TSTP Solution File: SET647^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET647^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 14:39:44 EDT 2023
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET647^3 : TPTP v8.1.2. Released v3.6.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.36 % Computer : n026.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 12:53:03 EDT 2023
% 0.20/0.36 % CPUTime :
% 0.21/0.49 %----Proving TH0
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 % File : SET647^3 : TPTP v8.1.2. Released v3.6.0.
% 0.21/0.50 % Domain : Set Theory
% 0.21/0.50 % Problem : Domain of R (X to Y) a subset of X => R is (X to range of R)
% 0.21/0.50 % Version : [BS+08] axioms.
% 0.21/0.50 % English : If the domain of a relation R from X to Y is a subset of X,
% 0.21/0.50 % R is a relation from X to the range of R.
% 0.21/0.50
% 0.21/0.50 % Refs : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
% 0.21/0.50 % : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
% 0.21/0.50 % : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% 0.21/0.50 % Source : [Ben08]
% 0.21/0.50 % Names :
% 0.21/0.50
% 0.21/0.50 % Status : Theorem
% 0.21/0.50 % Rating : 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 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, 0.33 v3.7.0
% 0.21/0.50 % Syntax : Number of formulae : 71 ( 35 unt; 35 typ; 35 def)
% 0.21/0.50 % Number of atoms : 91 ( 43 equ; 0 cnn)
% 0.21/0.50 % Maximal formula atoms : 5 ( 2 avg)
% 0.21/0.50 % Number of connectives : 133 ( 8 ~; 5 |; 18 &; 91 @)
% 0.21/0.50 % ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% 0.21/0.50 % Maximal formula depth : 7 ( 1 avg)
% 0.21/0.50 % Number of types : 2 ( 0 usr)
% 0.21/0.50 % Number of type conns : 215 ( 215 >; 0 *; 0 +; 0 <<)
% 0.21/0.50 % Number of symbols : 42 ( 40 usr; 6 con; 0-4 aty)
% 0.21/0.50 % Number of variables : 109 ( 80 ^; 21 !; 8 ?; 109 :)
% 0.21/0.50 % SPC : TH0_THM_EQU_NAR
% 0.21/0.50
% 0.21/0.50 % Comments :
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Include basic set theory definitions
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(in_decl,type,
% 0.21/0.50 in: $i > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(in,definition,
% 0.21/0.50 ( in
% 0.21/0.50 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(is_a_decl,type,
% 0.21/0.50 is_a: $i > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(is_a,definition,
% 0.21/0.50 ( is_a
% 0.21/0.50 = ( ^ [X: $i,M: $i > $o] : ( M @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(emptyset_decl,type,
% 0.21/0.50 emptyset: $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(emptyset,definition,
% 0.21/0.50 ( emptyset
% 0.21/0.50 = ( ^ [X: $i] : $false ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(unord_pair_decl,type,
% 0.21/0.50 unord_pair: $i > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(unord_pair,definition,
% 0.21/0.50 ( unord_pair
% 0.21/0.50 = ( ^ [X: $i,Y: $i,U: $i] :
% 0.21/0.50 ( ( U = X )
% 0.21/0.50 | ( U = Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(singleton_decl,type,
% 0.21/0.50 singleton: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(singleton,definition,
% 0.21/0.50 ( singleton
% 0.21/0.50 = ( ^ [X: $i,U: $i] : ( U = X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(union_decl,type,
% 0.21/0.50 union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(union,definition,
% 0.21/0.50 ( union
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 | ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(excl_union_decl,type,
% 0.21/0.50 excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(excl_union,definition,
% 0.21/0.50 ( excl_union
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.50 ( ( ( X @ U )
% 0.21/0.50 & ~ ( Y @ U ) )
% 0.21/0.50 | ( ~ ( X @ U )
% 0.21/0.50 & ( Y @ U ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(intersection_decl,type,
% 0.21/0.50 intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(intersection,definition,
% 0.21/0.50 ( intersection
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 & ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(setminus_decl,type,
% 0.21/0.50 setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(setminus,definition,
% 0.21/0.50 ( setminus
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 & ~ ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(complement_decl,type,
% 0.21/0.50 complement: ( $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(complement,definition,
% 0.21/0.50 ( complement
% 0.21/0.50 = ( ^ [X: $i > $o,U: $i] :
% 0.21/0.50 ~ ( X @ U ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(disjoint_decl,type,
% 0.21/0.50 disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(disjoint,definition,
% 0.21/0.50 ( disjoint
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.21/0.50 ( ( intersection @ X @ Y )
% 0.21/0.50 = emptyset ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(subset_decl,type,
% 0.21/0.50 subset: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(subset,definition,
% 0.21/0.50 ( subset
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.21/0.50 ! [U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 => ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(meets_decl,type,
% 0.21/0.50 meets: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(meets,definition,
% 0.21/0.50 ( meets
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.21/0.50 ? [U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 & ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(misses_decl,type,
% 0.21/0.50 misses: ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(misses,definition,
% 0.21/0.50 ( misses
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o] :
% 0.21/0.50 ~ ? [U: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 & ( Y @ U ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 %----Include definitions for relations
% 0.21/0.50 %------------------------------------------------------------------------------
% 0.21/0.50 thf(cartesian_product_decl,type,
% 0.21/0.50 cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(cartesian_product,definition,
% 0.21/0.50 ( cartesian_product
% 0.21/0.50 = ( ^ [X: $i > $o,Y: $i > $o,U: $i,V: $i] :
% 0.21/0.50 ( ( X @ U )
% 0.21/0.50 & ( Y @ V ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(pair_rel_decl,type,
% 0.21/0.50 pair_rel: $i > $i > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(pair_rel,definition,
% 0.21/0.50 ( pair_rel
% 0.21/0.50 = ( ^ [X: $i,Y: $i,U: $i,V: $i] :
% 0.21/0.50 ( ( U = X )
% 0.21/0.50 | ( V = Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(id_rel_decl,type,
% 0.21/0.50 id_rel: ( $i > $o ) > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(id_rel,definition,
% 0.21/0.50 ( id_rel
% 0.21/0.50 = ( ^ [S: $i > $o,X: $i,Y: $i] :
% 0.21/0.50 ( ( S @ X )
% 0.21/0.50 & ( X = Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(sub_rel_decl,type,
% 0.21/0.50 sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(sub_rel,definition,
% 0.21/0.50 ( sub_rel
% 0.21/0.50 = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] :
% 0.21/0.50 ! [X: $i,Y: $i] :
% 0.21/0.50 ( ( R1 @ X @ Y )
% 0.21/0.50 => ( R2 @ X @ Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(is_rel_on_decl,type,
% 0.21/0.50 is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(is_rel_on,definition,
% 0.21/0.50 ( is_rel_on
% 0.21/0.50 = ( ^ [R: $i > $i > $o,A: $i > $o,B: $i > $o] :
% 0.21/0.50 ! [X: $i,Y: $i] :
% 0.21/0.50 ( ( R @ X @ Y )
% 0.21/0.50 => ( ( A @ X )
% 0.21/0.50 & ( B @ Y ) ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(restrict_rel_domain_decl,type,
% 0.21/0.50 restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(restrict_rel_domain,definition,
% 0.21/0.50 ( restrict_rel_domain
% 0.21/0.50 = ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
% 0.21/0.50 ( ( S @ X )
% 0.21/0.50 & ( R @ X @ Y ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(rel_diagonal_decl,type,
% 0.21/0.50 rel_diagonal: $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(rel_diagonal,definition,
% 0.21/0.50 ( rel_diagonal
% 0.21/0.50 = ( ^ [X: $i,Y: $i] : ( X = Y ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(rel_composition_decl,type,
% 0.21/0.50 rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(rel_composition,definition,
% 0.21/0.50 ( rel_composition
% 0.21/0.50 = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o,X: $i,Z: $i] :
% 0.21/0.50 ? [Y: $i] :
% 0.21/0.50 ( ( R1 @ X @ Y )
% 0.21/0.50 & ( R2 @ Y @ Z ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(reflexive_decl,type,
% 0.21/0.50 reflexive: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(reflexive,definition,
% 0.21/0.50 ( reflexive
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(irreflexive_decl,type,
% 0.21/0.50 irreflexive: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(irreflexive,definition,
% 0.21/0.50 ( irreflexive
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [X: $i] :
% 0.21/0.50 ~ ( R @ X @ X ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(symmetric_decl,type,
% 0.21/0.50 symmetric: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(symmetric,definition,
% 0.21/0.50 ( symmetric
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [X: $i,Y: $i] :
% 0.21/0.50 ( ( R @ X @ Y )
% 0.21/0.50 => ( R @ Y @ X ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(transitive_decl,type,
% 0.21/0.50 transitive: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(transitive,definition,
% 0.21/0.50 ( transitive
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ! [X: $i,Y: $i,Z: $i] :
% 0.21/0.50 ( ( ( R @ X @ Y )
% 0.21/0.50 & ( R @ Y @ Z ) )
% 0.21/0.50 => ( R @ X @ Z ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(equiv_rel__decl,type,
% 0.21/0.50 equiv_rel: ( $i > $i > $o ) > $o ).
% 0.21/0.50
% 0.21/0.50 thf(equiv_rel,definition,
% 0.21/0.50 ( equiv_rel
% 0.21/0.50 = ( ^ [R: $i > $i > $o] :
% 0.21/0.50 ( ( reflexive @ R )
% 0.21/0.50 & ( symmetric @ R )
% 0.21/0.50 & ( transitive @ R ) ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(rel_codomain_decl,type,
% 0.21/0.50 rel_codomain: ( $i > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(rel_codomain,definition,
% 0.21/0.50 ( rel_codomain
% 0.21/0.50 = ( ^ [R: $i > $i > $o,Y: $i] :
% 0.21/0.50 ? [X: $i] : ( R @ X @ Y ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(rel_domain_decl,type,
% 0.21/0.50 rel_domain: ( $i > $i > $o ) > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(rel_domain,definition,
% 0.21/0.50 ( rel_domain
% 0.21/0.50 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.21/0.50 ? [Y: $i] : ( R @ X @ Y ) ) ) ).
% 0.21/0.50
% 0.21/0.50 thf(rel_inverse_decl,type,
% 0.21/0.50 rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
% 0.21/0.50
% 0.21/0.50 thf(rel_inverse,definition,
% 0.21/0.51 ( rel_inverse
% 0.21/0.51 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(equiv_classes_decl,type,
% 0.21/0.51 equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(equiv_classes,definition,
% 0.21/0.51 ( equiv_classes
% 0.21/0.51 = ( ^ [R: $i > $i > $o,S1: $i > $o] :
% 0.21/0.51 ? [X: $i] :
% 0.21/0.51 ( ( S1 @ X )
% 0.21/0.51 & ! [Y: $i] :
% 0.21/0.51 ( ( S1 @ Y )
% 0.21/0.51 <=> ( R @ X @ Y ) ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(restrict_rel_codomain_decl,type,
% 0.21/0.51 restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(restrict_rel_codomain,definition,
% 0.21/0.51 ( restrict_rel_codomain
% 0.21/0.51 = ( ^ [R: $i > $i > $o,S: $i > $o,X: $i,Y: $i] :
% 0.21/0.51 ( ( S @ Y )
% 0.21/0.51 & ( R @ X @ Y ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(rel_field_decl,type,
% 0.21/0.51 rel_field: ( $i > $i > $o ) > $i > $o ).
% 0.21/0.51
% 0.21/0.51 thf(rel_field,definition,
% 0.21/0.51 ( rel_field
% 0.21/0.51 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.21/0.51 ( ( rel_domain @ R @ X )
% 0.21/0.51 | ( rel_codomain @ R @ X ) ) ) ) ).
% 0.21/0.51
% 0.21/0.51 thf(well_founded_decl,type,
% 0.21/0.51 well_founded: ( $i > $i > $o ) > $o ).
% 0.21/0.51
% 0.21/0.51 thf(well_founded,definition,
% 0.21/0.52 ( well_founded
% 0.21/0.52 = ( ^ [R: $i > $i > $o] :
% 0.21/0.52 ! [X: $i > $o,Z: $i] :
% 0.21/0.52 ( ( X @ Z )
% 0.21/0.52 => ? [Y: $i] :
% 0.21/0.52 ( ( X @ Y )
% 0.21/0.52 & ! [W: $i] :
% 0.21/0.52 ( ( R @ Y @ W )
% 0.21/0.52 => ~ ( X @ W ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 thf(upwards_well_founded_decl,type,
% 0.21/0.52 upwards_well_founded: ( $i > $i > $o ) > $o ).
% 0.21/0.52
% 0.21/0.52 thf(upwards_well_founded,definition,
% 0.21/0.52 ( upwards_well_founded
% 0.21/0.52 = ( ^ [R: $i > $i > $o] :
% 0.21/0.52 ! [X: $i > $o,Z: $i] :
% 0.21/0.52 ( ( X @ Z )
% 0.21/0.52 => ? [Y: $i] :
% 0.21/0.52 ( ( X @ Y )
% 0.21/0.52 & ! [W: $i] :
% 0.21/0.52 ( ( R @ Y @ Y )
% 0.21/0.52 => ~ ( X @ W ) ) ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 thf(thm,conjecture,
% 0.21/0.52 ! [R: $i > $i > $o,X: $i > $o] :
% 0.21/0.52 ( ( subset @ ( rel_domain @ R ) @ X )
% 0.21/0.52 => ( sub_rel @ R @ ( cartesian_product @ X @ ( rel_codomain @ R ) ) ) ) ).
% 0.21/0.52
% 0.21/0.52 %------------------------------------------------------------------------------
% 0.21/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.8yYNwlh64z/cvc5---1.0.5_2280.p...
% 0.21/0.52 (declare-sort $$unsorted 0)
% 0.21/0.52 (declare-fun tptp.in ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.in (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.21/0.52 (declare-fun tptp.is_a ($$unsorted (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.is_a (lambda ((X $$unsorted) (M (-> $$unsorted Bool))) (@ M X))))
% 0.21/0.52 (declare-fun tptp.emptyset ($$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.emptyset (lambda ((X $$unsorted)) false)))
% 0.21/0.52 (declare-fun tptp.unord_pair ($$unsorted $$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.unord_pair (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (= U X) (= U Y)))))
% 0.21/0.52 (declare-fun tptp.singleton ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.singleton (lambda ((X $$unsorted) (U $$unsorted)) (= U X))))
% 0.21/0.52 (declare-fun tptp.union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (or (@ X U) (@ Y U)))))
% 0.21/0.52 (declare-fun tptp.excl_union ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.excl_union (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (let ((_let_1 (@ Y U))) (let ((_let_2 (@ X U))) (or (and _let_2 (not _let_1)) (and (not _let_2) _let_1)))))))
% 0.21/0.52 (declare-fun tptp.intersection ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.intersection (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (@ Y U)))))
% 0.21/0.52 (declare-fun tptp.setminus ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.setminus (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted)) (and (@ X U) (not (@ Y U))))))
% 0.21/0.52 (declare-fun tptp.complement ((-> $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.complement (lambda ((X (-> $$unsorted Bool)) (U $$unsorted)) (not (@ X U)))))
% 0.21/0.52 (declare-fun tptp.disjoint ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (@ (@ tptp.intersection X) Y) tptp.emptyset))))
% 0.21/0.52 (declare-fun tptp.subset ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.subset (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (forall ((U $$unsorted)) (=> (@ X U) (@ Y U))))))
% 0.21/0.52 (declare-fun tptp.meets ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.meets (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (exists ((U $$unsorted)) (and (@ X U) (@ Y U))))))
% 0.21/0.52 (declare-fun tptp.misses ((-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.misses (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (not (exists ((U $$unsorted)) (and (@ X U) (@ Y U)))))))
% 0.21/0.52 (declare-fun tptp.cartesian_product ((-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.cartesian_product (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (U $$unsorted) (V $$unsorted)) (and (@ X U) (@ Y V)))))
% 0.21/0.52 (declare-fun tptp.pair_rel ($$unsorted $$unsorted $$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.pair_rel (lambda ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (= U X) (= V Y)))))
% 0.21/0.52 (declare-fun tptp.id_rel ((-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.id_rel (lambda ((S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (= X Y)))))
% 0.21/0.52 (declare-fun tptp.sub_rel ((-> $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.sub_rel (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R1 X) Y) (@ (@ R2 X) Y))))))
% 0.21/0.52 (declare-fun tptp.is_rel_on ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.52 (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)))))))
% 0.21/0.52 (declare-fun tptp.restrict_rel_domain ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.restrict_rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S X) (@ (@ R X) Y)))))
% 0.21/0.52 (declare-fun tptp.rel_diagonal ($$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.rel_diagonal (lambda ((X $$unsorted) (Y $$unsorted)) (= X Y))))
% 0.21/0.52 (declare-fun tptp.rel_composition ((-> $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.rel_composition (lambda ((R1 (-> $$unsorted $$unsorted Bool)) (R2 (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Z $$unsorted)) (exists ((Y $$unsorted)) (and (@ (@ R1 X) Y) (@ (@ R2 Y) Z))))))
% 0.21/0.52 (declare-fun tptp.reflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.reflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))))
% 0.21/0.52 (declare-fun tptp.irreflexive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.irreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))
% 0.21/0.52 (declare-fun tptp.symmetric ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.symmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))))
% 0.21/0.52 (declare-fun tptp.transitive ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.transitive (lambda ((R (-> $$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)))))))
% 0.21/0.52 (declare-fun tptp.equiv_rel ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.52 (assert (= tptp.equiv_rel (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.reflexive R) (@ tptp.symmetric R) (@ tptp.transitive R)))))
% 0.21/0.52 (declare-fun tptp.rel_codomain ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.52 (assert (= tptp.rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (Y $$unsorted)) (exists ((X $$unsorted)) (@ (@ R X) Y)))))
% 0.21/0.55 (declare-fun tptp.rel_domain ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.rel_domain (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ R X) Y)))))
% 0.21/0.55 (declare-fun tptp.rel_inverse ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.rel_inverse (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))))
% 0.21/0.55 (declare-fun tptp.equiv_classes ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool)) Bool)
% 0.21/0.55 (assert (= tptp.equiv_classes (lambda ((R (-> $$unsorted $$unsorted Bool)) (S1 (-> $$unsorted Bool))) (exists ((X $$unsorted)) (and (@ S1 X) (forall ((Y $$unsorted)) (= (@ S1 Y) (@ (@ R X) Y))))))))
% 0.21/0.55 (declare-fun tptp.restrict_rel_codomain ((-> $$unsorted $$unsorted Bool) (-> $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.restrict_rel_codomain (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ S Y) (@ (@ R X) Y)))))
% 0.21/0.55 (declare-fun tptp.rel_field ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.21/0.55 (assert (= tptp.rel_field (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (or (@ (@ tptp.rel_domain R) X) (@ (@ tptp.rel_codomain R) X)))))
% 0.21/0.55 (declare-fun tptp.well_founded ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.55 (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)))))))))))
% 0.21/0.55 (declare-fun tptp.upwards_well_founded ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.21/0.55 (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)))))))))))
% 0.21/0.55 (assert (not (forall ((R (-> $$unsorted $$unsorted Bool)) (X (-> $$unsorted Bool))) (=> (@ (@ tptp.subset (@ tptp.rel_domain R)) X) (@ (@ tptp.sub_rel R) (@ (@ tptp.cartesian_product X) (@ tptp.rel_codomain R)))))))
% 0.21/0.55 (set-info :filename cvc5---1.0.5_2280)
% 0.21/0.55 (check-sat-assuming ( true ))
% 0.21/0.55 ------- get file name : TPTP file name is SET647^3
% 0.21/0.55 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2280.smt2...
% 0.21/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for SET647^3
% 0.21/0.55 % SZS output start Proof for SET647^3
% 0.21/0.55 (
% 0.21/0.55 (let ((_let_1 (not (forall ((R (-> $$unsorted $$unsorted Bool)) (X (-> $$unsorted Bool))) (=> (@ (@ tptp.subset (@ tptp.rel_domain R)) X) (@ (@ tptp.sub_rel R) (@ (@ tptp.cartesian_product X) (@ 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 (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_38 (forall ((X $$unsorted)) (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))))) (let ((_let_39 (not _let_38))) (let ((_let_40 (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_41 (and _let_40 _let_39))) (let ((_let_42 (not _let_37))) (let ((_let_43 (forall ((U $$unsorted) (BOUND_VARIABLE_1360 $$unsorted)) (or (not (ho_3 (ho_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 U) BOUND_VARIABLE_1360)) (ho_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 U))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42 _let_41))) (let ((_let_46 (forall ((BOUND_VARIABLE_1515 |u_(-> $$unsorted $$unsorted Bool)|) (BOUND_VARIABLE_1526 |u_(-> $$unsorted Bool)|) (BOUND_VARIABLE_1423 $$unsorted) (BOUND_VARIABLE_1421 $$unsorted)) (or (not (forall ((U $$unsorted) (BOUND_VARIABLE_1360 $$unsorted)) (or (not (ho_3 (ho_2 BOUND_VARIABLE_1515 U) BOUND_VARIABLE_1360)) (ho_3 BOUND_VARIABLE_1526 U)))) (not (ho_3 (ho_2 BOUND_VARIABLE_1515 BOUND_VARIABLE_1421) BOUND_VARIABLE_1423)) (and (ho_3 BOUND_VARIABLE_1526 BOUND_VARIABLE_1421) (not (forall ((X $$unsorted)) (not (ho_3 (ho_2 BOUND_VARIABLE_1515 X) BOUND_VARIABLE_1423))))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (not _let_46))) (let ((_let_49 (ASSUME :args (_let_36)))) (let ((_let_50 (ASSUME :args (_let_35)))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_32)) (MACRO_SR_EQ_INTRO :args (_let_32 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (ASSUME :args (_let_31)))) (let ((_let_55 (ASSUME :args (_let_30)))) (let ((_let_56 (ASSUME :args (_let_29)))) (let ((_let_57 (ASSUME :args (_let_28)))) (let ((_let_58 (ASSUME :args (_let_27)))) (let ((_let_59 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_26)) (MACRO_SR_EQ_INTRO :args (_let_26 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args ((= tptp.disjoint (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= tptp.emptyset (@ (@ tptp.intersection X) Y)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (ASSUME :args (_let_22)))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (ASSUME :args (_let_20)))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (ASSUME :args (_let_17)))) (let ((_let_69 (ASSUME :args (_let_16)))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (ASSUME :args (_let_14)))) (let ((_let_72 (ASSUME :args (_let_13)))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_78 (ASSUME :args (_let_7)))) (let ((_let_79 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_80 (ASSUME :args (_let_5)))) (let ((_let_81 (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_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49) :args ((not (forall ((R (-> $$unsorted $$unsorted Bool)) (X (-> $$unsorted Bool))) (or (not (@ (@ tptp.subset (@ tptp.rel_domain R)) X)) (@ (@ tptp.sub_rel R) (@ (@ tptp.cartesian_product X) (@ tptp.rel_codomain R)))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (forall ((R (-> $$unsorted $$unsorted Bool)) (X (-> $$unsorted Bool)) (BOUND_VARIABLE_1423 $$unsorted) (BOUND_VARIABLE_1421 $$unsorted)) (or (not (forall ((U $$unsorted) (BOUND_VARIABLE_1360 $$unsorted)) (or (not (@ (@ R U) BOUND_VARIABLE_1360)) (@ X U)))) (not (@ (@ R BOUND_VARIABLE_1421) BOUND_VARIABLE_1423)) (and (@ X BOUND_VARIABLE_1421) (not (forall ((X $$unsorted)) (not (@ (@ R X) BOUND_VARIABLE_1423)))))))) _let_48))))))) (let ((_let_82 (or))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_81) :args (_let_48))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_46))) (REFL :args (_let_47)) :args _let_82)) _let_81 :args (_let_47 true _let_46)))) (let ((_let_84 (REFL :args (_let_45)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_37))) :args _let_82)) :args ((or _let_37 _let_45))) _let_83 :args (_let_37 true _let_45)))) (let ((_let_86 (or _let_42 _let_40))) (let ((_let_87 (_let_43))) (let ((_let_88 (not _let_40))) (let ((_let_89 (_let_41))) (let ((_let_90 (_let_38))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_90) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_90)) :args ((or _let_42 _let_39))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_89) (CONG (REFL :args _let_89) (REFL :args (_let_88)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_82)) :args ((or _let_38 _let_41 _let_88))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 2)) _let_83 :args ((not _let_41) true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_86)) :args ((or _let_42 _let_40 (not _let_86)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_87) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_87)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG _let_84 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_82)) :args ((or _let_43 _let_45))) _let_83 :args (_let_43 true _let_45)) :args (_let_86 false _let_43)) :args (_let_40 false _let_37 false _let_86)) :args (_let_38 true _let_41 false _let_40)) _let_85 :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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56 )
% 0.21/0.56 % SZS output end Proof for SET647^3
% 0.21/0.56 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------