TSTP Solution File: PRO019^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : PRO019^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 : Tue May 7 08:03:24 EDT 2024
% Result : Theorem 17.56s 5.71s
% Output : Refutation 18.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 163
% Syntax : Number of formulae : 305 ( 134 unt; 23 typ; 0 def)
% Number of atoms : 806 ( 370 equ; 4 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 5508 ( 88 ~; 14 |; 76 &;4936 @)
% ( 0 <=>; 394 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 10 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 686 ( 686 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 24 usr; 6 con; 0-14 aty)
% Number of variables : 1691 ( 40 ^1603 !; 20 ?;1691 :)
% ( 28 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bNF_eq_onp_type,type,
bNF_eq_onp:
!>[TA: $tType] : ( ( TA > $o ) > TA > TA > $o ) ).
thf(comp_type,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(proces1525233512Action_type,type,
proces1525233512Action:
!>[TA: $tType] : ( TA > ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) ) ).
thf(proces1915862579Choice_type,type,
proces1915862579Choice:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) ) ).
thf(proces1406508781rocess_type,type,
proces1406508781rocess:
!>[TA: $tType,TB: $tType] : ( ( TB > ( proces634752977rocess @ TB ) > TA ) > ( ( proces634752977rocess @ TB ) > ( proces634752977rocess @ TB ) > TA ) > ( proces634752977rocess @ TB ) > TA ) ).
thf(proces979765041_ch1Of_type,type,
proces979765041_ch1Of:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) ) ).
thf(proces988026546_ch2Of_type,type,
proces988026546_ch2Of:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) ) ).
thf(proces1778668539contOf_type,type,
proces1778668539contOf:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) ) ).
thf(proces894737309rocess_type,type,
proces894737309rocess:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > $o ) > ( TB > ( proces634752977rocess @ TA ) ) > ( TB > TB ) > ( TB > $o ) > ( TB > ( proces634752977rocess @ TA ) ) > ( TB > TB ) > ( TB > $o ) > ( TB > ( proces634752977rocess @ TA ) ) > ( TB > TB ) > TB > ( proces634752977rocess @ TA ) ) ).
thf(proces10484146Action_type,type,
proces10484146Action:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > $o ) ).
thf(proces401113213Choice_type,type,
proces401113213Choice:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > $o ) ).
thf(proces370407749rocess_type,type,
proces370407749rocess:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( proces634752977rocess @ TB ) > ( proces634752977rocess @ TA ) ) ).
thf(proces1205983068rocess_type,type,
proces1205983068rocess:
!>[TA: $tType] : ( ( TA > $o ) > ( proces634752977rocess @ TA ) > $o ) ).
thf(proces745025900prefOf_type,type,
proces745025900prefOf:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > TA ) ).
thf(proces749077512rocess_type,type,
proces749077512rocess:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( proces634752977rocess @ TB ) > ( proces634752977rocess @ TA ) > $o ) ).
thf(proces1148692671rocess_type,type,
proces1148692671rocess:
!>[TA: $tType] : ( ( proces634752977rocess @ TA ) > ( set @ TA ) ) ).
thf(ball_type,type,
ball:
!>[TA: $tType] : ( ( set @ TA ) > ( TA > $o ) > $o ) ).
thf(image_type,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: proces634752977rocess @ a ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_rewriteR__comp__comp) ).
thf(316,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(108,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( proces1205983068rocess @ TA @ C @ A )
= ( proces1205983068rocess @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_process_Opred__cong) ).
thf(555,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: TA > $o,D: TA > $o] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( proces1205983068rocess @ TA @ C @ A )
= ( proces1205983068rocess @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( ( ( C @ B )
=> ( ( proces1778668539contOf @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ C @ E @ F @ G @ H @ I @ J @ K @ L @ B ) )
= ( E @ B ) ) )
& ( ~ ( C @ B )
=> ( ( proces1778668539contOf @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ C @ E @ F @ G @ H @ I @ J @ K @ L @ B ) )
= ( proces894737309rocess @ TA @ TB @ A @ D @ C @ E @ F @ G @ H @ I @ J @ K @ L @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_process_Ocorec__sel_I2_J) ).
thf(333,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( ( ( C @ B )
=> ( ( proces1778668539contOf @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ C @ E @ F @ G @ H @ I @ J @ K @ L @ B ) )
= ( E @ B ) ) )
& ( ~ ( C @ B )
=> ( ( proces1778668539contOf @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ C @ E @ F @ G @ H @ I @ J @ K @ L @ B ) )
= ( proces894737309rocess @ TA @ TB @ A @ D @ C @ E @ F @ G @ H @ I @ J @ K @ L @ ( F @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(35,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_mk__disjoint__insert) ).
thf(249,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(117,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( proces10484146Action @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_process_Odisc_I1_J) ).
thf(582,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( proces10484146Action @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ball__imageD) ).
thf(276,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insertI1) ).
thf(247,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1,conjecture,
( ( proces10484146Action @ a @ p )
| ( proces401113213Choice @ a @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( proces10484146Action @ a @ p )
| ( proces401113213Choice @ a @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(142,plain,
~ ( ( proces10484146Action @ a @ p )
| ( proces401113213Choice @ a @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: proces634752977rocess @ TB,D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
~ ( proces749077512rocess @ TB @ TA @ A @ ( proces1525233512Action @ TB @ B @ C ) @ ( proces1915862579Choice @ TA @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_process_Orel__distinct_I1_J) ).
thf(500,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: proces634752977rocess @ TB,D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
~ ( proces749077512rocess @ TB @ TA @ A @ ( proces1525233512Action @ TB @ B @ C ) @ ( proces1915862579Choice @ TA @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(88,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: TA > ( proces634752977rocess @ TA ) > $o] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( ! [D: TA,E: proces634752977rocess @ TA] : ( C @ D @ ( proces1525233512Action @ TA @ D @ E ) )
=> ( ! [D: TA,E: proces634752977rocess @ TA,F: TA] :
( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( proces1525233512Action @ TA @ D @ E ) ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: TA] :
( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ D ) )
=> ( ( C @ F @ D )
=> ( C @ F @ ( proces1915862579Choice @ TA @ D @ E ) ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: TA] :
( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( proces1915862579Choice @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_process_Oset__induct) ).
thf(472,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: TA > ( proces634752977rocess @ TA ) > $o] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( ! [D: TA,E: proces634752977rocess @ TA] : ( C @ D @ ( proces1525233512Action @ TA @ D @ E ) )
=> ( ! [D: TA,E: proces634752977rocess @ TA,F: TA] :
( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( proces1525233512Action @ TA @ D @ E ) ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: TA] :
( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ D ) )
=> ( ( C @ F @ D )
=> ( C @ F @ ( proces1915862579Choice @ TA @ D @ E ) ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: TA] :
( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( proces1915862579Choice @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: proces634752977rocess @ TB,E: proces634752977rocess @ TA] :
( ( A @ B @ C )
=> ( ( proces749077512rocess @ TB @ TA @ A @ D @ E )
=> ( proces749077512rocess @ TB @ TA @ A @ ( proces1525233512Action @ TB @ B @ D ) @ ( proces1525233512Action @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_process_Orel__intros_I1_J) ).
thf(340,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: proces634752977rocess @ TB,E: proces634752977rocess @ TA] :
( ( A @ B @ C )
=> ( ( proces749077512rocess @ TB @ TA @ A @ D @ E )
=> ( proces749077512rocess @ TB @ TA @ A @ ( proces1525233512Action @ TB @ B @ D ) @ ( proces1525233512Action @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(138,axiom,
! [TA: $tType,A: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A @ B @ C )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
( ( A @ D @ E )
=> ( ( ( proces10484146Action @ TA @ D )
= ( proces10484146Action @ TA @ E ) )
& ( ( proces10484146Action @ TA @ D )
=> ( ( proces10484146Action @ TA @ E )
=> ( ( ( proces745025900prefOf @ TA @ D )
= ( proces745025900prefOf @ TA @ E ) )
& ( A @ ( proces1778668539contOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ E ) ) ) ) )
& ( ( proces401113213Choice @ TA @ D )
=> ( ( proces401113213Choice @ TA @ E )
=> ( ( A @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces979765041_ch1Of @ TA @ E ) )
& ( A @ ( proces988026546_ch2Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_process_Ocoinduct) ).
thf(670,plain,
! [TA: $tType,A: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A @ B @ C )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
( ( A @ D @ E )
=> ( ( ( proces10484146Action @ TA @ D )
= ( proces10484146Action @ TA @ E ) )
& ( ( proces10484146Action @ TA @ D )
=> ( ( proces10484146Action @ TA @ E )
=> ( ( ( proces745025900prefOf @ TA @ D )
= ( proces745025900prefOf @ TA @ E ) )
& ( A @ ( proces1778668539contOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ E ) ) ) ) )
& ( ( proces401113213Choice @ TA @ D )
=> ( ( proces401113213Choice @ TA @ E )
=> ( ( A @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces979765041_ch1Of @ TA @ E ) )
& ( A @ ( proces988026546_ch2Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_comp__assoc) ).
thf(174,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_insert__absorb) ).
thf(320,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType] :
( ( proces749077512rocess @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TB] :
( ( ( proces10484146Action @ TA @ B )
= ( proces10484146Action @ TB @ C ) )
& ( ( proces10484146Action @ TA @ B )
=> ( ( proces10484146Action @ TB @ C )
=> ( ( A @ ( proces745025900prefOf @ TA @ B ) @ ( proces745025900prefOf @ TB @ C ) )
& ( proces749077512rocess @ TA @ TB @ A @ ( proces1778668539contOf @ TA @ B ) @ ( proces1778668539contOf @ TB @ C ) ) ) ) )
& ( ( proces401113213Choice @ TA @ B )
=> ( ( proces401113213Choice @ TB @ C )
=> ( ( proces749077512rocess @ TA @ TB @ A @ ( proces979765041_ch1Of @ TA @ B ) @ ( proces979765041_ch1Of @ TB @ C ) )
& ( proces749077512rocess @ TA @ TB @ A @ ( proces988026546_ch2Of @ TA @ B ) @ ( proces988026546_ch2Of @ TB @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_process_Orel__sel) ).
thf(565,plain,
! [TA: $tType,TB: $tType] :
( ( proces749077512rocess @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TB] :
( ( ( proces10484146Action @ TA @ B )
= ( proces10484146Action @ TB @ C ) )
& ( ( proces10484146Action @ TA @ B )
=> ( ( proces10484146Action @ TB @ C )
=> ( ( A @ ( proces745025900prefOf @ TA @ B ) @ ( proces745025900prefOf @ TB @ C ) )
& ( proces749077512rocess @ TA @ TB @ A @ ( proces1778668539contOf @ TA @ B ) @ ( proces1778668539contOf @ TB @ C ) ) ) ) )
& ( ( proces401113213Choice @ TA @ B )
=> ( ( proces401113213Choice @ TB @ C )
=> ( ( proces749077512rocess @ TA @ TB @ A @ ( proces979765041_ch1Of @ TA @ B ) @ ( proces979765041_ch1Of @ TB @ C ) )
& ( proces749077512rocess @ TA @ TB @ A @ ( proces988026546_ch2Of @ TA @ B ) @ ( proces988026546_ch2Of @ TB @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
= ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_type__copy__map__cong0) ).
thf(184,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TB,B: TA > TE,C: TA,D: TD > TB,E: TA > TD,F: TB > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TB @ TC @ TE @ F @ A ) @ B @ C )
= ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ F @ D ) @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(119,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ~ ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_process_Odistinct__disc_I1_J) ).
thf(587,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ~ ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_fun_Omap__comp) ).
thf(216,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_comp__eq__elim) ).
thf(253,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1778668539contOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_process_Osel_I2_J) ).
thf(485,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1778668539contOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(31,axiom,
! [TA: $tType,A: TA > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( proces1205983068rocess @ TA @ A @ ( proces1915862579Choice @ TA @ B @ C ) )
= ( ( proces1205983068rocess @ TA @ A @ B )
& ( proces1205983068rocess @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_process_Opred__inject_I2_J) ).
thf(238,plain,
! [TA: $tType,A: TA > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( proces1205983068rocess @ TA @ A @ ( proces1915862579Choice @ TA @ B @ C ) )
= ( ( proces1205983068rocess @ TA @ A @ B )
& ( proces1205983068rocess @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(97,axiom,
! [TA: $tType,A: TA > TA > $o,B: proces634752977rocess @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( proces749077512rocess @ TA @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_process_Orel__refl) ).
thf(514,plain,
! [TA: $tType,A: TA > TA > $o,B: proces634752977rocess @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( proces749077512rocess @ TA @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(113,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( proces401113213Choice @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_process_Odisc_I4_J) ).
thf(574,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( proces401113213Choice @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TB,D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ ( proces1915862579Choice @ TB @ B @ C ) @ ( proces1915862579Choice @ TA @ D @ E ) )
= ( ( proces749077512rocess @ TB @ TA @ A @ B @ D )
& ( proces749077512rocess @ TB @ TA @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_process_Orel__inject_I2_J) ).
thf(492,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TB,D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ ( proces1915862579Choice @ TB @ B @ C ) @ ( proces1915862579Choice @ TA @ D @ E ) )
= ( ( proces749077512rocess @ TB @ TA @ A @ B @ D )
& ( proces749077512rocess @ TB @ TA @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o,B: TA > TA > $o,C: TA] :
( ( ( bNF_eq_onp @ TA @ A )
= B )
=> ( ( A @ C )
= ( B @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_eq__onp__eqD) ).
thf(164,plain,
! [TA: $tType,A: TA > $o,B: TA > TA > $o,C: TA] :
( ( ( bNF_eq_onp @ TA @ A )
= B )
=> ( ( A @ C )
= ( B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(140,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( ( proces10484146Action @ TA @ A )
= ( proces10484146Action @ TA @ B ) )
=> ( ( ( proces10484146Action @ TA @ A )
=> ( ( proces10484146Action @ TA @ B )
=> ( ( ( proces745025900prefOf @ TA @ A )
= ( proces745025900prefOf @ TA @ B ) )
& ( ( proces1778668539contOf @ TA @ A )
= ( proces1778668539contOf @ TA @ B ) ) ) ) )
=> ( ( ( proces401113213Choice @ TA @ A )
=> ( ( proces401113213Choice @ TA @ B )
=> ( ( ( proces979765041_ch1Of @ TA @ A )
= ( proces979765041_ch1Of @ TA @ B ) )
& ( ( proces988026546_ch2Of @ TA @ A )
= ( proces988026546_ch2Of @ TA @ B ) ) ) ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_process_Oexpand) ).
thf(687,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( ( proces10484146Action @ TA @ A )
= ( proces10484146Action @ TA @ B ) )
=> ( ( ( proces10484146Action @ TA @ A )
=> ( ( proces10484146Action @ TA @ B )
=> ( ( ( proces745025900prefOf @ TA @ A )
= ( proces745025900prefOf @ TA @ B ) )
& ( ( proces1778668539contOf @ TA @ A )
= ( proces1778668539contOf @ TA @ B ) ) ) ) )
=> ( ( ( proces401113213Choice @ TA @ A )
=> ( ( proces401113213Choice @ TA @ B )
=> ( ( ( proces979765041_ch1Of @ TA @ A )
= ( proces979765041_ch1Of @ TA @ B ) )
& ( ( proces988026546_ch2Of @ TA @ A )
= ( proces988026546_ch2Of @ TA @ B ) ) ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(132,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1778668539contOf @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_process_Ocollapse_I1_J) ).
thf(634,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1778668539contOf @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_comp__eq__dest__lhs) ).
thf(293,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(453,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(74,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( ( proces1915862579Choice @ TA @ A @ B )
= ( proces1915862579Choice @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_process_Oinject_I2_J) ).
thf(396,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( ( proces1915862579Choice @ TA @ A @ B )
= ( proces1915862579Choice @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( proces401113213Choice @ TB @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_process_Ocorec__disc_I2_J) ).
thf(660,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( proces401113213Choice @ TB @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(76,axiom,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_Ball__def) ).
thf(428,plain,
! [TA: $tType] :
( ( ball @ TA )
= ( ^ [A: set @ TA,B: TA > $o] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1915862579Choice @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_process_Oset__intros_I3_J) ).
thf(527,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1915862579Choice @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( proces370407749rocess @ TA @ TB @ C @ A )
= ( proces370407749rocess @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_process_Omap__cong) ).
thf(380,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( proces370407749rocess @ TA @ TB @ C @ A )
= ( proces370407749rocess @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insert__eq__iff) ).
thf(270,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TA @ TB @ A @ ( proces1525233512Action @ TA @ B @ C ) )
= ( proces1525233512Action @ TB @ ( A @ B ) @ ( proces370407749rocess @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_process_Osimps_I15_J) ).
thf(529,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TA @ TB @ A @ ( proces1525233512Action @ TA @ B @ C ) )
= ( proces1525233512Action @ TB @ ( A @ B ) @ ( proces370407749rocess @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces979765041_ch1Of @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( proces370407749rocess @ TA @ TB @ B @ ( proces979765041_ch1Of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_process_Omap__sel_I3_J) ).
thf(598,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces979765041_ch1Of @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( proces370407749rocess @ TA @ TB @ B @ ( proces979765041_ch1Of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_insert__iff) ).
thf(297,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(131,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A
= ( proces1915862579Choice @ TA @ B @ C ) )
=> ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_process_OdiscI_I2_J) ).
thf(630,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A
= ( proces1915862579Choice @ TA @ B @ C ) )
=> ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) )
= ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_insert__image) ).
thf(229,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) )
= ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_insertI2) ).
thf(197,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TA @ TB @ A @ ( proces1915862579Choice @ TA @ B @ C ) )
= ( proces1915862579Choice @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) @ ( proces370407749rocess @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_process_Osimps_I16_J) ).
thf(361,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TA @ TB @ A @ ( proces1915862579Choice @ TA @ B @ C ) )
= ( proces1915862579Choice @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) @ ( proces370407749rocess @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TA > ( proces634752977rocess @ TA ) > TB,B: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,C: TA,D: proces634752977rocess @ TA] :
( ( proces1406508781rocess @ TA @ TB @ A @ B @ ( proces1525233512Action @ TA @ C @ D ) )
= ( A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_process_Osimps_I5_J) ).
thf(456,plain,
! [TA: $tType,TB: $tType,A: TA > ( proces634752977rocess @ TA ) > TB,B: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,C: TA,D: proces634752977rocess @ TA] :
( ( proces1406508781rocess @ TA @ TB @ A @ B @ ( proces1525233512Action @ TA @ C @ D ) )
= ( A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TB,D: TA,E: proces634752977rocess @ TA] :
~ ( proces749077512rocess @ TB @ TA @ A @ ( proces1915862579Choice @ TB @ B @ C ) @ ( proces1525233512Action @ TA @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_process_Orel__distinct_I2_J) ).
thf(519,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TB,D: TA,E: proces634752977rocess @ TA] :
~ ( proces749077512rocess @ TB @ TA @ A @ ( proces1915862579Choice @ TB @ B @ C ) @ ( proces1525233512Action @ TA @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(115,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
~ ( proces401113213Choice @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_process_Odisc_I3_J) ).
thf(578,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
~ ( proces401113213Choice @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Inf_OINF__cong) ).
thf(256,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(90,axiom,
! [TA: $tType,A: TA > $o,B: proces634752977rocess @ TA,C: TA > $o] :
( ( proces1205983068rocess @ TA @ A @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( proces1205983068rocess @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_process_Opred__mono__strong) ).
thf(488,plain,
! [TA: $tType,A: TA > $o,B: proces634752977rocess @ TA,C: TA > $o] :
( ( proces1205983068rocess @ TA @ A @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( A @ D )
=> ( C @ D ) ) )
=> ( proces1205983068rocess @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(133,axiom,
! [TA: $tType,A: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A @ B @ C )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
( ( A @ D @ E )
=> ( ( ( proces10484146Action @ TA @ D )
= ( proces10484146Action @ TA @ E ) )
& ( ( proces10484146Action @ TA @ D )
=> ( ( proces10484146Action @ TA @ E )
=> ( ( ( proces745025900prefOf @ TA @ D )
= ( proces745025900prefOf @ TA @ E ) )
& ( ( A @ ( proces1778668539contOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ E ) )
| ( ( proces1778668539contOf @ TA @ D )
= ( proces1778668539contOf @ TA @ E ) ) ) ) ) )
& ( ( proces401113213Choice @ TA @ D )
=> ( ( proces401113213Choice @ TA @ E )
=> ( ( ( A @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces979765041_ch1Of @ TA @ E ) )
| ( ( proces979765041_ch1Of @ TA @ D )
= ( proces979765041_ch1Of @ TA @ E ) ) )
& ( ( A @ ( proces988026546_ch2Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ E ) )
| ( ( proces988026546_ch2Of @ TA @ D )
= ( proces988026546_ch2Of @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_process_Ocoinduct__strong) ).
thf(637,plain,
! [TA: $tType,A: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > $o,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A @ B @ C )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA] :
( ( A @ D @ E )
=> ( ( ( proces10484146Action @ TA @ D )
= ( proces10484146Action @ TA @ E ) )
& ( ( proces10484146Action @ TA @ D )
=> ( ( proces10484146Action @ TA @ E )
=> ( ( ( proces745025900prefOf @ TA @ D )
= ( proces745025900prefOf @ TA @ E ) )
& ( ( A @ ( proces1778668539contOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ E ) )
| ( ( proces1778668539contOf @ TA @ D )
= ( proces1778668539contOf @ TA @ E ) ) ) ) ) )
& ( ( proces401113213Choice @ TA @ D )
=> ( ( proces401113213Choice @ TA @ E )
=> ( ( ( A @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces979765041_ch1Of @ TA @ E ) )
| ( ( proces979765041_ch1Of @ TA @ D )
= ( proces979765041_ch1Of @ TA @ E ) ) )
& ( ( A @ ( proces988026546_ch2Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ E ) )
| ( ( proces988026546_ch2Of @ TA @ D )
= ( proces988026546_ch2Of @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ ( proces1148692671rocess @ TA @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( proces370407749rocess @ TA @ TB @ B @ A )
= ( proces370407749rocess @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_process_Omap__cong0) ).
thf(547,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ ( proces1148692671rocess @ TA @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( proces370407749rocess @ TA @ TB @ B @ A )
= ( proces370407749rocess @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(128,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
~ ( proces10484146Action @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_process_Odisc_I2_J) ).
thf(622,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
~ ( proces10484146Action @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces1148692671rocess @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( image @ TA @ TB @ A @ ( proces1148692671rocess @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_process_Oset__map) ).
thf(393,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces1148692671rocess @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( image @ TA @ TB @ A @ ( proces1148692671rocess @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(33,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: proces634752977rocess @ TA] :
( ( proces1205983068rocess @ TA @ A @ ( proces1525233512Action @ TA @ B @ C ) )
= ( ( A @ B )
& ( proces1205983068rocess @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_process_Opred__inject_I1_J) ).
thf(244,plain,
! [TA: $tType,A: TA > $o,B: TA,C: proces634752977rocess @ TA] :
( ( proces1205983068rocess @ TA @ A @ ( proces1525233512Action @ TA @ B @ C ) )
= ( ( A @ B )
& ( proces1205983068rocess @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(135,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ( member @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1148692671rocess @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_process_Oset__sel_I1_J) ).
thf(662,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ( member @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1148692671rocess @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( comp @ TB @ $o @ TA @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Ball__image__comp) ).
thf(148,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( comp @ TB @ $o @ TA @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_eq__onp__to__eq) ).
thf(161,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_rewriteR__comp__comp2) ).
thf(279,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_rewriteL__comp__comp2) ).
thf(180,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > $o,F: TA > ( proces634752977rocess @ TB ),G: TA > TA,H: TA > $o,I: TA > ( proces634752977rocess @ TB ),J: TA > TA,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( proces988026546_ch2Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ H @ I @ J @ C @ K @ L @ B ) )
= ( K @ B ) ) )
& ( ~ ( C @ B )
=> ( ( proces988026546_ch2Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ H @ I @ J @ C @ K @ L @ B ) )
= ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ H @ I @ J @ C @ K @ L @ ( L @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_process_Ocorec__sel_I4_J) ).
thf(375,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > $o,F: TA > ( proces634752977rocess @ TB ),G: TA > TA,H: TA > $o,I: TA > ( proces634752977rocess @ TB ),J: TA > TA,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( proces988026546_ch2Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ H @ I @ J @ C @ K @ L @ B ) )
= ( K @ B ) ) )
& ( ~ ( C @ B )
=> ( ( proces988026546_ch2Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ H @ I @ J @ C @ K @ L @ B ) )
= ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ H @ I @ J @ C @ K @ L @ ( L @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( proces10484146Action @ TB @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_process_Ocorec__disc_I1_J) ).
thf(601,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( proces10484146Action @ TB @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces988026546_ch2Of @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( proces370407749rocess @ TA @ TB @ B @ ( proces988026546_ch2Of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_process_Omap__sel_I4_J) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces988026546_ch2Of @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( proces370407749rocess @ TA @ TB @ B @ ( proces988026546_ch2Of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(109,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ A ) @ ( proces988026546_ch2Of @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_process_Ocollapse_I2_J) ).
thf(562,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ A ) @ ( proces988026546_ch2Of @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TD @ TB @ TA @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_comp__apply__eq) ).
thf(191,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA,D: TC > TB,E: TA > TC] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp @ TD @ TB @ TA @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Sup_OSUP__cong) ).
thf(286,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1915862579Choice @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_process_Oset__intros_I4_J) ).
thf(445,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1915862579Choice @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_comp__apply) ).
thf(313,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_process_Oset__intros_I1_J) ).
thf(498,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_rewriteL__comp__comp) ).
thf(187,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TC @ TB @ A @ ( proces370407749rocess @ TA @ TC @ B @ C ) )
= ( proces370407749rocess @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_process_Omap__comp) ).
thf(219,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TC @ TB @ A @ ( proces370407749rocess @ TA @ TC @ B @ C ) )
= ( proces370407749rocess @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(78,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces745025900prefOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_process_Osel_I1_J) ).
thf(434,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces745025900prefOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(49,axiom,
! [TA: $tType,A: TA > $o,B: set @ TA] :
( ( ~ ( member @ $o @ $false @ ( image @ TA @ $o @ A @ B ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_not__False__in__image__Ball) ).
thf(303,plain,
! [TA: $tType,A: TA > $o,B: set @ TA] :
( ( ~ ( member @ $o @ $false @ ( image @ TA @ $o @ A @ B ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B )
= ( proces1915862579Choice @ TB @ ( if @ ( proces634752977rocess @ TB ) @ ( G @ B ) @ ( H @ B ) @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ ( I @ B ) ) ) @ ( if @ ( proces634752977rocess @ TB ) @ ( J @ B ) @ ( K @ B ) @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ ( L @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_process_Ocorec_I2_J) ).
thf(387,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B )
= ( proces1915862579Choice @ TB @ ( if @ ( proces634752977rocess @ TB ) @ ( G @ B ) @ ( H @ B ) @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ ( I @ B ) ) ) @ ( if @ ( proces634752977rocess @ TB ) @ ( J @ B ) @ ( K @ B ) @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ ( L @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(56,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Set_Oset__insert) ).
thf(323,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_image__comp) ).
thf(213,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(141,axiom,
! [TA: $tType] :
( ( proces401113213Choice @ TA )
= ( ^ [A: proces634752977rocess @ TA] :
? [B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( A
= ( proces1915862579Choice @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_isChoice__def) ).
thf(700,plain,
! [TA: $tType] :
( ( proces401113213Choice @ TA )
= ( ^ [A: proces634752977rocess @ TA] :
? [B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( A
= ( proces1915862579Choice @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(130,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA,C: proces634752977rocess @ TA] :
( ( A
= ( proces1525233512Action @ TA @ B @ C ) )
=> ( proces10484146Action @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_process_OdiscI_I1_J) ).
thf(626,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA,C: proces634752977rocess @ TA] :
( ( A
= ( proces1525233512Action @ TA @ B @ C ) )
=> ( proces10484146Action @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( proces634752977rocess @ TA ) > TB,C: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,D: proces634752977rocess @ TA] :
( ( A @ ( proces1406508781rocess @ TA @ TB @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) )
& ~ ( A @ ( B @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) ) )
| ( ( D
= ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) )
& ~ ( A @ ( C @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_process_Osplit__sel__asm) ).
thf(330,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( proces634752977rocess @ TA ) > TB,C: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,D: proces634752977rocess @ TA] :
( ( A @ ( proces1406508781rocess @ TA @ TB @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) )
& ~ ( A @ ( B @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) ) )
| ( ( D
= ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) )
& ~ ( A @ ( C @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TB,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA,E: TB > TA > $o,F: TB > TA > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ ( proces1148692671rocess @ TB @ B ) )
=> ( ( member @ TA @ H @ ( proces1148692671rocess @ TA @ D ) )
=> ( ( E @ G @ H )
= ( F @ G @ H ) ) ) )
=> ( ( proces749077512rocess @ TB @ TA @ E @ A @ C )
= ( proces749077512rocess @ TB @ TA @ F @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_process_Orel__cong) ).
thf(462,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TB,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA,E: TB > TA > $o,F: TB > TA > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ ( proces1148692671rocess @ TB @ B ) )
=> ( ( member @ TA @ H @ ( proces1148692671rocess @ TA @ D ) )
=> ( ( E @ G @ H )
= ( F @ G @ H ) ) ) )
=> ( ( proces749077512rocess @ TB @ TA @ E @ A @ C )
= ( proces749077512rocess @ TB @ TA @ F @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( ! [C: proces634752977rocess @ TA] :
( B
!= ( proces1525233512Action @ TA @ A @ C ) )
=> ( ! [C: TA,D: proces634752977rocess @ TA] :
( ( B
= ( proces1525233512Action @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ D ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ? [D: proces634752977rocess @ TA] :
( B
= ( proces1915862579Choice @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ C ) ) )
=> ~ ! [C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( B
= ( proces1915862579Choice @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_process_Oset__cases) ).
thf(345,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( ! [C: proces634752977rocess @ TA] :
( B
!= ( proces1525233512Action @ TA @ A @ C ) )
=> ( ! [C: TA,D: proces634752977rocess @ TA] :
( ( B
= ( proces1525233512Action @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ D ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ? [D: proces634752977rocess @ TA] :
( B
= ( proces1915862579Choice @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ C ) ) )
=> ~ ! [C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( B
= ( proces1915862579Choice @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(107,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( proces988026546_ch2Of @ TA @ ( proces1915862579Choice @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_process_Osel_I4_J) ).
thf(552,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( proces988026546_ch2Of @ TA @ ( proces1915862579Choice @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ B @ C )
=> ( ! [D: TB,E: proces634752977rocess @ TB] :
( ( B
= ( proces1525233512Action @ TB @ D @ E ) )
=> ! [F: TA,G: proces634752977rocess @ TA] :
( ( C
= ( proces1525233512Action @ TA @ F @ G ) )
=> ( ( A @ D @ F )
=> ~ ( proces749077512rocess @ TB @ TA @ A @ E @ G ) ) ) )
=> ~ ! [D: proces634752977rocess @ TB,E: proces634752977rocess @ TB] :
( ( B
= ( proces1915862579Choice @ TB @ D @ E ) )
=> ! [F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( C
= ( proces1915862579Choice @ TA @ F @ G ) )
=> ( ( proces749077512rocess @ TB @ TA @ A @ D @ F )
=> ~ ( proces749077512rocess @ TB @ TA @ A @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_process_Orel__cases) ).
thf(399,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ B @ C )
=> ( ! [D: TB,E: proces634752977rocess @ TB] :
( ( B
= ( proces1525233512Action @ TB @ D @ E ) )
=> ! [F: TA,G: proces634752977rocess @ TA] :
( ( C
= ( proces1525233512Action @ TA @ F @ G ) )
=> ( ( A @ D @ F )
=> ~ ( proces749077512rocess @ TB @ TA @ A @ E @ G ) ) ) )
=> ~ ! [D: proces634752977rocess @ TB,E: proces634752977rocess @ TB] :
( ( B
= ( proces1915862579Choice @ TB @ D @ E ) )
=> ! [F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( C
= ( proces1915862579Choice @ TA @ F @ G ) )
=> ( ( proces749077512rocess @ TB @ TA @ A @ D @ F )
=> ~ ( proces749077512rocess @ TB @ TA @ A @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Inf_OINF__image) ).
thf(306,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_image__iff) ).
thf(226,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: TA > TB,D: TA > TB] :
( ! [E: TA,F: TA] :
( ( member @ TA @ E @ ( proces1148692671rocess @ TA @ A ) )
=> ( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( proces370407749rocess @ TA @ TB @ C @ A )
= ( proces370407749rocess @ TA @ TB @ D @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_process_Oinj__map__strong) ).
thf(505,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: TA > TB,D: TA > TB] :
( ! [E: TA,F: TA] :
( ( member @ TA @ E @ ( proces1148692671rocess @ TA @ A ) )
=> ( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ B ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( proces370407749rocess @ TA @ TB @ C @ A )
= ( proces370407749rocess @ TA @ TB @ D @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(77,axiom,
! [TA: $tType] :
( ( proces1205983068rocess @ TA )
= ( ^ [A: TA > $o,B: proces634752977rocess @ TA] :
! [C: TA] :
( ( member @ TA @ C @ ( proces1148692671rocess @ TA @ B ) )
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_process_Opred__set) ).
thf(431,plain,
! [TA: $tType] :
( ( proces1205983068rocess @ TA )
= ( ^ [A: TA > $o,B: proces634752977rocess @ TA] :
! [C: TA] :
( ( member @ TA @ C @ ( proces1148692671rocess @ TA @ B ) )
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(32,axiom,
! [TA: $tType,A: TA > $o] :
( ( proces749077512rocess @ TA @ TA @ ( bNF_eq_onp @ TA @ A ) )
= ( bNF_eq_onp @ ( proces634752977rocess @ TA ) @ ( proces1205983068rocess @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_process_Orel__eq__onp) ).
thf(241,plain,
! [TA: $tType,A: TA > $o] :
( ( proces749077512rocess @ TA @ TA @ ( bNF_eq_onp @ TA @ A ) )
= ( bNF_eq_onp @ ( proces634752977rocess @ TA ) @ ( proces1205983068rocess @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(139,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( member @ TA @ B @ ( proces1148692671rocess @ TA @ ( proces988026546_ch2Of @ TA @ A ) ) )
=> ( member @ TA @ B @ ( proces1148692671rocess @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_process_Oset__sel_I4_J) ).
thf(685,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( member @ TA @ B @ ( proces1148692671rocess @ TA @ ( proces988026546_ch2Of @ TA @ A ) ) )
=> ( member @ TA @ B @ ( proces1148692671rocess @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(99,axiom,
! [TA: $tType] :
( ( proces749077512rocess @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( proces634752977rocess @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_process_Orel__eq) ).
thf(521,plain,
! [TA: $tType] :
( ( proces749077512rocess @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( proces634752977rocess @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( proces634752977rocess @ TB ),E: TA > TA,F: TA > $o,G: TA > ( proces634752977rocess @ TB ),H: TA > TA,I: TA > $o,J: TA > ( proces634752977rocess @ TB ),K: TA > TA,L: TA] :
( ( proces401113213Choice @ TB @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L ) )
= ( ~ ( A @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_process_Ocorec__disc__iff_I2_J) ).
thf(589,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( proces634752977rocess @ TB ),E: TA > TA,F: TA > $o,G: TA > ( proces634752977rocess @ TB ),H: TA > TA,I: TA > $o,J: TA > ( proces634752977rocess @ TB ),K: TA > TA,L: TA] :
( ( proces401113213Choice @ TB @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L ) )
= ( ~ ( A @ L ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( proces401113213Choice @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_process_Omap__disc__iff_I2_J) ).
thf(617,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( proces401113213Choice @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(62,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ! [B: TA,C: proces634752977rocess @ TA] :
( A
!= ( proces1525233512Action @ TA @ B @ C ) )
=> ~ ! [B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( A
!= ( proces1915862579Choice @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_process_Oexhaust) ).
thf(342,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ! [B: TA,C: proces634752977rocess @ TA] :
( A
!= ( proces1525233512Action @ TA @ B @ C ) )
=> ~ ! [B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( A
!= ( proces1915862579Choice @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__absorb2) ).
thf(194,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [TA: $tType] :
( ( proces1205983068rocess @ TA )
= ( ^ [A: TA > $o,B: proces634752977rocess @ TA] : ( proces749077512rocess @ TA @ TA @ ( bNF_eq_onp @ TA @ A ) @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_process_Opred__rel) ).
thf(145,plain,
! [TA: $tType] :
( ( proces1205983068rocess @ TA )
= ( ^ [A: TA > $o,B: proces634752977rocess @ TA] : ( proces749077512rocess @ TA @ TA @ ( bNF_eq_onp @ TA @ A ) @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(116,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ~ ( proces10484146Action @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_process_Odistinct__disc_I2_J) ).
thf(580,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ~ ( proces10484146Action @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: proces634752977rocess @ TB,D: TA,E: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ ( proces1525233512Action @ TB @ B @ C ) @ ( proces1525233512Action @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( proces749077512rocess @ TB @ TA @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_process_Orel__inject_I1_J) ).
thf(327,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: proces634752977rocess @ TB,D: TA,E: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ ( proces1525233512Action @ TB @ B @ C ) @ ( proces1525233512Action @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( proces749077512rocess @ TB @ TA @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_insertCI) ).
thf(263,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_image__eq__imp__comp) ).
thf(310,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_image__eqI) ).
thf(199,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_comp__def) ).
thf(177,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( proces1525233512Action @ TA @ A @ B )
!= ( proces1915862579Choice @ TA @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_process_Odistinct_I1_J) ).
thf(370,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( proces1525233512Action @ TA @ A @ B )
!= ( proces1915862579Choice @ TA @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(95,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( proces979765041_ch1Of @ TA @ ( proces1915862579Choice @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_process_Osel_I3_J) ).
thf(502,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( proces979765041_ch1Of @ TA @ ( proces1915862579Choice @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: proces634752977rocess @ TB,E: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ B @ C )
=> ( ( proces749077512rocess @ TB @ TA @ A @ D @ E )
=> ( proces749077512rocess @ TB @ TA @ A @ ( proces1915862579Choice @ TB @ B @ D ) @ ( proces1915862579Choice @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_process_Orel__intros_I2_J) ).
thf(338,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: proces634752977rocess @ TB,E: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ B @ C )
=> ( ( proces749077512rocess @ TB @ TA @ A @ D @ E )
=> ( proces749077512rocess @ TB @ TA @ A @ ( proces1915862579Choice @ TB @ B @ D ) @ ( proces1915862579Choice @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(114,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA] :
( ( proces10484146Action @ TA @ A )
=> ( ( member @ TA @ B @ ( proces1148692671rocess @ TA @ ( proces1778668539contOf @ TA @ A ) ) )
=> ( member @ TA @ B @ ( proces1148692671rocess @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_process_Oset__sel_I2_J) ).
thf(576,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA] :
( ( proces10484146Action @ TA @ A )
=> ( ( member @ TA @ B @ ( proces1148692671rocess @ TA @ ( proces1778668539contOf @ TA @ A ) ) )
=> ( member @ TA @ B @ ( proces1148692671rocess @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( proces634752977rocess @ TA ) > TB,C: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,D: proces634752977rocess @ TA] :
( ( A @ ( proces1406508781rocess @ TA @ TB @ B @ C @ D ) )
= ( ( ( D
= ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) )
=> ( A @ ( B @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) ) )
& ( ( D
= ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) )
=> ( A @ ( C @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_process_Osplit__sel) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > ( proces634752977rocess @ TA ) > TB,C: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,D: proces634752977rocess @ TA] :
( ( A @ ( proces1406508781rocess @ TA @ TB @ B @ C @ D ) )
= ( ( ( D
= ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) )
=> ( A @ ( B @ ( proces745025900prefOf @ TA @ D ) @ ( proces1778668539contOf @ TA @ D ) ) ) )
& ( ( D
= ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) )
=> ( A @ ( C @ ( proces979765041_ch1Of @ TA @ D ) @ ( proces988026546_ch2Of @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(6,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( bNF_eq_onp @ TA @ B @ D @ E )
=> ( bNF_eq_onp @ TA @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_eq__onp__mono0) ).
thf(154,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( bNF_eq_onp @ TA @ B @ D @ E )
=> ( bNF_eq_onp @ TA @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(112,axiom,
! [TA: $tType] :
( ( proces10484146Action @ TA )
= ( ^ [A: proces634752977rocess @ TA] :
? [B: TA,C: proces634752977rocess @ TA] :
( A
= ( proces1525233512Action @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_isAction__def) ).
thf(571,plain,
! [TA: $tType] :
( ( proces10484146Action @ TA )
= ( ^ [A: proces634752977rocess @ TA] :
? [B: TA,C: proces634752977rocess @ TA] :
( A
= ( proces1525233512Action @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces10484146Action @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( proces10484146Action @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_process_Omap__disc__iff_I1_J) ).
thf(595,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces10484146Action @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( proces10484146Action @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA > ( proces634752977rocess @ TA ) > TB,B: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( proces1406508781rocess @ TA @ TB @ A @ B @ ( proces1915862579Choice @ TA @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_process_Osimps_I6_J) ).
thf(450,plain,
! [TA: $tType,TB: $tType,A: TA > ( proces634752977rocess @ TA ) > TB,B: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,C: proces634752977rocess @ TA,D: proces634752977rocess @ TA] :
( ( proces1406508781rocess @ TA @ TB @ A @ B @ ( proces1915862579Choice @ TA @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > $o,F: TA > ( proces634752977rocess @ TB ),G: TA > TA,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( proces979765041_ch1Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ C @ H @ I @ J @ K @ L @ B ) )
= ( H @ B ) ) )
& ( ~ ( C @ B )
=> ( ( proces979765041_ch1Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ C @ H @ I @ J @ K @ L @ B ) )
= ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ C @ H @ I @ J @ K @ L @ ( I @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_process_Ocorec__sel_I3_J) ).
thf(539,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > $o,F: TA > ( proces634752977rocess @ TB ),G: TA > TA,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( proces979765041_ch1Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ C @ H @ I @ J @ K @ L @ B ) )
= ( H @ B ) ) )
& ( ~ ( C @ B )
=> ( ( proces979765041_ch1Of @ TB @ ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ C @ H @ I @ J @ K @ L @ B ) )
= ( proces894737309rocess @ TA @ TB @ A @ D @ E @ F @ G @ C @ H @ I @ J @ K @ L @ ( I @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_image__cong) ).
thf(203,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B )
= ( proces1525233512Action @ TB @ ( C @ B ) @ ( if @ ( proces634752977rocess @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_process_Ocorec_I1_J) ).
thf(524,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B )
= ( proces1525233512Action @ TB @ ( C @ B ) @ ( if @ ( proces634752977rocess @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ ( F @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( ( proces745025900prefOf @ TB @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_process_Ocorec__sel_I1_J) ).
thf(495,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( proces634752977rocess @ TB ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TB ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TB ),L: TA > TA] :
( ( A @ B )
=> ( ( proces745025900prefOf @ TB @ ( proces894737309rocess @ TA @ TB @ A @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(7,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_eq__onp__same__args) ).
thf(158,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( bNF_eq_onp @ TA @ A @ B @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: TA,D: proces634752977rocess @ TA] :
( ( ( proces1525233512Action @ TA @ A @ B )
= ( proces1525233512Action @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_process_Oinject_I1_J) ).
thf(390,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: TA,D: proces634752977rocess @ TA] :
( ( ( proces1525233512Action @ TA @ A @ B )
= ( proces1525233512Action @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_comp__eq__dest) ).
thf(171,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( proces634752977rocess @ TB ),E: TA > TA,F: TA > $o,G: TA > ( proces634752977rocess @ TB ),H: TA > TA,I: TA > $o,J: TA > ( proces634752977rocess @ TB ),K: TA > TA,L: TA] :
( ( proces10484146Action @ TB @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L ) )
= ( A @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_process_Ocorec__disc__iff_I1_J) ).
thf(568,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( proces634752977rocess @ TB ),E: TA > TA,F: TA > $o,G: TA > ( proces634752977rocess @ TB ),H: TA > TA,I: TA > $o,J: TA > ( proces634752977rocess @ TB ),K: TA > TA,L: TA] :
( ( proces10484146Action @ TB @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L ) )
= ( A @ L ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_bex__imageD) ).
thf(235,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces1778668539contOf @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( proces370407749rocess @ TA @ TB @ B @ ( proces1778668539contOf @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_process_Omap__sel_I2_J) ).
thf(667,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces1778668539contOf @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( proces370407749rocess @ TA @ TB @ B @ ( proces1778668539contOf @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: proces634752977rocess @ TA] :
( ( proces1205983068rocess @ TB @ A @ ( proces370407749rocess @ TA @ TB @ B @ C ) )
= ( proces1205983068rocess @ TA @ ( comp @ TB @ $o @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_process_Opred__map) ).
thf(151,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: proces634752977rocess @ TA] :
( ( proces1205983068rocess @ TB @ A @ ( proces370407749rocess @ TA @ TB @ B @ C ) )
= ( proces1205983068rocess @ TA @ ( comp @ TB @ $o @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_insert__ident) ).
thf(300,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(127,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ~ ( proces10484146Action @ TA @ A )
=> ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_process_Oexhaust__disc) ).
thf(620,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ~ ( proces10484146Action @ TA @ A )
=> ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > $o,C: TA > TC,D: TA > $o,E: TA > ( proces634752977rocess @ TC ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TC ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TC ),L: TA > TA] :
( ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ ( proces894737309rocess @ TA @ TC @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L ) )
= ( proces894737309rocess @ TA @ TB @ B @ ( comp @ TC @ TB @ TA @ A @ C ) @ D @ ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ E ) @ F @ G @ ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ H ) @ I @ J @ ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ K ) @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_process_Omap__o__corec) ).
thf(447,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > $o,C: TA > TC,D: TA > $o,E: TA > ( proces634752977rocess @ TC ),F: TA > TA,G: TA > $o,H: TA > ( proces634752977rocess @ TC ),I: TA > TA,J: TA > $o,K: TA > ( proces634752977rocess @ TC ),L: TA > TA] :
( ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ ( proces894737309rocess @ TA @ TC @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ L ) )
= ( proces894737309rocess @ TA @ TB @ B @ ( comp @ TC @ TB @ TA @ A @ C ) @ D @ ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ E ) @ F @ G @ ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ H ) @ I @ J @ ( comp @ ( proces634752977rocess @ TC ) @ ( proces634752977rocess @ TB ) @ TA @ ( proces370407749rocess @ TC @ TB @ A ) @ K ) @ L ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__commute) ).
thf(168,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Sup_OSUP__image) ).
thf(273,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_process_Oset__intros_I2_J) ).
thf(373,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA,C: TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: ( proces634752977rocess @ TB ) > ( proces634752977rocess @ TA ) > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: proces634752977rocess @ TB,F: proces634752977rocess @ TA] :
( ( A @ E @ F )
=> ( ( ( proces10484146Action @ TB @ E )
= ( proces10484146Action @ TA @ F ) )
& ( ( proces10484146Action @ TB @ E )
=> ( ( proces10484146Action @ TA @ F )
=> ( ( D @ ( proces745025900prefOf @ TB @ E ) @ ( proces745025900prefOf @ TA @ F ) )
& ( A @ ( proces1778668539contOf @ TB @ E ) @ ( proces1778668539contOf @ TA @ F ) ) ) ) )
& ( ( proces401113213Choice @ TB @ E )
=> ( ( proces401113213Choice @ TA @ F )
=> ( ( A @ ( proces979765041_ch1Of @ TB @ E ) @ ( proces979765041_ch1Of @ TA @ F ) )
& ( A @ ( proces988026546_ch2Of @ TB @ E ) @ ( proces988026546_ch2Of @ TA @ F ) ) ) ) ) ) )
=> ( proces749077512rocess @ TB @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_process_Orel__coinduct) ).
thf(603,plain,
! [TA: $tType,TB: $tType,A: ( proces634752977rocess @ TB ) > ( proces634752977rocess @ TA ) > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ! [E: proces634752977rocess @ TB,F: proces634752977rocess @ TA] :
( ( A @ E @ F )
=> ( ( ( proces10484146Action @ TB @ E )
= ( proces10484146Action @ TA @ F ) )
& ( ( proces10484146Action @ TB @ E )
=> ( ( proces10484146Action @ TA @ F )
=> ( ( D @ ( proces745025900prefOf @ TB @ E ) @ ( proces745025900prefOf @ TA @ F ) )
& ( A @ ( proces1778668539contOf @ TB @ E ) @ ( proces1778668539contOf @ TA @ F ) ) ) ) )
& ( ( proces401113213Choice @ TB @ E )
=> ( ( proces401113213Choice @ TA @ F )
=> ( ( A @ ( proces979765041_ch1Of @ TB @ E ) @ ( proces979765041_ch1Of @ TA @ F ) )
& ( A @ ( proces988026546_ch2Of @ TB @ E ) @ ( proces988026546_ch2Of @ TA @ F ) ) ) ) ) ) )
=> ( proces749077512rocess @ TB @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_image__insert) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_imageI) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(358,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: TB > TA > $o] :
( ( proces749077512rocess @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( member @ TB @ E @ ( proces1148692671rocess @ TB @ B ) )
=> ( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ C ) )
=> ( ( A @ E @ F )
=> ( D @ E @ F ) ) ) )
=> ( proces749077512rocess @ TB @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_process_Orel__mono__strong) ).
thf(437,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: proces634752977rocess @ TB,C: proces634752977rocess @ TA,D: TB > TA > $o] :
( ( proces749077512rocess @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( member @ TB @ E @ ( proces1148692671rocess @ TB @ B ) )
=> ( ( member @ TA @ F @ ( proces1148692671rocess @ TA @ C ) )
=> ( ( A @ E @ F )
=> ( D @ E @ F ) ) ) )
=> ( proces749077512rocess @ TB @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces745025900prefOf @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( B @ ( proces745025900prefOf @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_process_Omap__sel_I1_J) ).
thf(664,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA > TB] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces745025900prefOf @ TB @ ( proces370407749rocess @ TA @ TB @ B @ A ) )
= ( B @ ( proces745025900prefOf @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(103,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_ball__reg) ).
thf(532,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
=> ( C @ D ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insertE) ).
thf(283,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(129,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( member @ TA @ B @ ( proces1148692671rocess @ TA @ ( proces979765041_ch1Of @ TA @ A ) ) )
=> ( member @ TA @ B @ ( proces1148692671rocess @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_process_Oset__sel_I3_J) ).
thf(624,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( member @ TA @ B @ ( proces1148692671rocess @ TA @ ( proces979765041_ch1Of @ TA @ A ) ) )
=> ( member @ TA @ B @ ( proces1148692671rocess @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( proces1148692671rocess @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_process_Osimps_I21_J) ).
thf(459,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( proces1148692671rocess @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(80,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( A
!= ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1778668539contOf @ TA @ A ) ) )
=> ( A
= ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ A ) @ ( proces988026546_ch2Of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_process_Oexhaust__sel) ).
thf(442,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( A
!= ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1778668539contOf @ TA @ A ) ) )
=> ( A
= ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ A ) @ ( proces988026546_ch2Of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(51,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(309,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_rev__image__eqI) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType] :
( ( proces1406508781rocess @ TA @ TB )
= ( ^ [A: TA > ( proces634752977rocess @ TA ) > TB,B: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,C: proces634752977rocess @ TA] : ( if @ TB @ ( proces10484146Action @ TA @ C ) @ ( A @ ( proces745025900prefOf @ TA @ C ) @ ( proces1778668539contOf @ TA @ C ) ) @ ( B @ ( proces979765041_ch1Of @ TA @ C ) @ ( proces988026546_ch2Of @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_process_Ocase__eq__if) ).
thf(592,plain,
! [TA: $tType,TB: $tType] :
( ( proces1406508781rocess @ TA @ TB )
= ( ^ [A: TA > ( proces634752977rocess @ TA ) > TB,B: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TB,C: proces634752977rocess @ TA] : ( if @ TB @ ( proces10484146Action @ TA @ C ) @ ( A @ ( proces745025900prefOf @ TA @ C ) @ ( proces1778668539contOf @ TA @ C ) ) @ ( B @ ( proces979765041_ch1Of @ TA @ C ) @ ( proces988026546_ch2Of @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(66,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( proces1148692671rocess @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( proces749077512rocess @ TA @ TA @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_process_Orel__refl__strong) ).
thf(364,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( proces1148692671rocess @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( proces749077512rocess @ TA @ TA @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_comp__cong) ).
thf(232,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(706,plain,
$false,
inference(e,[status(thm)],[316,555,333,249,582,276,247,142,500,472,340,670,174,320,565,184,587,216,253,485,238,514,574,492,164,687,634,293,453,396,660,428,527,380,270,529,598,297,630,229,197,361,456,519,578,256,488,637,547,622,393,244,662,148,161,279,180,375,601,584,562,191,286,445,313,498,187,219,434,303,387,323,213,700,626,330,462,345,552,399,306,226,505,431,241,685,521,589,617,342,194,145,580,327,263,310,199,177,370,502,338,576,544,154,571,595,450,539,203,524,495,158,390,171,568,235,667,151,300,620,447,168,273,373,603,210,268,358,437,664,532,283,624,459,442,309,222,592,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PRO019^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n010.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 15:57:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.66/1.15 % [INFO] Parsing done (270ms).
% 1.66/1.16 % [INFO] Running in sequential loop mode.
% 2.82/1.39 % [INFO] eprover registered as external prover.
% 2.82/1.39 % [INFO] cvc4 registered as external prover.
% 2.82/1.39 % [INFO] Scanning for conjecture ...
% 3.02/1.50 % [INFO] Found a conjecture and 283 axioms. Running axiom selection ...
% 3.18/1.59 % [INFO] Axiom selection finished. Selected 139 axioms (removed 144 axioms).
% 4.10/1.82 % [INFO] Problem is higher-order (TPTP THF).
% 4.14/1.84 % [INFO] Type checking passed.
% 4.14/1.84 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 17.56/5.71 % External prover 'e' found a proof!
% 17.56/5.71 % [INFO] Killing All external provers ...
% 17.56/5.71 % Time passed: 5185ms (effective reasoning time: 4550ms)
% 17.56/5.71 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 17.56/5.71 % Axioms used in derivation (139): fact_98_insert__iff, fact_37_process_Ocase__eq__if, fact_103_image__cong, fact_53_process_Oset__sel_I3_J, fact_54_process_Oinj__map__strong, fact_28_process_Omap__sel_I2_J, fact_93_insert__image, fact_71_process_Osimps_I21_J, fact_61_process_Osel_I2_J, fact_117_Ball__def, fact_67_process_Ocorec__sel_I4_J, fact_70_process_Orel__sel, fact_81_process_Orel__refl, fact_3_process_Ocorec__disc__iff_I2_J, fact_23_isAction__def, fact_16_process_Oinject_I1_J, fact_165_rewriteR__comp__comp, fact_175_eq__onp__to__eq, fact_56_process_Omap__cong, fact_155_image__comp, fact_8_process_Ocorec__disc_I1_J, fact_84_process_Orel__mono__strong, fact_49_process_Ocoinduct__strong, fact_77_process_Orel__distinct_I1_J, fact_87_process_Orel__intros_I1_J, fact_35_process_Ocollapse_I1_J, fact_57_process_Oset__intros_I1_J, fact_62_process_Osel_I3_J, fact_89_process_Orel__distinct_I2_J, fact_42_process_Oexhaust__sel, fact_116_comp__apply__eq, fact_154_comp__eq__dest__lhs, fact_79_process_Orel__inject_I1_J, fact_163_rewriteR__comp__comp2, fact_110_insert__absorb, fact_104_bex__imageD, fact_94_Ball__image__comp, fact_82_process_Omap__o__corec, fact_157_Inf_OINF__image, fact_78_process_Orel__inject_I2_J, fact_166_rewriteL__comp__comp, fact_150_comp__def, fact_58_process_Oset__intros_I2_J, fact_11_process_OdiscI_I2_J, fact_26_process_Omap__sel_I3_J, fact_114_insertI1, fact_162_type__copy__map__cong0, fact_43_process_Oexpand, fact_66_process_Ocorec__sel_I3_J, fact_2_process_Oexhaust__disc, fact_164_rewriteL__comp__comp2, fact_50_process_Oset__sel_I2_J, fact_96_image__eqI, fact_109_insert__eq__iff, fact_152_comp__eq__dest, help_If_1_1_T, fact_55_process_Omap__cong0, fact_86_process_Orel__intros_I2_J, fact_21_process_Odistinct_I1_J, fact_10_process_Odisc_I3_J, fact_9_process_Odisc_I4_J, fact_113_insertI2, fact_59_process_Oset__intros_I3_J, fact_33_process_Osimps_I6_J, fact_69_process_Orel__coinduct, fact_105_image__iff, fact_15_process_Oinject_I2_J, fact_151_comp__assoc, fact_158_Sup_OSUP__image, fact_51_process_Oset__sel_I1_J, fact_80_process_Orel__eq, fact_25_process_Omap__sel_I1_J, fact_156_image__eq__imp__comp, fact_137_Inf_OINF__cong, fact_107_mk__disjoint__insert, fact_29_process_Oset__cases, fact_63_process_Osel_I4_J, fact_101_rev__image__eqI, fact_19_process_Osimps_I16_J, fact_153_comp__eq__elim, fact_97_insert__absorb2, fact_38_process_Opred__mono__strong, fact_41_process_Osplit__sel, fact_39_process_Opred__cong, fact_22_process_Oexhaust, fact_68_process_Ocorec__sel_I1_J, fact_159_ball__reg, fact_75_process_Oset__map, fact_102_ball__imageD, help_If_3_1_T, fact_40_process_Osplit__sel__asm, help_If_2_1_T, fact_44_process_Ocoinduct, fact_161_fun_Omap__comp, fact_20_process_Osimps_I15_J, fact_111_insert__ident, fact_14_process_Odisc_I1_J, fact_83_process_Orel__cong, fact_30_process_Oset__induct, fact_167_process_Opred__rel, fact_34_process_Osimps_I5_J, fact_7_process_Ocorec__disc_I2_J, fact_17_process_Ocorec_I2_J, fact_32_process_Opred__inject_I1_J, fact_176_eq__onp__same__args, fact_52_process_Oset__sel_I4_J, fact_27_process_Omap__sel_I4_J, fact_0_process_Odistinct__disc_I2_J, fact_64_process_Osel_I1_J, fact_92_image__insert, fact_74_process_Opred__set, fact_76_process_Orel__cases, fact_174_eq__onp__mono0, fact_85_process_Orel__refl__strong, fact_12_isChoice__def, fact_1_process_Odistinct__disc_I1_J, fact_24_process_OdiscI_I1_J, fact_112_Set_Oset__insert, fact_115_insertE, fact_73_process_Opred__map, fact_173_eq__onp__eqD, fact_88_process_Omap__comp, fact_13_process_Odisc_I2_J, fact_106_imageI, fact_18_process_Ocorec_I1_J, fact_172_process_Orel__eq__onp, fact_4_process_Ocorec__disc__iff_I1_J, fact_130_comp__apply, fact_31_process_Opred__inject_I2_J, fact_6_process_Omap__disc__iff_I1_J, fact_36_process_Ocollapse_I2_J, fact_138_Sup_OSUP__cong, fact_60_process_Oset__intros_I4_J, fact_129_not__False__in__image__Ball, fact_99_insertCI, fact_65_process_Ocorec__sel_I2_J, fact_5_process_Omap__disc__iff_I2_J, fact_160_comp__cong, fact_108_insert__commute
% 17.56/5.71 % No. of inferences in proof: 282
% 17.56/5.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5185 ms resp. 4550 ms w/o parsing
% 18.32/5.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.32/5.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------