TSTP Solution File: SEV140^5 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV140^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 19:21:40 EDT 2023
% Result : Theorem 0.22s 0.57s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV140^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.19/0.35 % Computer : n029.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Thu Aug 24 02:13:38 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.22/0.49 %----Proving TH0
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 % File : SEV140^5 : TPTP v8.1.2. Released v4.0.0.
% 0.22/0.50 % Domain : Set Theory (Relations)
% 0.22/0.50 % Problem : TPS problem THM250C
% 0.22/0.50 % Version : Especial.
% 0.22/0.50 % English :
% 0.22/0.50
% 0.22/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.22/0.50 % Source : [Bro09]
% 0.22/0.50 % Names : tps_0517 [Bro09]
% 0.22/0.50 % : THM250C [TPS]
% 0.22/0.50
% 0.22/0.50 % Status : Theorem
% 0.22/0.50 % Rating : 0.09 v8.1.0, 0.17 v7.5.0, 0.33 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 v6.1.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% 0.22/0.50 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.22/0.50 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.22/0.50 % Maximal formula atoms : 0 ( 0 avg)
% 0.22/0.50 % Number of connectives : 71 ( 0 ~; 2 |; 8 &; 48 @)
% 0.22/0.50 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.22/0.50 % Maximal formula depth : 23 ( 23 avg)
% 0.22/0.50 % Number of types : 2 ( 1 usr)
% 0.22/0.50 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.22/0.50 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.22/0.50 % Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% 0.22/0.50 % SPC : TH0_THM_NEQ_NAR
% 0.22/0.50
% 0.22/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.22/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.22/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.22/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.22/0.50 % : Polymorphic definitions expanded.
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 thf(a_type,type,
% 0.22/0.50 a: $tType ).
% 0.22/0.50
% 0.22/0.50 thf(cTHM250C_pme,conjecture,
% 0.22/0.50 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.22/0.50 ( ! [Xp1: a > a > $o] :
% 0.22/0.50 ( ( ! [Xx0: a,Xy0: a] :
% 0.22/0.50 ( ( ! [Xp10: a > a > $o] :
% 0.22/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.22/0.50 ( ( R @ Xx1 @ Xy1 )
% 0.22/0.50 => ( Xp10 @ Xx1 @ Xy1 ) )
% 0.22/0.50 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.22/0.50 ( ( ( Xp10 @ Xx1 @ Xy1 )
% 0.22/0.50 & ( Xp10 @ Xy1 @ Xz ) )
% 0.22/0.50 => ( Xp10 @ Xx1 @ Xz ) ) )
% 0.22/0.50 => ( Xp10 @ Xx0 @ Xy0 ) )
% 0.22/0.50 | ! [Xp10: a > a > $o] :
% 0.22/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.22/0.50 ( ( S @ Xx1 @ Xy1 )
% 0.22/0.50 => ( Xp10 @ Xx1 @ Xy1 ) )
% 0.22/0.50 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.22/0.50 ( ( ( Xp10 @ Xx1 @ Xy1 )
% 0.22/0.50 & ( Xp10 @ Xy1 @ Xz ) )
% 0.22/0.50 => ( Xp10 @ Xx1 @ Xz ) ) )
% 0.22/0.50 => ( Xp10 @ Xx0 @ Xy0 ) ) )
% 0.22/0.50 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.22/0.50 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.22/0.50 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.22/0.50 & ( Xp1 @ Xy0 @ Xz ) )
% 0.22/0.50 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.22/0.50 => ( Xp1 @ Xx @ Xy ) )
% 0.22/0.50 => ! [Xp1: a > a > $o] :
% 0.22/0.50 ( ( ! [Xx0: a,Xy0: a] :
% 0.22/0.50 ( ( ( R @ Xx0 @ Xy0 )
% 0.22/0.50 | ( S @ Xx0 @ Xy0 ) )
% 0.22/0.50 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.22/0.50 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.22/0.50 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.22/0.50 & ( Xp1 @ Xy0 @ Xz ) )
% 0.22/0.50 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.22/0.50 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 0.22/0.50
% 0.22/0.50 %------------------------------------------------------------------------------
% 0.22/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.csQvh8QDib/cvc5---1.0.5_32687.p...
% 0.22/0.50 (declare-sort $$unsorted 0)
% 0.22/0.50 (declare-sort tptp.a 0)
% 0.22/0.50 (assert (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ R Xx1) Xy1) (@ (@ Xp10 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp10 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0))) (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ S Xx1) Xy1) (@ (@ Xp10 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp10 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (@ (@ R Xx0) Xy0) (@ (@ S Xx0) Xy0)) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy)))))))
% 0.22/0.57 (set-info :filename cvc5---1.0.5_32687)
% 0.22/0.57 (check-sat-assuming ( true ))
% 0.22/0.57 ------- get file name : TPTP file name is SEV140^5
% 0.22/0.57 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32687.smt2...
% 0.22/0.57 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.57 % SZS status Theorem for SEV140^5
% 0.22/0.57 % SZS output start Proof for SEV140^5
% 0.22/0.57 (
% 0.22/0.57 (let ((_let_1 (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ R Xx1) Xy1) (@ (@ Xp10 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp10 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0))) (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ S Xx1) Xy1) (@ (@ Xp10 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp10 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (@ (@ R Xx0) Xy0) (@ (@ S Xx0) Xy0)) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy)))))))) (let ((_let_2 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_3 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_4 (not _let_3))) (let ((_let_5 (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21)) _let_4))) (let ((_let_6 (or _let_5 _let_2))) (let ((_let_7 (or _let_4 _let_2))) (let ((_let_8 (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx1) Xy1))))) (let ((_let_9 (not _let_7))) (let ((_let_10 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_11 (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy1) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_12 (not _let_11))) (let ((_let_13 (not _let_8))) (let ((_let_14 (or _let_13 _let_12 _let_10))) (let ((_let_15 (forall ((BOUND_VARIABLE_858 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_858 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_858 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_858 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((BOUND_VARIABLE_883 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_883 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_883 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_883 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (and _let_18 _let_16))) (let ((_let_20 (or _let_19 _let_10))) (let ((_let_21 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (forall ((BOUND_VARIABLE_883 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_883 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_883 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx0) Xy0)))) (not (forall ((BOUND_VARIABLE_858 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_858 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_858 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx0) Xy0))))) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) Xy0))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_24 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (not _let_21))) (let ((_let_27 (or _let_26 _let_25 _let_23))) (let ((_let_28 (forall ((BOUND_VARIABLE_843 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (forall ((BOUND_VARIABLE_883 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_883 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_883 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx0) Xy0)))) (not (forall ((BOUND_VARIABLE_858 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_858 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_858 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx0) Xy0))))) (ho_3 (ho_2 BOUND_VARIABLE_843 Xx0) Xy0)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_843 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_843 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_843 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))) (let ((_let_29 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy0) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx0) Xy0)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx0) Xy0))) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx0) Xy0))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (not _let_28))) (let ((_let_34 (or _let_33 _let_32 _let_30 _let_23))) (let ((_let_35 (forall ((BOUND_VARIABLE_835 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_831 |u_(-> tptp.a tptp.a Bool)|) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_811 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((BOUND_VARIABLE_843 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (forall ((BOUND_VARIABLE_883 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_835 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_883 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_883 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_883 Xx0) Xy0)))) (not (forall ((BOUND_VARIABLE_858 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_831 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_858 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_858 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_858 Xx0) Xy0))))) (ho_3 (ho_2 BOUND_VARIABLE_843 Xx0) Xy0)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_843 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_843 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_843 Xx) Xy)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (ho_3 (ho_2 BOUND_VARIABLE_835 Xx0) Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_831 Xx0) Xy0))) (ho_3 (ho_2 BOUND_VARIABLE_811 Xx0) Xy0)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_811 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_811 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_811 Xx) Xy))))) (let ((_let_36 (not _let_34))) (let ((_let_37 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_39 (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_2 v ii) (ite (= i ii) e (ho_2 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_2 x z) (ho_2 y z)))) (= x y))))) (let ((_let_41 (not _let_35))) (let ((_let_42 (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_784 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xp1 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (@ (@ R Xx1) Xy1)) (@ (@ Xp10 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx1))) (or (not (@ _let_1 Xy1)) (not (@ (@ Xp10 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0)))) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (@ (@ S Xx1) Xy1)) (@ (@ Xp10 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx1))) (or (not (@ _let_1 Xy1)) (not (@ (@ Xp10 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp10 Xx0) Xy0))))) (@ (@ Xp1 Xx0) Xy0)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp1 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx) Xy)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (@ (@ R Xx0) Xy0)) (not (@ (@ S Xx0) Xy0))) (@ (@ BOUND_VARIABLE_784 Xx0) Xy0)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ BOUND_VARIABLE_784 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ BOUND_VARIABLE_784 Xy0) Xz)) (@ _let_1 Xz))))) (@ (@ BOUND_VARIABLE_784 Xx) Xy)))) _let_41))))))) (let ((_let_43 (or))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_41))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_35))) (REFL :args (_let_36)) :args _let_43)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_42 (PREPROCESS :args ((and _let_40 _let_39 _let_38 _let_37)))) :args ((and _let_41 _let_40 _let_39 _let_38 _let_37))) :args (0)) :args (_let_36 true _let_35)))) (let ((_let_45 (REFL :args (_let_34)))) (let ((_let_46 (_let_28))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 2)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_43)) :args ((or _let_29 _let_34))) _let_44 :args (_let_29 true _let_34)))) (let ((_let_48 (_let_26))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_48)) :args _let_48)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_21))) (REFL :args (_let_22)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_23 _let_26 _let_25 (not _let_27)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_34 3)) _let_44 :args ((not _let_23) true _let_34)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_29 (= Xx0 Xx0) (= Xz Xz) (= Xy0 Xy0)))) _let_47 :args (_let_24 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_46) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 BOUND_VARIABLE_843 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)))) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 0)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_28))) :args _let_43)) :args ((or _let_28 _let_34))) _let_44 :args (_let_28 true _let_34)) :args (_let_27 false _let_28)) :args (_let_26 true _let_23 false _let_24 false _let_27)) :args (_let_22 true _let_21)))) (let ((_let_50 (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xy1) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_51 (not _let_50))) (let ((_let_52 (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 Xx1) Xy1))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51 _let_10))) (let ((_let_55 (not _let_54))) (let ((_let_56 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_57 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56))) (let ((_let_60 (and _let_58 (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_61 (or _let_60 _let_56))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_34 1)) (CONG _let_45 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_43)) :args ((or _let_31 _let_34))) _let_44 :args (_let_31 true _let_34)))) (let ((_let_63 (_let_31))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (_let_53))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 1)) _let_49 :args ((not _let_10) true _let_20)))) (let ((_let_67 (_let_17))) (let ((_let_68 (_let_19))) (let ((_let_69 (_let_15))) (let ((_let_70 (_let_13))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_70)) :args _let_70)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_8))) (REFL :args (_let_9)) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_10 _let_13 _let_12 (not _let_14)))) _let_66 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_29 (= Xx0 Xx1) (= Xz Xz) (= Xy0 Xy1)))) _let_47 :args (_let_11 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_69) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 BOUND_VARIABLE_858 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) :args _let_69)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_68) (CONG (REFL :args _let_68) (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_43)) :args ((or _let_17 _let_15 _let_19))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_67) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_2 BOUND_VARIABLE_883 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11)))) :args _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_10 _let_53 _let_51 _let_55))) _let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) (REFL :args ((not _let_59))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_56 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63)) _let_62 :args (_let_61 false _let_31)) (REORDERING (CNF_AND_POS :args (_let_60 0)) :args ((or _let_58 (not _let_60)))) (CNF_OR_NEG :args (_let_59 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG (REFL :args (_let_59)) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_43)) :args ((or _let_57 _let_59))) :args (_let_59 false _let_61 true _let_60 true _let_56 false _let_57)) :args (_let_52 false _let_59)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_29 (= Xx0 Xx1) (= Xz Xz) (= Xy0 Xy1)))) _let_47 :args (_let_50 false _let_29)) :args (_let_55 true _let_10 false _let_52 false _let_50)) :args (_let_18 true _let_54)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 0)) _let_49 :args ((not _let_19) true _let_20)) :args (_let_15 true _let_17 true _let_19)) :args (_let_14 false _let_15)) :args (_let_13 true _let_10 false _let_11 false _let_14)) :args (_let_9 true _let_8)))) (let ((_let_72 (not _let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_2 _let_5 (not _let_6)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_63)) _let_62 :args (_let_6 false _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_5 1)) :args ((or _let_4 _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_4) _let_3))) :args _let_43)) :args ((or _let_3 _let_7))) _let_71 :args (_let_3 true _let_7)) :args (_let_72 false _let_3)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_7 1)) _let_71 :args ((not _let_2) true _let_7)) :args (false false _let_6 true _let_5 true _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.57 )
% 0.22/0.57 % SZS output end Proof for SEV140^5
% 0.22/0.57 % cvc5---1.0.5 exiting
% 0.22/0.57 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------