> (and (@ X0 Xx) (forall ((Xz0 tptp.a)) (=> (@ X0 Xz0) (@ X0 (@ tptp.cL Xz0))))) (exists ((Xv tptp.a)) (and (@ X0 Xv) (= (@ tptp.cR Xv) Xx_18))))) (@ tptp.cX Xx_18))) (@ tptp.cF (@ (@ tptp.cP Xx) Xz)))) (exists ((Xx tptp.a)) (and (forall ((Xx_19 tptp.a)) (=> (forall ((X0 (-> tptp.a Bool))) (=> (and (@ X0 Xx) (forall ((Xz0 tptp.a)) (=> (@ X0 Xz0) (@ X0 (@ tptp.cL Xz0))))) (exists ((Xv tptp.a)) (and (@ X0 Xv) (= (@ tptp.cR Xv) Xx_19))))) (@ tptp.cX Xx_19))) (@ tptp.cG (@ (@ tptp.cP Xx) Xz))))))))))) (let ((_let_4 (ho_8 (ho_7 k_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (let ((_let_5 (ho_5 k_10 _let_4))) (let ((_let_6 (not _let_5))) (let ((_let_7 (and _let_6 (not (ho_5 k_9 _let_4))))) (let ((_let_8 (forall ((Xx_17 tptp.a)) (or (not (forall ((BOUND_VARIABLE_994 |u_(-> tptp.a Bool)|)) (or (not (ho_5 BOUND_VARIABLE_994 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54)) (not (forall ((Xz tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xz)) (ho_5 BOUND_VARIABLE_994 (ho_8 k_13 Xz))))) (not (forall ((Xv tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xv)) (not (= Xx_17 (ho_8 k_12 Xv))))))))) (ho_5 k_11 Xx_17))))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (forall ((Xx tptp.a)) (let ((_let_1 (ho_8 (ho_7 k_6 Xx) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (or (not (forall ((Xx_17 tptp.a)) (or (not (forall ((BOUND_VARIABLE_994 |u_(-> tptp.a Bool)|)) (or (not (ho_5 BOUND_VARIABLE_994 Xx)) (not (forall ((Xz tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xz)) (ho_5 BOUND_VARIABLE_994 (ho_8 k_13 Xz))))) (not (forall ((Xv tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xv)) (not (= Xx_17 (ho_8 k_12 Xv))))))))) (ho_5 k_11 Xx_17)))) (and (not (ho_5 k_10 _let_1)) (not (ho_5 k_9 _let_1)))))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_39))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (forall ((BOUND_VARIABLE_944 tptp.a)) (= (ho_5 k_4 BOUND_VARIABLE_944) (not (forall ((Xx tptp.a)) (let ((_let_1 (ho_8 (ho_7 k_6 Xx) BOUND_VARIABLE_944))) (or (not (forall ((Xx_17 tptp.a)) (or (not (forall ((BOUND_VARIABLE_994 |u_(-> tptp.a Bool)|)) (or (not (ho_5 BOUND_VARIABLE_994 Xx)) (not (forall ((Xz tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xz)) (ho_5 BOUND_VARIABLE_994 (ho_8 k_13 Xz))))) (not (forall ((Xv tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xv)) (not (= Xx_17 (ho_8 k_12 Xv))))))))) (ho_5 k_11 Xx_17)))) (and (not (ho_5 k_10 _let_1)) (not (ho_5 k_9 _let_1))))))))))) (let ((_let_16 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_17 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_18 (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_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_19 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_20 (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_7 v ii) (ite (= i ii) e (ho_7 u ii)))))))))) (let ((_let_21 (forall ((x |u_(-> tptp.a tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_7 x z) (ho_7 y z)))) (= x y))))) (let ((_let_22 (forall ((BOUND_VARIABLE_926 tptp.a)) (= (ho_5 k_14 BOUND_VARIABLE_926) (or (not (forall ((Xx tptp.a)) (or (not (forall ((Xx_18 tptp.a)) (or (not (forall ((BOUND_VARIABLE_1066 |u_(-> tptp.a Bool)|)) (or (not (ho_5 BOUND_VARIABLE_1066 Xx)) (not (forall ((Xz0 tptp.a)) (or (not (ho_5 BOUND_VARIABLE_1066 Xz0)) (ho_5 BOUND_VARIABLE_1066 (ho_8 k_13 Xz0))))) (not (forall ((Xv tptp.a)) (or (not (ho_5 BOUND_VARIABLE_1066 Xv)) (not (= Xx_18 (ho_8 k_12 Xv))))))))) (ho_5 k_11 Xx_18)))) (not (ho_5 k_10 (ho_8 (ho_7 k_6 Xx) BOUND_VARIABLE_926)))))) (not (forall ((Xx tptp.a)) (or (not (forall ((Xx_19 tptp.a)) (or (not (forall ((BOUND_VARIABLE_1033 |u_(-> tptp.a Bool)|)) (or (not (ho_5 BOUND_VARIABLE_1033 Xx)) (not (forall ((Xz0 tptp.a)) (or (not (ho_5 BOUND_VARIABLE_1033 Xz0)) (ho_5 BOUND_VARIABLE_1033 (ho_8 k_13 Xz0))))) (not (forall ((Xv tptp.a)) (or (not (ho_5 BOUND_VARIABLE_1033 Xv)) (not (= Xx_19 (ho_8 k_12 Xv))))))))) (ho_5 k_11 Xx_19)))) (not (ho_5 k_9 (ho_8 (ho_7 k_6 Xx) BOUND_VARIABLE_926))))))))))) (let ((_let_23 (= k_4 k_14))) (let ((_let_24 (not (=> (and (= tptp.cZ (ho_8 k_13 tptp.cZ)) (= tptp.cZ (ho_8 k_12 tptp.cZ)) (forall ((Xx tptp.a) (Xy tptp.a)) (= Xx (ho_8 k_13 (ho_8 (ho_7 k_6 Xx) Xy)))) (forall ((Xx tptp.a) (Xy tptp.a)) (= Xy (ho_8 k_12 (ho_8 (ho_7 k_6 Xx) Xy)))) (forall ((Xt tptp.a)) (= (not (= tptp.cZ Xt)) (= Xt (ho_8 (ho_7 k_6 (ho_8 k_13 Xt)) (ho_8 k_12 Xt))))) (forall ((BOUND_VARIABLE_1095 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_771 tptp.a)) (or (not (forall ((Xu tptp.a)) (or (not (ho_5 BOUND_VARIABLE_1095 Xu)) (ho_5 BOUND_VARIABLE_1095 (ho_8 k_13 Xu))))) (not (ho_5 BOUND_VARIABLE_1095 BOUND_VARIABLE_771)) (ho_5 BOUND_VARIABLE_1095 tptp.cZ)))) _let_23)))) (let ((_let_25 (forall ((BOUND_VARIABLE_944 tptp.a)) (= (not (forall ((Xx tptp.a)) (let ((_let_1 (@ (@ tptp.cP Xx) BOUND_VARIABLE_944))) (or (not (forall ((Xx_17 tptp.a)) (or (not (forall ((X0 (-> tptp.a Bool))) (or (not (@ X0 Xx)) (not (forall ((Xz tptp.a)) (or (not (@ X0 Xz)) (@ X0 (@ tptp.cL Xz))))) (not (forall ((Xv tptp.a)) (or (not (@ X0 Xv)) (not (= Xx_17 (@ tptp.cR Xv))))))))) (@ tptp.cX Xx_17)))) (and (not (@ tptp.cF _let_1)) (not (@ tptp.cG _let_1))))))) (ll_3 BOUND_VARIABLE_944))))) (let ((_let_26 (forall ((BOUND_VARIABLE_926 tptp.a)) (= (or (not (forall ((Xx tptp.a)) (or (not (forall ((Xx_18 tptp.a)) (or (not (forall ((X0 (-> tptp.a Bool))) (or (not (@ X0 Xx)) (not (forall ((Xz0 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SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62)) (not (forall ((Xz tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xz)) (ho_5 BOUND_VARIABLE_994 (ho_8 k_13 Xz))))) (not (forall ((Xv tptp.a)) (or (not (ho_5 BOUND_VARIABLE_994 Xv)) (not (= Xx_17 (ho_8 k_12 Xv))))))))) (ho_5 k_11 Xx_17))))) (let ((_let_98 (and (not (ho_5 k_10 _let_91)) _let_93))) (let ((_let_99 (not _let_97))) (let ((_let_100 (or _let_99 _let_98))) (let ((_let_101 (REFL :args (_let_96)))) (let ((_let_102 (_let_37))) (let ((_let_103 (_let_39))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_103)) :args _let_103)) (CONG _let_73 (REFL :args (_let_90)) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args _let_74) :args ((or _let_39 _let_37 _let_69))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_102)) :args _let_102)) (CONG _let_76 (REFL :args ((not _let_96))) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_99 _let_98 (not _let_100)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args (_let_100 false _let_11)) (REORDERING (CNF_AND_POS :args (_let_98 1)) :args ((or _let_93 (not _let_98)))) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_94 (= Xz0 Xz) (= Xv Xv) (= BOUND_VARIABLE_1033 BOUND_VARIABLE_994) (= Xx_19 Xx_17)))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 1)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_92))) :args _let_62)) :args ((or _let_92 _let_96))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 0)) (CONG _let_101 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_94))) :args _let_62)) :args ((or _let_94 _let_96))) :args (_let_96 false _let_100 true _let_98 false _let_97 false _let_92 false _let_94)) :args (_let_36 false _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_70) :args ((or (not _let_33) _let_40 _let_68))) _let_82 _let_67 :args (_let_40 false _let_33 false _let_41)) :args (_let_39 false _let_36 false _let_40)) :args (_let_90 true _let_38)))) (let ((_let_105 (REFL :args (_let_89)))) (let ((_let_106 (not _let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 (not _let_10)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_7 0)) :args ((or _let_6 _let_106))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_89 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_62)) :args ((or _let_5 _let_89))) _let_104 :args (_let_5 true _let_89)) :args (_let_106 false _let_5)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_87 (= Xz0 Xz) (= Xv Xv) (= BOUND_VARIABLE_1066 BOUND_VARIABLE_994) (= Xx_18 Xx_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_89 0)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_87))) :args _let_62)) :args ((or _let_87 _let_89))) _let_104 :args (_let_87 true _let_89)) :args (_let_8 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_54 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_85)) :args _let_84)) _let_83 :args (_let_10 false _let_11)) :args (false true _let_7 false _let_8 false _let_10)) :args (_let_3 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.67 )
% 0.20/0.67 % SZS output end Proof for ALG290^5
% 0.20/0.67 % cvc5---1.0.5 exiting
% 0.20/0.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------