TSTP Solution File: SEV155^5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV155^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 0.20s 0.84s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV155^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 02:34:56 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.49 %----Proving TH0
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 % File : SEV155^5 : TPTP v8.1.2. Released v4.0.0.
% 0.20/0.49 % Domain : Set Theory (Relations)
% 0.20/0.49 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.20/0.49 % Version : Especial.
% 0.20/0.49 % English :
% 0.20/0.49
% 0.20/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.49 % Source : [Bro09]
% 0.20/0.49 % Names : tps_1232 [Bro09]
% 0.20/0.49
% 0.20/0.49 % Status : Theorem
% 0.20/0.49 % 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, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.20/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.20/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.20/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.20/0.49 % Number of connectives : 161 ( 0 ~; 7 |; 18 &; 108 @)
% 0.20/0.49 % ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% 0.20/0.49 % Maximal formula depth : 23 ( 23 avg)
% 0.20/0.49 % Number of types : 2 ( 1 usr)
% 0.20/0.49 % Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% 0.20/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.20/0.49 % Number of variables : 57 ( 0 ^; 57 !; 0 ?; 57 :)
% 0.20/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.49
% 0.20/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.49 %------------------------------------------------------------------------------
% 0.20/0.49 thf(a_type,type,
% 0.20/0.49 a: $tType ).
% 0.20/0.49
% 0.20/0.49 thf(cTHM250D_pme,conjecture,
% 0.20/0.49 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.20/0.49 ( ( ( ! [Xx0: a,Xy0: a] :
% 0.20/0.49 ( ( ! [Xp1: a > a > $o] :
% 0.20/0.49 ( ( ! [Xx1: a,Xy1: a] :
% 0.20/0.49 ( ( R @ Xx1 @ Xy1 )
% 0.20/0.49 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.20/0.49 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.20/0.49 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.20/0.50 & ( Xp1 @ Xy1 @ Xz ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.20/0.50 | ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.20/0.50 ( ( S @ Xx1 @ Xy1 )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.20/0.50 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.20/0.50 & ( Xp1 @ Xy1 @ Xz ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.20/0.50 => ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.20/0.50 ( ( ( R @ Xx1 @ Xy1 )
% 0.20/0.50 | ( S @ Xx1 @ Xy1 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.20/0.50 & ! [Xx1: a,Xy1: a,Xz: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.20/0.50 & ( Xp1 @ Xy1 @ Xz ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xz ) ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xy0 ) ) )
% 0.20/0.50 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.20/0.50 ( ( ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.20/0.50 ( ( ( R @ Xx1 @ Xy1 )
% 0.20/0.50 | ( S @ Xx1 @ Xy1 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.20/0.50 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.20/0.50 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.20/0.50 & ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.20/0.50 ( ( ( R @ Xx1 @ Xy1 )
% 0.20/0.50 | ( S @ Xx1 @ Xy1 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.20/0.50 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.20/0.50 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.20/0.50 => ( Xp1 @ Xy0 @ Xz ) ) )
% 0.20/0.50 => ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx1: a,Xy1: a] :
% 0.20/0.50 ( ( ( R @ Xx1 @ Xy1 )
% 0.20/0.50 | ( S @ Xx1 @ Xy1 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xy1 ) )
% 0.20/0.50 & ! [Xx1: a,Xy1: a,Xz0: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx1 @ Xy1 )
% 0.20/0.50 & ( Xp1 @ Xy1 @ Xz0 ) )
% 0.20/0.50 => ( Xp1 @ Xx1 @ Xz0 ) ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xz ) ) ) )
% 0.20/0.50 => ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx0: a,Xy0: a] :
% 0.20/0.50 ( ( ( R @ Xx0 @ Xy0 )
% 0.20/0.50 | ( S @ Xx0 @ Xy0 ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.20/0.50 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.20/0.50 & ( Xp1 @ Xy0 @ Xz ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.20/0.50 => ( Xp1 @ Xx @ Xy ) ) )
% 0.20/0.50 => ! [Xp1: a > a > $o] :
% 0.20/0.50 ( ( ! [Xx0: a,Xy0: a] :
% 0.20/0.50 ( ( ( R @ Xx0 @ Xy0 )
% 0.20/0.50 | ( S @ Xx0 @ Xy0 ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xy0 ) )
% 0.20/0.50 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.20/0.50 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.20/0.50 & ( Xp1 @ Xy0 @ Xz ) )
% 0.20/0.50 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.20/0.50 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 0.20/0.50
% 0.20/0.50 %------------------------------------------------------------------------------
% 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dMwirFsSv2/cvc5---1.0.5_1108.p...
% 0.20/0.50 (declare-sort $$unsorted 0)
% 0.20/0.50 (declare-sort tptp.a 0)
% 0.20/0.50 (assert (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ R Xx1) Xy1) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ S Xx1) Xy1) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx0) Xy0)))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx0) Xy0))))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (=> (and (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz0)) (@ _let_1 Xz0))))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz0)) (@ _let_1 Xz0))))) (@ (@ Xp1 Xy0) Xz)))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz0)) (@ _let_1 Xz0))))) (@ (@ Xp1 Xx0) Xz)))))) (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)))) (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)))))))
% 0.20/0.84 (set-info :filename cvc5---1.0.5_1108)
% 0.20/0.84 (check-sat-assuming ( true ))
% 0.20/0.84 ------- get file name : TPTP file name is SEV155^5
% 0.20/0.84 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_1108.smt2...
% 0.20/0.84 --- Run --ho-elim --full-saturate-quant at 10...
% 0.20/0.84 % SZS status Theorem for SEV155^5
% 0.20/0.84 % SZS output start Proof for SEV155^5
% 0.20/0.84 (
% 0.20/0.84 (let ((_let_1 (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool)) (Xx tptp.a) (Xy tptp.a)) (=> (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (or (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ R Xx1) Xy1) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (@ (@ S Xx1) Xy1) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx0) Xy0)))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz)) (@ _let_1 Xz))))) (@ (@ Xp1 Xx0) Xy0))))) (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (=> (and (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz0)) (@ _let_1 Xz0))))) (@ (@ Xp1 Xx0) Xy0))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz0)) (@ _let_1 Xz0))))) (@ (@ Xp1 Xy0) Xz)))) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (=> (or (@ (@ R Xx1) Xy1) (@ (@ S Xx1) Xy1)) (@ (@ Xp1 Xx1) Xy1))) (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (@ Xp1 Xx1))) (=> (and (@ _let_1 Xy1) (@ (@ Xp1 Xy1) Xz0)) (@ _let_1 Xz0))))) (@ (@ Xp1 Xx0) Xz)))))) (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)))) (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_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_3 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36))) (let ((_let_4 (not _let_3))) (let ((_let_5 (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36)) _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_11 Xx1) Xy1))))) (let ((_let_9 (not _let_7))) (let ((_let_10 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_11 (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 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_1349 |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_1349 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1349 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1349 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_1349 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((BOUND_VARIABLE_1374 |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_1374 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1374 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1374 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_1374 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (and _let_18 _let_16))) (let ((_let_20 (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Xy1) Xz)) (ho_3 _let_1 Xz)))))) (let ((_let_21 (not _let_20))) (let ((_let_22 (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1))) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 Xx1) Xy1))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_19 _let_23 _let_21 _let_10))) (let ((_let_25 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_26 (ho_3 _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_27 (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xy1) Xz0)) (ho_3 _let_1 Xz0)))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1))) (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xx1) Xy1))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (forall ((BOUND_VARIABLE_1265 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1))) (ho_3 (ho_2 BOUND_VARIABLE_1265 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1265 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1265 Xy1) Xz0)) (ho_3 _let_1 Xz0))))) (ho_3 (ho_2 BOUND_VARIABLE_1265 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (forall ((BOUND_VARIABLE_1294 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (and (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Xx1) Xy1)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Xx1) Xy1))) (ho_3 (ho_2 BOUND_VARIABLE_1294 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1294 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1294 Xy1) Xz0)) (ho_3 _let_1 Xz0))))) (ho_3 (ho_2 BOUND_VARIABLE_1294 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_30 _let_28 _let_26))) (let ((_let_36 (forall ((BOUND_VARIABLE_1211 |u_(-> tptp.a tptp.a Bool)|)) (or (not (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 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(or _let_53 _let_52 _let_26))) (let ((_let_55 (or))) (let ((_let_56 (REFL :args (_let_35)))) (let ((_let_57 (_let_33))) (let ((_let_58 (_let_31))) (let ((_let_59 (_let_27))) (let ((_let_60 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 Xx1))) (let ((_let_61 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_62 (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_63 (not _let_62))) (let ((_let_64 (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_65 (not _let_64))) (let ((_let_66 (or _let_38 _let_65 _let_63 _let_61))) (let ((_let_67 (forall ((BOUND_VARIABLE_1203 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_1199 |u_(-> tptp.a tptp.a Bool)|) (Xx tptp.a) (Xy tptp.a) (BOUND_VARIABLE_1179 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_1117 tptp.a) (BOUND_VARIABLE_1115 tptp.a) (BOUND_VARIABLE_1324 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_1240 |u_(-> tptp.a tptp.a Bool)|) (BOUND_VARIABLE_1082 tptp.a) (BOUND_VARIABLE_1119 tptp.a) (BOUND_VARIABLE_1080 tptp.a)) (or (and (or (and (not (forall ((BOUND_VARIABLE_1374 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_1203 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_1374 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1374 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1374 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_1374 BOUND_VARIABLE_1080) BOUND_VARIABLE_1082)))) (not (forall ((BOUND_VARIABLE_1349 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_1199 Xx1) Xy1)) (ho_3 (ho_2 BOUND_VARIABLE_1349 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1349 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1349 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_1349 BOUND_VARIABLE_1080) BOUND_VARIABLE_1082))))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (and (not (ho_3 (ho_2 BOUND_VARIABLE_1203 Xx1) Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1199 Xx1) Xy1))) (ho_3 (ho_2 BOUND_VARIABLE_1324 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1324 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1324 Xy1) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_1324 BOUND_VARIABLE_1080) BOUND_VARIABLE_1082)) (or (not (forall ((BOUND_VARIABLE_1294 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (or (and (not (ho_3 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(ho_3 (ho_2 BOUND_VARIABLE_1203 Xx1) Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1199 Xx1) Xy1))) (ho_3 (ho_2 BOUND_VARIABLE_1240 Xx1) Xy1)))) (not (forall ((Xx1 tptp.a) (Xy1 tptp.a) (Xz0 tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1240 Xx1))) (or (not (ho_3 _let_1 Xy1)) (not (ho_3 (ho_2 BOUND_VARIABLE_1240 Xy1) Xz0)) (ho_3 _let_1 Xz0))))) (ho_3 (ho_2 BOUND_VARIABLE_1240 BOUND_VARIABLE_1115) BOUND_VARIABLE_1119)) (not (forall ((BOUND_VARIABLE_1211 |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (ho_3 (ho_2 BOUND_VARIABLE_1203 Xx0) Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_1199 Xx0) Xy0))) (ho_3 (ho_2 BOUND_VARIABLE_1211 Xx0) Xy0)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (ho_2 BOUND_VARIABLE_1211 Xx0))) (or (not (ho_3 _let_1 Xy0)) (not (ho_3 (ho_2 BOUND_VARIABLE_1211 Xy0) Xz)) (ho_3 _let_1 Xz))))) (ho_3 (ho_2 BOUND_VARIABLE_1211 Xx) Xy))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (and (not (ho_3 (ho_2 BOUND_VARIABLE_1203 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_let_69))) :args (0)) :args (_let_68 true _let_67)))) (let ((_let_76 (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_77 (not _let_76))) (let ((_let_78 (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_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_77 _let_61))) (let ((_let_81 (not _let_80))) (let ((_let_82 (REFL :args (_let_66)))) (let ((_let_83 (_let_36))) (let ((_let_84 (not _let_35))) (let ((_let_85 (_let_38))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_85) (CONG (REFL :args _let_85) (REFL :args (_let_39)) (REFL :args (_let_84)) (MACRO_SR_PRED_INTRO :args ((= 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(or _let_97 _let_95))) (let ((_let_99 (and _let_97 (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))))) (let ((_let_100 (or _let_99 _let_95))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 1)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_55)) :args ((or _let_22 _let_24))) _let_86 :args (_let_22 true _let_24)))) (let ((_let_102 (_let_22))) (let ((_let_103 (ASSUME :args _let_102))) (let ((_let_104 (not _let_100))) (let ((_let_105 (_let_90))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 3)) _let_86 :args ((not _let_10) true _let_24)))) (let ((_let_107 (_let_17))) (let ((_let_108 (_let_19))) (let ((_let_109 (_let_15))) (let ((_let_110 (_let_13))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_110)) :args _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not 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(SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_102)) _let_101 :args (_let_100 false _let_22)) :args (_let_98 false _let_100)) :args (_let_89 false _let_98)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_20 (= Xx1 Xx1) (= Xy1 Xy1) (= Xz Xz)))) _let_94 :args (_let_87 false _let_20)) :args (_let_92 true _let_10 false _let_89 false _let_87)) :args (_let_18 true _let_91)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 0)) _let_86 :args ((not _let_19) true _let_24)) :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_112 (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_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 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% 0.20/0.84 )
% 0.20/0.84 % SZS output end Proof for SEV155^5
% 0.20/0.84 % cvc5---1.0.5 exiting
% 0.20/0.85 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------