TSTP Solution File: SEV441^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEV441^1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 19:22:32 EDT 2023
% Result : Satisfiable 0.15s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV441^1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.10 % Command : do_cvc5 %s %d
% 0.10/0.30 % Computer : n004.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 24 02:07:23 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.41 %----Proving TH0
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : SEV441^1 : TPTP v8.1.2. Released v6.4.0.
% 0.15/0.41 % Domain : Set Theory
% 0.15/0.41 % Problem : Binary relations
% 0.15/0.41 % Version : [Nei08] axioms.
% 0.15/0.41 % English :
% 0.15/0.41
% 0.15/0.41 % Refs : [BN99] Baader & Nipkow (1999), Term Rewriting and All That
% 0.15/0.41 % : [Nei08] Neis (2008), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [TPTP]
% 0.15/0.41 % Names :
% 0.15/0.41
% 0.15/0.41 % Status : Satisfiable
% 0.15/0.41 % Rating : 0.00 v7.4.0, 0.33 v6.4.0
% 0.15/0.41 % Syntax : Number of formulae : 58 ( 29 unt; 29 typ; 29 def)
% 0.15/0.41 % Number of atoms : 91 ( 33 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 1 ( 3 avg)
% 0.15/0.41 % Number of connectives : 158 ( 4 ~; 4 |; 12 &; 122 @)
% 0.15/0.41 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 1 ( 1 avg)
% 0.15/0.41 % Number of types : 2 ( 0 usr)
% 0.15/0.41 % Number of type conns : 197 ( 197 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 30 ( 29 usr; 0 con; 1-3 aty)
% 0.15/0.41 % Number of variables : 86 ( 43 ^; 38 !; 5 ?; 86 :)
% 0.15/0.41 % SPC : TH0_SAT_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments :
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 %----Binary relations
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 %----BASICS
% 0.15/0.41 %----Subrelation
% 0.15/0.41 thf(subrel_type,type,
% 0.15/0.41 subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(subrel,definition,
% 0.15/0.41 ( subrel
% 0.15/0.41 = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i] :
% 0.15/0.41 ( ( R @ X @ Y )
% 0.15/0.41 => ( S @ X @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Inverse
% 0.15/0.41 thf(inv_type,type,
% 0.15/0.41 inv: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(inverse,definition,
% 0.15/0.41 ( inv
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] : ( R @ Y @ X ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----IDEMPOTENCY, INFLATION, MONOTONICITY
% 0.15/0.41 %----Idempotency
% 0.15/0.41 thf(idem_type,type,
% 0.15/0.41 idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(idempotent,definition,
% 0.15/0.41 ( idem
% 0.15/0.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.15/0.41 ! [R: $i > $i > $o] :
% 0.15/0.41 ( ( F @ ( F @ R ) )
% 0.15/0.41 = ( F @ R ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Being inflationary
% 0.15/0.41 thf(infl_type,type,
% 0.15/0.41 infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(inflationary,definition,
% 0.15/0.41 ( infl
% 0.15/0.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.15/0.41 ! [R: $i > $i > $o] : ( subrel @ R @ ( F @ R ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Monotonicity
% 0.15/0.41 thf(mono_type,type,
% 0.15/0.41 mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(monotonic,definition,
% 0.15/0.41 ( mono
% 0.15/0.41 = ( ^ [F: ( $i > $i > $o ) > $i > $i > $o] :
% 0.15/0.41 ! [R: $i > $i > $o,S: $i > $i > $o] :
% 0.15/0.41 ( ( subrel @ R @ S )
% 0.15/0.41 => ( subrel @ ( F @ R ) @ ( F @ S ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----REFLEXIVITY, IRREFLEXIVITY, AND REFLEXIVE CLOSURE
% 0.15/0.41 %----Reflexivity
% 0.15/0.41 thf(refl_type,type,
% 0.15/0.41 refl: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(reflexive,definition,
% 0.15/0.41 ( refl
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i] : ( R @ X @ X ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Irreflexivity
% 0.15/0.41 thf(irrefl_type,type,
% 0.15/0.41 irrefl: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(irreflexive,definition,
% 0.15/0.41 ( irrefl
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i] :
% 0.15/0.41 ~ ( R @ X @ X ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Reflexive closure
% 0.15/0.41 thf(rc_type,type,
% 0.15/0.41 rc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(reflexive_closure,definition,
% 0.15/0.41 ( rc
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.15/0.41 ( ( X = Y )
% 0.15/0.41 | ( R @ X @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----SYMMETRY, ANTISYMMETRY, ASYMMETRY, AND SYMMETRIC CLOSURE
% 0.15/0.41 %----Symmetry
% 0.15/0.41 thf(symm_type,type,
% 0.15/0.41 symm: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(symmetric,definition,
% 0.15/0.41 ( symm
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i] :
% 0.15/0.41 ( ( R @ X @ Y )
% 0.15/0.41 => ( R @ Y @ X ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Antisymmetry
% 0.15/0.41 thf(antisymm_type,type,
% 0.15/0.41 antisymm: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(antisymmetric,definition,
% 0.15/0.41 ( antisymm
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i] :
% 0.15/0.41 ( ( ( R @ X @ Y )
% 0.15/0.41 & ( R @ Y @ X ) )
% 0.15/0.41 => ( X = Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Asymmetry
% 0.15/0.41 thf(asymm_type,type,
% 0.15/0.41 asymm: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(asymmetric,definition,
% 0.15/0.41 ( asymm
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i] :
% 0.15/0.41 ( ( R @ X @ Y )
% 0.15/0.41 => ~ ( R @ Y @ X ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Symmetric closure
% 0.15/0.41 thf(sc_type,type,
% 0.15/0.41 sc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(symmetric_closure,definition,
% 0.15/0.41 ( sc
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.15/0.41 ( ( R @ Y @ X )
% 0.15/0.41 | ( R @ X @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----TRANSITIVITY AND TRANSITIVE CLOSURE
% 0.15/0.41 %----Transitivity
% 0.15/0.41 thf(trans_type,type,
% 0.15/0.41 trans: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(transitive,definition,
% 0.15/0.41 ( trans
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i,Z: $i] :
% 0.15/0.41 ( ( ( R @ X @ Y )
% 0.15/0.41 & ( R @ Y @ Z ) )
% 0.15/0.41 => ( R @ X @ Z ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Transitive closure
% 0.15/0.41 thf(tc_type,type,
% 0.15/0.41 tc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 % the transitive closure of R is the smallest transitive
% 0.15/0.41 % relation containing R (thanks, Chad!)
% 0.15/0.41 thf(transitive_closure,definition,
% 0.15/0.41 ( tc
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.15/0.41 ! [S: $i > $i > $o] :
% 0.15/0.41 ( ( ( trans @ S )
% 0.15/0.41 & ( subrel @ R @ S ) )
% 0.15/0.41 => ( S @ X @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----TRANSITIVE REFLEXIVE CLOSURE AND TRANSITIVE REFLEXIVE SYMMETRIC CLOSURE
% 0.15/0.41 %----Transitive reflexive closure
% 0.15/0.41 thf(trc_type,type,
% 0.15/0.41 trc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(transitive_reflexive_closure,definition,
% 0.15/0.41 ( trc
% 0.15/0.41 = ( ^ [R: $i > $i > $o] : ( rc @ ( tc @ R ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Transitive reflexive symmetric closure
% 0.15/0.41 thf(trsc_type,type,
% 0.15/0.41 trsc: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(transitive_reflexive_symmetric_closure,definition,
% 0.15/0.41 ( trsc
% 0.15/0.41 = ( ^ [R: $i > $i > $o] : ( sc @ ( rc @ ( tc @ R ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----ORDERS
% 0.15/0.41 %----Being a partial order
% 0.15/0.41 thf(po_type,type,
% 0.15/0.41 po: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(partial_order,definition,
% 0.15/0.41 ( po
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ( ( refl @ R )
% 0.15/0.41 & ( antisymm @ R )
% 0.15/0.41 & ( trans @ R ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Being a strict (partial) order
% 0.15/0.41 thf(so_type,type,
% 0.15/0.41 so: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(strict_order,definition,
% 0.15/0.41 ( so
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ( ( asymm @ R )
% 0.15/0.41 & ( trans @ R ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Totality
% 0.15/0.41 thf(total_type,type,
% 0.15/0.41 total: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(total,definition,
% 0.15/0.41 ( total
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i] :
% 0.15/0.41 ( ( X = Y )
% 0.15/0.41 | ( R @ X @ Y )
% 0.15/0.41 | ( R @ Y @ X ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----TERMINATION AND INDUCTION
% 0.15/0.41 %----Termination
% 0.15/0.41 thf(term_type,type,
% 0.15/0.41 term: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 % axiomatisation: any non-empty subset has an R-maximal element
% 0.15/0.41 thf(terminating,definition,
% 0.15/0.41 ( term
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [A: $i > $o] :
% 0.15/0.41 ( ? [X: $i] : ( A @ X )
% 0.15/0.41 => ? [X: $i] :
% 0.15/0.41 ( ( A @ X )
% 0.15/0.41 & ! [Y: $i] :
% 0.15/0.41 ( ( A @ Y )
% 0.15/0.41 => ~ ( R @ X @ Y ) ) ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Satisfying the induction principle
% 0.15/0.41 thf(ind_type,type,
% 0.15/0.41 ind: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(satisfying_the_induction_principle,definition,
% 0.15/0.41 ( ind
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [P: $i > $o] :
% 0.15/0.41 ( ! [X: $i] :
% 0.15/0.41 ( ! [Y: $i] :
% 0.15/0.41 ( ( tc @ R @ X @ Y )
% 0.15/0.41 => ( P @ Y ) )
% 0.15/0.41 => ( P @ X ) )
% 0.15/0.41 => ! [X: $i] : ( P @ X ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----NORMALIZATION
% 0.15/0.41 %----In normal form
% 0.15/0.41 thf(innf_type,type,
% 0.15/0.41 innf: ( $i > $i > $o ) > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(in_normal_form,definition,
% 0.15/0.41 ( innf
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i] :
% 0.15/0.41 ~ ? [Y: $i] : ( R @ X @ Y ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Normal form of
% 0.15/0.41 thf(nfof_type,type,
% 0.15/0.41 nfof: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(normal_form_of,definition,
% 0.15/0.41 ( nfof
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.15/0.41 ( ( trc @ R @ Y @ X )
% 0.15/0.41 & ( innf @ R @ X ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Normalization
% 0.15/0.41 thf(norm_type,type,
% 0.15/0.41 norm: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(normalizing,definition,
% 0.15/0.41 ( norm
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i] :
% 0.15/0.41 ? [Y: $i] : ( nfof @ R @ Y @ X ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----CONFLUENCE AND FRIENDS
% 0.15/0.41 %----Joinability
% 0.15/0.41 thf(join_type,type,
% 0.15/0.41 join: ( $i > $i > $o ) > $i > $i > $o ).
% 0.15/0.41
% 0.15/0.41 thf(joinable,definition,
% 0.15/0.41 ( join
% 0.15/0.41 = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
% 0.15/0.41 ? [Z: $i] :
% 0.15/0.41 ( ( trc @ R @ X @ Z )
% 0.15/0.41 & ( trc @ R @ Y @ Z ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Local confluence
% 0.15/0.41 thf(lconfl_type,type,
% 0.15/0.41 lconfl: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(locally_confluent,definition,
% 0.15/0.41 ( lconfl
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i,Z: $i] :
% 0.15/0.41 ( ( ( R @ X @ Z )
% 0.15/0.41 & ( R @ X @ Y ) )
% 0.15/0.41 => ( join @ R @ Z @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Semi confluence
% 0.15/0.41 thf(sconfl_type,type,
% 0.15/0.41 sconfl: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(semi_confluent,definition,
% 0.15/0.41 ( sconfl
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i,Z: $i] :
% 0.15/0.41 ( ( ( R @ X @ Z )
% 0.15/0.41 & ( trc @ R @ X @ Y ) )
% 0.15/0.41 => ( join @ R @ Z @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Confluence
% 0.15/0.41 thf(confl_type,type,
% 0.15/0.41 confl: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(confluent,definition,
% 0.15/0.41 ( confl
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i,Z: $i] :
% 0.15/0.41 ( ( ( trc @ R @ X @ Z )
% 0.15/0.41 & ( trc @ R @ X @ Y ) )
% 0.15/0.41 => ( join @ R @ Z @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %----Church-Rosser property
% 0.15/0.41 thf(cr_type,type,
% 0.15/0.41 cr: ( $i > $i > $o ) > $o ).
% 0.15/0.41
% 0.15/0.41 thf(church_rosser,definition,
% 0.15/0.41 ( cr
% 0.15/0.41 = ( ^ [R: $i > $i > $o] :
% 0.15/0.41 ! [X: $i,Y: $i] :
% 0.15/0.41 ( ( trsc @ R @ X @ Y )
% 0.15/0.41 => ( join @ R @ X @ Y ) ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.pf4wQkyzIu/cvc5---1.0.5_979.p...
% 0.15/0.42 (declare-sort $$unsorted 0)
% 0.15/0.42 (declare-fun tptp.subrel ((-> $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.subrel (lambda ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ S X) Y))))))
% 0.15/0.42 (declare-fun tptp.inv ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.inv (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (@ (@ R Y) X))))
% 0.15/0.42 (declare-fun tptp.idem ((-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.idem (lambda ((F (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) (forall ((R (-> $$unsorted $$unsorted Bool))) (let ((_let_1 (@ F R))) (= (@ F _let_1) _let_1))))))
% 0.15/0.42 (declare-fun tptp.infl ((-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.infl (lambda ((F (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) (forall ((R (-> $$unsorted $$unsorted Bool))) (@ (@ tptp.subrel R) (@ F R))))))
% 0.15/0.42 (declare-fun tptp.mono ((-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.mono (lambda ((F (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) (forall ((R (-> $$unsorted $$unsorted Bool)) (S (-> $$unsorted $$unsorted Bool))) (=> (@ (@ tptp.subrel R) S) (@ (@ tptp.subrel (@ F R)) (@ F S)))))))
% 0.15/0.42 (declare-fun tptp.refl ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.refl (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (@ (@ R X) X)))))
% 0.15/0.42 (declare-fun tptp.irrefl ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.irrefl (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (not (@ (@ R X) X))))))
% 0.15/0.42 (declare-fun tptp.rc ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.rc (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (or (= X Y) (@ (@ R X) Y)))))
% 0.15/0.42 (declare-fun tptp.symm ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.symm (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (@ (@ R Y) X))))))
% 0.15/0.42 (declare-fun tptp.antisymm ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.antisymm (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (@ (@ R X) Y) (@ (@ R Y) X)) (= X Y))))))
% 0.15/0.42 (declare-fun tptp.asymm ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.asymm (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ R X) Y) (not (@ (@ R Y) X)))))))
% 0.15/0.42 (declare-fun tptp.sc ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.sc (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (or (@ (@ R Y) X) (@ (@ R X) Y)))))
% 0.15/0.42 (declare-fun tptp.trans ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.trans (lambda ((R (-> $$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)))))))
% 0.15/0.42 (declare-fun tptp.tc ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.tc (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (forall ((S (-> $$unsorted $$unsorted Bool))) (=> (and (@ tptp.trans S) (@ (@ tptp.subrel R) S)) (@ (@ S X) Y))))))
% 0.15/0.42 (declare-fun tptp.trc ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.trc (lambda ((R (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ (@ tptp.rc (@ tptp.tc R)) __flatten_var_0) __flatten_var_1))))
% 0.15/0.42 (declare-fun tptp.trsc ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.trsc (lambda ((R (-> $$unsorted $$unsorted Bool)) (__flatten_var_0 $$unsorted) (__flatten_var_1 $$unsorted)) (@ (@ (@ tptp.sc (@ tptp.rc (@ tptp.tc R))) __flatten_var_0) __flatten_var_1))))
% 0.15/0.42 (declare-fun tptp.po ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.po (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.refl R) (@ tptp.antisymm R) (@ tptp.trans R)))))
% 0.15/0.42 (declare-fun tptp.so ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.so (lambda ((R (-> $$unsorted $$unsorted Bool))) (and (@ tptp.asymm R) (@ tptp.trans R)))))
% 0.15/0.42 (declare-fun tptp.total ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.total (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (@ (@ R X) Y) (@ (@ R Y) X))))))
% 0.15/0.42 (declare-fun tptp.term ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.term (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((A (-> $$unsorted Bool))) (=> (exists ((X $$unsorted)) (@ A X)) (exists ((X $$unsorted)) (and (@ A X) (forall ((Y $$unsorted)) (=> (@ A Y) (not (@ (@ R X) Y)))))))))))
% 0.15/0.42 (declare-fun tptp.ind ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.ind (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((P (-> $$unsorted Bool))) (=> (forall ((X $$unsorted)) (=> (forall ((Y $$unsorted)) (=> (@ (@ (@ tptp.tc R) X) Y) (@ P Y))) (@ P X))) (forall ((X $$unsorted)) (@ P X)))))))
% 0.15/0.42 (declare-fun tptp.innf ((-> $$unsorted $$unsorted Bool) $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.innf (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted)) (not (exists ((Y $$unsorted)) (@ (@ R X) Y))))))
% 0.15/0.42 (declare-fun tptp.nfof ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.nfof (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (and (@ (@ (@ tptp.trc R) Y) X) (@ (@ tptp.innf R) X)))))
% 0.15/0.42 (declare-fun tptp.norm ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.norm (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted)) (exists ((Y $$unsorted)) (@ (@ (@ tptp.nfof R) Y) X))))))
% 0.15/0.42 (declare-fun tptp.join ((-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted) Bool)
% 0.15/0.42 (assert (= tptp.join (lambda ((R (-> $$unsorted $$unsorted Bool)) (X $$unsorted) (Y $$unsorted)) (exists ((Z $$unsorted)) (let ((_let_1 (@ tptp.trc R))) (and (@ (@ _let_1 X) Z) (@ (@ _let_1 Y) Z)))))))
% 0.15/0.42 (declare-fun tptp.lconfl ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.lconfl (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ R X))) (=> (and (@ _let_1 Z) (@ _let_1 Y)) (@ (@ (@ tptp.join R) Z) Y)))))))
% 0.15/0.42 (declare-fun tptp.sconfl ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.sconfl (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (@ (@ R X) Z) (@ (@ (@ tptp.trc R) X) Y)) (@ (@ (@ tptp.join R) Z) Y))))))
% 0.15/0.42 (declare-fun tptp.confl ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.confl (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (let ((_let_1 (@ (@ tptp.trc R) X))) (=> (and (@ _let_1 Z) (@ _let_1 Y)) (@ (@ (@ tptp.join R) Z) Y)))))))
% 0.15/0.42 (declare-fun tptp.cr ((-> $$unsorted $$unsorted Bool)) Bool)
% 0.15/0.42 (assert (= tptp.cr (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (@ (@ (@ tptp.trsc R) X) Y) (@ (@ (@ tptp.join R) X) Y))))))
% 0.15/0.42 (set-info :filename cvc5---1.0.5_979)
% 0.15/0.42 (check-sat)
% 0.15/0.42 ------- get file name : TPTP file name is SEV441^1
% 0.15/0.42 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_979.smt2...
% 0.15/0.42 --- Run --ho-elim --full-saturate-quant at 10...
% 0.15/0.47 % SZS status Satisfiable for SEV441^1
% 0.15/0.47 % cvc5---1.0.5 exiting
% 0.15/0.47 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------