TSTP Solution File: SET669^3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n006.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 14:39:49 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% 0.12/0.14 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 08:26:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.48 %----Proving TH0
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 % File : SET669^3 : TPTP v8.1.2. Released v3.6.0.
% 0.19/0.48 % Domain : Set Theory
% 0.19/0.48 % Problem : Id on Y subset of R => Y subset of domain R & Y is range R
% 0.19/0.48 % Version : [BS+08] axioms.
% 0.19/0.48 % English : If the identity relation on Y is a subset of a relation R from X
% 0.19/0.48 % to Y then Y is a subset of the domain of R and Y is the range of R.
% 0.19/0.48
% 0.19/0.48 % Refs : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
% 0.19/0.48 % : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
% 0.19/0.48 % : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% 0.19/0.48 % Source : [Ben08]
% 0.19/0.48 % Names :
% 0.19/0.48
% 0.19/0.48 % Status : Theorem
% 0.19/0.48 % Rating : 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.19/0.48 % Syntax : Number of formulae : 71 ( 35 unt; 35 typ; 35 def)
% 0.19/0.48 % Number of atoms : 95 ( 44 equ; 0 cnn)
% 0.19/0.48 % Maximal formula atoms : 7 ( 2 avg)
% 0.19/0.48 % Number of connectives : 133 ( 8 ~; 5 |; 19 &; 90 @)
% 0.19/0.48 % ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% 0.19/0.48 % Maximal formula depth : 7 ( 1 avg)
% 0.19/0.48 % Number of types : 2 ( 0 usr)
% 0.19/0.48 % Number of type conns : 214 ( 214 >; 0 *; 0 +; 0 <<)
% 0.19/0.48 % Number of symbols : 43 ( 40 usr; 7 con; 0-4 aty)
% 0.19/0.48 % Number of variables : 111 ( 83 ^; 20 !; 8 ?; 111 :)
% 0.19/0.48 % SPC : TH0_THM_EQU_NAR
% 0.19/0.48
% 0.19/0.48 % Comments :
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 %----Include basic set theory definitions
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(in_decl,type,
% 0.19/0.48 in: $i > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(in,definition,
% 0.19/0.48 ( in
% 0.19/0.48 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(is_a_decl,type,
% 0.19/0.48 is_a: $i > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(is_a,definition,
% 0.19/0.48 ( is_a
% 0.19/0.48 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(emptyset_decl,type,
% 0.19/0.48 emptyset: $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(emptyset,definition,
% 0.19/0.48 ( emptyset
% 0.19/0.48 = ( ^ [X: $i] : $false ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(unord_pair_decl,type,
% 0.19/0.48 unord_pair: $i > $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(unord_pair,definition,
% 0.19/0.48 ( unord_pair
% 0.19/0.48 = ( ^ [X: $i,Y: $i,U: $i] :
% 0.19/0.48 ( ( U = X )
% 0.19/0.48 | ( U = Y ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(singleton_decl,type,
% 0.19/0.48 singleton: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(singleton,definition,
% 0.19/0.48 ( singleton
% 0.19/0.48 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(union_decl,type,
% 0.19/0.48 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(union,definition,
% 0.19/0.48 ( union
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 | ( Y @ U ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(excl_union_decl,type,
% 0.19/0.48 excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(excl_union,definition,
% 0.19/0.48 ( excl_union
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.48 ( ( ( X @ U )
% 0.19/0.48 & ~ ( Y @ U ) )
% 0.19/0.48 | ( ~ ( X @ U )
% 0.19/0.48 & ( Y @ U ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(intersection_decl,type,
% 0.19/0.48 intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(intersection,definition,
% 0.19/0.48 ( intersection
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 & ( Y @ U ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(setminus_decl,type,
% 0.19/0.48 setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(setminus,definition,
% 0.19/0.48 ( setminus
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 & ~ ( Y @ U ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(complement_decl,type,
% 0.19/0.48 complement: ( $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(complement,definition,
% 0.19/0.48 ( complement
% 0.19/0.48 = ( ^ [X: $i > $o,U: $i] :
% 0.19/0.48 ~ ( X @ U ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(disjoint_decl,type,
% 0.19/0.48 disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(disjoint,definition,
% 0.19/0.48 ( disjoint
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.19/0.48 ( ( intersection @ X @ Y )
% 0.19/0.48 = emptyset ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(subset_decl,type,
% 0.19/0.48 subset: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(subset,definition,
% 0.19/0.48 ( subset
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.19/0.48 ! [U: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 => ( Y @ U ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(meets_decl,type,
% 0.19/0.48 meets: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(meets,definition,
% 0.19/0.48 ( meets
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.19/0.48 ? [U: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 & ( Y @ U ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(misses_decl,type,
% 0.19/0.48 misses: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(misses,definition,
% 0.19/0.48 ( misses
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.19/0.48 ~ ? [U: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 & ( Y @ U ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 %----Include definitions for relations
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 thf(cartesian_product_decl,type,
% 0.19/0.48 cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(cartesian_product,definition,
% 0.19/0.48 ( cartesian_product
% 0.19/0.48 = ( ^ [X: $i > $o,Y: $i > $o,U: $i,V: $i] :
% 0.19/0.48 ( ( X @ U )
% 0.19/0.48 & ( Y @ V ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(pair_rel_decl,type,
% 0.19/0.48 pair_rel: $i > $i > $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(pair_rel,definition,
% 0.19/0.48 ( pair_rel
% 0.19/0.48 = ( ^ [X: $i,Y: $i,U: $i,V: $i] :
% 0.19/0.48 ( ( U = X )
% 0.19/0.48 | ( V = Y ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(id_rel_decl,type,
% 0.19/0.48 id_rel: ( $i > $o ) > $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(id_rel,definition,
% 0.19/0.48 ( id_rel
% 0.19/0.48 = ( ^ [S: $i > $o,X: $i,Y: $i] :
% 0.19/0.48 ( ( S @ X )
% 0.19/0.48 & ( X = Y ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(sub_rel_decl,type,
% 0.19/0.48 sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(sub_rel,definition,
% 0.19/0.48 ( sub_rel
% 0.19/0.48 = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
% 0.19/0.48 ! [X: $i,Y: $i] :
% 0.19/0.48 ( ( R1 @ X @ Y )
% 0.19/0.48 => ( R2 @ X @ Y ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(is_rel_on_decl,type,
% 0.19/0.48 is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(is_rel_on,definition,
% 0.19/0.48 ( is_rel_on
% 0.19/0.48 = ( ^ [R: $i > $i > $o,A: $i > $o,B: $i > $o] :
% 0.19/0.48 ! [X: $i,Y: $i] :
% 0.19/0.48 ( ( R @ X @ Y )
% 0.19/0.48 => ( ( A @ X )
% 0.19/0.48 & ( B @ Y ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(restrict_rel_domain_decl,type,
% 0.19/0.48 restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(restrict_rel_domain,definition,
% 0.19/0.48 ( restrict_rel_domain
% 0.19/0.48 = ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
% 0.19/0.48 ( ( S @ X )
% 0.19/0.48 & ( R @ X @ Y ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(rel_diagonal_decl,type,
% 0.19/0.48 rel_diagonal: $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(rel_diagonal,definition,
% 0.19/0.48 ( rel_diagonal
% 0.19/0.48 = ( ^ [X: $i,Y: $i] : ( X = Y ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(rel_composition_decl,type,
% 0.19/0.48 rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(rel_composition,definition,
% 0.19/0.48 ( rel_composition
% 0.19/0.48 = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o,X: $i,Z: $i] :
% 0.19/0.48 ? [Y: $i] :
% 0.19/0.48 ( ( R1 @ X @ Y )
% 0.19/0.48 & ( R2 @ Y @ Z ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(reflexive_decl,type,
% 0.19/0.48 reflexive: ( $i > $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(reflexive,definition,
% 0.19/0.48 ( reflexive
% 0.19/0.48 = ( ^ [R: $i > $i > $o] :
% 0.19/0.48 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(irreflexive_decl,type,
% 0.19/0.48 irreflexive: ( $i > $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(irreflexive,definition,
% 0.19/0.48 ( irreflexive
% 0.19/0.48 = ( ^ [R: $i > $i > $o] :
% 0.19/0.48 ! [X: $i] :
% 0.19/0.48 ~ ( R @ X @ X ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(symmetric_decl,type,
% 0.19/0.48 symmetric: ( $i > $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(symmetric,definition,
% 0.19/0.48 ( symmetric
% 0.19/0.48 = ( ^ [R: $i > $i > $o] :
% 0.19/0.48 ! [X: $i,Y: $i] :
% 0.19/0.48 ( ( R @ X @ Y )
% 0.19/0.48 => ( R @ Y @ X ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(transitive_decl,type,
% 0.19/0.48 transitive: ( $i > $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(transitive,definition,
% 0.19/0.48 ( transitive
% 0.19/0.48 = ( ^ [R: $i > $i > $o] :
% 0.19/0.48 ! [X: $i,Y: $i,Z: $i] :
% 0.19/0.48 ( ( ( R @ X @ Y )
% 0.19/0.48 & ( R @ Y @ Z ) )
% 0.19/0.48 => ( R @ X @ Z ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(equiv_rel__decl,type,
% 0.19/0.48 equiv_rel: ( $i > $i > $o ) > $o ).
% 0.19/0.48
% 0.19/0.48 thf(equiv_rel,definition,
% 0.19/0.48 ( equiv_rel
% 0.19/0.48 = ( ^ [R: $i > $i > $o] :
% 0.19/0.48 ( ( reflexive @ R )
% 0.19/0.48 & ( symmetric @ R )
% 0.19/0.48 & ( transitive @ R ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(rel_codomain_decl,type,
% 0.19/0.48 rel_codomain: ( $i > $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(rel_codomain,definition,
% 0.19/0.48 ( rel_codomain
% 0.19/0.48 = ( ^ [R: $i > $i > $o,Y: $i] :
% 0.19/0.48 ? [X: $i] : ( R @ X @ Y ) ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(rel_domain_decl,type,
% 0.19/0.48 rel_domain: ( $i > $i > $o ) > $i > $o ).
% 0.19/0.48
% 0.19/0.48 thf(rel_domain,definition,
% 0.19/0.48 ( rel_domain
% 0.19/0.48 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.19/0.48 ? [Y: $i] : ( R @ X @ Y ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(rel_inverse_decl,type,
% 0.19/0.50 rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(rel_inverse,definition,
% 0.19/0.50 ( rel_inverse
% 0.19/0.50 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(equiv_classes_decl,type,
% 0.19/0.50 equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(equiv_classes,definition,
% 0.19/0.50 ( equiv_classes
% 0.19/0.50 = ( ^ [R: $i > $i > $o,S1: $i > $o] :
% 0.19/0.50 ? [X: $i] :
% 0.19/0.50 ( ( S1 @ X )
% 0.19/0.50 & ! [Y: $i] :
% 0.19/0.50 ( ( S1 @ Y )
% 0.19/0.50 <=> ( R @ X @ Y ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(restrict_rel_codomain_decl,type,
% 0.19/0.50 restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(restrict_rel_codomain,definition,
% 0.19/0.50 ( restrict_rel_codomain
% 0.19/0.50 = ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
% 0.19/0.50 ( ( S @ Y )
% 0.19/0.50 & ( R @ X @ Y ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(rel_field_decl,type,
% 0.19/0.50 rel_field: ( $i > $i > $o ) > $i > $o ).
% 0.19/0.50
% 0.19/0.50 thf(rel_field,definition,
% 0.19/0.50 ( rel_field
% 0.19/0.50 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.19/0.50 ( ( rel_domain @ R @ X )
% 0.19/0.50 | ( rel_codomain @ R @ X ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(well_founded_decl,type,
% 0.19/0.50 well_founded: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(well_founded,definition,
% 0.19/0.50 ( well_founded
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [X: $i > $o,Z: $i] :
% 0.19/0.50 ( ( X @ Z )
% 0.19/0.50 => ? [Y: $i] :
% 0.19/0.50 ( ( X @ Y )
% 0.19/0.50 & ! [W: $i] :
% 0.19/0.50 ( ( R @ Y @ W )
% 0.19/0.50 => ~ ( X @ W ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 thf(upwards_well_founded_decl,type,
% 0.19/0.50 upwards_well_founded: ( $i > $i > $o ) > $o ).
% 0.19/0.50
% 0.19/0.50 thf(upwards_well_founded,definition,
% 0.19/0.50 ( upwards_well_founded
% 0.19/0.50 = ( ^ [R: $i > $i > $o] :
% 0.19/0.50 ! [X: $i > $o,Z: $i] :
% 0.19/0.50 ( ( X @ Z )
% 0.19/0.50 => ? [Y: $i] :
% 0.19/0.50 ( ( X @ Y )
% 0.19/0.50 & ! [W: $i] :
% 0.19/0.50 ( ( R @ Y @ Y )
% 0.19/0.50 => ~ ( X @ W ) ) ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 thf(thm,conjecture,
% 0.19/0.50 ! [R: $i > $i > $o] :
% 0.19/0.50 ( ( sub_rel
% 0.19/0.50 @ ( id_rel
% 0.19/0.50 @ ^ [X: $i] : $true )
% 0.19/0.50 @ R )
% 0.19/0.50 => ( ( subset
% 0.19/0.50 @ ^ [X: $i] : $true
% 0.19/0.50 @ ( rel_domain @ R ) )
% 0.19/0.50 & ( ( ^ [X: $i] : $true )
% 0.19/0.50 = ( rel_codomain @ R ) ) ) ) ).
% 0.19/0.50
% 0.19/0.50 %------------------------------------------------------------------------------
% 0.19/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MioKwsycPE/cvc5---1.0.5_12148.p...
% 0.19/0.50 (declare-sort $$unsorted 0)
% 0.19/0.50 (declare-fun tptp.in ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.19/0.50 (declare-fun tptp.is_a ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.19/0.50 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.19/0.50 (declare-fun tptp.unord_pair ($$unsorted $$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.19/0.50 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.19/0.50 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.19/0.50 (declare-fun tptp.excl_union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))
% 0.19/0.50 (declare-fun tptp.intersection ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.19/0.50 (declare-fun tptp.setminus ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.19/0.50 (declare-fun tptp.complement ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.19/0.50 (declare-fun tptp.disjoint ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.19/0.50 (declare-fun tptp.subset ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.19/0.50 (declare-fun tptp.meets ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.19/0.50 (declare-fun tptp.misses ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.19/0.50 (declare-fun tptp.cartesian_product ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))))
% 0.19/0.50 (declare-fun tptp.pair_rel ($$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))))
% 0.19/0.50 (declare-fun tptp.id_rel ((-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))))
% 0.19/0.50 (declare-fun tptp.sub_rel ((-> $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))))
% 0.19/0.50 (declare-fun tptp.is_rel_on ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))))
% 0.19/0.50 (declare-fun tptp.restrict_rel_domain ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))))
% 0.19/0.50 (declare-fun tptp.rel_diagonal ($$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))))
% 0.19/0.50 (declare-fun tptp.rel_composition ((-> $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.19/0.50 (assert (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))
% 0.19/0.50 (declare-fun tptp.reflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))))
% 0.19/0.50 (declare-fun tptp.irreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))
% 0.19/0.50 (declare-fun tptp.symmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))))
% 0.19/0.50 (declare-fun tptp.transitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ R X))) (=> (and (@ _let_1 Y) (@ (@ R Y) Z)) (@ _let_1 Z)))))))
% 0.19/0.50 (declare-fun tptp.equiv_rel ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.50 (assert (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))))
% 0.19/0.58 (declare-fun tptp.rel_codomain ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))))
% 0.19/0.58 (declare-fun tptp.rel_domain ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))))
% 0.19/0.58 (declare-fun tptp.rel_inverse ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))))
% 0.19/0.58 (declare-fun tptp.equiv_classes ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.19/0.58 (assert (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))
% 0.19/0.58 (declare-fun tptp.restrict_rel_codomain ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))))
% 0.19/0.58 (declare-fun tptp.rel_field ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.19/0.58 (assert (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))))
% 0.19/0.58 (declare-fun tptp.well_founded ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.58 (assert (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))))))
% 0.19/0.58 (declare-fun tptp.upwards_well_founded ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.19/0.58 (assert (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))))))
% 0.19/0.58 (assert (not (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ (@ tptp.sub_rel (@ tptp.id_rel (lambda ((X $$unsorted)) true))) R) (and (@ (@ tptp.subset (lambda ((X $$unsorted)) true)) (@ tptp.rel_domain R)) (= (lambda ((X $$unsorted)) true) (@ tptp.rel_codomain R)))))))
% 0.19/0.58 (set-info :filename cvc5---1.0.5_12148)
% 0.19/0.58 (check-sat-assuming ( true ))
% 0.19/0.58 ------- get file name : TPTP file name is SET669^3
% 0.19/0.58 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12148.smt2...
% 0.19/0.58 --- Run --ho-elim --full-saturate-quant at 10...
% 0.19/0.58 % SZS status Theorem for SET669^3
% 0.19/0.58 % SZS output start Proof for SET669^3
% 0.19/0.58 (
% 0.19/0.58 (let ((_let_1 (not (forall ((R (-> $$unsorted $$unsorted Bool))) (=> (@ (@ tptp.sub_rel (@ tptp.id_rel (lambda ((X $$unsorted)) true))) R) (and (@ (@ tptp.subset (lambda ((X $$unsorted)) true)) (@ tptp.rel_domain R)) (= (lambda ((X $$unsorted)) true) (@ tptp.rel_codomain R)))))))) (let ((_let_2 (= tptp.upwards_well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) Y) (not (@ X W)))))))))))) (let ((_let_3 (= tptp.well_founded (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X (-> $$unsorted Bool)) (Z $$unsorted)) (=> (@ X Z) (exists ((Y $$unsorted)) (and (@ X Y) (forall ((W $$unsorted)) (=> (@ (@ R Y) W) (not (@ X W)))))))))))) (let ((_let_4 (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))))) (let ((_let_5 (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))))) (let ((_let_6 (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))) (let ((_let_7 (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))))) (let ((_let_8 (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))))) (let ((_let_9 (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))))) (let ((_let_10 (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))))) (let ((_let_11 (= tptp.transitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ R X))) (=> (and (@ _let_1 Y) (@ (@ R Y) Z)) (@ _let_1 Z)))))))) (let ((_let_12 (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))))) (let ((_let_13 (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))) (let ((_let_14 (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))))) (let ((_let_15 (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))) (let ((_let_16 (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))))) (let ((_let_17 (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))))) (let ((_let_18 (= tptp.is_rel_on (lambda ((R (-> $$unsorted $$unsorted Bool)) (A (-> $$unsorted Bool)) (B (-> $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (and (@ A X) (@ B Y)))))))) (let ((_let_19 (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))))) (let ((_let_20 (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))))) (let ((_let_21 (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))))) (let ((_let_22 (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))))) (let ((_let_23 (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))) (let ((_let_24 (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))) (let ((_let_25 (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))) (let ((_let_26 (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))) (let ((_let_27 (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))) (let ((_let_28 (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))) (let ((_let_29 (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))) (let ((_let_30 (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))) (let ((_let_31 (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))) (let ((_let_32 (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))) (let ((_let_33 (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))) (let ((_let_34 (= tptp.emptyset (lambda ((X $$unsorted)) false)))) (let ((_let_35 (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_36 (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))) (let ((_let_37 (forall ((X $$unsorted)) (not (ho_5 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 X) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))))) (let ((_let_38 (ho_5 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_39 (not _let_37))) (let ((_let_40 (ho_8 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_41 (ho_5 _let_40 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_42 (= _let_41 _let_39))) (let ((_let_43 (forall ((BOUND_VARIABLE_1579 |u_(-> $$unsorted $$unsorted Bool)|) (BOUND_VARIABLE_1548 $$unsorted)) (= (ho_5 (ho_8 k_7 BOUND_VARIABLE_1579) BOUND_VARIABLE_1548) (not (forall ((X $$unsorted)) (not (ho_5 (ho_6 BOUND_VARIABLE_1579 X) BOUND_VARIABLE_1548)))))))) (let ((_let_44 (forall ((u |u_(-> $$unsorted Bool)|) (e Bool) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> $$unsorted Bool)|) (y |u_(-> $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> $$unsorted $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i $$unsorted)) (not (forall ((v |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((ii $$unsorted)) (= (ho_6 v ii) (ite (= i ii) e (ho_6 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> $$unsorted $$unsorted Bool)|) (y |u_(-> $$unsorted $$unsorted Bool)|)) (or (not (forall ((z $$unsorted)) (= (ho_6 x z) (ho_6 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (e |u_(-> $$unsorted Bool)|) (i |u_(-> $$unsorted $$unsorted Bool)|)) (not (forall ((v |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (not (forall ((ii |u_(-> $$unsorted $$unsorted Bool)|)) (= (ho_8 v ii) (ite (= i ii) e (ho_8 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|) (y |u_(-> _u_(-> $$unsorted $$unsorted Bool)_ $$unsorted Bool)|)) (or (not (forall ((z |u_(-> $$unsorted $$unsorted Bool)|)) (= (ho_8 x z) (ho_8 y z)))) (= x y))))) (let ((_let_50 (forall ((BOUND_VARIABLE_1558 $$unsorted)) (ho_5 k_4 BOUND_VARIABLE_1558)))) (let ((_let_51 (and (forall ((BOUND_VARIABLE_1547 (-> $$unsorted $$unsorted Bool)) (BOUND_VARIABLE_1548 $$unsorted)) (= (not (forall ((X $$unsorted)) (not (@ (@ BOUND_VARIABLE_1547 X) BOUND_VARIABLE_1548)))) (ll_2 BOUND_VARIABLE_1547 BOUND_VARIABLE_1548))) (forall ((BOUND_VARIABLE_1558 $$unsorted)) (ll_3 BOUND_VARIABLE_1558))))) (let ((_let_52 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (PREPROCESS_LEMMA :args (_let_51)) (PREPROCESS :args ((= _let_51 (and _let_43 _let_50))))) (PREPROCESS :args ((and _let_49 _let_48 _let_47 _let_46 _let_45 _let_44)))) :args ((and _let_43 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44))))) (let ((_let_53 (AND_ELIM _let_52 :args (0)))) (let ((_let_54 (ho_5 k_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31))) (let ((_let_55 (= _let_41 _let_54))) (let ((_let_56 (AND_ELIM _let_52 :args (1)))) (let ((_let_57 (forall ((z $$unsorted)) (= (ho_5 (ho_8 k_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9) z) (ho_5 k_4 z))))) (let ((_let_58 (not _let_55))) (let ((_let_59 (= k_4 _let_40))) (let ((_let_60 (not _let_57))) (let ((_let_61 (or _let_60 _let_59))) (let ((_let_62 (AND_ELIM _let_52 :args (6)))) (let ((_let_63 (forall ((Y $$unsorted)) (not (ho_5 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) Y))))) (let ((_let_64 (not _let_63))) (let ((_let_65 (and _let_64 _let_59))) (let ((_let_66 (not _let_59))) (let ((_let_67 (forall ((Y $$unsorted)) (ho_5 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y) Y)))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_65))) (let ((_let_70 (forall ((BOUND_VARIABLE_1602 |u_(-> $$unsorted $$unsorted Bool)|) (BOUND_VARIABLE_1440 $$unsorted)) (or (not (forall ((Y $$unsorted)) (ho_5 (ho_6 BOUND_VARIABLE_1602 Y) Y))) (and (not (forall ((Y $$unsorted)) (not (ho_5 (ho_6 BOUND_VARIABLE_1602 BOUND_VARIABLE_1440) Y)))) (= k_4 (ho_8 k_7 BOUND_VARIABLE_1602))))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (not _let_70))) (let ((_let_73 (not (forall ((R (-> $$unsorted $$unsorted Bool)) (BOUND_VARIABLE_1440 $$unsorted)) (or (not (forall ((Y $$unsorted)) (@ (@ R Y) Y))) (and (not (forall ((Y $$unsorted)) (not (@ (@ R BOUND_VARIABLE_1440) Y)))) (= (@ ll_2 R) ll_3))))))) (let ((_let_74 (ASSUME :args (_let_36)))) (let ((_let_75 (ASSUME :args (_let_35)))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (ASSUME :args (_let_31)))) (let ((_let_80 (ASSUME :args (_let_30)))) (let ((_let_81 (ASSUME :args (_let_29)))) (let ((_let_82 (ASSUME :args (_let_28)))) (let ((_let_83 (ASSUME :args (_let_27)))) (let ((_let_84 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args ((= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (ASSUME :args (_let_22)))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (ASSUME :args (_let_20)))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (ASSUME :args (_let_17)))) (let ((_let_94 (ASSUME :args (_let_16)))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (ASSUME :args (_let_14)))) (let ((_let_97 (ASSUME :args (_let_13)))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (ASSUME :args (_let_7)))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (ASSUME :args (_let_5)))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74) :args ((not (forall ((R (-> $$unsorted $$unsorted Bool))) (or (not (@ (@ tptp.sub_rel (@ tptp.id_rel (lambda ((BOUND_VARIABLE_1365 $$unsorted)) true))) R)) (and (@ (@ tptp.subset (lambda ((BOUND_VARIABLE_1365 $$unsorted)) true)) (@ tptp.rel_domain R)) (= (@ tptp.rel_codomain R) (lambda ((BOUND_VARIABLE_1365 $$unsorted)) true)))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((R (-> $$unsorted $$unsorted Bool)) (BOUND_VARIABLE_1440 $$unsorted)) (or (not (forall ((Y $$unsorted)) (@ (@ R Y) Y))) (and (not (forall ((Y $$unsorted)) (not (@ (@ R BOUND_VARIABLE_1440) Y)))) (= (lambda ((BOUND_VARIABLE_1365 $$unsorted)) true) (lambda ((Y $$unsorted)) (not (forall ((X $$unsorted)) (not (@ (@ R X) Y)))))))))) _let_73))) (PREPROCESS :args ((= _let_73 _let_72))))))) (let ((_let_107 (or))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_106) :args (_let_72))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_70))) (REFL :args (_let_71)) :args _let_107)) _let_106 :args (_let_71 true _let_70)))) (let ((_let_109 (ho_5 (ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_110 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG (REFL :args (_let_69)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_107)) :args ((or _let_67 _let_69))) _let_108 :args (_let_67 true _let_69)))) (let ((_let_111 (_let_67))) (let ((_let_112 (ASSUME :args _let_111))) (let ((_let_113 (_let_63))) (let ((_let_114 (_let_65))) (let ((_let_115 (_let_60))) (let ((_let_116 (not _let_42))) (let ((_let_117 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_ENUM))) (let ((_let_118 (_let_37))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_118) :args _let_117) :args _let_118)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args _let_117) :args _let_111)) _let_110 :args (_let_38 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_42)) (CONG (REFL :args (_let_116)) (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_37))) :args _let_107)) :args ((or _let_41 _let_37 _let_116))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args (_let_55)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_115)) :args _let_115)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_57))) (REFL :args (_let_58)) :args _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_59 _let_60 (not _let_61)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_114) (CONG (REFL :args _let_114) (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) (REFL :args (_let_66)) :args _let_107)) :args ((or _let_63 _let_65 _let_66))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_113) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_113)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 Y)))) :args _let_111)) _let_110 :args (_let_109 false _let_67)) :args (_let_64 false _let_109)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_69 1)) _let_108 :args ((not _let_65) true _let_69)) :args (_let_66 true _let_63 true _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_40 k_4 QUANTIFIERS_INST_ENUM)) :args (_let_45)))) _let_62 :args (_let_61 false _let_45)) :args (_let_60 true _let_59 false _let_61)) :args (_let_58 true _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_50))) _let_56 :args (_let_54 false _let_50)) :args ((not _let_41) true _let_55 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_53 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_31 QUANTIFIERS_INST_E_MATCHING ((ho_5 (ho_8 k_7 BOUND_VARIABLE_1579) BOUND_VARIABLE_1548)))) :args (_let_43))) _let_53 :args (_let_42 false _let_43)) :args (_let_37 true _let_41 false _let_42)) :args (false false _let_38 false _let_37)) :args (_let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_4 _let_3 _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.58 )
% 0.19/0.58 % SZS output end Proof for SET669^3
% 0.19/0.58 % cvc5---1.0.5 exiting
% 0.19/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------