TSTP Solution File: SEV149^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV149^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 19:21:41 EDT 2023
% Result : Theorem 0.16s 0.58s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV149^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : do_cvc5 %s %d
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Aug 24 03:49:51 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.16/0.44 %----Proving TH0
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 % File : SEV149^5 : TPTP v8.1.2. Released v4.0.0.
% 0.16/0.45 % Domain : Set Theory (Relations)
% 0.16/0.45 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.16/0.45 % Version : Especial.
% 0.16/0.45 % English :
% 0.16/0.45
% 0.16/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.45 % Source : [Bro09]
% 0.16/0.45 % Names : tps_1187 [Bro09]
% 0.16/0.45
% 0.16/0.45 % Status : Theorem
% 0.16/0.45 % Rating : 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 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 v5.2.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.16/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.16/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.16/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.16/0.45 % Number of connectives : 83 ( 0 ~; 4 |; 12 &; 48 @)
% 0.16/0.45 % ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% 0.16/0.45 % Maximal formula depth : 23 ( 23 avg)
% 0.16/0.45 % Number of types : 2 ( 1 usr)
% 0.16/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.16/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.45 % Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% 0.16/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.45
% 0.16/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 thf(a_type,type,
% 0.16/0.45 a: $tType ).
% 0.16/0.45
% 0.16/0.45 thf(cTHM251B_pme,conjecture,
% 0.16/0.45 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.16/0.45 ( ! [Xq: a > $o] :
% 0.16/0.45 ( ( ! [Xw: a] :
% 0.16/0.45 ( ( ( R @ Xx @ Xw )
% 0.16/0.45 | ( S @ Xx @ Xw ) )
% 0.16/0.45 => ( Xq @ Xw ) )
% 0.16/0.45 & ! [Xu: a,Xv: a] :
% 0.16/0.45 ( ( ( Xq @ Xu )
% 0.16/0.45 & ( ( R @ Xu @ Xv )
% 0.16/0.45 | ( S @ Xu @ Xv ) ) )
% 0.16/0.45 => ( Xq @ Xv ) ) )
% 0.16/0.45 => ( Xq @ Xy ) )
% 0.16/0.45 => ! [Xq: a > $o] :
% 0.16/0.45 ( ( ! [Xw: a] :
% 0.16/0.45 ( ( ! [Xq0: a > $o] :
% 0.16/0.45 ( ( ! [Xw0: a] :
% 0.16/0.45 ( ( R @ Xx @ Xw0 )
% 0.16/0.45 => ( Xq0 @ Xw0 ) )
% 0.16/0.45 & ! [Xu: a,Xv: a] :
% 0.16/0.45 ( ( ( Xq0 @ Xu )
% 0.16/0.45 & ( R @ Xu @ Xv ) )
% 0.16/0.45 => ( Xq0 @ Xv ) ) )
% 0.16/0.45 => ( Xq0 @ Xw ) )
% 0.16/0.45 | ! [Xq0: a > $o] :
% 0.16/0.45 ( ( ! [Xw0: a] :
% 0.16/0.45 ( ( S @ Xx @ Xw0 )
% 0.16/0.45 => ( Xq0 @ Xw0 ) )
% 0.16/0.45 & ! [Xu: a,Xv: a] :
% 0.16/0.45 ( ( ( Xq0 @ Xu )
% 0.16/0.45 & ( S @ Xu @ Xv ) )
% 0.16/0.45 => ( Xq0 @ Xv ) ) )
% 0.16/0.45 => ( Xq0 @ Xw ) ) )
% 0.16/0.45 => ( Xq @ Xw ) )
% 0.16/0.45 & ! [Xu: a,Xv: a] :
% 0.16/0.45 ( ( ( Xq @ Xu )
% 0.16/0.45 & ( ! [Xq0: a > $o] :
% 0.16/0.45 ( ( ! [Xw: a] :
% 0.16/0.45 ( ( R @ Xu @ Xw )
% 0.16/0.45 => ( Xq0 @ Xw ) )
% 0.16/0.45 & ! [Xu0: a,Xv0: a] :
% 0.16/0.45 ( ( ( Xq0 @ Xu0 )
% 0.16/0.45 & ( R @ Xu0 @ Xv0 ) )
% 0.16/0.45 => ( Xq0 @ Xv0 ) ) )
% 0.16/0.45 => ( Xq0 @ Xv ) )
% 0.16/0.45 | ! [Xq0: a > $o] :
% 0.16/0.45 ( ( ! [Xw: a] :
% 0.16/0.45 ( ( S @ Xu @ Xw )
% 0.16/0.45 => ( Xq0 @ Xw ) )
% 0.16/0.45 & ! [Xu0: a,Xv0: a] :
% 0.16/0.45 ( ( ( Xq0 @ Xu0 )
% 0.16/0.45 & ( S @ Xu0 @ Xv0 ) )
% 0.16/0.45 => ( Xq0 @ Xv0 ) ) )
% 0.16/0.45 => ( Xq0 @ Xv ) ) ) )
% 0.16/0.45 => ( Xq @ Xv ) ) )
% 0.16/0.45 => ( Xq @ Xy ) ) ) ).
% 0.16/0.45
% 0.16/0.45 %------------------------------------------------------------------------------
% 0.16/0.45 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.TTwV3MuLzx/cvc5---1.0.5_15643.p...
% 0.16/0.58 (declare-sort $$unsorted 0)
% 0.16/0.58 (declare-sort tptp.a 0)
% 0.16/0.58 (assert (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (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))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw0 tptp.a)) (=> (@ (@ R Xx) Xw0) (@ Xq0 Xw0))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq0 Xu) (@ (@ R Xu) Xv)) (@ Xq0 Xv)))) (@ Xq0 Xw))) (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw0 tptp.a)) (=> (@ (@ S Xx) Xw0) (@ Xq0 Xw0))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq0 Xu) (@ (@ S Xu) Xv)) (@ Xq0 Xv)))) (@ Xq0 Xw)))) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ R Xu) Xw) (@ Xq0 Xw))) (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (=> (and (@ Xq0 Xu0) (@ (@ R Xu0) Xv0)) (@ Xq0 Xv0)))) (@ Xq0 Xv))) (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ S Xu) Xw) (@ Xq0 Xw))) (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (=> (and (@ Xq0 Xu0) (@ (@ S Xu0) Xv0)) (@ Xq0 Xv0)))) (@ Xq0 Xv))))) (@ Xq Xv)))) (@ Xq Xy)))))))
% 0.16/0.58 (set-info :filename cvc5---1.0.5_15643)
% 0.16/0.58 (check-sat-assuming ( true ))
% 0.16/0.58 ------- get file name : TPTP file name is SEV149^5
% 0.16/0.58 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15643.smt2...
% 0.16/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.16/0.58 % SZS status Theorem for SEV149^5
% 0.16/0.58 % SZS output start Proof for SEV149^5
% 0.16/0.58 (
% 0.16/0.58 (let ((_let_1 (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (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))) (forall ((Xq (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (or (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw0 tptp.a)) (=> (@ (@ R Xx) Xw0) (@ Xq0 Xw0))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq0 Xu) (@ (@ R Xu) Xv)) (@ Xq0 Xv)))) (@ Xq0 Xw))) (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw0 tptp.a)) (=> (@ (@ S Xx) Xw0) (@ Xq0 Xw0))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq0 Xu) (@ (@ S Xu) Xv)) (@ Xq0 Xv)))) (@ Xq0 Xw)))) (@ Xq Xw))) (forall ((Xu tptp.a) (Xv tptp.a)) (=> (and (@ Xq Xu) (or (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ R Xu) Xw) (@ Xq0 Xw))) (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (=> (and (@ Xq0 Xu0) (@ (@ R Xu0) Xv0)) (@ Xq0 Xv0)))) (@ Xq0 Xv))) (forall ((Xq0 (-> tptp.a Bool))) (=> (and (forall ((Xw tptp.a)) (=> (@ (@ S Xu) Xw) (@ Xq0 Xw))) (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (=> (and (@ Xq0 Xu0) (@ (@ S Xu0) Xv0)) (@ Xq0 Xv0)))) (@ Xq0 Xv))))) (@ Xq Xv)))) (@ Xq Xy)))))))) (let ((_let_2 (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) Xw)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 Xw))))) (let ((_let_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_4 (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (not _let_2))) (let ((_let_8 (or _let_7 (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 Xu0)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu0) Xv0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_37 Xv0)))) _let_3))) (let ((_let_9 (forall ((BOUND_VARIABLE_882 |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_18) Xw)) (ho_2 BOUND_VARIABLE_882 Xw)))) (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 BOUND_VARIABLE_882 Xu0)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu0) Xv0)) (ho_2 BOUND_VARIABLE_882 Xv0)))) (ho_2 BOUND_VARIABLE_882 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))))) (let ((_let_10 (not _let_8))) (let ((_let_11 (not _let_9))) (let ((_let_12 (forall ((BOUND_VARIABLE_908 |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_18) Xw)) (ho_2 BOUND_VARIABLE_908 Xw)))) (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 BOUND_VARIABLE_908 Xu0)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu0) Xv0)) (ho_2 BOUND_VARIABLE_908 Xv0)))) (ho_2 BOUND_VARIABLE_908 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))))) (let ((_let_13 (not _let_12))) (let ((_let_14 (and _let_13 _let_11))) (let ((_let_15 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_16 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_14 _let_15))) (let ((_let_19 (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xu)) (and (not (forall ((BOUND_VARIABLE_908 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xw)) (ho_2 BOUND_VARIABLE_908 Xw)))) (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 BOUND_VARIABLE_908 Xu0)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu0) Xv0)) (ho_2 BOUND_VARIABLE_908 Xv0)))) (ho_2 BOUND_VARIABLE_908 Xv)))) (not (forall ((BOUND_VARIABLE_882 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xw)) (ho_2 BOUND_VARIABLE_882 Xw)))) (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 BOUND_VARIABLE_882 Xu0)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu0) Xv0)) (ho_2 BOUND_VARIABLE_882 Xv0)))) (ho_2 BOUND_VARIABLE_882 Xv))))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xv))))) (let ((_let_20 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_21 (not _let_19))) (let ((_let_22 (forall ((Xw tptp.a)) (or (and (not (forall ((BOUND_VARIABLE_960 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw0)) (ho_2 BOUND_VARIABLE_960 Xw0)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_960 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (ho_2 BOUND_VARIABLE_960 Xv)))) (ho_2 BOUND_VARIABLE_960 Xw)))) (not (forall ((BOUND_VARIABLE_938 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw0)) (ho_2 BOUND_VARIABLE_938 Xw0)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_938 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv)) (ho_2 BOUND_VARIABLE_938 Xv)))) (ho_2 BOUND_VARIABLE_938 Xw))))) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xw))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (forall ((BOUND_VARIABLE_986 |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_986 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_986 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_986 Xv)))) (ho_2 BOUND_VARIABLE_986 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_21 _let_20))) (let ((_let_27 (forall ((BOUND_VARIABLE_911 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_886 |u_(-> tptp.a tptp.a Bool)|) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_877 |u_(-> tptp.a Bool)|)) (or (not (forall ((BOUND_VARIABLE_986 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (and (not (ho_2 (ho_3 BOUND_VARIABLE_911 Xx) Xw)) (not (ho_2 (ho_3 BOUND_VARIABLE_886 Xx) Xw))) (ho_2 BOUND_VARIABLE_986 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_986 Xu)) (and (not (ho_2 (ho_3 BOUND_VARIABLE_911 Xu) Xv)) (not (ho_2 (ho_3 BOUND_VARIABLE_886 Xu) Xv))) (ho_2 BOUND_VARIABLE_986 Xv)))) (ho_2 BOUND_VARIABLE_986 Xy)))) (not (forall ((Xw tptp.a)) (or (and (not (forall ((BOUND_VARIABLE_960 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_911 Xx) Xw0)) (ho_2 BOUND_VARIABLE_960 Xw0)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_960 Xu)) (not (ho_2 (ho_3 BOUND_VARIABLE_911 Xu) Xv)) (ho_2 BOUND_VARIABLE_960 Xv)))) (ho_2 BOUND_VARIABLE_960 Xw)))) (not (forall ((BOUND_VARIABLE_938 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_886 Xx) Xw0)) (ho_2 BOUND_VARIABLE_938 Xw0)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_938 Xu)) (not (ho_2 (ho_3 BOUND_VARIABLE_886 Xu) Xv)) (ho_2 BOUND_VARIABLE_938 Xv)))) (ho_2 BOUND_VARIABLE_938 Xw))))) (ho_2 BOUND_VARIABLE_877 Xw)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_877 Xu)) (and (not (forall ((BOUND_VARIABLE_908 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 BOUND_VARIABLE_911 Xu) Xw)) (ho_2 BOUND_VARIABLE_908 Xw)))) (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 BOUND_VARIABLE_908 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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_32 (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_33 (not _let_27))) (let ((_let_34 (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_856 (-> tptp.a Bool))) (or (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 (forall ((Xq0 (-> tptp.a Bool))) (or (not (forall ((Xw0 tptp.a)) (or (not (@ (@ R Xx) 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((_let_35 (or))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_33))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_27))) (REFL :args (_let_28)) :args _let_35)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_34 (PREPROCESS :args ((and _let_32 _let_31 _let_30 _let_29)))) :args ((and _let_33 _let_32 _let_31 _let_30 _let_29))) :args (0)) :args (_let_28 true _let_27)))) (let ((_let_37 (REFL :args (_let_26)))) (let ((_let_38 (_let_19))) (let ((_let_39 (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_40 (not _let_39))) (let ((_let_41 (and _let_40 _let_5))) (let ((_let_42 (or _let_17 _let_41 _let_15))) (let ((_let_43 (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_44 (not _let_42))) (let ((_let_45 (not _let_43))) (let ((_let_46 (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_8 Xw))))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_47 _let_45 _let_20))) (let ((_let_49 (_let_24))) (let ((_let_50 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_51 (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_52 (not _let_51))) (let ((_let_53 (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_54 (not _let_53))) (let ((_let_55 (and _let_54 _let_52))) (let ((_let_56 (or _let_55 _let_50))) (let ((_let_57 (forall ((BOUND_VARIABLE_938 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw0)) (ho_2 BOUND_VARIABLE_938 Xw0)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_938 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xu) Xv)) (ho_2 BOUND_VARIABLE_938 Xv)))) (ho_2 BOUND_VARIABLE_938 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_58 (not _let_57))) (let ((_let_59 (forall ((BOUND_VARIABLE_960 |u_(-> tptp.a Bool)|)) (or (not (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw0)) (ho_2 BOUND_VARIABLE_960 Xw0)))) (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 BOUND_VARIABLE_960 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (ho_2 BOUND_VARIABLE_960 Xv)))) (ho_2 BOUND_VARIABLE_960 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_60 (not _let_59))) (let ((_let_61 (and _let_60 _let_58))) (let ((_let_62 (or _let_61 _let_50))) (let ((_let_63 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_64 (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Xw0))))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 (not (forall ((Xu tptp.a) (Xv tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Xu)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu) Xv)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 Xv)))) _let_63))) (let ((_let_67 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_68 (forall ((Xw0 tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) Xw0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 Xw0))))) (let ((_let_69 (not _let_68))) (let ((_let_70 (or _let_69 (not (forall ((Xu tptp.a) (Xv 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:args ((not _let_20) true _let_26)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_81)) :args _let_81)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) (REFL :args ((not _let_56))) :args _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args _let_78) :args _let_80)) (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_52 _let_67 (not _let_72)))) (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_79) (CONG (REFL :args _let_79) (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_51))) :args _let_35)) :args ((or _let_53 _let_51 _let_55))) (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_54 _let_63 (not _let_71)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_77) :args _let_78) :args _let_77)) (CNF_OR_NEG :args (_let_70 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG (REFL :args (_let_70)) 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:args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_35)) :args ((or _let_24 _let_26))) _let_36 :args (_let_24 true _let_26)) :args (_let_48 false _let_24)) :args (_let_45 true _let_20 false _let_46 false _let_48)) :args (_let_44 true _let_43)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_17 _let_15 _let_14 (not _let_18)))) (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_17) _let_16))) :args _let_35)) :args ((or _let_16 _let_42))) _let_83 :args (_let_16 true _let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 2)) _let_83 :args ((not _let_15) true _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xu) false)) (not (= (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xv) true))))) :args _let_38)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 2)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_19))) :args _let_35)) :args ((or _let_19 _let_26))) _let_36 :args (_let_19 true _let_26)) :args (_let_18 false _let_19)) :args (_let_14 false _let_16 true _let_15 false _let_18)))) (let ((_let_85 (not _let_14))) (let ((_let_86 (_let_11))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_86)) :args _let_86)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_9))) (REFL :args (_let_10)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_14 1)) :args ((or _let_11 _let_85))) _let_84 :args (_let_11 false _let_14)) :args (_let_10 true _let_9)))) (let ((_let_88 (not _let_6))) (let ((_let_89 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_90 (or _let_40 _let_89))) (let ((_let_91 (forall ((Xw tptp.a)) (or (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) Xw)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 Xw))))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 (not (forall ((Xu0 tptp.a) (Xv0 tptp.a)) (or (not (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 Xu0)) (not (ho_2 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xu0) Xv0)) (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 Xv0)))) _let_89))) (let ((_let_94 (not _let_93))) (let ((_let_95 (_let_13))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_95)) :args _let_95)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) (REFL :args (_let_94)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_14 0)) :args ((or _let_13 _let_85))) _let_84 :args (_let_13 false _let_14)) :args (_let_94 true _let_12)))) (let ((_let_97 (_let_91))) (let ((_let_98 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_CBQI_CONFLICT))) (let ((_let_99 (_let_41))) (let ((_let_100 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_100) :args _let_98) :args _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_5 _let_3 _let_88))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_99) (CONG (REFL :args _let_99) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_35)) :args ((or _let_39 _let_4 _let_41))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_40 _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_93 2)) _let_96 :args ((not _let_89) true _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_97) :args _let_98) :args _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_93 0)) (CONG (REFL :args (_let_93)) (MACRO_SR_PRED_INTRO :args ((= (not _let_92) _let_91))) :args _let_35)) :args ((or _let_91 _let_93))) _let_96 :args (_let_91 true _let_93)) :args (_let_90 false _let_91)) :args (_let_40 true _let_89 false _let_90)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_42 1)) _let_83 :args ((not _let_41) true _let_42)) :args (_let_4 true _let_39 true _let_41)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_8 2)) _let_87 :args ((not _let_3) true _let_8)) :args (_let_88 false _let_4 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_8 0)) (CONG (REFL :args (_let_8)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_2))) :args _let_35)) :args ((or _let_2 _let_8))) _let_87 :args (_let_2 true _let_8)) :args (false true _let_6 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.58 )
% 0.16/0.58 % SZS output end Proof for SEV149^5
% 0.16/0.58 % cvc5---1.0.5 exiting
% 0.16/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------