TSTP Solution File: SEV154^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 19:21:42 EDT 2023
% Result : Theorem 0.52s 0.82s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n014.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 03:32:04 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 % File : SEV154^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.49 % Domain : Set Theory (Relations)
% 0.21/0.49 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.21/0.49 % Version : Especial.
% 0.21/0.49 % English :
% 0.21/0.49
% 0.21/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.49 % Source : [Bro09]
% 0.21/0.49 % Names : tps_1221 [Bro09]
% 0.21/0.49
% 0.21/0.49 % Status : Theorem
% 0.21/0.49 % Rating : 0.27 v8.1.0, 0.42 v7.5.0, 0.58 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.62 v6.4.0, 0.71 v6.3.0, 0.83 v6.1.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v5.2.0, 1.00 v5.0.0, 0.75 v4.1.0, 1.00 v4.0.0
% 0.21/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.21/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.21/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.21/0.49 % Number of connectives : 148 ( 1 ~; 14 |; 18 &; 88 @)
% 0.21/0.49 % ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% 0.21/0.49 % Maximal formula depth : 24 ( 24 avg)
% 0.21/0.49 % Number of types : 2 ( 1 usr)
% 0.21/0.49 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.21/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.49 % Number of variables : 41 ( 0 ^; 41 !; 0 ?; 41 :)
% 0.21/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.21/0.49
% 0.21/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 thf(a_type,type,
% 0.21/0.49 a: $tType ).
% 0.21/0.49
% 0.21/0.49 thf(cTHM251G_pme,conjecture,
% 0.21/0.49 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.21/0.49 ( ! [Xq: a > $o] :
% 0.21/0.49 ( ( ! [Xw: a] :
% 0.21/0.49 ( ( ( R @ Xx @ Xw )
% 0.21/0.49 | ( S @ Xx @ Xw ) )
% 0.21/0.49 => ( Xq @ Xw ) )
% 0.21/0.49 & ! [Xu: a,Xv: a] :
% 0.21/0.49 ( ( ( Xq @ Xu )
% 0.21/0.49 & ( ( R @ Xu @ Xv )
% 0.21/0.49 | ( S @ Xu @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xy ) )
% 0.21/0.49 | ~ ( ( ! [Xx0: a,Xy0: a] :
% 0.21/0.49 ( ( ! [Xq: a > $o] :
% 0.21/0.49 ( ( ! [Xw: a] :
% 0.21/0.49 ( ( R @ Xx0 @ Xw )
% 0.21/0.49 => ( Xq @ Xw ) )
% 0.21/0.49 & ! [Xu: a,Xv: a] :
% 0.21/0.49 ( ( ( Xq @ Xu )
% 0.21/0.49 & ( R @ Xu @ Xv ) )
% 0.21/0.49 => ( Xq @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xy0 ) )
% 0.21/0.49 | ! [Xq: a > $o] :
% 0.21/0.49 ( ( ! [Xw: a] :
% 0.21/0.49 ( ( S @ Xx0 @ Xw )
% 0.21/0.49 => ( Xq @ Xw ) )
% 0.21/0.49 & ! [Xu: a,Xv: a] :
% 0.21/0.49 ( ( ( Xq @ Xu )
% 0.21/0.49 & ( S @ Xu @ Xv ) )
% 0.21/0.49 => ( Xq @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xy0 ) ) )
% 0.21/0.49 => ! [Xq: a > $o] :
% 0.21/0.49 ( ( ! [Xw: a] :
% 0.21/0.49 ( ( ( R @ Xx0 @ Xw )
% 0.21/0.49 | ( S @ Xx0 @ Xw ) )
% 0.21/0.49 => ( Xq @ Xw ) )
% 0.21/0.49 & ! [Xu: a,Xv: a] :
% 0.21/0.49 ( ( ( Xq @ Xu )
% 0.21/0.49 & ( ( R @ Xu @ Xv )
% 0.21/0.49 | ( S @ Xu @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xy0 ) ) )
% 0.21/0.49 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.21/0.49 ( ( ! [Xq: a > $o] :
% 0.21/0.49 ( ( ! [Xw: a] :
% 0.21/0.49 ( ( ( R @ Xx0 @ Xw )
% 0.21/0.49 | ( S @ Xx0 @ Xw ) )
% 0.21/0.49 => ( Xq @ Xw ) )
% 0.21/0.49 & ! [Xu: a,Xv: a] :
% 0.21/0.49 ( ( ( Xq @ Xu )
% 0.21/0.49 & ( ( R @ Xu @ Xv )
% 0.21/0.49 | ( S @ Xu @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xv ) ) )
% 0.21/0.49 => ( Xq @ Xy0 ) )
% 0.21/0.49 & ! [Xq: a > $o] :
% 0.21/0.49 ( ( ! [Xw: a] :
% 0.21/0.49 ( ( ( R @ Xy0 @ Xw )
% 0.52/0.82 | ( S @ Xy0 @ Xw ) )
% 0.52/0.82 => ( Xq @ Xw ) )
% 0.52/0.82 & ! [Xu: a,Xv: a] :
% 0.52/0.82 ( ( ( Xq @ Xu )
% 0.52/0.82 & ( ( R @ Xu @ Xv )
% 0.52/0.82 | ( S @ Xu @ Xv ) ) )
% 0.52/0.82 => ( Xq @ Xv ) ) )
% 0.52/0.82 => ( Xq @ Xz ) ) )
% 0.52/0.82 => ! [Xq: a > $o] :
% 0.52/0.82 ( ( ! [Xw: a] :
% 0.52/0.82 ( ( ( R @ Xx0 @ Xw )
% 0.52/0.82 | ( S @ Xx0 @ Xw ) )
% 0.52/0.82 => ( Xq @ Xw ) )
% 0.52/0.82 & ! [Xu: a,Xv: a] :
% 0.52/0.82 ( ( ( Xq @ Xu )
% 0.52/0.82 & ( ( R @ Xu @ Xv )
% 0.52/0.82 | ( S @ Xu @ Xv ) ) )
% 0.52/0.82 => ( Xq @ Xv ) ) )
% 0.52/0.82 => ( Xq @ Xz ) ) ) )
% 0.52/0.82 => ! [Xq: a > $o] :
% 0.52/0.82 ( ( ! [Xw: a] :
% 0.52/0.82 ( ( ( R @ Xx @ Xw )
% 0.52/0.82 | ( S @ Xx @ Xw ) )
% 0.52/0.82 => ( Xq @ Xw ) )
% 0.52/0.82 & ! [Xu: a,Xv: a] :
% 0.52/0.82 ( ( ( Xq @ Xu )
% 0.52/0.82 & ( ( R @ Xu @ Xv )
% 0.52/0.82 | ( S @ Xu @ Xv ) ) )
% 0.52/0.82 => ( Xq @ Xv ) ) )
% 0.52/0.82 => ( Xq @ Xy ) ) ) ) ).
% 0.52/0.82
% 0.52/0.82 %------------------------------------------------------------------------------
% 0.52/0.82 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lnNPmvvwmz/cvc5---1.0.5_8704.p...
% 0.52/0.82 (declare-sort $$unsorted 0)
% 0.52/0.82 (declare-sort tptp.a 0)
% 0.52/0.82 (assert (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (or (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx) Xw) (@ (@ S Xx) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy))) (not (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ R Xx0) Xw) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (@ (@ R Xu) Xv)) (@ Xq Xv)))) (@ Xq Xy0))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ S Xx0) Xw) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (@ (@ S Xu) Xv)) (@ Xq Xv)))) (@ Xq Xy0)))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx0) Xw) (@ (@ S Xx0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy0))))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (=> (and (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx0) Xw) (@ (@ S Xx0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy0))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xy0) Xw) (@ (@ S Xy0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xz)))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx0) Xw) (@ (@ S Xx0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xz)))))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx) Xw) (@ (@ S Xx) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy)))))))))
% 0.52/0.82 (set-info :filename cvc5---1.0.5_8704)
% 0.52/0.82 (check-sat-assuming ( true ))
% 0.52/0.82 ------- get file name : TPTP file name is SEV154^5
% 0.52/0.82 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_8704.smt2...
% 0.52/0.82 --- Run --ho-elim --full-saturate-quant at 10...
% 0.52/0.82 % SZS status Theorem for SEV154^5
% 0.52/0.82 % SZS output start Proof for SEV154^5
% 0.52/0.82 (
% 0.52/0.82 (let ((_let_1 (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (or (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx) Xw) (@ (@ S Xx) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy))) (not (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ R Xx0) Xw) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (@ (@ R Xu) Xv)) (@ Xq Xv)))) (@ Xq Xy0))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ S Xx0) Xw) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (@ (@ S Xu) Xv)) (@ Xq Xv)))) (@ Xq Xy0)))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx0) Xw) (@ (@ S Xx0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy0))))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (=> (and (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx0) Xw) (@ (@ S Xx0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy0))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xy0) Xw) (@ (@ S Xy0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xz)))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx0) Xw) (@ (@ S Xx0) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xz)))))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (@ (@ R Xx) Xw) (@ (@ S Xx) Xw)) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (@ (@ R Xu) Xv) (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy)))))))))) (let ((_let_2 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62))) (let ((_let_4 (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62))) (let ((_let_5 (not _let_4))) (let ((_let_6 (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62)) _let_5))) (let ((_let_7 (not _let_2))) (let ((_let_8 (or _let_7 _let_6 _let_3))) (let ((_let_9 (or _let_7 _let_5 _let_3))) (let ((_let_10 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xv))))) (let ((_let_11 (not _let_9))) (let ((_let_12 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_13 (not _let_10))) (let ((_let_14 (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xw)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xw))))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_12))) (let ((_let_17 (forall ((BOUND_VARIABLE_1350 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xw)) (ho_2 BOUND_VARIABLE_1350 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1350 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv)) (ho_2 BOUND_VARIABLE_1350 Xv)))) (ho_2 BOUND_VARIABLE_1350 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (forall ((BOUND_VARIABLE_1371 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xw)) (ho_2 BOUND_VARIABLE_1371 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1371 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (ho_2 BOUND_VARIABLE_1371 Xv)))) (ho_2 BOUND_VARIABLE_1371 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_20 (not _let_19))) (let ((_let_21 (and _let_20 _let_18))) (let ((_let_22 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xv))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xw))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xw))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_21 _let_25 _let_23 _let_12))) (let ((_let_27 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_28 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xv))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) Xw))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xw))))) (let ((_let_31 (not _let_30))) (let ((_let_32 (forall ((BOUND_VARIABLE_1265 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Xw))) (ho_2 BOUND_VARIABLE_1265 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1265 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 BOUND_VARIABLE_1265 Xv)))) (ho_2 BOUND_VARIABLE_1265 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))))) (let ((_let_33 (not _let_32))) (let ((_let_34 (forall ((BOUND_VARIABLE_1295 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) Xw))) (ho_2 BOUND_VARIABLE_1295 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1295 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 BOUND_VARIABLE_1295 Xv)))) (ho_2 BOUND_VARIABLE_1295 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_31 _let_29 _let_27))) (let ((_let_37 (forall ((BOUND_VARIABLE_1211 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw))) (ho_2 BOUND_VARIABLE_1211 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1211 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 BOUND_VARIABLE_1211 Xv)))) (ho_2 BOUND_VARIABLE_1211 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_38 (not _let_37))) (let ((_let_39 (and _let_26 _let_36 _let_38))) (let ((_let_40 (not _let_26))) (let ((_let_41 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_42 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xv))))) (let ((_let_43 (not _let_42))) (let ((_let_44 (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) Xw))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xw))))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43 _let_41))) (let ((_let_47 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xv))))) (let ((_let_48 (not _let_47))) (let ((_let_49 (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Xw))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xw))))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_27))) (let ((_let_52 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_53 (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))))) (let ((_let_54 (not _let_41))) (let ((_let_55 (or _let_54 _let_53 _let_52))) (let ((_let_56 (or _let_53 _let_52))) (let ((_let_57 (or))) (let ((_let_58 (REFL :args (_let_36)))) (let ((_let_59 (_let_34))) (let ((_let_60 (_let_32))) (let ((_let_61 (_let_28))) (let ((_let_62 (_let_50))) (let ((_let_63 (not _let_55))) (let ((_let_64 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_65 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xv))))) (let ((_let_66 (not _let_65))) (let ((_let_67 (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xw))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_39 _let_68 _let_66 _let_64))) (let ((_let_70 (forall ((BOUND_VARIABLE_1190 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_1184 |u_(-> tptp.a tptp.a Bool)|) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_1239 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_1121 tptp.a) (BOUND_VARIABLE_1119 tptp.a) (BOUND_VARIABLE_1117 tptp.a) (BOUND_VARIABLE_1324 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_1075 tptp.a) (BOUND_VARIABLE_1073 tptp.a) (BOUND_VARIABLE_1178 |u_(-> tptp.a Bool)|)) (or (and (or (and (not (forall ((BOUND_VARIABLE_1371 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_1190 BOUND_VARIABLE_1073) Xw)) (ho_2 BOUND_VARIABLE_1371 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1371 Xu)) (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (ho_2 BOUND_VARIABLE_1371 Xv)))) (ho_2 BOUND_VARIABLE_1371 BOUND_VARIABLE_1075)))) (not (forall ((BOUND_VARIABLE_1350 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_1184 BOUND_VARIABLE_1073) Xw)) (ho_2 BOUND_VARIABLE_1350 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1350 Xu)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv)) (ho_2 BOUND_VARIABLE_1350 Xv)))) (ho_2 BOUND_VARIABLE_1350 BOUND_VARIABLE_1075))))) (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 BOUND_VARIABLE_1073) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 BOUND_VARIABLE_1073) Xw))) (ho_2 BOUND_VARIABLE_1324 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1324 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv))) (ho_2 BOUND_VARIABLE_1324 Xv)))) (ho_2 BOUND_VARIABLE_1324 BOUND_VARIABLE_1075)) (or (not (forall ((BOUND_VARIABLE_1295 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 BOUND_VARIABLE_1117) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 BOUND_VARIABLE_1117) Xw))) (ho_2 BOUND_VARIABLE_1295 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1295 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv))) (ho_2 BOUND_VARIABLE_1295 Xv)))) (ho_2 BOUND_VARIABLE_1295 BOUND_VARIABLE_1119)))) (not (forall ((BOUND_VARIABLE_1265 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 BOUND_VARIABLE_1119) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 BOUND_VARIABLE_1119) Xw))) (ho_2 BOUND_VARIABLE_1265 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1265 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv))) (ho_2 BOUND_VARIABLE_1265 Xv)))) (ho_2 BOUND_VARIABLE_1265 BOUND_VARIABLE_1121)))) (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 BOUND_VARIABLE_1117) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 BOUND_VARIABLE_1117) Xw))) (ho_2 BOUND_VARIABLE_1239 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1239 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv))) (ho_2 BOUND_VARIABLE_1239 Xv)))) (ho_2 BOUND_VARIABLE_1239 BOUND_VARIABLE_1121)) (not (forall ((BOUND_VARIABLE_1211 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xx) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xx) Xw))) (ho_2 BOUND_VARIABLE_1211 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1211 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv))) (ho_2 BOUND_VARIABLE_1211 Xv)))) (ho_2 BOUND_VARIABLE_1211 Xy))))) (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xx) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xx) Xw))) (ho_2 BOUND_VARIABLE_1178 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_1178 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_1190 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_1184 Xu) Xv))) (ho_2 BOUND_VARIABLE_1178 Xv)))) (ho_2 BOUND_VARIABLE_1178 Xy))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_76 (not _let_70))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_1123 (-> tptp.a Bool)) (BOUND_VARIABLE_1121 tptp.a) (BOUND_VARIABLE_1119 tptp.a) (BOUND_VARIABLE_1117 tptp.a) (BOUND_VARIABLE_1077 (-> tptp.a Bool)) (BOUND_VARIABLE_1075 tptp.a) (BOUND_VARIABLE_1073 tptp.a) (BOUND_VARIABLE_1059 (-> tptp.a Bool))) (or (and (or (and (not (forall ((Xq (-> tptp.a Bool))) (or (not (forall ((Xw tptp.a)) (or (not (@ (@ R BOUND_VARIABLE_1073) Xw)) (@ Xq Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ Xq Xu)) (not (@ (@ R Xu) Xv)) (@ Xq Xv)))) (@ Xq BOUND_VARIABLE_1075)))) (not (forall ((Xq (-> tptp.a Bool))) (or (not (forall ((Xw tptp.a)) (or (not (@ (@ S BOUND_VARIABLE_1073) Xw)) (@ Xq Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ Xq Xu)) (not (@ (@ S Xu) Xv)) (@ Xq Xv)))) (@ Xq BOUND_VARIABLE_1075))))) (not (forall ((Xw tptp.a)) (or (and (not (@ (@ R BOUND_VARIABLE_1073) Xw)) (not (@ (@ S BOUND_VARIABLE_1073) Xw))) (@ BOUND_VARIABLE_1077 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ BOUND_VARIABLE_1077 Xu)) (and (not (@ (@ R Xu) Xv)) (not (@ (@ S Xu) Xv))) (@ BOUND_VARIABLE_1077 Xv)))) (@ BOUND_VARIABLE_1077 BOUND_VARIABLE_1075)) (or (not (forall ((Xq (-> tptp.a Bool))) (or (not (forall ((Xw tptp.a)) (or (and (not (@ (@ R BOUND_VARIABLE_1117) Xw)) (not (@ (@ S BOUND_VARIABLE_1117) Xw))) (@ Xq Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ Xq Xu)) (and (not (@ (@ R Xu) Xv)) (not (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq BOUND_VARIABLE_1119)))) (not (forall ((Xq (-> tptp.a Bool))) (or (not (forall ((Xw tptp.a)) (or (and (not (@ (@ R BOUND_VARIABLE_1119) Xw)) (not (@ (@ S BOUND_VARIABLE_1119) Xw))) (@ Xq Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ Xq Xu)) (and (not (@ (@ R Xu) Xv)) (not (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq BOUND_VARIABLE_1121)))) (not (forall ((Xw tptp.a)) (or (and (not (@ (@ R BOUND_VARIABLE_1117) Xw)) (not (@ (@ S BOUND_VARIABLE_1117) Xw))) (@ BOUND_VARIABLE_1123 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ BOUND_VARIABLE_1123 Xu)) (and (not (@ (@ R Xu) Xv)) (not (@ (@ S Xu) Xv))) (@ BOUND_VARIABLE_1123 Xv)))) (@ BOUND_VARIABLE_1123 BOUND_VARIABLE_1121)) (not (forall ((Xq (-> tptp.a Bool))) (or (not (forall ((Xw tptp.a)) (or (and (not (@ (@ R Xx) Xw)) (not (@ (@ S Xx) Xw))) (@ Xq Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ Xq Xu)) (and (not (@ (@ R Xu) Xv)) (not (@ (@ S Xu) Xv))) (@ Xq Xv)))) (@ Xq Xy))))) (not (forall ((Xw tptp.a)) (or (and (not (@ (@ R Xx) Xw)) (not (@ (@ S Xx) Xw))) (@ BOUND_VARIABLE_1059 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (@ BOUND_VARIABLE_1059 Xu)) (and (not (@ (@ R Xu) Xv)) (not (@ (@ S Xu) Xv))) (@ BOUND_VARIABLE_1059 Xv)))) (@ BOUND_VARIABLE_1059 Xy)))) _let_76))))))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_77) :args (_let_76))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_70))) (REFL :args (_let_71)) :args _let_57)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_77 (PREPROCESS :args ((and _let_75 _let_74 _let_73 _let_72)))) :args ((and _let_76 _let_75 _let_74 _let_73 _let_72))) :args (0)) :args (_let_71 true _let_70)))) (let ((_let_79 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xu)) (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xv))))) (let ((_let_80 (not _let_79))) (let ((_let_81 (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xw))))) (let ((_let_82 (not _let_81))) (let ((_let_83 (or _let_82 _let_80 _let_64))) (let ((_let_84 (not _let_83))) (let ((_let_85 (REFL :args (_let_69)))) (let ((_let_86 (_let_37))) (let ((_let_87 (not _let_36))) (let ((_let_88 (_let_39))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_88) (CONG (REFL :args _let_88) (REFL :args (_let_40)) (REFL :args (_let_87)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_57)) :args ((or _let_37 _let_39 _let_40 _let_87))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_86) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_1211 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) true))))) :args _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_64 _let_82 _let_80 _let_84))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_69 3)) _let_78 :args ((not _let_64) true _let_69)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_67 (= Xw Xw)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 1)) (CONG _let_85 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_57)) :args ((or _let_67 _let_69))) _let_78 :args (_let_67 true _let_69)) :args (_let_81 false 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(REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_41 _let_45 _let_43 (not _let_46)))) (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_27 _let_50 _let_48 (not _let_51)))) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_28 (= Xu Xu) (= Xv Xv)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_61) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27 QUANTIFIERS_INST_E_MATCHING ((ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)))) :args _let_61)) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_28 (= Xu Xu) (= Xv Xv)))) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_30 (= Xw Xw)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_60) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_1265 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) true))))) :args _let_60)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 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_let_34)) :args (_let_40 true _let_37 true _let_39 false _let_36)))) (let ((_let_90 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xv))))) (let ((_let_91 (not _let_90))) (let ((_let_92 (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) Xw)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xw))))) (let ((_let_93 (not _let_92))) (let ((_let_94 (or _let_93 _let_91 _let_12))) (let ((_let_95 (not _let_94))) (let ((_let_96 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_97 (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_98 (not _let_97))) (let ((_let_99 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_100 _let_98 _let_96))) (let ((_let_102 (and _let_98 (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))))) (let ((_let_103 (or _let_100 _let_102 _let_96))) (let ((_let_104 (REFL :args (_let_26)))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 2)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_57)) :args ((or _let_22 _let_26))) _let_89 :args (_let_22 true _let_26)))) (let ((_let_106 (_let_22))) (let ((_let_107 (ASSUME :args _let_106))) (let ((_let_108 (not _let_103))) (let ((_let_109 (REFL :args (_let_101)))) (let ((_let_110 (_let_91))) (let ((_let_111 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_112 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_113 (ho_2 _let_112 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))) (let ((_let_114 (not _let_113))) (let ((_let_115 (or _let_114 _let_111))) (let ((_let_116 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_117 (and _let_114 (not (ho_2 _let_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22))))) (let ((_let_118 (or _let_117 _let_111))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_57)) :args ((or _let_24 _let_26))) _let_89 :args (_let_24 true _let_26)))) (let ((_let_120 (_let_24))) (let ((_let_121 (ASSUME :args _let_120))) (let ((_let_122 (not _let_118))) (let ((_let_123 (_let_93))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 3)) _let_89 :args ((not _let_12) true _let_26)))) (let ((_let_125 (_let_19))) (let ((_let_126 (_let_21))) (let ((_let_127 (_let_17))) (let ((_let_128 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49))) (let ((_let_129 (ho_2 _let_116 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49))) (let ((_let_130 (not _let_129))) (let ((_let_131 (or _let_130 _let_128))) (let ((_let_132 (and (not (ho_2 _let_112 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49)) _let_130))) (let ((_let_133 (or _let_132 _let_128))) (let ((_let_134 (_let_15))) (let ((_let_135 (_let_13))) (let ((_let_136 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_135)) :args _let_135)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_10))) (REFL :args (_let_11)) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_12 _let_15 _let_13 (not _let_16)))) _let_124 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_134)) :args _let_134)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) (REFL :args ((not _let_131))) :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_133)) :args ((or _let_128 _let_132 (not _let_133)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_49 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_120)) _let_119 :args (_let_133 false _let_24)) (REORDERING (CNF_AND_POS :args (_let_132 1)) :args ((or _let_130 (not _let_132)))) (CNF_OR_NEG :args (_let_131 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_131 0)) (CONG (REFL :args (_let_131)) (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_129))) :args _let_57)) :args ((or _let_129 _let_131))) :args (_let_131 false _let_133 true _let_132 true _let_128 false _let_129)) :args (_let_14 false _let_131)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_127) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_1350 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) true))))) :args _let_127)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_126) (CONG (REFL :args _let_126) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_57)) :args ((or _let_19 _let_17 _let_21))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_125) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_2 BOUND_VARIABLE_1371 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) true))))) :args _let_125)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_12 _let_93 _let_91 _let_95))) _let_124 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_123)) :args _let_123)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_92))) (REFL :args ((not _let_115))) :args _let_57)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_111 _let_117 _let_122))) (REORDERING (CNF_AND_POS :args (_let_117 0)) :args ((or _let_114 (not _let_117)))) (CNF_OR_NEG :args (_let_115 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_115 0)) (CONG (REFL :args (_let_115)) (MACRO_SR_PRED_INTRO :args ((= (not _let_114) _let_113))) :args _let_57)) :args ((or _let_113 _let_115))) :args ((or _let_115 _let_122) true _let_117 true _let_111 false _let_113)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_22 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_120)) _let_119 :args (_let_118 false _let_24)) :args (_let_115 false _let_118)) :args (_let_92 false _let_115)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_110)) :args _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) (REFL :args ((not _let_101))) :args _let_57)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_100 _let_96 _let_102 _let_108))) (REORDERING (CNF_AND_POS :args (_let_102 0)) :args ((or _let_98 (not _let_102)))) (CNF_OR_NEG :args (_let_101 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_101 1)) (CONG _let_109 (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_97))) :args _let_57)) :args ((or _let_97 _let_101))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_101 0)) (CONG _let_109 (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_99))) :args _let_57)) :args ((or _let_99 _let_101))) :args ((or _let_101 _let_108) true _let_102 true _let_96 false _let_97 false _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_106)) _let_105 :args (_let_103 false _let_22)) :args (_let_101 false _let_103)) :args (_let_90 false _let_101)) :args (_let_95 true _let_12 false _let_92 false _let_90)) :args (_let_20 true _let_94)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_26 0)) _let_89 :args ((not _let_21) true _let_26)) :args (_let_17 true _let_19 true _let_21)) :args (_let_16 false _let_17)) :args (_let_13 true _let_12 false _let_14 false _let_16)) :args (_let_11 true _let_10)))) (let ((_let_137 (REFL :args (_let_9)))) (let ((_let_138 (not _let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_7 _let_3 _let_6 (not _let_8)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_61 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_62 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_106)) _let_105 :args (_let_8 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_6 1)) :args ((or _let_5 _let_138))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 1)) (CONG _let_137 (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_57)) :args ((or _let_4 _let_9))) _let_136 :args (_let_4 true _let_9)) :args (_let_138 false _let_4)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_9 2)) _let_136 :args ((not _let_3) true _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 0)) (CONG _let_137 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_2))) :args _let_57)) :args ((or _let_2 _let_9))) _let_136 :args (_let_2 true _let_9)) :args (false false _let_8 true _let_6 true _let_3 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.52/0.83 )
% 0.52/0.83 % SZS output end Proof for SEV154^5
% 0.52/0.83 % cvc5---1.0.5 exiting
% 0.52/0.83 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------