TSTP Solution File: SEV031^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV031^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 19:21:23 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 : SEV031^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 03:27:27 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 % File : SEV031^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.51 % Domain : Set Theory (Relations)
% 0.22/0.51 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.22/0.51 % Version : Especial.
% 0.22/0.51 % English :
% 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_1127 [Bro09]
% 0.22/0.51
% 0.22/0.51 % Status : Theorem
% 0.22/0.51 % Rating : 0.09 v8.1.0, 0.17 v7.5.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.22/0.51 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.22/0.51 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.22/0.51 % Maximal formula atoms : 0 ( 0 avg)
% 0.22/0.51 % Number of connectives : 61 ( 0 ~; 0 |; 6 &; 43 @)
% 0.22/0.51 % ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% 0.22/0.51 % Maximal formula depth : 16 ( 16 avg)
% 0.22/0.51 % Number of types : 3 ( 2 usr)
% 0.22/0.51 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.22/0.51 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.22/0.51 % Number of variables : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 0.22/0.51 % SPC : TH0_THM_NEQ_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 %------------------------------------------------------------------------------
% 0.22/0.51 thf(a_type,type,
% 0.22/0.51 a: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(b_type,type,
% 0.22/0.51 b: $tType ).
% 0.22/0.51
% 0.22/0.51 thf(cTHM512_pme,conjecture,
% 0.22/0.51 ! [Xp: a > $o,Xe: a > ( a > b ) > ( a > b ) > $o] :
% 0.22/0.51 ( ! [Xx: a] :
% 0.22/0.51 ( ( Xp @ Xx )
% 0.22/0.51 => ( ! [Xx0: a > b] : ( Xe @ Xx @ Xx0 @ Xx0 )
% 0.22/0.51 & ! [Xx0: a > b,Xy: a > b] :
% 0.22/0.51 ( ( Xe @ Xx @ Xx0 @ Xy )
% 0.22/0.51 => ( Xe @ Xx @ Xy @ Xx0 ) )
% 0.22/0.51 & ! [Xx0: a > b,Xy: a > b,Xz: a > b] :
% 0.22/0.51 ( ( ( Xe @ Xx @ Xx0 @ Xy )
% 0.22/0.51 & ( Xe @ Xx @ Xy @ Xz ) )
% 0.22/0.51 => ( Xe @ Xx @ Xx0 @ Xz ) ) ) )
% 0.22/0.51 => ( ! [Xx: a > b,Xx0: a] :
% 0.22/0.51 ( ( Xp @ Xx0 )
% 0.22/0.51 => ( Xe @ Xx0 @ Xx @ Xx ) )
% 0.22/0.51 & ! [Xx: a > b,Xy: a > b] :
% 0.22/0.51 ( ! [Xx0: a] :
% 0.22/0.51 ( ( Xp @ Xx0 )
% 0.22/0.51 => ( Xe @ Xx0 @ Xx @ Xy ) )
% 0.22/0.51 => ! [Xx0: a] :
% 0.22/0.51 ( ( Xp @ Xx0 )
% 0.22/0.51 => ( Xe @ Xx0 @ Xy @ Xx ) ) )
% 0.22/0.51 & ! [Xx: a > b,Xy: a > b,Xz: a > b] :
% 0.22/0.51 ( ( ! [Xx0: a] :
% 0.22/0.51 ( ( Xp @ Xx0 )
% 0.22/0.51 => ( Xe @ Xx0 @ Xx @ Xy ) )
% 0.22/0.51 & ! [Xx0: a] :
% 0.22/0.51 ( ( Xp @ Xx0 )
% 0.22/0.51 => ( Xe @ Xx0 @ Xy @ Xz ) ) )
% 0.22/0.51 => ! [Xx0: a] :
% 0.22/0.51 ( ( Xp @ Xx0 )
% 0.22/0.51 => ( Xe @ Xx0 @ Xx @ Xz ) ) ) ) ) ).
% 0.22/0.51
% 0.22/0.51 %------------------------------------------------------------------------------
% 0.22/0.51 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.C5TXXG3bmZ/cvc5---1.0.5_15986.p...
% 0.22/0.51 (declare-sort $$unsorted 0)
% 0.22/0.51 (declare-sort tptp.a 0)
% 0.22/0.51 (declare-sort tptp.b 0)
% 0.22/0.51 (assert (not (forall ((Xp (-> tptp.a Bool)) (Xe (-> tptp.a (-> tptp.a tptp.b) (-> tptp.a tptp.b) Bool))) (=> (forall ((Xx tptp.a)) (=> (@ Xp Xx) (and (forall ((Xx0 (-> tptp.a tptp.b))) (@ (@ (@ Xe Xx) Xx0) Xx0)) (forall ((Xx0 (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b))) (let ((_let_1 (@ Xe Xx))) (=> (@ (@ _let_1 Xx0) Xy) (@ (@ _let_1 Xy) Xx0)))) (forall ((Xx0 (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b)) (Xz (-> tptp.a tptp.b))) (let ((_let_1 (@ Xe Xx))) (let ((_let_2 (@ _let_1 Xx0))) (=> (and (@ _let_2 Xy) (@ (@ _let_1 Xy) Xz)) (@ _let_2 Xz)))))))) (and (forall ((Xx (-> tptp.a tptp.b)) (Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xx))) (forall ((Xx (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b))) (=> (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xy))) (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xy) Xx))))) (forall ((Xx (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b)) (Xz (-> tptp.a tptp.b))) (=> (and (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xy))) (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xy) Xz)))) (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xz))))))))))
% 0.22/0.56 (set-info :filename cvc5---1.0.5_15986)
% 0.22/0.56 (check-sat-assuming ( true ))
% 0.22/0.56 ------- get file name : TPTP file name is SEV031^5
% 0.22/0.56 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15986.smt2...
% 0.22/0.56 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.56 % SZS status Theorem for SEV031^5
% 0.22/0.56 % SZS output start Proof for SEV031^5
% 0.22/0.56 (
% 0.22/0.56 (let ((_let_1 (not (forall ((Xp (-> tptp.a Bool)) (Xe (-> tptp.a (-> tptp.a tptp.b) (-> tptp.a tptp.b) Bool))) (=> (forall ((Xx tptp.a)) (=> (@ Xp Xx) (and (forall ((Xx0 (-> tptp.a tptp.b))) (@ (@ (@ Xe Xx) Xx0) Xx0)) (forall ((Xx0 (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b))) (let ((_let_1 (@ Xe Xx))) (=> (@ (@ _let_1 Xx0) Xy) (@ (@ _let_1 Xy) Xx0)))) (forall ((Xx0 (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b)) (Xz (-> tptp.a tptp.b))) (let ((_let_1 (@ Xe Xx))) (let ((_let_2 (@ _let_1 Xx0))) (=> (and (@ _let_2 Xy) (@ (@ _let_1 Xy) Xz)) (@ _let_2 Xz)))))))) (and (forall ((Xx (-> tptp.a tptp.b)) (Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xx))) (forall ((Xx (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b))) (=> (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xy))) (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xy) Xx))))) (forall ((Xx (-> tptp.a tptp.b)) (Xy (-> tptp.a tptp.b)) (Xz (-> tptp.a tptp.b))) (=> (and (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xy))) (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xy) Xz)))) (forall ((Xx0 tptp.a)) (=> (@ Xp Xx0) (@ (@ (@ Xe Xx0) Xx) Xz))))))))))) (let ((_let_2 (ho_5 (ho_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_3 (not _let_2))) (let ((_let_4 (and _let_2 (or _let_3 _let_2) (or _let_3 _let_3 _let_2)))) (let ((_let_5 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_6 (not _let_5))) (let ((_let_7 (or _let_6 _let_2))) (let ((_let_8 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_9 (ho_4 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_10 (ho_5 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_11 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_12 (not _let_11))) (let ((_let_13 (forall ((Xx0 tptp.a)) (or (not (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0)) (ho_5 (ho_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (forall ((Xx0 tptp.a)) (or (not (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0)) (ho_5 (ho_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (or _let_16 _let_14 _let_12 _let_10))) (let ((_let_18 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_19 (ho_5 (ho_4 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_20 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_21 (not _let_20))) (let ((_let_22 (forall ((Xx0 tptp.a)) (or (not (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0)) (ho_5 (ho_4 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_21 _let_19))) (let ((_let_25 (and _let_7 _let_24 _let_17))) (let ((_let_26 (ho_5 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_27 (or _let_12 _let_26))) (let ((_let_28 (ho_5 (ho_4 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_29 (or _let_12 _let_28))) (let ((_let_30 (not _let_28))) (let ((_let_31 (not _let_26))) (let ((_let_32 (or _let_31 _let_30 _let_10))) (let ((_let_33 (ho_5 (ho_4 _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_34 (and _let_33 (or (not _let_33) _let_33) _let_32))) (let ((_let_35 (or _let_12 _let_34))) (let ((_let_36 (or))) (let ((_let_37 (REFL :args (_let_17)))) (let ((_let_38 (_let_15))) (let ((_let_39 (_let_13))) (let ((_let_40 (forall ((Xx tptp.a) (BOUND_VARIABLE_917 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_922 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_918 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_930 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_929 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_937 |u_(-> tptp.a tptp.b)|)) (let ((_let_1 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx))) (let ((_let_2 (ho_4 _let_1 BOUND_VARIABLE_918))) (or (not (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx)) (and (ho_5 (ho_4 _let_1 BOUND_VARIABLE_937) BOUND_VARIABLE_937) (or (not (ho_5 (ho_4 _let_1 BOUND_VARIABLE_929) BOUND_VARIABLE_930)) (ho_5 (ho_4 _let_1 BOUND_VARIABLE_930) BOUND_VARIABLE_929)) (or (not (ho_5 _let_2 BOUND_VARIABLE_922)) (not (ho_5 (ho_4 _let_1 BOUND_VARIABLE_922) BOUND_VARIABLE_917)) (ho_5 _let_2 BOUND_VARIABLE_917))))))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_25))) (let ((_let_43 (forall ((BOUND_VARIABLE_870 |u_(-> tptp.a Bool)|) (BOUND_VARIABLE_855 |u_(-> tptp.a _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|) (BOUND_VARIABLE_825 tptp.a) (BOUND_VARIABLE_849 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_875 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_852 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_806 tptp.a) (BOUND_VARIABLE_894 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_893 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_794 tptp.a) (BOUND_VARIABLE_909 |u_(-> tptp.a tptp.b)|)) (or (not (forall ((Xx tptp.a) (BOUND_VARIABLE_917 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_922 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_918 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_930 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_929 |u_(-> tptp.a tptp.b)|) (BOUND_VARIABLE_937 |u_(-> tptp.a tptp.b)|)) (let ((_let_1 (ho_3 BOUND_VARIABLE_855 Xx))) (let ((_let_2 (ho_4 _let_1 BOUND_VARIABLE_918))) (or (not (ho_6 BOUND_VARIABLE_870 Xx)) (and (ho_5 (ho_4 _let_1 BOUND_VARIABLE_937) BOUND_VARIABLE_937) (or (not (ho_5 (ho_4 _let_1 BOUND_VARIABLE_929) BOUND_VARIABLE_930)) (ho_5 (ho_4 _let_1 BOUND_VARIABLE_930) BOUND_VARIABLE_929)) (or (not (ho_5 _let_2 BOUND_VARIABLE_922)) (not (ho_5 (ho_4 _let_1 BOUND_VARIABLE_922) BOUND_VARIABLE_917)) (ho_5 _let_2 BOUND_VARIABLE_917)))))))) (and (or (not (ho_6 BOUND_VARIABLE_870 BOUND_VARIABLE_794)) (ho_5 (ho_4 (ho_3 BOUND_VARIABLE_855 BOUND_VARIABLE_794) BOUND_VARIABLE_909) BOUND_VARIABLE_909)) (or (not (forall ((Xx0 tptp.a)) (or (not (ho_6 BOUND_VARIABLE_870 Xx0)) (ho_5 (ho_4 (ho_3 BOUND_VARIABLE_855 Xx0) BOUND_VARIABLE_893) BOUND_VARIABLE_894)))) (not (ho_6 BOUND_VARIABLE_870 BOUND_VARIABLE_806)) (ho_5 (ho_4 (ho_3 BOUND_VARIABLE_855 BOUND_VARIABLE_806) BOUND_VARIABLE_894) BOUND_VARIABLE_893)) (or (not (forall ((Xx0 tptp.a)) (or (not (ho_6 BOUND_VARIABLE_870 Xx0)) (ho_5 (ho_4 (ho_3 BOUND_VARIABLE_855 Xx0) BOUND_VARIABLE_852) BOUND_VARIABLE_875)))) (not (forall ((Xx0 tptp.a)) (or (not (ho_6 BOUND_VARIABLE_870 Xx0)) (ho_5 (ho_4 (ho_3 BOUND_VARIABLE_855 Xx0) BOUND_VARIABLE_875) BOUND_VARIABLE_849)))) (not (ho_6 BOUND_VARIABLE_870 BOUND_VARIABLE_825)) (ho_5 (ho_4 (ho_3 BOUND_VARIABLE_855 BOUND_VARIABLE_825) BOUND_VARIABLE_852) BOUND_VARIABLE_849))))))) (let ((_let_44 (not _let_42))) (let ((_let_45 (forall ((u |u_(-> tptp.a tptp.b)|) (e tptp.b) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.b)|)) (not (forall ((ii tptp.a)) (= (ho_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> tptp.a tptp.b)|) (y |u_(-> tptp.a tptp.b)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> _u_(-> tptp.a tptp.b)_ Bool)|) (e Bool) (i |u_(-> tptp.a tptp.b)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.b)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.b)|)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> _u_(-> tptp.a tptp.b)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.b)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.b)|)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> tptp.a _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|) (e |u_(-> _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> tptp.a _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|) (y |u_(-> tptp.a _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|) (e |u_(-> _u_(-> tptp.a tptp.b)_ Bool)|) (i |u_(-> tptp.a tptp.b)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.b)|)) (= (ho_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|) (y |u_(-> _u_(-> tptp.a tptp.b)_ _u_(-> tptp.a tptp.b)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.b)|)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_55 (not _let_43))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((Xp (-> tptp.a Bool)) (Xe (-> tptp.a (-> tptp.a tptp.b) (-> tptp.a tptp.b) Bool)) (BOUND_VARIABLE_825 tptp.a) (BOUND_VARIABLE_823 (-> tptp.a tptp.b)) (BOUND_VARIABLE_821 (-> tptp.a tptp.b)) (BOUND_VARIABLE_819 (-> tptp.a tptp.b)) (BOUND_VARIABLE_806 tptp.a) (BOUND_VARIABLE_804 (-> tptp.a tptp.b)) (BOUND_VARIABLE_802 (-> tptp.a tptp.b)) (BOUND_VARIABLE_794 tptp.a) (BOUND_VARIABLE_792 (-> tptp.a tptp.b))) (or (not (forall ((Xx tptp.a) (BOUND_VARIABLE_714 (-> tptp.a tptp.b)) (BOUND_VARIABLE_712 (-> tptp.a tptp.b)) (BOUND_VARIABLE_710 (-> tptp.a tptp.b)) (BOUND_VARIABLE_702 (-> tptp.a tptp.b)) (BOUND_VARIABLE_700 (-> tptp.a tptp.b)) (BOUND_VARIABLE_696 (-> tptp.a tptp.b))) (let ((_let_1 (@ Xe Xx))) (let ((_let_2 (@ _let_1 BOUND_VARIABLE_710))) (or (not (@ Xp Xx)) (and (@ (@ _let_1 BOUND_VARIABLE_696) BOUND_VARIABLE_696) (or (not (@ (@ _let_1 BOUND_VARIABLE_700) BOUND_VARIABLE_702)) (@ (@ _let_1 BOUND_VARIABLE_702) BOUND_VARIABLE_700)) (or (not (@ _let_2 BOUND_VARIABLE_712)) (not (@ (@ _let_1 BOUND_VARIABLE_712) BOUND_VARIABLE_714)) (@ _let_2 BOUND_VARIABLE_714)))))))) (and (or (not (@ Xp BOUND_VARIABLE_794)) (@ (@ (@ Xe BOUND_VARIABLE_794) BOUND_VARIABLE_792) BOUND_VARIABLE_792)) (or (not (forall ((Xx0 tptp.a)) (or (not (@ Xp Xx0)) (@ (@ (@ Xe Xx0) BOUND_VARIABLE_802) BOUND_VARIABLE_804)))) (not (@ Xp BOUND_VARIABLE_806)) (@ (@ (@ Xe BOUND_VARIABLE_806) BOUND_VARIABLE_804) BOUND_VARIABLE_802)) (or (not (forall ((Xx0 tptp.a)) (or (not (@ Xp Xx0)) (@ (@ (@ Xe Xx0) BOUND_VARIABLE_819) BOUND_VARIABLE_821)))) (not (forall ((Xx0 tptp.a)) (or (not (@ Xp Xx0)) (@ (@ (@ Xe Xx0) BOUND_VARIABLE_821) BOUND_VARIABLE_823)))) (not (@ Xp BOUND_VARIABLE_825)) (@ (@ (@ Xe BOUND_VARIABLE_825) BOUND_VARIABLE_819) BOUND_VARIABLE_823)))))) _let_55))))))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_56) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_43))) (REFL :args (_let_44)) :args _let_36)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_56 (PREPROCESS :args ((and _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45)))) :args ((and _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45))) :args (0)) :args (_let_44 true _let_43)))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_36)) :args ((or _let_40 _let_42))) _let_57 :args (_let_40 true _let_42)))) (let ((_let_59 (_let_40))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (ho_5 (ho_4 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_62 (or _let_21 _let_61))) (let ((_let_63 (ho_5 (ho_4 _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_61))) (let ((_let_66 (or _let_65 _let_19))) (let ((_let_67 (and _let_63 _let_66 (or _let_64 _let_64 _let_63)))) (let ((_let_68 (or _let_21 _let_67))) (let ((_let_69 (REFL :args (_let_24)))) (let ((_let_70 (_let_22))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_25)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 1)) _let_57 :args ((not _let_25) true _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 1)) :args ((or _let_66 (not _let_67)))) (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_19 _let_65 (not _let_66)))) (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_21 _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59)) _let_58 :args (_let_68 false _let_40)) (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_21 _let_61 (not _let_62)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_70) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0) false))))) :args _let_70)) (CNF_OR_NEG :args (_let_24 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_36)) :args ((or _let_20 _let_24))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG _let_69 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_36)) :args ((or _let_22 _let_24))) :args (_let_24 true _let_66 false _let_67 false _let_68 false _let_61 false _let_62 true _let_19 false _let_20 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_10 _let_31 _let_30 (not _let_32)))) (REORDERING (CNF_AND_POS :args (_let_34 2)) :args ((or _let_32 (not _let_34)))) (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_12 _let_28 (not _let_29)))) (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_12 _let_26 (not _let_27)))) (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_12 _let_34 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59)) _let_58 :args (_let_35 false _let_40)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_39) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0) false))))) :args _let_39)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Xx0) false))))) :args _let_38)) (CNF_OR_NEG :args (_let_17 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 2)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_36)) :args ((or _let_11 _let_17))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_36)) :args ((or _let_13 _let_17))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_36)) :args ((or _let_15 _let_17))) :args (_let_17 false _let_32 false _let_28 false _let_26 false _let_34 false _let_35 false _let_29 false _let_27 true _let_10 false _let_11 false _let_13 false _let_15)) :args ((not _let_7) true _let_25 false _let_24 false _let_17)))) (let ((_let_72 (or _let_6 _let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_4 0)) :args ((or _let_2 (not _let_4)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_6 _let_4 (not _let_72)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_7 0)) (CONG (REFL :args (_let_7)) (MACRO_SR_PRED_INTRO :args ((= (not _let_6) _let_5))) :args _let_36)) :args ((or _let_5 _let_7))) _let_71 :args (_let_5 true _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59)) _let_58 :args (_let_72 false _let_40)) :args (_let_4 false _let_5 false _let_72)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_7 1)) _let_71 :args (_let_3 true _let_7)) :args (false false _let_4 true _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.56 )
% 0.22/0.56 % SZS output end Proof for SEV031^5
% 0.22/0.56 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------