TSTP Solution File: SEV192^5 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV192^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 19:21:49 EDT 2023
% Result : Theorem 36.14s 36.37s
% Output : Proof 36.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV192^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 03:25:10 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 % File : SEV192^5 : TPTP v8.1.2. Released v4.0.0.
% 0.21/0.49 % Domain : Set Theory (Sets of sets)
% 0.21/0.49 % Problem : TPS problem CS-DUC-RELNS
% 0.21/0.49 % Version : Especial.
% 0.21/0.49 % English : Given a pairing algebra B (with zero element 0(B) and pairing
% 0.21/0.49 % operation P(BBB)), we can define a notion of join and a notion of
% 0.21/0.49 % inclusion. A subset of the pairing algebra is a DUC-set (downward
% 0.21/0.49 % union closed) if it is downward closed with respect to
% 0.21/0.49 % inclusion, and closed with respect to joins. A relation R between
% 0.21/0.49 % any set C and the pairing algebra is DUC-valued if for any c in
% 0.21/0.49 % C, {y | R(c,y)} is a DUC-set. The theorem states that the
% 0.21/0.49 % DUC-valued relations form a closure system, i.e., an arbitrary
% 0.21/0.49 % intersection of DUC-valued relations is a DUC-valued relation.
% 0.21/0.49
% 0.21/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.49 % Source : [Bro09]
% 0.21/0.49 % Names : tps_0573 [Bro09]
% 0.21/0.49 % : CS-DUC-RELNS [TPS]
% 0.21/0.49
% 0.21/0.49 % Status : Theorem
% 0.21/0.49 % Rating : 0.77 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.44 v7.2.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v4.0.0
% 0.21/0.49 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.21/0.49 % Number of atoms : 32 ( 28 equ; 0 cnn)
% 0.21/0.49 % Maximal formula atoms : 32 ( 32 avg)
% 0.21/0.49 % Number of connectives : 169 ( 0 ~; 8 |; 38 &; 103 @)
% 0.21/0.49 % ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% 0.21/0.49 % Maximal formula depth : 36 ( 36 avg)
% 0.21/0.49 % Number of types : 3 ( 2 usr)
% 0.21/0.49 % Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% 0.21/0.49 % Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% 0.21/0.49 % Number of variables : 60 ( 0 ^; 36 !; 24 ?; 60 :)
% 0.21/0.49 % SPC : TH0_THM_EQU_NAR
% 0.21/0.49
% 0.21/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.49 % : Polymorphic definitions expanded.
% 0.21/0.49 %------------------------------------------------------------------------------
% 0.21/0.49 thf(b_type,type,
% 0.21/0.49 b: $tType ).
% 0.21/0.49
% 0.21/0.49 thf(c_type,type,
% 0.21/0.49 c: $tType ).
% 0.21/0.49
% 0.21/0.49 thf(cP,type,
% 0.21/0.49 cP: b > b > b ).
% 0.21/0.49
% 0.21/0.49 thf(c0,type,
% 0.21/0.49 c0: b ).
% 0.21/0.49
% 0.21/0.49 thf(cCS_DUC_RELNS_pme,conjecture,
% 0.21/0.49 ! [S: ( c > b > $o ) > $o] :
% 0.21/0.49 ( ! [Xx: c > b > $o] :
% 0.21/0.49 ( ( S @ Xx )
% 0.21/0.49 => ! [Xc: c] :
% 0.21/0.49 ( ( Xx @ Xc @ c0 )
% 0.21/0.49 & ! [Xx0: b,Xy: b] :
% 0.21/0.49 ( ( ( Xx @ Xc @ Xy )
% 0.21/0.49 & ! [R: b > b > b > $o] :
% 0.21/0.49 ( ( $true
% 0.21/0.49 & ! [Xa: b,Xb: b,Xc0: b] :
% 0.21/0.49 ( ( ( ( Xa = c0 )
% 0.21/0.49 & ( Xb = Xc0 ) )
% 0.21/0.49 | ( ( Xb = c0 )
% 0.21/0.49 & ( Xa = Xc0 ) )
% 0.21/0.49 | ? [Xx1: b,Xx2: b,Xy1: b,Xy2: b,Xz1: b,Xz2: b] :
% 0.21/0.49 ( ( Xa
% 0.21/0.49 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.49 & ( Xb
% 0.21/0.49 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.49 & ( Xc0
% 0.21/0.49 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.49 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.49 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.49 => ( R @ Xa @ Xb @ Xc0 ) ) )
% 0.21/0.49 => ( R @ Xx0 @ Xy @ Xy ) ) )
% 0.21/0.49 => ( Xx @ Xc @ Xx0 ) )
% 0.21/0.49 & ! [Xx0: b,Xy: b,Xz: b] :
% 0.21/0.49 ( ( ( Xx @ Xc @ Xx0 )
% 0.21/0.49 & ( Xx @ Xc @ Xy )
% 0.21/0.49 & ! [R: b > b > b > $o] :
% 0.21/0.49 ( ( $true
% 0.21/0.49 & ! [Xa: b,Xb: b,Xc0: b] :
% 0.21/0.49 ( ( ( ( Xa = c0 )
% 0.21/0.49 & ( Xb = Xc0 ) )
% 0.21/0.50 | ( ( Xb = c0 )
% 0.21/0.50 & ( Xa = Xc0 ) )
% 0.21/0.50 | ? [Xx1: b,Xx2: b,Xy1: b,Xy2: b,Xz1: b,Xz2: b] :
% 0.21/0.50 ( ( Xa
% 0.21/0.50 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.50 & ( Xb
% 0.21/0.50 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.50 & ( Xc0
% 0.21/0.50 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.50 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.50 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.50 => ( R @ Xa @ Xb @ Xc0 ) ) )
% 0.21/0.50 => ( R @ Xx0 @ Xy @ Xz ) ) )
% 0.21/0.50 => ( Xx @ Xc @ Xz ) ) ) )
% 0.21/0.50 => ! [Xc: c] :
% 0.21/0.50 ( ! [R: c > b > $o] :
% 0.21/0.50 ( ( S @ R )
% 0.21/0.50 => ( R @ Xc @ c0 ) )
% 0.21/0.50 & ! [Xx: b,Xy: b] :
% 0.21/0.50 ( ( ! [R: c > b > $o] :
% 0.21/0.50 ( ( S @ R )
% 0.21/0.50 => ( R @ Xc @ Xy ) )
% 0.21/0.50 & ! [R: b > b > b > $o] :
% 0.21/0.50 ( ( $true
% 0.21/0.50 & ! [Xa: b,Xb: b,Xc0: b] :
% 0.21/0.50 ( ( ( ( Xa = c0 )
% 0.21/0.50 & ( Xb = Xc0 ) )
% 0.21/0.50 | ( ( Xb = c0 )
% 0.21/0.50 & ( Xa = Xc0 ) )
% 0.21/0.50 | ? [Xx1: b,Xx2: b,Xy1: b,Xy2: b,Xz1: b,Xz2: b] :
% 0.21/0.50 ( ( Xa
% 0.21/0.50 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.50 & ( Xb
% 0.21/0.50 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.50 & ( Xc0
% 0.21/0.50 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.50 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.50 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.50 => ( R @ Xa @ Xb @ Xc0 ) ) )
% 0.21/0.50 => ( R @ Xx @ Xy @ Xy ) ) )
% 0.21/0.50 => ! [R: c > b > $o] :
% 0.21/0.50 ( ( S @ R )
% 0.21/0.50 => ( R @ Xc @ Xx ) ) )
% 0.21/0.50 & ! [Xx: b,Xy: b,Xz: b] :
% 0.21/0.50 ( ( ! [R: c > b > $o] :
% 0.21/0.50 ( ( S @ R )
% 0.21/0.50 => ( R @ Xc @ Xx ) )
% 0.21/0.50 & ! [R: c > b > $o] :
% 0.21/0.50 ( ( S @ R )
% 0.21/0.50 => ( R @ Xc @ Xy ) )
% 0.21/0.50 & ! [R: b > b > b > $o] :
% 0.21/0.50 ( ( $true
% 0.21/0.50 & ! [Xa: b,Xb: b,Xc0: b] :
% 0.21/0.50 ( ( ( ( Xa = c0 )
% 0.21/0.50 & ( Xb = Xc0 ) )
% 0.21/0.50 | ( ( Xb = c0 )
% 0.21/0.50 & ( Xa = Xc0 ) )
% 0.21/0.50 | ? [Xx1: b,Xx2: b,Xy1: b,Xy2: b,Xz1: b,Xz2: b] :
% 0.21/0.50 ( ( Xa
% 0.21/0.50 = ( cP @ Xx1 @ Xx2 ) )
% 0.21/0.50 & ( Xb
% 0.21/0.50 = ( cP @ Xy1 @ Xy2 ) )
% 0.21/0.50 & ( Xc0
% 0.21/0.50 = ( cP @ Xz1 @ Xz2 ) )
% 0.21/0.50 & ( R @ Xx1 @ Xy1 @ Xz1 )
% 0.21/0.50 & ( R @ Xx2 @ Xy2 @ Xz2 ) ) )
% 0.21/0.50 => ( R @ Xa @ Xb @ Xc0 ) ) )
% 0.21/0.50 => ( R @ Xx @ Xy @ Xz ) ) )
% 0.21/0.50 => ! [R: c > b > $o] :
% 0.21/0.50 ( ( S @ R )
% 0.21/0.50 => ( R @ Xc @ Xz ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.IrxZStHYNE/cvc5---1.0.5_11611.p...
% 0.21/0.50 (declare-sort $$unsorted 0)
% 0.21/0.50 (declare-sort tptp.b 0)
% 0.21/0.50 (declare-sort tptp.c 0)
% 0.21/0.50 (declare-fun tptp.cP (tptp.b tptp.b) tptp.b)
% 0.21/0.50 (declare-fun tptp.c0 () tptp.b)
% 0.21/0.50 (assert (not (forall ((S (-> (-> tptp.c tptp.b Bool) Bool))) (=> (forall ((Xx (-> tptp.c tptp.b Bool))) (=> (@ S Xx) (forall ((Xc tptp.c)) (and (@ (@ Xx Xc) tptp.c0) (forall ((Xx0 tptp.b) (Xy tptp.b)) (let ((_let_1 (@ Xx Xc))) (=> (and (@ _let_1 Xy) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx0) Xy) Xy)))) (@ _let_1 Xx0)))) (forall ((Xx0 tptp.b) (Xy tptp.b) (Xz tptp.b)) (let ((_let_1 (@ Xx Xc))) (=> (and (@ _let_1 Xx0) (@ _let_1 Xy) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx0) Xy) Xz)))) (@ _let_1 Xz)))))))) (forall ((Xc tptp.c)) (and (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) tptp.c0))) (forall ((Xx tptp.b) (Xy tptp.b)) (=> (and (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xy))) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx) Xy) Xy)))) (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xx))))) (forall ((Xx tptp.b) (Xy tptp.b) (Xz tptp.b)) (=> (and (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xx))) (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xy))) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx) Xy) Xz)))) (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xz)))))))))))
% 36.14/36.37 (set-info :filename cvc5---1.0.5_11611)
% 36.14/36.37 (check-sat-assuming ( true ))
% 36.14/36.37 ------- get file name : TPTP file name is SEV192^5
% 36.14/36.37 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11611.smt2...
% 36.14/36.37 --- Run --ho-elim --full-saturate-quant at 10...
% 36.14/36.37 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 36.14/36.37 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 36.14/36.37 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 36.14/36.37 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 36.14/36.37 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 36.14/36.37 % SZS status Theorem for SEV192^5
% 36.14/36.37 % SZS output start Proof for SEV192^5
% 36.14/36.37 (
% 36.14/36.37 (let ((_let_1 (not (forall ((S (-> (-> tptp.c tptp.b Bool) Bool))) (=> (forall ((Xx (-> tptp.c tptp.b Bool))) (=> (@ S Xx) (forall ((Xc tptp.c)) (and (@ (@ Xx Xc) tptp.c0) (forall ((Xx0 tptp.b) (Xy tptp.b)) (let ((_let_1 (@ Xx Xc))) (=> (and (@ _let_1 Xy) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx0) Xy) Xy)))) (@ _let_1 Xx0)))) (forall ((Xx0 tptp.b) (Xy tptp.b) (Xz tptp.b)) (let ((_let_1 (@ Xx Xc))) (=> (and (@ _let_1 Xx0) (@ _let_1 Xy) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx0) Xy) Xz)))) (@ _let_1 Xz)))))))) (forall ((Xc tptp.c)) (and (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) tptp.c0))) (forall ((Xx tptp.b) (Xy tptp.b)) (=> (and (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xy))) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx) Xy) Xy)))) (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xx))))) (forall ((Xx tptp.b) (Xy tptp.b) (Xz tptp.b)) (=> (and (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xx))) (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xy))) (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (=> (and true (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b)) (=> (or (and (= Xa tptp.c0) (= Xb Xc0)) (and (= Xb tptp.c0) (= Xa Xc0)) (exists ((Xx1 tptp.b) (Xx2 tptp.b) (Xy1 tptp.b) (Xy2 tptp.b) (Xz1 tptp.b) (Xz2 tptp.b)) (and (= Xa (@ (@ tptp.cP Xx1) Xx2)) (= Xb (@ (@ tptp.cP Xy1) Xy2)) (= Xc0 (@ (@ tptp.cP Xz1) Xz2)) (@ (@ (@ R Xx1) Xy1) Xz1) (@ (@ (@ R Xx2) Xy2) Xz2)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R Xx) Xy) Xz)))) (forall ((R (-> tptp.c tptp.b Bool))) (=> (@ S R) (@ (@ R Xc) Xz)))))))))))) (let ((_let_2 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 tptp.c0))) (let ((_let_3 (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_990 tptp.b) (BOUND_VARIABLE_988 tptp.b) (BOUND_VARIABLE_986 tptp.b) (BOUND_VARIABLE_984 tptp.b) (BOUND_VARIABLE_982 tptp.b) (BOUND_VARIABLE_980 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_980) BOUND_VARIABLE_982))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_984) BOUND_VARIABLE_986))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_988) BOUND_VARIABLE_990))) (not (@ (@ (@ R BOUND_VARIABLE_980) BOUND_VARIABLE_984) BOUND_VARIABLE_988)) (not (@ (@ (@ R BOUND_VARIABLE_982) BOUND_VARIABLE_986) BOUND_VARIABLE_990)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R tptp.c0) tptp.c0) tptp.c0)))))) (let ((_let_4 (not _let_2))) (let ((_let_5 (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_909 tptp.b) (BOUND_VARIABLE_907 tptp.b) (BOUND_VARIABLE_905 tptp.b) (BOUND_VARIABLE_903 tptp.b) (BOUND_VARIABLE_901 tptp.b) (BOUND_VARIABLE_899 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_899) BOUND_VARIABLE_901))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_903) BOUND_VARIABLE_905))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_907) BOUND_VARIABLE_909))) (not (@ (@ (@ R BOUND_VARIABLE_899) BOUND_VARIABLE_903) BOUND_VARIABLE_907)) (not (@ (@ (@ R BOUND_VARIABLE_901) BOUND_VARIABLE_905) BOUND_VARIABLE_909)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R tptp.c0) tptp.c0) tptp.c0)))))) (let ((_let_6 (and _let_2 (or _let_4 _let_5 _let_2) (or _let_4 _let_4 _let_3 _let_2)))) (let ((_let_7 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_2))) (let ((_let_10 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_11 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_12 (not _let_11))) (let ((_let_13 (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_1267 tptp.b) (BOUND_VARIABLE_1265 tptp.b) (BOUND_VARIABLE_1263 tptp.b) (BOUND_VARIABLE_1261 tptp.b) (BOUND_VARIABLE_1259 tptp.b) (BOUND_VARIABLE_1257 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_1257) BOUND_VARIABLE_1259))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_1261) BOUND_VARIABLE_1263))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_1265) BOUND_VARIABLE_1267))) (not (@ (@ (@ R BOUND_VARIABLE_1257) BOUND_VARIABLE_1261) BOUND_VARIABLE_1265)) (not (@ (@ (@ R BOUND_VARIABLE_1259) BOUND_VARIABLE_1263) BOUND_VARIABLE_1267)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (forall ((R (-> tptp.c tptp.b Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 R)) (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_16 (not _let_15))) (let ((_let_17 (forall ((R (-> tptp.c tptp.b Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 R)) (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14 _let_12 _let_10))) (let ((_let_20 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_22 (not _let_21))) (let ((_let_23 (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_1165 tptp.b) (BOUND_VARIABLE_1163 tptp.b) (BOUND_VARIABLE_1161 tptp.b) (BOUND_VARIABLE_1159 tptp.b) (BOUND_VARIABLE_1157 tptp.b) (BOUND_VARIABLE_1155 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_1155) BOUND_VARIABLE_1157))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_1159) BOUND_VARIABLE_1161))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_1163) BOUND_VARIABLE_1165))) (not (@ (@ (@ R BOUND_VARIABLE_1155) BOUND_VARIABLE_1159) BOUND_VARIABLE_1163)) (not (@ (@ (@ R BOUND_VARIABLE_1157) BOUND_VARIABLE_1161) BOUND_VARIABLE_1165)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_24 (not _let_23))) (let ((_let_25 (forall ((R (-> tptp.c tptp.b Bool))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 R)) (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_22 _let_20))) (let ((_let_28 (and _let_9 _let_27 _let_19))) (let ((_let_29 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_30 (or _let_12 _let_29))) (let ((_let_31 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_32 (or _let_12 _let_31))) (let ((_let_33 (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_990 tptp.b) (BOUND_VARIABLE_988 tptp.b) (BOUND_VARIABLE_986 tptp.b) (BOUND_VARIABLE_984 tptp.b) (BOUND_VARIABLE_982 tptp.b) (BOUND_VARIABLE_980 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_980) BOUND_VARIABLE_982))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_984) BOUND_VARIABLE_986))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_988) BOUND_VARIABLE_990))) (not (@ (@ (@ R BOUND_VARIABLE_980) BOUND_VARIABLE_984) BOUND_VARIABLE_988)) (not (@ (@ (@ R BOUND_VARIABLE_982) BOUND_VARIABLE_986) BOUND_VARIABLE_990)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))))) (let ((_let_34 (not _let_33))) (let ((_let_35 (not _let_31))) (let ((_let_36 (not _let_29))) (let ((_let_37 (or _let_36 _let_35 _let_34 _let_10))) (let ((_let_38 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.c0))) (let ((_let_39 (and _let_38 (or (not _let_38) _let_5 _let_38) _let_37))) (let ((_let_40 (or _let_12 _let_39))) (let ((_let_41 (or))) (let ((_let_42 (REFL :args (_let_19)))) (let ((_let_43 (=>))) (let ((_let_44 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_45 (THEORY_PREPROCESS :args ((= (@ _let_44 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_29))))) (let ((_let_46 (not))) (let ((_let_47 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) _let_11))) :args _let_46))) (let ((_let_48 (_let_17))) (let ((_let_49 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING))) (let ((_let_50 (THEORY_PREPROCESS :args ((= (@ _let_44 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) _let_31))))) (let ((_let_51 (_let_15))) (let ((_let_52 (forall ((Xx (-> tptp.c tptp.b Bool)) (BOUND_VARIABLE_1100 tptp.b) (BOUND_VARIABLE_1098 tptp.b) (BOUND_VARIABLE_1096 tptp.b) (BOUND_VARIABLE_1094 tptp.c) (BOUND_VARIABLE_1081 tptp.b) (BOUND_VARIABLE_1079 tptp.b) (BOUND_VARIABLE_1077 tptp.c) (BOUND_VARIABLE_1073 tptp.c)) (let ((_let_1 (@ Xx BOUND_VARIABLE_1094))) (let ((_let_2 (@ Xx BOUND_VARIABLE_1077))) (or (not (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx)) (and (@ (@ Xx BOUND_VARIABLE_1073) tptp.c0) (or (not (@ _let_2 BOUND_VARIABLE_1081)) (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_909 tptp.b) (BOUND_VARIABLE_907 tptp.b) (BOUND_VARIABLE_905 tptp.b) (BOUND_VARIABLE_903 tptp.b) (BOUND_VARIABLE_901 tptp.b) (BOUND_VARIABLE_899 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_899) BOUND_VARIABLE_901))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_903) BOUND_VARIABLE_905))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_907) BOUND_VARIABLE_909))) (not (@ (@ (@ R BOUND_VARIABLE_899) BOUND_VARIABLE_903) BOUND_VARIABLE_907)) (not (@ (@ (@ R BOUND_VARIABLE_901) BOUND_VARIABLE_905) BOUND_VARIABLE_909)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R BOUND_VARIABLE_1079) BOUND_VARIABLE_1081) BOUND_VARIABLE_1081)))) (@ _let_2 BOUND_VARIABLE_1079)) (or (not (@ _let_1 BOUND_VARIABLE_1096)) (not (@ _let_1 BOUND_VARIABLE_1098)) (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_990 tptp.b) (BOUND_VARIABLE_988 tptp.b) (BOUND_VARIABLE_986 tptp.b) (BOUND_VARIABLE_984 tptp.b) (BOUND_VARIABLE_982 tptp.b) (BOUND_VARIABLE_980 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_980) BOUND_VARIABLE_982))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_984) BOUND_VARIABLE_986))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_988) BOUND_VARIABLE_990))) (not (@ (@ (@ R BOUND_VARIABLE_980) BOUND_VARIABLE_984) BOUND_VARIABLE_988)) (not (@ (@ (@ R BOUND_VARIABLE_982) BOUND_VARIABLE_986) BOUND_VARIABLE_990)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R BOUND_VARIABLE_1096) BOUND_VARIABLE_1098) BOUND_VARIABLE_1100)))) (@ _let_1 BOUND_VARIABLE_1100))))))))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_28))) (let ((_let_55 (forall ((S (-> (-> tptp.c tptp.b Bool) Bool)) (BOUND_VARIABLE_1411 tptp.c) (BOUND_VARIABLE_1415 tptp.b) (BOUND_VARIABLE_1389 tptp.b) (BOUND_VARIABLE_1413 tptp.b) (BOUND_VARIABLE_1387 tptp.c) (BOUND_VARIABLE_1419 (-> tptp.c tptp.b Bool)) (BOUND_VARIABLE_1393 (-> tptp.c tptp.b Bool)) (BOUND_VARIABLE_1380 (-> tptp.c tptp.b Bool)) (BOUND_VARIABLE_1417 tptp.b) (BOUND_VARIABLE_1391 tptp.b) (BOUND_VARIABLE_1378 tptp.c)) (or (not (forall ((Xx (-> tptp.c tptp.b Bool)) (BOUND_VARIABLE_1100 tptp.b) (BOUND_VARIABLE_1098 tptp.b) (BOUND_VARIABLE_1096 tptp.b) (BOUND_VARIABLE_1094 tptp.c) (BOUND_VARIABLE_1081 tptp.b) (BOUND_VARIABLE_1079 tptp.b) (BOUND_VARIABLE_1077 tptp.c) (BOUND_VARIABLE_1073 tptp.c)) (let ((_let_1 (@ Xx BOUND_VARIABLE_1094))) (let ((_let_2 (@ Xx BOUND_VARIABLE_1077))) (or (not (@ S Xx)) (and (@ (@ Xx BOUND_VARIABLE_1073) tptp.c0) (or (not (@ _let_2 BOUND_VARIABLE_1081)) (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_909 tptp.b) (BOUND_VARIABLE_907 tptp.b) (BOUND_VARIABLE_905 tptp.b) (BOUND_VARIABLE_903 tptp.b) (BOUND_VARIABLE_901 tptp.b) (BOUND_VARIABLE_899 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_899) BOUND_VARIABLE_901))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_903) BOUND_VARIABLE_905))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_907) BOUND_VARIABLE_909))) (not (@ (@ (@ R BOUND_VARIABLE_899) BOUND_VARIABLE_903) BOUND_VARIABLE_907)) (not (@ (@ (@ R BOUND_VARIABLE_901) BOUND_VARIABLE_905) BOUND_VARIABLE_909)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R BOUND_VARIABLE_1079) BOUND_VARIABLE_1081) BOUND_VARIABLE_1081)))) (@ _let_2 BOUND_VARIABLE_1079)) (or (not (@ _let_1 BOUND_VARIABLE_1096)) (not (@ _let_1 BOUND_VARIABLE_1098)) (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_990 tptp.b) (BOUND_VARIABLE_988 tptp.b) (BOUND_VARIABLE_986 tptp.b) (BOUND_VARIABLE_984 tptp.b) (BOUND_VARIABLE_982 tptp.b) (BOUND_VARIABLE_980 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_980) BOUND_VARIABLE_982))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_984) BOUND_VARIABLE_986))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_988) BOUND_VARIABLE_990))) (not (@ (@ (@ R BOUND_VARIABLE_980) BOUND_VARIABLE_984) BOUND_VARIABLE_988)) (not (@ (@ (@ R BOUND_VARIABLE_982) BOUND_VARIABLE_986) BOUND_VARIABLE_990)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R BOUND_VARIABLE_1096) BOUND_VARIABLE_1098) BOUND_VARIABLE_1100)))) (@ _let_1 BOUND_VARIABLE_1100)))))))) (and (or (not (@ S BOUND_VARIABLE_1380)) (@ (@ BOUND_VARIABLE_1380 BOUND_VARIABLE_1378) tptp.c0)) (or (not (forall ((R (-> tptp.c tptp.b Bool))) (or (not (@ S R)) (@ (@ R BOUND_VARIABLE_1387) BOUND_VARIABLE_1391)))) (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_1165 tptp.b) (BOUND_VARIABLE_1163 tptp.b) (BOUND_VARIABLE_1161 tptp.b) (BOUND_VARIABLE_1159 tptp.b) (BOUND_VARIABLE_1157 tptp.b) (BOUND_VARIABLE_1155 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_1155) BOUND_VARIABLE_1157))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_1159) BOUND_VARIABLE_1161))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_1163) BOUND_VARIABLE_1165))) (not (@ (@ (@ R BOUND_VARIABLE_1155) BOUND_VARIABLE_1159) BOUND_VARIABLE_1163)) (not (@ (@ (@ R BOUND_VARIABLE_1157) BOUND_VARIABLE_1161) BOUND_VARIABLE_1165)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R BOUND_VARIABLE_1389) BOUND_VARIABLE_1391) BOUND_VARIABLE_1391)))) (not (@ S BOUND_VARIABLE_1393)) (@ (@ BOUND_VARIABLE_1393 BOUND_VARIABLE_1387) BOUND_VARIABLE_1389)) (or (not (forall ((R (-> tptp.c tptp.b Bool))) (or (not (@ S R)) (@ (@ R BOUND_VARIABLE_1411) BOUND_VARIABLE_1413)))) (not (forall ((R (-> tptp.c tptp.b Bool))) (or (not (@ S R)) (@ (@ R BOUND_VARIABLE_1411) BOUND_VARIABLE_1415)))) (not (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_1267 tptp.b) (BOUND_VARIABLE_1265 tptp.b) (BOUND_VARIABLE_1263 tptp.b) (BOUND_VARIABLE_1261 tptp.b) (BOUND_VARIABLE_1259 tptp.b) (BOUND_VARIABLE_1257 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_1257) BOUND_VARIABLE_1259))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_1261) BOUND_VARIABLE_1263))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_1265) BOUND_VARIABLE_1267))) (not (@ (@ (@ R BOUND_VARIABLE_1257) BOUND_VARIABLE_1261) BOUND_VARIABLE_1265)) (not (@ (@ (@ R BOUND_VARIABLE_1259) BOUND_VARIABLE_1263) BOUND_VARIABLE_1267)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R BOUND_VARIABLE_1413) BOUND_VARIABLE_1415) BOUND_VARIABLE_1417)))) (not (@ S BOUND_VARIABLE_1419)) (@ (@ BOUND_VARIABLE_1419 BOUND_VARIABLE_1411) BOUND_VARIABLE_1417))))))) (let ((_let_56 (not _let_54))) (let ((_let_57 (forall ((u (-> tptp.b Bool)) (e Bool) (i tptp.b)) (not (forall ((v (-> tptp.b Bool))) (not (forall ((ii tptp.b)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_58 (forall ((u (-> tptp.c tptp.b Bool)) (e (-> tptp.b Bool)) (i tptp.c)) (not (forall ((v (-> tptp.c tptp.b Bool))) (not (forall ((ii tptp.c)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_59 (forall ((u (-> (-> tptp.c tptp.b Bool) Bool)) (e Bool) (i (-> tptp.c tptp.b Bool))) (not (forall ((v (-> (-> tptp.c tptp.b Bool) Bool))) (not (forall ((ii (-> tptp.c tptp.b Bool))) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_60 (forall ((u (-> tptp.b tptp.b Bool)) (e (-> tptp.b Bool)) (i tptp.b)) (not (forall ((v (-> tptp.b tptp.b Bool))) (not (forall ((ii tptp.b)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_61 (forall ((u (-> tptp.b tptp.b tptp.b Bool)) (e (-> tptp.b tptp.b Bool)) (i tptp.b)) (not (forall ((v (-> tptp.b tptp.b tptp.b Bool))) (not (forall ((ii tptp.b)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_62 (forall ((u (-> tptp.b tptp.b)) (e tptp.b) (i tptp.b)) (not (forall ((v (-> tptp.b tptp.b))) (not (forall ((ii tptp.b)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_63 (forall ((u (-> tptp.b tptp.b tptp.b)) (e (-> tptp.b tptp.b)) (i tptp.b)) (not (forall ((v (-> tptp.b tptp.b tptp.b))) (not (forall ((ii tptp.b)) (= (@ v ii) (ite (= i ii) e (@ u ii)))))))))) (let ((_let_64 (not _let_55))) (let ((_let_65 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_66 (and))) (let ((_let_67 (THEORY_PREPROCESS :args ((= (@ _let_44 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11) _let_10))))) (let ((_let_68 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_69 (THEORY_PREPROCESS :args ((= (@ _let_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) _let_20))))) (let ((_let_70 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) _let_21))) :args _let_46))) (let ((_let_71 (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13) tptp.c0) _let_2))))) (let ((_let_72 (CONG (THEORY_PREPROCESS :args ((= (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) _let_7))) :args _let_46))) (let ((_let_73 (_let_64))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_65) :args _let_73) (CONG (REFL :args _let_73) (CONG (CONG (REFL :args (_let_53)) (CONG (CONG _let_72 _let_71 :args _let_41) (CONG (REFL :args (_let_26)) (REFL :args (_let_24)) _let_70 _let_69 :args _let_41) (CONG (REFL :args (_let_18)) (REFL :args (_let_16)) (REFL :args (_let_14)) _let_47 _let_67 :args _let_41) :args _let_66) :args _let_41) :args _let_46) :args _let_43))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_55))) (REFL :args (_let_56)) :args _let_41)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO _let_65 (PREPROCESS :args ((and _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57)))) :args ((and _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57))) :args (0)) :args (_let_56 true _let_55)))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 0)) (CONG (REFL :args (_let_54)) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_41)) :args ((or _let_52 _let_54))) _let_74 :args (_let_52 true _let_54)))) (let ((_let_76 (THEORY_PREPROCESS :args ((= (@ _let_44 tptp.c0) _let_38))))) (let ((_let_77 (REFL :args (_let_5)))) (let ((_let_78 (_let_52))) (let ((_let_79 (REFL :args _let_78))) (let ((_let_80 (ASSUME :args _let_78))) (let ((_let_81 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_82 (or _let_22 _let_81))) (let ((_let_83 (forall ((R (-> tptp.b tptp.b tptp.b Bool))) (or (not (forall ((Xa tptp.b) (Xb tptp.b) (Xc0 tptp.b) (BOUND_VARIABLE_909 tptp.b) (BOUND_VARIABLE_907 tptp.b) (BOUND_VARIABLE_905 tptp.b) (BOUND_VARIABLE_903 tptp.b) (BOUND_VARIABLE_901 tptp.b) (BOUND_VARIABLE_899 tptp.b)) (or (and (or (not (= tptp.c0 Xa)) (not (= Xb Xc0))) (or (not (= tptp.c0 Xb)) (not (= Xa Xc0))) (or (not (= Xa (@ (@ tptp.cP BOUND_VARIABLE_899) BOUND_VARIABLE_901))) (not (= Xb (@ (@ tptp.cP BOUND_VARIABLE_903) BOUND_VARIABLE_905))) (not (= Xc0 (@ (@ tptp.cP BOUND_VARIABLE_907) BOUND_VARIABLE_909))) (not (@ (@ (@ R BOUND_VARIABLE_899) BOUND_VARIABLE_903) BOUND_VARIABLE_907)) (not (@ (@ (@ R BOUND_VARIABLE_901) BOUND_VARIABLE_905) BOUND_VARIABLE_909)))) (@ (@ (@ R Xa) Xb) Xc0)))) (@ (@ (@ R SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))))) (let ((_let_84 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 tptp.c0))) (let ((_let_85 (not _let_84))) (let ((_let_86 (not _let_83))) (let ((_let_87 (not _let_81))) (let ((_let_88 (or _let_87 _let_86 _let_20))) (let ((_let_89 (and _let_84 _let_88 (or _let_85 _let_85 _let_3 _let_84)))) (let ((_let_90 (or _let_22 _let_89))) (let ((_let_91 (REFL :args (_let_27)))) (let ((_let_92 (THEORY_PREPROCESS :args ((= (@ _let_68 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) _let_81))))) (let ((_let_93 (_let_25))) (let ((_let_94 (THEORY_PREPROCESS :args ((= (@ _let_68 tptp.c0) _let_84))))) (let ((_let_95 (REFL :args (_let_3)))) (let ((_let_96 (CONG _let_94 :args _let_46))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_28)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_54 1)) _let_74 :args ((not _let_28) true _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_89 1)) :args ((or _let_88 (not _let_89)))) (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_20 _let_87 _let_86 (not _let_88)))) (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_22 _let_89 (not _let_90)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.c0 tptp.c0 tptp.c0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING)) :args _let_78) (CONG _let_79 (CONG _let_70 (CONG _let_94 (CONG (CONG _let_92 :args _let_46) (REFL :args (_let_86)) _let_69 :args _let_41) (CONG _let_96 _let_96 _let_95 _let_94 :args _let_41) :args _let_66) :args _let_41) :args _let_43))) _let_75 :args (_let_90 false _let_52)) (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_22 _let_81 (not _let_82)))) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_23 (= Xa Xa) (= R R) (= Xb Xb) (= Xc0 Xc0) (= BOUND_VARIABLE_1165 BOUND_VARIABLE_909) (= BOUND_VARIABLE_1163 BOUND_VARIABLE_907) (= BOUND_VARIABLE_1161 BOUND_VARIABLE_905) (= BOUND_VARIABLE_1159 BOUND_VARIABLE_903) (= BOUND_VARIABLE_1157 BOUND_VARIABLE_901) (= BOUND_VARIABLE_1155 BOUND_VARIABLE_899)))) (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_93) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING)) :args _let_93) (CONG (REFL :args _let_93) (CONG _let_70 _let_92 :args _let_41) :args _let_43))) (CNF_OR_NEG :args (_let_27 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 2)) (CONG _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_41)) :args ((or _let_21 _let_27))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_41)) :args ((or _let_23 _let_27))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_41)) :args ((or _let_25 _let_27))) :args (_let_27 true _let_88 false _let_89 false _let_90 false _let_81 false _let_83 false _let_82 true _let_20 false _let_21 false _let_23 false _let_25)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 2)) :args ((or _let_37 (not _let_39)))) (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_10 _let_36 _let_35 _let_34 (not _let_37)))) (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_12 _let_31 (not _let_32)))) (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_12 _let_29 (not _let_30)))) (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_12 _let_39 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 tptp.c0 tptp.c0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING)) :args _let_78) (CONG _let_79 (CONG _let_47 (CONG _let_76 (CONG (CONG _let_76 :args _let_46) _let_77 _let_76 :args _let_41) (CONG (CONG _let_45 :args _let_46) (CONG _let_50 :args _let_46) (REFL :args (_let_34)) _let_67 :args _let_41) :args _let_66) :args _let_41) :args _let_43))) _let_75 :args (_let_40 false _let_52)) (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_13 (= Xa Xa) (= R R) (= Xb Xb) (= Xc0 Xc0) (= BOUND_VARIABLE_1267 BOUND_VARIABLE_990) (= BOUND_VARIABLE_1265 BOUND_VARIABLE_988) (= BOUND_VARIABLE_1263 BOUND_VARIABLE_986) (= BOUND_VARIABLE_1261 BOUND_VARIABLE_984) (= BOUND_VARIABLE_1259 BOUND_VARIABLE_982) (= BOUND_VARIABLE_1257 BOUND_VARIABLE_980)))) (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_51) :args _let_49) :args _let_51) (CONG (REFL :args _let_51) (CONG _let_47 _let_50 :args _let_41) :args _let_43))) (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_48) :args _let_49) :args _let_48) (CONG (REFL :args _let_48) (CONG _let_47 _let_45 :args _let_41) :args _let_43))) (CNF_OR_NEG :args (_let_19 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 3)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_41)) :args ((or _let_11 _let_19))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 2)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_41)) :args ((or _let_13 _let_19))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 1)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_41)) :args ((or _let_15 _let_19))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_19 0)) (CONG _let_42 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_41)) :args ((or _let_17 _let_19))) :args (_let_19 true _let_37 false _let_31 false _let_29 false _let_39 false _let_40 false _let_33 false _let_32 false _let_30 true _let_10 false _let_11 false _let_13 false _let_15 false _let_17)) :args ((not _let_9) true _let_28 false _let_27 false _let_19)))) (let ((_let_98 (or _let_8 _let_6))) (let ((_let_99 (CONG _let_71 :args _let_46))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_6 0)) :args ((or _let_2 (not _let_6)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_8 _let_6 (not _let_98)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 0)) (CONG (REFL :args (_let_9)) (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_41)) :args ((or _let_7 _let_9))) _let_97 :args (_let_7 true _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.c0 tptp.c0 tptp.c0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 tptp.c0 tptp.c0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING)) :args _let_78) (CONG _let_79 (CONG _let_72 (CONG _let_71 (CONG _let_99 _let_77 _let_71 :args _let_41) (CONG _let_99 _let_99 _let_95 _let_71 :args _let_41) :args _let_66) :args _let_41) :args _let_43))) _let_75 :args (_let_98 false _let_52)) :args (_let_6 false _let_7 false _let_98)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_9 1)) _let_97 :args (_let_4 true _let_9)) :args (false false _let_6 true _let_2)) :args (_let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 36.22/36.37 )
% 36.22/36.37 % SZS output end Proof for SEV192^5
% 36.22/36.37 % cvc5---1.0.5 exiting
% 36.22/36.38 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------