TSTP Solution File: PRO023^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : PRO023^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 08:03:25 EDT 2024
% Result : Theorem 51.83s 26.02s
% Output : Refutation 52.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 286
% Syntax : Number of formulae : 526 ( 258 unt; 48 typ; 0 def)
% Number of atoms : 2100 ( 770 equ; 10 cnn)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 14380 ( 348 ~; 21 |; 95 &;13030 @)
% ( 0 <=>; 886 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1308 (1308 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 11 con; 0-14 aty)
% Number of variables : 3605 ( 364 ^3115 !; 46 ?;3605 :)
% ( 80 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(undefined_type,type,
undefined:
!>[TA: $tType] : TA ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(proces1239275103le_CH1_type,type,
proces1239275103le_CH1:
!>[TA: $tType,TB: $tType] : ( ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) ) ).
thf(proces1869379930H1_rel_type,type,
proces1869379930H1_rel:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) > ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) > $o ) ).
thf(proces1239275104le_CH2_type,type,
proces1239275104le_CH2:
!>[TA: $tType,TB: $tType] : ( ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) ) ).
thf(proces93903513H2_rel_type,type,
proces93903513H2_rel:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) > ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) > $o ) ).
thf(proces126235999e_CONT_type,type,
proces126235999e_CONT:
!>[TA: $tType,TB: $tType] : ( ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) ) ).
thf(proces1004198490NT_rel_type,type,
proces1004198490NT_rel:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) > ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) > $o ) ).
thf(proces1708129104e_PREF_type,type,
proces1708129104e_PREF:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( proces554692349s_term @ TB @ TA ) ) > ( proces554692349s_term @ TB @ TC ) > TB ) ).
thf(proces527360425EF_rel_type,type,
proces527360425EF_rel:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( product_prod @ ( TC > ( proces554692349s_term @ TB @ TA ) ) @ ( proces554692349s_term @ TB @ TC ) ) > ( product_prod @ ( TC > ( proces554692349s_term @ TB @ TA ) ) @ ( proces554692349s_term @ TB @ TC ) ) > $o ) ).
thf(proces1121166967uarded_type,type,
proces1121166967uarded:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > ( proces554692349s_term @ TB @ TA ) ) > $o ) ).
thf(proces687458811_isACT_type,type,
proces687458811_isACT:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > ( proces554692349s_term @ TC @ TB ) ) > ( proces554692349s_term @ TA @ TD ) > $o ) ).
thf(proces896239806CT_rel_type,type,
proces896239806CT_rel:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( product_prod @ ( TD > ( proces554692349s_term @ TC @ TB ) ) @ ( proces554692349s_term @ TA @ TD ) ) > ( product_prod @ ( TD > ( proces554692349s_term @ TC @ TB ) ) @ ( proces554692349s_term @ TA @ TD ) ) > $o ) ).
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(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(proces1454156180ss_ACT_type,type,
proces1454156180ss_ACT:
!>[TA: $tType,TB: $tType] : ( TB > ( proces554692349s_term @ TB @ TA ) > ( proces554692349s_term @ TB @ TA ) ) ).
thf(proces89589571ess_CH_type,type,
proces89589571ess_CH:
!>[TA: $tType,TB: $tType] : ( ( proces554692349s_term @ TB @ TA ) > ( proces554692349s_term @ TB @ TA ) > ( proces554692349s_term @ TB @ TA ) ) ).
thf(proces1062592052s_PROC_type,type,
proces1062592052s_PROC:
!>[TA: $tType,TB: $tType] : ( ( proces634752977rocess @ TB ) > ( proces554692349s_term @ TB @ TA ) ) ).
thf(proces1627516585ss_VAR_type,type,
proces1627516585ss_VAR:
!>[TA: $tType,TB: $tType] : ( TB > ( proces554692349s_term @ TA @ TB ) ) ).
thf(proces460752237s_term_type,type,
proces460752237s_term:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( ( proces634752977rocess @ TA ) > TB ) > ( TA > ( proces554692349s_term @ TA @ TC ) > TB ) > ( ( proces554692349s_term @ TA @ TC ) > ( proces554692349s_term @ TA @ TC ) > TB ) > ( proces554692349s_term @ TA @ TC ) > TB ) ).
thf(proces224683037s_term_type,type,
proces224683037s_term:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( proces554692349s_term @ TD @ TB ) > ( proces554692349s_term @ TC @ TA ) ) ).
thf(proces2118920028s_term_type,type,
proces2118920028s_term:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( proces554692349s_term @ TB @ TA ) > $o ) ).
thf(proces2029722208s_term_type,type,
proces2029722208s_term:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC > $o ) > ( TB > TA > $o ) > ( proces554692349s_term @ TD @ TB ) > ( proces554692349s_term @ TC @ TA ) > $o ) ).
thf(proces1264666542s_term_type,type,
proces1264666542s_term:
!>[TA: $tType,TB: $tType] : ( ( proces554692349s_term @ TB @ TA ) > ( set @ TB ) ) ).
thf(proces1493547885s_term_type,type,
proces1493547885s_term:
!>[TA: $tType,TB: $tType] : ( ( proces554692349s_term @ TB @ TA ) > ( set @ TA ) ) ).
thf(proces1652378886lution_type,type,
proces1652378886lution:
!>[TA: $tType,TB: $tType] : ( ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > ( proces634752977rocess @ TA ) ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(accp_type,type,
accp:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: proces634752977rocess @ a ).
thf(p2_type,type,
p2: proces634752977rocess @ a ).
thf(pa_type,type,
pa: proces634752977rocess @ a ).
thf(q_type,type,
q: proces634752977rocess @ a ).
thf(sys_type,type,
sys: b > ( proces554692349s_term @ a @ b ) ).
thf(121,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/sandbox/benchmark/theBenchmark.p',fact_108_process_Omap__cong0) ).
thf(892,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)],[121]) ).
thf(31,axiom,
! [TA: $tType] :
( ( proces988026546_ch2Of @ TA )
= ( proces1406508781rocess @ TA @ ( proces634752977rocess @ TA )
@ ^ [A: TA,B: proces634752977rocess @ TA] : ( undefined @ ( proces634752977rocess @ TA ) )
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ch2Of__def) ).
thf(365,plain,
! [TA: $tType] :
( ( proces988026546_ch2Of @ TA )
= ( proces1406508781rocess @ TA @ ( proces634752977rocess @ TA )
@ ^ [A: TA,B: proces634752977rocess @ TA] : ( undefined @ ( proces634752977rocess @ TA ) )
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_22_process_Ocorec_I2_J) ).
thf(760,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)],[94]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_56_process_Ocoinduct) ).
thf(1559,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)],[233]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces1708129104e_PREF @ TC @ TA @ TB @ A @ ( proces1062592052s_PROC @ TA @ TC @ B ) )
= ( proces745025900prefOf @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_PREF_Osimps_I2_J) ).
thf(846,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces1708129104e_PREF @ TC @ TA @ TB @ A @ ( proces1062592052s_PROC @ TA @ TC @ B ) )
= ( proces745025900prefOf @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: TA,C: proces554692349s_term @ TA @ TB] :
( ( proces126235999e_CONT @ TB @ TA @ A @ ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_CONT_Osimps_I3_J) ).
thf(333,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: TA,C: proces554692349s_term @ TA @ TB] :
( ( proces126235999e_CONT @ TB @ TA @ A @ ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > $o,B: proces634752977rocess @ TC,C: TA > TB,D: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TC @ TB @ A @ B @ ( proces370407749rocess @ TA @ TB @ C @ D ) )
= ( proces749077512rocess @ TC @ TA
@ ^ [E: TC,F: TA] : ( A @ E @ ( C @ F ) )
@ B
@ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_process_Orel__map_I2_J) ).
thf(518,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB > $o,B: proces634752977rocess @ TC,C: TA > TB,D: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TC @ TB @ A @ B @ ( proces370407749rocess @ TA @ TB @ C @ D ) )
= ( proces749077512rocess @ TC @ TA
@ ^ [E: TC,F: TA] : ( A @ E @ ( C @ F ) )
@ B
@ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(229,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ( ( proces1525233512Action @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1778668539contOf @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_process_Ocollapse_I1_J) ).
thf(1549,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)],[229]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',fact_96_process_Oset__sel_I4_J) ).
thf(1554,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)],[231]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TA > $o,B: TD > TB > $o,C: TD,D: proces634752977rocess @ TA] :
~ ( proces2029722208s_term @ TC @ TA @ TD @ TB @ A @ B @ ( proces1627516585ss_VAR @ TD @ TC @ C ) @ ( proces1062592052s_PROC @ TA @ TB @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_process__term_Orel__distinct_I1_J) ).
thf(523,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TA > $o,B: TD > TB > $o,C: TD,D: proces634752977rocess @ TA] :
~ ( proces2029722208s_term @ TC @ TA @ TD @ TB @ A @ B @ ( proces1627516585ss_VAR @ TD @ TC @ C ) @ ( proces1062592052s_PROC @ TA @ TB @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(190,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ B )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ~ ( proces460752237s_term @ TC @ $o @ TD
@ ^ [D: TC] : $false
@ ( proces10484146Action @ TD )
@ ^ [D: TD,E: proces554692349s_term @ TD @ TC] : $true
@ ^ [D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TD @ TC] : $false
@ ( A @ C ) ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ~ ( proces10484146Action @ TA @ C ) ) )
=> ~ ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_isACT_Opelims_I2_J) ).
thf(1290,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ B )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ~ ( proces460752237s_term @ TC @ $o @ TD
@ ^ [D: TC] : $false
@ ( proces10484146Action @ TD )
@ ^ [D: TD,E: proces554692349s_term @ TD @ TC] : $true
@ ^ [D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TD @ TC] : $false
@ ( A @ C ) ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ~ ( proces10484146Action @ TA @ C ) ) )
=> ~ ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(236,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( ( A
= ( proces1915862579Choice @ TA @ B @ C ) )
=> ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_process_OdiscI_I2_J) ).
thf(1591,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)],[236]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: TA] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_process__term_Oset__intros_I3_J) ).
thf(1269,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: TA] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: TA,F: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_process__term_Orel__distinct_I12_J) ).
thf(614,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: TA,F: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(191,axiom,
( q
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062) ).
thf(1305,plain,
( q
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(216,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ~ ( proces10484146Action @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_process_Odistinct__disc_I2_J) ).
thf(1486,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ~ ( proces10484146Action @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275103le_CH1 @ TB @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : E
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C = D )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_CH1_Opelims) ).
thf(1137,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275103le_CH1 @ TB @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : E
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C = D )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1869379930H1_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',fact_27_process_Oexhaust) ).
thf(1233,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)],[168]) ).
thf(106,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/sandbox/benchmark/theBenchmark.p',fact_66_process_Ocorec__sel_I1_J) ).
thf(814,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)],[106]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: ( proces634752977rocess @ TC ) > TB,C: TC > ( proces554692349s_term @ TC @ TA ) > TB,D: ( proces554692349s_term @ TC @ TA ) > ( proces554692349s_term @ TC @ TA ) > TB,E: TA] :
( ( proces460752237s_term @ TA @ TB @ TC @ A @ B @ C @ D @ ( proces1627516585ss_VAR @ TA @ TC @ E ) )
= ( A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_process__term_Osimps_I17_J) ).
thf(913,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: ( proces634752977rocess @ TC ) > TB,C: TC > ( proces554692349s_term @ TC @ TA ) > TB,D: ( proces554692349s_term @ TC @ TA ) > ( proces554692349s_term @ TC @ TA ) > TB,E: TA] :
( ( proces460752237s_term @ TA @ TB @ TC @ A @ B @ C @ D @ ( proces1627516585ss_VAR @ TA @ TC @ E ) )
= ( A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1239275104le_CH2 @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces460752237s_term @ TA @ ( proces554692349s_term @ TB @ TA ) @ TB
@ ^ [C: TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces634752977rocess @ TB] : ( proces1062592052s_PROC @ TB @ TA @ ( proces988026546_ch2Of @ TB @ C ) )
@ ^ [C: TB,D: proces554692349s_term @ TB @ TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces554692349s_term @ TB @ TA,D: proces554692349s_term @ TB @ TA] : D
@ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_CH2_Osimps_I1_J) ).
thf(1095,plain,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1239275104le_CH2 @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces460752237s_term @ TA @ ( proces554692349s_term @ TB @ TA ) @ TB
@ ^ [C: TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces634752977rocess @ TB] : ( proces1062592052s_PROC @ TB @ TA @ ( proces988026546_ch2Of @ TB @ C ) )
@ ^ [C: TB,D: proces554692349s_term @ TB @ TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces554692349s_term @ TB @ TA,D: proces554692349s_term @ TB @ TA] : D
@ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_PREF_Ocases) ).
thf(1243,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TA @ TC ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',fact_24_process_Osimps_I16_J) ).
thf(1046,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)],[138]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: TA,D: proces554692349s_term @ TA @ TB] :
( ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
= ( proces1454156180ss_ACT @ TC @ TD @ ( A @ C ) @ ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_process__term_Osimps_I27_J) ).
thf(320,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: TA,D: proces554692349s_term @ TA @ TB] :
( ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
= ( proces1454156180ss_ACT @ TC @ TD @ ( A @ C ) @ ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',fact_95_process_Oset__sel_I3_J) ).
thf(1518,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)],[220]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: proces554692349s_term @ TA @ TB] :
( ( proces1627516585ss_VAR @ TB @ TA @ A )
!= ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_process__term_Odistinct_I3_J) ).
thf(504,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: proces554692349s_term @ TA @ TB] :
( ( proces1627516585ss_VAR @ TB @ TA @ A )
!= ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( TB > ( proces554692349s_term @ TA @ TC ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TA @ TC ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_PREF_Oinduct) ).
thf(1264,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( TB > ( proces554692349s_term @ TA @ TC ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TA @ TC ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TC ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_82_process_Orel__intros_I1_J) ).
thf(619,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)],[75]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_isACT_Ocases) ).
thf(751,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TD @ TC ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(212,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/sandbox/benchmark/theBenchmark.p',fact_40_process_Omap__sel_I3_J) ).
thf(1462,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)],[212]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( member @ TD @ G @ ( proces1264666542s_term @ TD @ TC @ C ) )
=> ( ( member @ TA @ H @ ( proces1264666542s_term @ TA @ TB @ D ) )
=> ( ( A @ G @ H )
=> ( E @ G @ H ) ) ) )
=> ( ! [G: TC,H: TB] :
( ( member @ TC @ G @ ( proces1493547885s_term @ TD @ TC @ C ) )
=> ( ( member @ TB @ H @ ( proces1493547885s_term @ TA @ TB @ D ) )
=> ( ( B @ G @ H )
=> ( F @ G @ H ) ) ) )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_process__term_Orel__mono__strong) ).
thf(460,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB,E: TD > TA > $o,F: TC > TB > $o] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [G: TD,H: TA] :
( ( member @ TD @ G @ ( proces1264666542s_term @ TD @ TC @ C ) )
=> ( ( member @ TA @ H @ ( proces1264666542s_term @ TA @ TB @ D ) )
=> ( ( A @ G @ H )
=> ( E @ G @ H ) ) ) )
=> ( ! [G: TC,H: TB] :
( ( member @ TC @ G @ ( proces1493547885s_term @ TD @ TC @ C ) )
=> ( ( member @ TB @ H @ ( proces1493547885s_term @ TA @ TB @ D ) )
=> ( ( B @ G @ H )
=> ( F @ G @ H ) ) ) )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ E @ F @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_89_process_Orel__cases) ).
thf(817,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)],[107]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces126235999e_CONT @ TB @ TA @ A @ ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_CONT_Osimps_I2_J) ).
thf(606,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces126235999e_CONT @ TB @ TA @ A @ ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
= ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ E )
& ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_process__term_Orel__inject_I4_J) ).
thf(325,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
= ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ E )
& ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: TA,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
= ( ( A @ C @ E )
& ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_process__term_Orel__inject_I3_J) ).
thf(289,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: TA,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
= ( ( A @ C @ E )
& ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TF > TD,D: TE > TC,E: proces554692349s_term @ TF @ TE,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces224683037s_term @ TF @ TD @ TE @ TC @ C @ D @ E ) @ F )
= ( proces2029722208s_term @ TF @ TA @ TE @ TB
@ ^ [G: TF] : ( A @ ( C @ G ) )
@ ^ [G: TE] : ( B @ ( D @ G ) )
@ E
@ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_process__term_Orel__map_I1_J) ).
thf(448,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TF > TD,D: TE > TC,E: proces554692349s_term @ TF @ TE,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces224683037s_term @ TF @ TD @ TE @ TC @ C @ D @ E ) @ F )
= ( proces2029722208s_term @ TF @ TA @ TE @ TB
@ ^ [G: TF] : ( A @ ( C @ G ) )
@ ^ [G: TE] : ( B @ ( D @ G ) )
@ E
@ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_19_process_Oinject_I1_J) ).
thf(1100,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)],[150]) ).
thf(8,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_insertI2) ).
thf(284,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)],[8]) ).
thf(98,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( proces988026546_ch2Of @ TA @ ( proces1915862579Choice @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_process_Osel_I4_J) ).
thf(770,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)],[98]) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',fact_101_process_Orel__mono__strong) ).
thf(924,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)],[128]) ).
thf(213,axiom,
! [TA: $tType] :
( ( proces10484146Action @ TA )
= ( ^ [A: proces634752977rocess @ TA] :
? [B: TA,C: proces634752977rocess @ TA] :
( A
= ( proces1525233512Action @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_isAction__def) ).
thf(1465,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)],[213]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',fact_51_process_Osplit__sel) ).
thf(1109,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)],[152]) ).
thf(203,axiom,
( p2
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_iss) ).
thf(1418,plain,
( p2
= ( proces1652378886lution @ b @ a @ sys @ ( proces1062592052s_PROC @ a @ b @ pa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',fact_106_process_Oset__intros_I4_J) ).
thf(514,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)],[56]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB > $o,B: TC > TA > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: TA] :
~ ( proces2029722208s_term @ TD @ TB @ TC @ TA @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces1627516585ss_VAR @ TA @ TB @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_process__term_Orel__distinct_I4_J) ).
thf(806,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB > $o,B: TC > TA > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: TA] :
~ ( proces2029722208s_term @ TD @ TB @ TC @ TA @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces1627516585ss_VAR @ TA @ TB @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',fact_142_insertE) ).
thf(353,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)],[27]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ E @ F )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ E ) @ ( proces89589571ess_CH @ TA @ TB @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_process__term_Orel__intros_I4_J) ).
thf(480,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ E @ F )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ E ) @ ( proces89589571ess_CH @ TA @ TB @ D @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',fact_23_process_Ocorec_I1_J) ).
thf(1183,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)],[161]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_7_process_Ocorec__disc__iff_I1_J) ).
thf(1283,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)],[187]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',fact_88_process_Orel__distinct_I1_J) ).
thf(766,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)],[96]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces634752977rocess @ TD,D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1062592052s_PROC @ TD @ TC @ C ) @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_process__term_Orel__distinct_I9_J) ).
thf(877,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces634752977rocess @ TD,D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1062592052s_PROC @ TD @ TC @ C ) @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces126235999e_CONT @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces460752237s_term @ TA @ ( proces554692349s_term @ TB @ TA ) @ TB
@ ^ [C: TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces634752977rocess @ TB] : ( proces1062592052s_PROC @ TB @ TA @ ( proces1778668539contOf @ TB @ C ) )
@ ^ [C: TB,D: proces554692349s_term @ TB @ TA] : D
@ ^ [C: proces554692349s_term @ TB @ TA,D: proces554692349s_term @ TB @ TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_CONT_Osimps_I1_J) ).
thf(1072,plain,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces126235999e_CONT @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces460752237s_term @ TA @ ( proces554692349s_term @ TB @ TA ) @ TB
@ ^ [C: TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces634752977rocess @ TB] : ( proces1062592052s_PROC @ TB @ TA @ ( proces1778668539contOf @ TB @ C ) )
@ ^ [C: TB,D: proces554692349s_term @ TB @ TA] : D
@ ^ [C: proces554692349s_term @ TB @ TA,D: proces554692349s_term @ TB @ TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_process__term_Oset__intros_I4_J) ).
thf(1119,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > TC,D: TA > TC,E: TB > TD,F: TB > TD] :
( ( A = B )
=> ( ( proces2118920028s_term @ TA @ TB
@ ^ [G: TA] :
( ( C @ G )
= ( D @ G ) )
@ ^ [G: TB] :
( ( E @ G )
= ( F @ G ) )
@ B )
=> ( ( proces224683037s_term @ TA @ TC @ TB @ TD @ C @ E @ A )
= ( proces224683037s_term @ TA @ TC @ TB @ TD @ D @ F @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_process__term_Omap__cong__pred) ).
thf(396,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > TC,D: TA > TC,E: TB > TD,F: TB > TD] :
( ( A = B )
=> ( ( proces2118920028s_term @ TA @ TB
@ ^ [G: TA] :
( ( C @ G )
= ( D @ G ) )
@ ^ [G: TB] :
( ( E @ G )
= ( F @ G ) )
@ B )
=> ( ( proces224683037s_term @ TA @ TC @ TB @ TD @ C @ E @ A )
= ( proces224683037s_term @ TA @ TC @ TB @ TD @ D @ F @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',fact_98_process_Oset__sel_I2_J) ).
thf(1351,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)],[197]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > ( proces554692349s_term @ TC @ TB ),B: TA] :
( ( proces687458811_isACT @ TA @ TC @ TB @ TD @ A @ ( proces1627516585ss_VAR @ TA @ TD @ B ) )
= ( proces460752237s_term @ TB @ $o @ TC
@ ^ [C: TB] : $false
@ ( proces10484146Action @ TC )
@ ^ [C: TC,D: proces554692349s_term @ TC @ TB] : $true
@ ^ [C: proces554692349s_term @ TC @ TB,D: proces554692349s_term @ TC @ TB] : $false
@ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_isACT_Osimps_I1_J) ).
thf(1345,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > ( proces554692349s_term @ TC @ TB ),B: TA] :
( ( proces687458811_isACT @ TA @ TC @ TB @ TD @ A @ ( proces1627516585ss_VAR @ TA @ TD @ B ) )
= ( proces460752237s_term @ TB @ $o @ TC
@ ^ [C: TB] : $false
@ ( proces10484146Action @ TC )
@ ^ [C: TC,D: proces554692349s_term @ TC @ TB] : $true
@ ^ [C: proces554692349s_term @ TC @ TB,D: proces554692349s_term @ TC @ TB] : $false
@ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(3,axiom,
! [TA: $tType] :
( ( proces1778668539contOf @ TA )
= ( proces1406508781rocess @ TA @ ( proces634752977rocess @ TA )
@ ^ [A: TA,B: proces634752977rocess @ TA] : B
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( undefined @ ( proces634752977rocess @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_contOf__def) ).
thf(243,plain,
! [TA: $tType] :
( ( proces1778668539contOf @ TA )
= ( proces1406508781rocess @ TA @ ( proces634752977rocess @ TA )
@ ^ [A: TA,B: proces634752977rocess @ TA] : B
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( undefined @ ( proces634752977rocess @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(239,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TA @ A )
=> ( ( proces1915862579Choice @ TA @ ( proces979765041_ch1Of @ TA @ A ) @ ( proces988026546_ch2Of @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_process_Ocollapse_I2_J) ).
thf(1600,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)],[239]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_99_process_Oset__cases) ).
thf(849,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)],[109]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,A: ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_CH2_Oinduct) ).
thf(507,plain,
! [TA: $tType,TB: $tType,A: ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( proces2029722208s_term @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( proces554692349s_term @ TA @ TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_process__term_Orel__eq) ).
thf(292,plain,
! [TA: $tType,TB: $tType] :
( ( proces2029722208s_term @ TA @ TA @ TB @ TB @ ( (=) @ TA ) @ ( (=) @ TB ) )
= ( (=) @ ( proces554692349s_term @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > TC,D: TA > TC,E: TB > TD,F: TB > TD] :
( ( A = B )
=> ( ! [G: TA] :
( ( member @ TA @ G @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ! [G: TB] :
( ( member @ TB @ G @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( proces224683037s_term @ TA @ TC @ TB @ TD @ C @ E @ A )
= ( proces224683037s_term @ TA @ TC @ TB @ TD @ D @ F @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_process__term_Omap__cong) ).
thf(380,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > TC,D: TA > TC,E: TB > TD,F: TB > TD] :
( ( A = B )
=> ( ! [G: TA] :
( ( member @ TA @ G @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ! [G: TB] :
( ( member @ TB @ G @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( proces224683037s_term @ TA @ TC @ TB @ TD @ C @ E @ A )
= ( proces224683037s_term @ TA @ TC @ TB @ TD @ D @ F @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_104_process_Oset__intros_I2_J) ).
thf(512,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)],[55]) ).
thf(209,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ( member @ TA @ ( proces745025900prefOf @ TA @ A ) @ ( proces1148692671rocess @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_process_Oset__sel_I1_J) ).
thf(1438,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)],[209]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_process__term_Oset__intros_I5_J) ).
thf(798,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_63_process_Ocorec__sel_I2_J) ).
thf(1057,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)],[142]) ).
thf(123,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( proces979765041_ch1Of @ TA @ ( proces1915862579Choice @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_process_Osel_I3_J) ).
thf(910,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)],[123]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType] :
( ( proces894737309rocess @ TA @ TB )
= ( ^ [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] : ( if @ ( proces634752977rocess @ TB ) @ ( A @ L ) @ ( proces1525233512Action @ TB @ ( B @ L ) @ ( if @ ( proces634752977rocess @ TB ) @ ( C @ L ) @ ( D @ L ) @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ ( E @ L ) ) ) ) @ ( proces1915862579Choice @ TB @ ( if @ ( proces634752977rocess @ TB ) @ ( F @ L ) @ ( G @ L ) @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ ( H @ L ) ) ) @ ( if @ ( proces634752977rocess @ TB ) @ ( I @ L ) @ ( J @ L ) @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ ( K @ L ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_process_Ocorec__code) ).
thf(957,plain,
! [TA: $tType,TB: $tType] :
( ( proces894737309rocess @ TA @ TB )
= ( ^ [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] : ( if @ ( proces634752977rocess @ TB ) @ ( A @ L ) @ ( proces1525233512Action @ TB @ ( B @ L ) @ ( if @ ( proces634752977rocess @ TB ) @ ( C @ L ) @ ( D @ L ) @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ ( E @ L ) ) ) ) @ ( proces1915862579Choice @ TB @ ( if @ ( proces634752977rocess @ TB ) @ ( F @ L ) @ ( G @ L ) @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ ( H @ L ) ) ) @ ( if @ ( proces634752977rocess @ TB ) @ ( I @ L ) @ ( J @ L ) @ ( proces894737309rocess @ TA @ TB @ A @ B @ C @ D @ E @ F @ G @ H @ I @ J @ K @ ( K @ L ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1627516585ss_VAR @ TB @ TA @ A )
!= ( proces89589571ess_CH @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_process__term_Odistinct_I5_J) ).
thf(1255,plain,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1627516585ss_VAR @ TB @ TA @ A )
!= ( proces89589571ess_CH @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: ( proces634752977rocess @ TA ) > TB,C: TA > ( proces554692349s_term @ TA @ TC ) > TB,D: ( proces554692349s_term @ TA @ TC ) > ( proces554692349s_term @ TA @ TC ) > TB,E: proces634752977rocess @ TA] :
( ( proces460752237s_term @ TC @ TB @ TA @ A @ B @ C @ D @ ( proces1062592052s_PROC @ TA @ TC @ E ) )
= ( B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_process__term_Osimps_I18_J) ).
thf(862,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: ( proces634752977rocess @ TA ) > TB,C: TA > ( proces554692349s_term @ TA @ TC ) > TB,D: ( proces554692349s_term @ TA @ TC ) > ( proces554692349s_term @ TA @ TC ) > TB,E: proces634752977rocess @ TA] :
( ( proces460752237s_term @ TC @ TB @ TA @ A @ B @ C @ D @ ( proces1062592052s_PROC @ TA @ TC @ E ) )
= ( B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( proces554692349s_term @ TA @ TC ),B: proces554692349s_term @ TA @ TB,C: TA] :
( ( ( proces1708129104e_PREF @ TB @ TA @ TC @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TC @ TA @ TA
@ ^ [E: TC] : ( undefined @ TA )
@ ( proces745025900prefOf @ TA )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TC] : E
@ ^ [E: proces554692349s_term @ TA @ TC,F: proces554692349s_term @ TA @ TC] : ( undefined @ TA )
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces745025900prefOf @ TA @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C = D )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ TA ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_PREF_Opelims) ).
thf(693,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( proces554692349s_term @ TA @ TC ),B: proces554692349s_term @ TA @ TB,C: TA] :
( ( ( proces1708129104e_PREF @ TB @ TA @ TC @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TC @ TA @ TA
@ ^ [E: TC] : ( undefined @ TA )
@ ( proces745025900prefOf @ TA )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TC] : E
@ ^ [E: proces554692349s_term @ TA @ TC,F: proces554692349s_term @ TA @ TC] : ( undefined @ TA )
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces745025900prefOf @ TA @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C = D )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ TA ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces527360425EF_rel @ TB @ TA @ TC ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces634752977rocess @ TD,D: TA,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1062592052s_PROC @ TD @ TC @ C ) @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_process__term_Orel__distinct_I7_J) ).
thf(1238,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces634752977rocess @ TD,D: TA,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1062592052s_PROC @ TD @ TC @ C ) @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',fact_10_process_Ocorec__disc_I2_J) ).
thf(1423,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)],[205]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_process__term_Oset__intros_I9_J) ).
thf(916,plain,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_25_process_Osimps_I15_J) ).
thf(879,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)],[116]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TB,B: TD > TC,C: proces634752977rocess @ TA] :
( ( proces224683037s_term @ TA @ TB @ TD @ TC @ A @ B @ ( proces1062592052s_PROC @ TA @ TD @ C ) )
= ( proces1062592052s_PROC @ TB @ TC @ ( proces370407749rocess @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_process__term_Osimps_I26_J) ).
thf(583,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TB,B: TD > TC,C: proces634752977rocess @ TA] :
( ( proces224683037s_term @ TA @ TB @ TD @ TC @ A @ B @ ( proces1062592052s_PROC @ TA @ TD @ C ) )
= ( proces1062592052s_PROC @ TB @ TC @ ( proces370407749rocess @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > ( proces634752977rocess @ TA ) > TC,C: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TC,D: proces634752977rocess @ TA] :
( ( A @ ( proces1406508781rocess @ TA @ TC @ B @ C @ D ) )
= ( proces1406508781rocess @ TA @ TB
@ ^ [E: TA,F: proces634752977rocess @ TA] : ( A @ ( B @ E @ F ) )
@ ^ [E: proces634752977rocess @ TA,F: proces634752977rocess @ TA] : ( A @ ( C @ E @ F ) )
@ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_process_Ocase__distrib) ).
thf(889,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > ( proces634752977rocess @ TA ) > TC,C: ( proces634752977rocess @ TA ) > ( proces634752977rocess @ TA ) > TC,D: proces634752977rocess @ TA] :
( ( A @ ( proces1406508781rocess @ TA @ TC @ B @ C @ D ) )
= ( proces1406508781rocess @ TA @ TB
@ ^ [E: TA,F: proces634752977rocess @ TA] : ( A @ ( B @ E @ F ) )
@ ^ [E: proces634752977rocess @ TA,F: proces634752977rocess @ TA] : ( A @ ( C @ E @ F ) )
@ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > $o,B: TC > TB,C: proces634752977rocess @ TC,D: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ ( proces370407749rocess @ TC @ TB @ B @ C ) @ D )
= ( proces749077512rocess @ TC @ TA
@ ^ [E: TC] : ( A @ ( B @ E ) )
@ C
@ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_process_Orel__map_I1_J) ).
thf(757,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA > $o,B: TC > TB,C: proces634752977rocess @ TC,D: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TB @ TA @ A @ ( proces370407749rocess @ TC @ TB @ B @ C ) @ D )
= ( proces749077512rocess @ TC @ TA
@ ^ [E: TC] : ( A @ ( B @ E ) )
@ C
@ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1062592052s_PROC @ TA @ TB @ A )
!= ( proces89589571ess_CH @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_process__term_Odistinct_I9_J) ).
thf(1128,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1062592052s_PROC @ TA @ TB @ A )
!= ( proces89589571ess_CH @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(186,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
~ ( ( proces10484146Action @ TA @ A )
& ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__isAction__isChoice) ).
thf(1281,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
~ ( ( proces10484146Action @ TA @ A )
& ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(200,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 ) )
& ( ( proces401113213Choice @ TA @ D )
= ( proces401113213Choice @ TA @ E ) ) ) )
=> ( ! [D: TA,E: TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1525233512Action @ TA @ D @ F ) @ ( proces1525233512Action @ TA @ E @ G ) )
=> ( ( D = E )
& ( A @ F @ G ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1915862579Choice @ TA @ D @ E ) @ ( proces1915862579Choice @ TA @ F @ G ) )
=> ( ( A @ D @ F )
& ( A @ E @ G ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_process__coind) ).
thf(1402,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 ) )
& ( ( proces401113213Choice @ TA @ D )
= ( proces401113213Choice @ TA @ E ) ) ) )
=> ( ! [D: TA,E: TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1525233512Action @ TA @ D @ F ) @ ( proces1525233512Action @ TA @ E @ G ) )
=> ( ( D = E )
& ( A @ F @ G ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1915862579Choice @ TA @ D @ E ) @ ( proces1915862579Choice @ TA @ F @ G ) )
=> ( ( A @ D @ F )
& ( A @ E @ G ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( proces1652378886lution @ TA @ TB )
= ( ^ [A: TA > ( proces554692349s_term @ TB @ TA ),B: proces554692349s_term @ TB @ TA] : ( if @ ( proces634752977rocess @ TB ) @ ( proces687458811_isACT @ TA @ TB @ TA @ TB @ A @ B ) @ ( proces1525233512Action @ TB @ ( proces1708129104e_PREF @ TA @ TB @ TA @ A @ B ) @ ( proces1652378886lution @ TA @ TB @ A @ ( proces126235999e_CONT @ TA @ TB @ A @ B ) ) ) @ ( proces1915862579Choice @ TB @ ( proces1652378886lution @ TA @ TB @ A @ ( proces1239275103le_CH1 @ TA @ TB @ A @ B ) ) @ ( proces1652378886lution @ TA @ TB @ A @ ( proces1239275104le_CH2 @ TA @ TB @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_solution_Ocode) ).
thf(742,plain,
! [TA: $tType,TB: $tType] :
( ( proces1652378886lution @ TA @ TB )
= ( ^ [A: TA > ( proces554692349s_term @ TB @ TA ),B: proces554692349s_term @ TB @ TA] : ( if @ ( proces634752977rocess @ TB ) @ ( proces687458811_isACT @ TA @ TB @ TA @ TB @ A @ B ) @ ( proces1525233512Action @ TB @ ( proces1708129104e_PREF @ TA @ TB @ TA @ A @ B ) @ ( proces1652378886lution @ TA @ TB @ A @ ( proces126235999e_CONT @ TA @ TB @ A @ B ) ) ) @ ( proces1915862579Choice @ TB @ ( proces1652378886lution @ TA @ TB @ A @ ( proces1239275103le_CH1 @ TA @ TB @ A @ B ) ) @ ( proces1652378886lution @ TA @ TB @ A @ ( proces1239275104le_CH2 @ TA @ TB @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(226,axiom,
( ( proces10484146Action @ a @ pa )
| ( proces401113213Choice @ a @ pa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062) ).
thf(1541,plain,
( ( proces10484146Action @ a @ pa )
| ( proces401113213Choice @ a @ pa ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces745025900prefOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_process_Osel_I1_J) ).
thf(874,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces745025900prefOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',fact_109_process_Omap__cong) ).
thf(1121,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)],[156]) ).
thf(206,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ~ ( proces10484146Action @ TA @ A )
=> ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_process_Oexhaust__disc) ).
thf(1425,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ~ ( proces10484146Action @ TA @ A )
=> ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( proces2029722208s_term @ TC @ TD @ TB @ TA @ A @ B @ ( proces1627516585ss_VAR @ TB @ TC @ C ) @ ( proces1627516585ss_VAR @ TA @ TD @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_process__term_Orel__inject_I1_J) ).
thf(356,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( proces2029722208s_term @ TC @ TD @ TB @ TA @ A @ B @ ( proces1627516585ss_VAR @ TB @ TC @ C ) @ ( proces1627516585ss_VAR @ TA @ TD @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: TA,C: proces554692349s_term @ TA @ TB] : ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_isACT_Osimps_I3_J) ).
thf(499,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: TA,C: proces554692349s_term @ TA @ TB] : ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD,C: TA,D: TC > TB > $o] :
( ( A @ B @ C )
=> ( proces2029722208s_term @ TC @ TB @ TD @ TA @ D @ A @ ( proces1627516585ss_VAR @ TD @ TC @ B ) @ ( proces1627516585ss_VAR @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_process__term_Orel__intros_I1_J) ).
thf(328,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD,C: TA,D: TC > TB > $o] :
( ( A @ B @ C )
=> ( proces2029722208s_term @ TC @ TB @ TD @ TA @ D @ A @ ( proces1627516585ss_VAR @ TD @ TC @ B ) @ ( proces1627516585ss_VAR @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(118,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/sandbox/benchmark/theBenchmark.p',fact_54_process_Oexhaust__sel) ).
thf(884,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)],[118]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
= ( proces89589571ess_CH @ TC @ TD @ ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ C ) @ ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_process__term_Osimps_I28_J) ).
thf(339,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
= ( proces89589571ess_CH @ TC @ TD @ ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ C ) @ ( proces224683037s_term @ TA @ TC @ TB @ TD @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(81,axiom,
! [TA: $tType,A: TA > TA > $o,B: proces634752977rocess @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( proces749077512rocess @ TA @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_process_Orel__refl) ).
thf(679,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)],[81]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA] : ( member @ TA @ A @ ( proces1493547885s_term @ TB @ TA @ ( proces1627516585ss_VAR @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_process__term_Oset__intros_I6_J) ).
thf(686,plain,
! [TA: $tType,TB: $tType,A: TA] : ( member @ TA @ A @ ( proces1493547885s_term @ TB @ TA @ ( proces1627516585ss_VAR @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
~ ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_isACT_Osimps_I4_J) ).
thf(1075,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
~ ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] :
( ( proces1493547885s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ A @ B ) )
= ( proces1493547885s_term @ TA @ TB @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_process__term_Osimps_I51_J) ).
thf(393,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] :
( ( proces1493547885s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ A @ B ) )
= ( proces1493547885s_term @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > ( proces554692349s_term @ TB @ TC ),B: proces634752977rocess @ TA] :
( ( proces687458811_isACT @ TD @ TB @ TC @ TA @ A @ ( proces1062592052s_PROC @ TA @ TD @ B ) )
= ( proces10484146Action @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_isACT_Osimps_I2_J) ).
thf(1588,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > ( proces554692349s_term @ TB @ TC ),B: proces634752977rocess @ TA] :
( ( proces687458811_isACT @ TD @ TB @ TC @ TA @ A @ ( proces1062592052s_PROC @ TA @ TD @ B ) )
= ( proces10484146Action @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces1778668539contOf @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1652378886lution @ TB @ TA @ A @ ( proces126235999e_CONT @ TB @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_solution_Osimps_I4_J) ).
thf(1249,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces1778668539contOf @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1652378886lution @ TB @ TA @ A @ ( proces126235999e_CONT @ TB @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( proces554692349s_term @ TC @ TB ),B: TA] :
( ( proces1708129104e_PREF @ TA @ TC @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TC @ B ) )
= ( proces460752237s_term @ TB @ TC @ TC
@ ^ [C: TB] : ( undefined @ TC )
@ ( proces745025900prefOf @ TC )
@ ^ [C: TC,D: proces554692349s_term @ TC @ TB] : C
@ ^ [C: proces554692349s_term @ TC @ TB,D: proces554692349s_term @ TC @ TB] : ( undefined @ TC )
@ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_PREF_Osimps_I1_J) ).
thf(1266,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( proces554692349s_term @ TC @ TB ),B: TA] :
( ( proces1708129104e_PREF @ TA @ TC @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TC @ B ) )
= ( proces460752237s_term @ TB @ TC @ TC
@ ^ [C: TB] : ( undefined @ TC )
@ ( proces745025900prefOf @ TC )
@ ^ [C: TC,D: proces554692349s_term @ TC @ TB] : C
@ ^ [C: proces554692349s_term @ TC @ TB,D: proces554692349s_term @ TC @ TB] : ( undefined @ TC )
@ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( proces2118920028s_term @ TA @ TB
@ ^ [A: TA] : $true
@ ^ [A: TB] : $true )
= ( ^ [A: proces554692349s_term @ TA @ TB] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_process__term_Opred__True) ).
thf(1131,plain,
! [TA: $tType,TB: $tType] :
( ( proces2118920028s_term @ TA @ TB
@ ^ [A: TA] : $true
@ ^ [A: TB] : $true )
= ( ^ [A: proces554692349s_term @ TA @ TB] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( proces10484146Action @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_solution_Odisc_I1_J) ).
thf(1552,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( proces10484146Action @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TA] :
( ( proces224683037s_term @ TD @ TC @ TA @ TB @ A @ B @ ( proces1627516585ss_VAR @ TA @ TD @ C ) )
= ( proces1627516585ss_VAR @ TB @ TC @ ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_process__term_Osimps_I25_J) ).
thf(457,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TA] :
( ( proces224683037s_term @ TD @ TC @ TA @ TB @ A @ B @ ( proces1627516585ss_VAR @ TA @ TD @ C ) )
= ( proces1627516585ss_VAR @ TB @ TC @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TC @ TD ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TC @ TD @ TA @ A @ B )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( proces460752237s_term @ TD @ $o @ TC
@ ^ [D: TD] : $false
@ ( proces10484146Action @ TC )
@ ^ [D: TC,E: proces554692349s_term @ TC @ TD] : $true
@ ^ [D: proces554692349s_term @ TC @ TD,E: proces554692349s_term @ TC @ TD] : $false
@ ( A @ C ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( proces10484146Action @ TA @ C ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( B
!= ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_isACT_Oelims_I3_J) ).
thf(1429,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TC @ TD ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TC @ TD @ TA @ A @ B )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( proces460752237s_term @ TD @ $o @ TC
@ ^ [D: TD] : $false
@ ( proces10484146Action @ TC )
@ ^ [D: TC,E: proces554692349s_term @ TC @ TD] : $true
@ ^ [D: proces554692349s_term @ TC @ TD,E: proces554692349s_term @ TC @ TD] : $false
@ ( A @ C ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( proces10484146Action @ TA @ C ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( B
!= ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_CH2_Ocases) ).
thf(1246,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',fact_43_process_Omap__sel_I2_J) ).
thf(1525,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)],[223]) ).
thf(127,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_process_Omap__ident) ).
thf(921,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces370407749rocess @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',fact_68_process_Osimps_I6_J) ).
thf(1054,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)],[141]) ).
thf(188,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
~ ( proces10484146Action @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_process_Odisc_I2_J) ).
thf(1286,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
~ ( proces10484146Action @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces10484146Action @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( proces10484146Action @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_process_Omap__disc__iff_I1_J) ).
thf(1515,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)],[219]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275103le_CH1 @ TB @ TA @ A @ B )
= C )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : E
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( C
!= ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ D ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB] :
( ? [E: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( C != D ) )
=> ~ ( ? [D: TA,E: proces554692349s_term @ TA @ TB] :
( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C
!= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_CH1_Oelims) ).
thf(773,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275103le_CH1 @ TB @ TA @ A @ B )
= C )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : E
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( C
!= ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ D ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB] :
( ? [E: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( C != D ) )
=> ~ ( ? [D: TA,E: proces554692349s_term @ TA @ TB] :
( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C
!= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB,E: ( proces554692349s_term @ TD @ TC ) > ( proces554692349s_term @ TA @ TB ) > $o] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [F: TC,G: TB] :
( ( B @ F @ G )
=> ( E @ ( proces1627516585ss_VAR @ TC @ TD @ F ) @ ( proces1627516585ss_VAR @ TB @ TA @ G ) ) )
=> ( ! [F: proces634752977rocess @ TD,G: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TD @ TA @ A @ F @ G )
=> ( E @ ( proces1062592052s_PROC @ TD @ TC @ F ) @ ( proces1062592052s_PROC @ TA @ TB @ G ) ) )
=> ( ! [F: TD,G: proces554692349s_term @ TD @ TC,H: TA,I: proces554692349s_term @ TA @ TB] :
( ( A @ F @ H )
=> ( ( E @ G @ I )
=> ( E @ ( proces1454156180ss_ACT @ TD @ TC @ F @ G ) @ ( proces1454156180ss_ACT @ TA @ TB @ H @ I ) ) ) )
=> ( ! [F: proces554692349s_term @ TD @ TC,G: proces554692349s_term @ TD @ TC,H: proces554692349s_term @ TA @ TB,I: proces554692349s_term @ TA @ TB] :
( ( E @ F @ H )
=> ( ( E @ G @ I )
=> ( E @ ( proces89589571ess_CH @ TD @ TC @ F @ G ) @ ( proces89589571ess_CH @ TA @ TB @ H @ I ) ) ) )
=> ( E @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_process__term_Orel__induct) ).
thf(586,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB,E: ( proces554692349s_term @ TD @ TC ) > ( proces554692349s_term @ TA @ TB ) > $o] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [F: TC,G: TB] :
( ( B @ F @ G )
=> ( E @ ( proces1627516585ss_VAR @ TC @ TD @ F ) @ ( proces1627516585ss_VAR @ TB @ TA @ G ) ) )
=> ( ! [F: proces634752977rocess @ TD,G: proces634752977rocess @ TA] :
( ( proces749077512rocess @ TD @ TA @ A @ F @ G )
=> ( E @ ( proces1062592052s_PROC @ TD @ TC @ F ) @ ( proces1062592052s_PROC @ TA @ TB @ G ) ) )
=> ( ! [F: TD,G: proces554692349s_term @ TD @ TC,H: TA,I: proces554692349s_term @ TA @ TB] :
( ( A @ F @ H )
=> ( ( E @ G @ I )
=> ( E @ ( proces1454156180ss_ACT @ TD @ TC @ F @ G ) @ ( proces1454156180ss_ACT @ TA @ TB @ H @ I ) ) ) )
=> ( ! [F: proces554692349s_term @ TD @ TC,G: proces554692349s_term @ TD @ TC,H: proces554692349s_term @ TA @ TB,I: proces554692349s_term @ TA @ TB] :
( ( E @ F @ H )
=> ( ( E @ G @ I )
=> ( E @ ( proces89589571ess_CH @ TD @ TC @ F @ G ) @ ( proces89589571ess_CH @ TA @ TB @ H @ I ) ) ) )
=> ( E @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > TD,D: TA > TD,E: TB > TC,F: TB > TC] :
( ! [G: TA,H: TA] :
( ( member @ TA @ G @ ( proces1264666542s_term @ TA @ TB @ A ) )
=> ( ( member @ TA @ H @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ( ( C @ G )
= ( D @ H ) )
=> ( G = H ) ) ) )
=> ( ! [G: TB,H: TB] :
( ( member @ TB @ G @ ( proces1493547885s_term @ TA @ TB @ A ) )
=> ( ( member @ TB @ H @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( ( E @ G )
= ( F @ H ) )
=> ( G = H ) ) ) )
=> ( ( ( proces224683037s_term @ TA @ TD @ TB @ TC @ C @ E @ A )
= ( proces224683037s_term @ TA @ TD @ TB @ TC @ D @ F @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_process__term_Oinj__map__strong) ).
thf(412,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > TD,D: TA > TD,E: TB > TC,F: TB > TC] :
( ! [G: TA,H: TA] :
( ( member @ TA @ G @ ( proces1264666542s_term @ TA @ TB @ A ) )
=> ( ( member @ TA @ H @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ( ( C @ G )
= ( D @ H ) )
=> ( G = H ) ) ) )
=> ( ! [G: TB,H: TB] :
( ( member @ TB @ G @ ( proces1493547885s_term @ TA @ TB @ A ) )
=> ( ( member @ TB @ H @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( ( E @ G )
= ( F @ H ) )
=> ( G = H ) ) ) )
=> ( ( ( proces224683037s_term @ TA @ TD @ TB @ TC @ C @ E @ A )
= ( proces224683037s_term @ TA @ TD @ TB @ TC @ D @ F @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: ( proces554692349s_term @ TA @ TB ) > $o,B: proces554692349s_term @ TA @ TB] :
( ! [C: TB] : ( A @ ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( ! [C: proces634752977rocess @ TA] : ( A @ ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( A @ D )
=> ( A @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_process__term_Oinduct) ).
thf(965,plain,
! [TA: $tType,TB: $tType,A: ( proces554692349s_term @ TA @ TB ) > $o,B: proces554692349s_term @ TA @ TB] :
( ! [C: TB] : ( A @ ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( ! [C: proces634752977rocess @ TA] : ( A @ ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( A @ D )
=> ( A @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',fact_100_process_Orel__refl__strong) ).
thf(1103,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)],[151]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_6_process_Ocorec__disc__iff_I2_J) ).
thf(1483,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)],[215]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_pred__equals__eq2) ).
thf(1273,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= ( insert @ TA @ A @ ( proces1148692671rocess @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_process_Osimps_I21_J) ).
thf(745,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)],[89]) ).
thf(237,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces10484146Action @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_solution_Odisc__iff_I1_J) ).
thf(1595,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces10484146Action @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(1278,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TB > TB > $o,C: proces554692349s_term @ TA @ TB] :
( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TB] : ( B @ D @ D )
=> ( proces2029722208s_term @ TA @ TA @ TB @ TB @ A @ B @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_process__term_Orel__refl) ).
thf(298,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TB > TB > $o,C: proces554692349s_term @ TA @ TB] :
( ! [D: TA] : ( A @ D @ D )
=> ( ! [D: TB] : ( B @ D @ D )
=> ( proces2029722208s_term @ TA @ TA @ TB @ TB @ A @ B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275104le_CH2 @ TB @ TA @ A @ B )
= C )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : F
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( C
!= ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ D ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( C != E ) )
=> ~ ( ? [D: TA,E: proces554692349s_term @ TA @ TB] :
( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C
!= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_CH2_Oelims) ).
thf(975,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275104le_CH2 @ TB @ TA @ A @ B )
= C )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : F
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( C
!= ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ D ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( C != E ) )
=> ~ ( ? [D: TA,E: proces554692349s_term @ TA @ TB] :
( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C
!= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fact_131_insert__iff) ).
thf(286,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)],[9]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',fact_39_process_Omap__sel_I1_J) ).
thf(1520,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)],[221]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_insert__absorb2) ).
thf(281,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)],[7]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > ( proces554692349s_term @ TB @ TA ),B: proces554692349s_term @ TD @ TC,C: $o] :
( ( ( proces687458811_isACT @ TC @ TB @ TA @ TD @ A @ B )
= C )
=> ( ! [D: TC] :
( ( B
= ( proces1627516585ss_VAR @ TC @ TD @ D ) )
=> ( C
= ( ~ ( proces460752237s_term @ TA @ $o @ TB
@ ^ [E: TA] : $false
@ ( proces10484146Action @ TB )
@ ^ [E: TB,F: proces554692349s_term @ TB @ TA] : $true
@ ^ [E: proces554692349s_term @ TB @ TA,F: proces554692349s_term @ TB @ TA] : $false
@ ( A @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TD] :
( ( B
= ( proces1062592052s_PROC @ TD @ TC @ D ) )
=> ( C
= ( ~ ( proces10484146Action @ TD @ D ) ) ) )
=> ( ( ? [D: TD,E: proces554692349s_term @ TD @ TC] :
( B
= ( proces1454156180ss_ACT @ TD @ TC @ D @ E ) )
=> ~ C )
=> ~ ( ? [D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TD @ TC] :
( B
= ( proces89589571ess_CH @ TD @ TC @ D @ E ) )
=> C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_isACT_Oelims_I1_J) ).
thf(1488,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > ( proces554692349s_term @ TB @ TA ),B: proces554692349s_term @ TD @ TC,C: $o] :
( ( ( proces687458811_isACT @ TC @ TB @ TA @ TD @ A @ B )
= C )
=> ( ! [D: TC] :
( ( B
= ( proces1627516585ss_VAR @ TC @ TD @ D ) )
=> ( C
= ( ~ ( proces460752237s_term @ TA @ $o @ TB
@ ^ [E: TA] : $false
@ ( proces10484146Action @ TB )
@ ^ [E: TB,F: proces554692349s_term @ TB @ TA] : $true
@ ^ [E: proces554692349s_term @ TB @ TA,F: proces554692349s_term @ TB @ TA] : $false
@ ( A @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TD] :
( ( B
= ( proces1062592052s_PROC @ TD @ TC @ D ) )
=> ( C
= ( ~ ( proces10484146Action @ TD @ D ) ) ) )
=> ( ( ? [D: TD,E: proces554692349s_term @ TD @ TC] :
( B
= ( proces1454156180ss_ACT @ TD @ TC @ D @ E ) )
=> ~ C )
=> ~ ( ? [D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TD @ TC] :
( B
= ( proces89589571ess_CH @ TD @ TC @ D @ E ) )
=> C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TA] :
( ( proces2118920028s_term @ TB @ TA @ A @ B @ ( proces1627516585ss_VAR @ TA @ TB @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_process__term_Opred__inject_I1_J) ).
thf(445,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > $o,C: TA] :
( ( proces2118920028s_term @ TB @ TA @ A @ B @ ( proces1627516585ss_VAR @ TA @ TB @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',fact_105_process_Oset__intros_I3_J) ).
thf(1271,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)],[182]) ).
thf(194,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/sandbox/benchmark/theBenchmark.p',fact_55_process_Oexpand) ).
thf(1332,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)],[194]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1121166967uarded @ TA @ TB @ TA @ A )
=> ( ( proces1652378886lution @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces1652378886lution @ TA @ TB @ A @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_solution__VAR) ).
thf(1258,plain,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1121166967uarded @ TA @ TB @ TA @ A )
=> ( ( proces1652378886lution @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces1652378886lution @ TA @ TB @ A @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',fact_107_process_Oinj__map__strong) ).
thf(1224,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)],[167]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB,C: $o] :
( ( ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TC @ $o @ TD
@ ^ [E: TC] : $false
@ ( proces10484146Action @ TD )
@ ^ [E: TD,F: proces554692349s_term @ TD @ TC] : $true
@ ^ [E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TD @ TC] : $false
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces10484146Action @ TA @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ~ C
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_isACT_Opelims_I1_J) ).
thf(1356,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB,C: $o] :
( ( ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TC @ $o @ TD
@ ^ [E: TC] : $false
@ ( proces10484146Action @ TD )
@ ^ [E: TD,F: proces554692349s_term @ TD @ TC] : $true
@ ^ [E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TD @ TC] : $false
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces10484146Action @ TA @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ~ C
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_136_insert__eq__iff) ).
thf(350,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)],[26]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_139_Set_Oset__insert) ).
thf(274,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)],[5]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TA > $o,B: TD > TB > $o,C: TD,D: TA,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TC @ TA @ TD @ TB @ A @ B @ ( proces1627516585ss_VAR @ TD @ TC @ C ) @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_process__term_Orel__distinct_I3_J) ).
thf(1117,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TA > $o,B: TD > TB > $o,C: TD,D: TA,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TC @ TA @ TD @ TB @ A @ B @ ( proces1627516585ss_VAR @ TD @ TC @ C ) @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_74_process_Orel__coinduct) ).
thf(1574,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)],[234]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces1239275104le_CH2 @ TB @ TA @ A @ ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_CH2_Osimps_I2_J) ).
thf(509,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces1239275104le_CH2 @ TB @ TA @ A @ ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( proces401113213Choice @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_solution_Odisc_I2_J) ).
thf(1307,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( proces401113213Choice @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1239275103le_CH1 @ TB @ TA @ A @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_CH1_Osimps_I3_J) ).
thf(362,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1239275103le_CH1 @ TB @ TA @ A @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] :
( ( proces1264666542s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ A @ B ) )
= ( insert @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_process__term_Osimps_I47_J) ).
thf(451,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] :
( ( proces1264666542s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ A @ B ) )
= ( insert @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(73,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(616,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_138_insert__ident) ).
thf(303,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)],[14]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB] :
( ( proces224683037s_term @ TA @ TA @ TB @ TB
@ ^ [B: TA] : B
@ ^ [B: TB] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_process__term_Omap__ident) ).
thf(477,plain,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB] :
( ( proces224683037s_term @ TA @ TA @ TB @ TB
@ ^ [B: TA] : B
@ ^ [B: TB] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces988026546_ch2Of @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275104le_CH2 @ TB @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_solution_Osimps_I6_J) ).
thf(811,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces988026546_ch2Of @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275104le_CH2 @ TB @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_130_insertCI) ).
thf(345,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)],[25]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_20_process_Oinject_I2_J) ).
thf(609,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)],[70]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_insertI1) ).
thf(323,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_26_process_Odistinct_I1_J) ).
thf(621,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)],[76]) ).
thf(1,conjecture,
( ( ( proces10484146Action @ a @ pa )
= ( proces10484146Action @ a @ p2 ) )
& ( ( proces401113213Choice @ a @ pa )
= ( proces401113213Choice @ a @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( proces10484146Action @ a @ pa )
= ( proces10484146Action @ a @ p2 ) )
& ( ( proces401113213Choice @ a @ pa )
= ( proces401113213Choice @ a @ p2 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(240,plain,
~ ( ( ( proces10484146Action @ a @ pa )
= ( proces10484146Action @ a @ p2 ) )
& ( ( proces401113213Choice @ a @ pa )
= ( proces401113213Choice @ a @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',fact_52_process_Ocase__eq__if) ).
thf(1556,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)],[232]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: TA,D: proces554692349s_term @ TA @ TB] :
( ( proces2118920028s_term @ TA @ TB @ A @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
= ( ( A @ C )
& ( proces2118920028s_term @ TA @ TB @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_process__term_Opred__inject_I3_J) ).
thf(330,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: TA,D: proces554692349s_term @ TA @ TB] :
( ( proces2118920028s_term @ TA @ TB @ A @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
= ( ( A @ C )
& ( proces2118920028s_term @ TA @ TB @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TC,C: TA] :
( ( ( proces1708129104e_PREF @ TC @ TA @ TB @ A @ B )
= C )
=> ( ! [D: TC] :
( ( B
= ( proces1627516585ss_VAR @ TC @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ TA @ TA
@ ^ [E: TB] : ( undefined @ TA )
@ ( proces745025900prefOf @ TA )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : E
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( undefined @ TA )
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TC @ D ) )
=> ( C
!= ( proces745025900prefOf @ TA @ D ) ) )
=> ( ! [D: TA] :
( ? [E: proces554692349s_term @ TA @ TC] :
( B
= ( proces1454156180ss_ACT @ TA @ TC @ D @ E ) )
=> ( C != D ) )
=> ~ ( ? [D: proces554692349s_term @ TA @ TC,E: proces554692349s_term @ TA @ TC] :
( B
= ( proces89589571ess_CH @ TA @ TC @ D @ E ) )
=> ( C
!= ( undefined @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_PREF_Oelims) ).
thf(932,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TC,C: TA] :
( ( ( proces1708129104e_PREF @ TC @ TA @ TB @ A @ B )
= C )
=> ( ! [D: TC] :
( ( B
= ( proces1627516585ss_VAR @ TC @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ TA @ TA
@ ^ [E: TB] : ( undefined @ TA )
@ ( proces745025900prefOf @ TA )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : E
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( undefined @ TA )
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TC @ D ) )
=> ( C
!= ( proces745025900prefOf @ TA @ D ) ) )
=> ( ! [D: TA] :
( ? [E: proces554692349s_term @ TA @ TC] :
( B
= ( proces1454156180ss_ACT @ TA @ TC @ D @ E ) )
=> ( C != D ) )
=> ~ ( ? [D: proces554692349s_term @ TA @ TC,E: proces554692349s_term @ TA @ TC] :
( B
= ( proces89589571ess_CH @ TA @ TC @ D @ E ) )
=> ( C
!= ( undefined @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_65_process_Ocorec__sel_I4_J) ).
thf(1112,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)],[153]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_CONT_Oinduct) ).
thf(521,plain,
! [TA: $tType,TB: $tType,A: ( TB > ( proces554692349s_term @ TA @ TB ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TA @ TB ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB,B: TA > TA > $o,C: TB > TB > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ ( proces1264666542s_term @ TA @ TB @ A ) )
=> ( B @ D @ D ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ ( proces1493547885s_term @ TA @ TB @ A ) )
=> ( C @ D @ D ) )
=> ( proces2029722208s_term @ TA @ TA @ TB @ TB @ B @ C @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_process__term_Orel__refl__strong) ).
thf(306,plain,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB,B: TA > TA > $o,C: TB > TB > $o] :
( ! [D: TA] :
( ( member @ TA @ D @ ( proces1264666542s_term @ TA @ TB @ A ) )
=> ( B @ D @ D ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ ( proces1493547885s_term @ TA @ TB @ A ) )
=> ( C @ D @ D ) )
=> ( proces2029722208s_term @ TA @ TA @ TB @ TB @ B @ C @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces126235999e_CONT @ TB @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : F
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C = E )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_CONT_Opelims) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces126235999e_CONT @ TB @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : F
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C = E )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces1004198490NT_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',fact_64_process_Ocorec__sel_I3_J) ).
thf(1213,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)],[164]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: TA] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_process__term_Oset__intros_I7_J) ).
thf(768,plain,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: TA] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6,axiom,
! [TA: $tType] :
( ( proces979765041_ch1Of @ TA )
= ( proces1406508781rocess @ TA @ ( proces634752977rocess @ TA )
@ ^ [A: TA,B: proces634752977rocess @ TA] : ( undefined @ ( proces634752977rocess @ TA ) )
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ch1Of__def) ).
thf(278,plain,
! [TA: $tType] :
( ( proces979765041_ch1Of @ TA )
= ( proces1406508781rocess @ TA @ ( proces634752977rocess @ TA )
@ ^ [A: TA,B: proces634752977rocess @ TA] : ( undefined @ ( proces634752977rocess @ TA ) )
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TC @ TD ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TC @ TD @ TA @ A @ B )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ~ ( proces460752237s_term @ TD @ $o @ TC
@ ^ [D: TD] : $false
@ ( proces10484146Action @ TC )
@ ^ [D: TC,E: proces554692349s_term @ TC @ TD] : $true
@ ^ [D: proces554692349s_term @ TC @ TD,E: proces554692349s_term @ TC @ TD] : $false
@ ( A @ C ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ~ ( proces10484146Action @ TA @ C ) )
=> ~ ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( B
!= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_isACT_Oelims_I2_J) ).
thf(1528,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TC @ TD ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TC @ TD @ TA @ A @ B )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ~ ( proces460752237s_term @ TD @ $o @ TC
@ ^ [D: TD] : $false
@ ( proces10484146Action @ TC )
@ ^ [D: TC,E: proces554692349s_term @ TC @ TD] : $true
@ ^ [D: proces554692349s_term @ TC @ TD,E: proces554692349s_term @ TC @ TD] : $false
@ ( A @ C ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ~ ( proces10484146Action @ TA @ C ) )
=> ~ ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( B
!= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( ( proces89589571ess_CH @ TA @ TB @ A @ B )
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_process__term_Oinject_I4_J) ).
thf(868,plain,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( ( proces89589571ess_CH @ TA @ TB @ A @ B )
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(201,axiom,
! [TA: $tType] :
( ( proces10484146Action @ TA )
= ( proces1406508781rocess @ TA @ $o
@ ^ [A: TA,B: proces634752977rocess @ TA] : $true
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_process_Odisc__eq__case_I1_J) ).
thf(1413,plain,
! [TA: $tType] :
( ( proces10484146Action @ TA )
= ( proces1406508781rocess @ TA @ $o
@ ^ [A: TA,B: proces634752977rocess @ TA] : $true
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( B
!= ( proces1627516585ss_VAR @ TB @ TA @ A ) )
=> ( ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
=> ~ ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ D ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB] :
( ? [D: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ C ) ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_process__term_Oset__cases_I2_J) ).
thf(531,plain,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( B
!= ( proces1627516585ss_VAR @ TB @ TA @ A ) )
=> ( ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
=> ~ ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ D ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB] :
( ? [D: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ C ) ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(204,axiom,
! [TA: $tType] :
( ( proces401113213Choice @ TA )
= ( ^ [A: proces634752977rocess @ TA] :
? [B: proces634752977rocess @ TA,C: proces634752977rocess @ TA] :
( A
= ( proces1915862579Choice @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_isChoice__def) ).
thf(1420,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)],[204]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_79_process_Orel__inject_I2_J) ).
thf(1134,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)],[159]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > TD > $o,B: TE > TC > $o,C: proces554692349s_term @ TF @ TE,D: TA > TD,E: TB > TC,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TF @ TD @ TE @ TC @ A @ B @ C @ ( proces224683037s_term @ TA @ TD @ TB @ TC @ D @ E @ F ) )
= ( proces2029722208s_term @ TF @ TA @ TE @ TB
@ ^ [G: TF,H: TA] : ( A @ G @ ( D @ H ) )
@ ^ [G: TE,H: TB] : ( B @ G @ ( E @ H ) )
@ C
@ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_process__term_Orel__map_I2_J) ).
thf(342,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF > TD > $o,B: TE > TC > $o,C: proces554692349s_term @ TF @ TE,D: TA > TD,E: TB > TC,F: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TF @ TD @ TE @ TC @ A @ B @ C @ ( proces224683037s_term @ TA @ TD @ TB @ TC @ D @ E @ F ) )
= ( proces2029722208s_term @ TF @ TA @ TE @ TB
@ ^ [G: TF,H: TA] : ( A @ G @ ( D @ H ) )
@ ^ [G: TE,H: TB] : ( B @ G @ ( E @ H ) )
@ C
@ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(754,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA,C: proces554692349s_term @ TA @ TB] :
( ( proces1062592052s_PROC @ TA @ TB @ A )
!= ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_process__term_Odistinct_I7_J) ).
thf(1049,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: TA,C: proces554692349s_term @ TA @ TB] :
( ( proces1062592052s_PROC @ TA @ TB @ A )
!= ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] : ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_process__term_Oset__intros_I2_J) ).
thf(617,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] : ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces1454156180ss_ACT @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TB > ( proces554692349s_term @ TD @ TC ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TD @ TC ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_isACT_Oinduct) ).
thf(516,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( TB > ( proces554692349s_term @ TD @ TC ) ) > ( proces554692349s_term @ TA @ TB ) > $o,B: TB > ( proces554692349s_term @ TD @ TC ),C: proces554692349s_term @ TA @ TB] :
( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: TB] : ( A @ D @ ( proces1627516585ss_VAR @ TB @ TA @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: proces634752977rocess @ TA] : ( A @ D @ ( proces1062592052s_PROC @ TA @ TB @ E ) )
=> ( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: TA,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
=> ( ! [D: TB > ( proces554692349s_term @ TD @ TC ),E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( A @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
=> ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB] :
( ! [B: TB] :
( A
!= ( proces1627516585ss_VAR @ TB @ TA @ B ) )
=> ( ! [B: proces634752977rocess @ TA] :
( A
!= ( proces1062592052s_PROC @ TA @ TB @ B ) )
=> ( ! [B: TA,C: proces554692349s_term @ TA @ TB] :
( A
!= ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) )
=> ~ ! [B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( A
!= ( proces89589571ess_CH @ TA @ TB @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_process__term_Oexhaust) ).
thf(525,plain,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB] :
( ! [B: TB] :
( A
!= ( proces1627516585ss_VAR @ TB @ TA @ B ) )
=> ( ! [B: proces634752977rocess @ TA] :
( A
!= ( proces1062592052s_PROC @ TA @ TB @ B ) )
=> ( ! [B: TA,C: proces554692349s_term @ TA @ TB] :
( A
!= ( proces1454156180ss_ACT @ TA @ TB @ B @ C ) )
=> ~ ! [B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( A
!= ( proces89589571ess_CH @ TA @ TB @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(238,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
~ ( proces401113213Choice @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_process_Odisc_I3_J) ).
thf(1598,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
~ ( proces401113213Choice @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_insert__absorb) ).
thf(295,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)],[12]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_87_process_Orel__distinct_I2_J) ).
thf(887,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)],[119]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: ( proces634752977rocess @ TA ) > TD,D: TA > ( proces554692349s_term @ TA @ TB ) > TD,E: ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) > TD,F: proces554692349s_term @ TA @ TB] :
( ( A @ ( proces460752237s_term @ TB @ TD @ TA @ B @ C @ D @ E @ F ) )
= ( proces460752237s_term @ TB @ TC @ TA
@ ^ [G: TB] : ( A @ ( B @ G ) )
@ ^ [G: proces634752977rocess @ TA] : ( A @ ( C @ G ) )
@ ^ [G: TA,H: proces554692349s_term @ TA @ TB] : ( A @ ( D @ G @ H ) )
@ ^ [G: proces554692349s_term @ TA @ TB,H: proces554692349s_term @ TA @ TB] : ( A @ ( E @ G @ H ) )
@ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_process__term_Ocase__distrib) ).
thf(1252,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: ( proces634752977rocess @ TA ) > TD,D: TA > ( proces554692349s_term @ TA @ TB ) > TD,E: ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) > TD,F: proces554692349s_term @ TA @ TB] :
( ( A @ ( proces460752237s_term @ TB @ TD @ TA @ B @ C @ D @ E @ F ) )
= ( proces460752237s_term @ TB @ TC @ TA
@ ^ [G: TB] : ( A @ ( B @ G ) )
@ ^ [G: proces634752977rocess @ TA] : ( A @ ( C @ G ) )
@ ^ [G: TA,H: proces554692349s_term @ TA @ TB] : ( A @ ( D @ G @ H ) )
@ ^ [G: proces554692349s_term @ TA @ TB,H: proces554692349s_term @ TA @ TB] : ( A @ ( E @ G @ H ) )
@ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',fact_53_process_Osplit__sel__asm) ).
thf(739,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)],[87]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( proces2118920028s_term @ TA @ TB @ A @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
= ( ( proces2118920028s_term @ TA @ TB @ A @ B @ C )
& ( proces2118920028s_term @ TA @ TB @ A @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_process__term_Opred__inject_I4_J) ).
thf(409,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( proces2118920028s_term @ TA @ TB @ A @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
= ( ( proces2118920028s_term @ TA @ TB @ A @ B @ C )
& ( proces2118920028s_term @ TA @ TB @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(149,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( member @ TA @ A @ ( proces1148692671rocess @ TA @ ( proces1525233512Action @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_process_Oset__intros_I1_J) ).
thf(1098,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)],[149]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1778668539contOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_process_Osel_I2_J) ).
thf(673,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( proces1778668539contOf @ TA @ ( proces1525233512Action @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces979765041_ch1Of @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275103le_CH1 @ TB @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_solution_Osimps_I5_J) ).
thf(808,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces979765041_ch1Of @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275103le_CH1 @ TB @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1239275104le_CH2 @ TB @ TA @ A @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_CH2_Osimps_I3_J) ).
thf(359,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( proces1239275104le_CH2 @ TB @ TA @ A @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces1239275103le_CH1 @ TB @ TA @ A @ ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_CH1_Osimps_I2_J) ).
thf(1218,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces634752977rocess @ TA] :
( ( proces1239275103le_CH1 @ TB @ TA @ A @ ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( proces1062592052s_PROC @ TA @ TB @ ( proces979765041_ch1Of @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [E: TC] :
( ( C
= ( proces1627516585ss_VAR @ TC @ TD @ E ) )
=> ! [F: TB] :
( ( D
= ( proces1627516585ss_VAR @ TB @ TA @ F ) )
=> ~ ( B @ E @ F ) ) )
=> ( ! [E: proces634752977rocess @ TD] :
( ( C
= ( proces1062592052s_PROC @ TD @ TC @ E ) )
=> ! [F: proces634752977rocess @ TA] :
( ( D
= ( proces1062592052s_PROC @ TA @ TB @ F ) )
=> ~ ( proces749077512rocess @ TD @ TA @ A @ E @ F ) ) )
=> ( ! [E: TD,F: proces554692349s_term @ TD @ TC] :
( ( C
= ( proces1454156180ss_ACT @ TD @ TC @ E @ F ) )
=> ! [G: TA,H: proces554692349s_term @ TA @ TB] :
( ( D
= ( proces1454156180ss_ACT @ TA @ TB @ G @ H ) )
=> ( ( A @ E @ G )
=> ~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ F @ H ) ) ) )
=> ~ ! [E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TD @ TC] :
( ( C
= ( proces89589571ess_CH @ TD @ TC @ E @ F ) )
=> ! [G: proces554692349s_term @ TA @ TB,H: proces554692349s_term @ TA @ TB] :
( ( D
= ( proces89589571ess_CH @ TA @ TB @ G @ H ) )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ E @ G )
=> ~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ F @ H ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_process__term_Orel__cases) ).
thf(544,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TA @ TB] :
( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ C @ D )
=> ( ! [E: TC] :
( ( C
= ( proces1627516585ss_VAR @ TC @ TD @ E ) )
=> ! [F: TB] :
( ( D
= ( proces1627516585ss_VAR @ TB @ TA @ F ) )
=> ~ ( B @ E @ F ) ) )
=> ( ! [E: proces634752977rocess @ TD] :
( ( C
= ( proces1062592052s_PROC @ TD @ TC @ E ) )
=> ! [F: proces634752977rocess @ TA] :
( ( D
= ( proces1062592052s_PROC @ TA @ TB @ F ) )
=> ~ ( proces749077512rocess @ TD @ TA @ A @ E @ F ) ) )
=> ( ! [E: TD,F: proces554692349s_term @ TD @ TC] :
( ( C
= ( proces1454156180ss_ACT @ TD @ TC @ E @ F ) )
=> ! [G: TA,H: proces554692349s_term @ TA @ TB] :
( ( D
= ( proces1454156180ss_ACT @ TA @ TB @ G @ H ) )
=> ( ( A @ E @ G )
=> ~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ F @ H ) ) ) )
=> ~ ! [E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TD @ TC] :
( ( C
= ( proces89589571ess_CH @ TD @ TC @ E @ F ) )
=> ! [G: proces554692349s_term @ TA @ TB,H: proces554692349s_term @ TA @ TB] :
( ( D
= ( proces89589571ess_CH @ TA @ TB @ G @ H ) )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ E @ G )
=> ~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ F @ H ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces126235999e_CONT @ TB @ TA @ A @ B )
= C )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : F
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( C
!= ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ D ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C != E ) )
=> ~ ( ? [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( C
!= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_CONT_Oelims) ).
thf(1188,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces126235999e_CONT @ TB @ TA @ A @ B )
= C )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( C
!= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : F
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ( A @ D ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( C
!= ( proces1062592052s_PROC @ TA @ TB @ ( proces1778668539contOf @ TA @ D ) ) ) )
=> ( ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( C != E ) )
=> ~ ( ? [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( C
!= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TA > $o,B: TD > TB > $o,C: TD,D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TC @ TA @ TD @ TB @ A @ B @ ( proces1627516585ss_VAR @ TD @ TC @ C ) @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_process__term_Orel__distinct_I5_J) ).
thf(1186,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TA > $o,B: TD > TB > $o,C: TD,D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TC @ TA @ TD @ TB @ A @ B @ ( proces1627516585ss_VAR @ TD @ TC @ C ) @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA] :
( ( proces1264666542s_term @ TA @ TB @ ( proces1062592052s_PROC @ TA @ TB @ A ) )
= ( proces1148692671rocess @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_process__term_Osimps_I46_J) ).
thf(1221,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA] :
( ( proces1264666542s_term @ TA @ TB @ ( proces1062592052s_PROC @ TA @ TB @ A ) )
= ( proces1148692671rocess @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_process__term_Oset__intros_I8_J) ).
thf(1052,plain,
! [TA: $tType,TB: $tType,A: TB,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( member @ TB @ A @ ( proces1493547885s_term @ TA @ TB @ ( proces89589571ess_CH @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(207,axiom,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( proces10484146Action @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_process_Odisc_I1_J) ).
thf(1427,plain,
! [TA: $tType,A: TA,B: proces634752977rocess @ TA] : ( proces10484146Action @ TA @ ( proces1525233512Action @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: proces634752977rocess @ TA] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces1062592052s_PROC @ TA @ TB @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_process__term_Orel__distinct_I10_J) ).
thf(612,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: proces634752977rocess @ TA] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces1062592052s_PROC @ TA @ TB @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(171,axiom,
! [TA: $tType] :
( ( proces749077512rocess @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( proces634752977rocess @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_process_Orel__eq) ).
thf(1240,plain,
! [TA: $tType] :
( ( proces749077512rocess @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( proces634752977rocess @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',fact_41_process_Omap__sel_I4_J) ).
thf(1543,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)],[227]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',fact_135_insert__commute) ).
thf(336,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)],[22]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: proces634752977rocess @ TA] :
( ( proces401113213Choice @ TB @ ( proces370407749rocess @ TA @ TB @ A @ B ) )
= ( proces401113213Choice @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_process_Omap__disc__iff_I2_J) ).
thf(1353,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)],[198]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: ( proces634752977rocess @ TA ) > TC,C: TA > ( proces554692349s_term @ TA @ TB ) > TC,D: ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) > TC,E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] :
( ( proces460752237s_term @ TB @ TC @ TA @ A @ B @ C @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
= ( D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_process__term_Osimps_I20_J) ).
thf(600,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: ( proces634752977rocess @ TA ) > TC,C: TA > ( proces554692349s_term @ TA @ TB ) > TC,D: ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) > TC,E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] :
( ( proces460752237s_term @ TB @ TC @ TA @ A @ B @ C @ D @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) )
= ( D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275104le_CH2 @ TB @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : F
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C = E )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_CH2_Opelims) ).
thf(627,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB] :
( ( ( proces1239275104le_CH2 @ TB @ TA @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [D: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ D ) )
=> ( ( C
= ( proces460752237s_term @ TB @ ( proces554692349s_term @ TA @ TB ) @ TA
@ ^ [E: TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces634752977rocess @ TA] : ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ E ) )
@ ^ [E: TA,F: proces554692349s_term @ TA @ TB] : ( undefined @ ( proces554692349s_term @ TA @ TB ) )
@ ^ [E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] : F
@ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ D ) ) ) ) )
=> ( ! [D: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ D ) )
=> ( ( C
= ( proces1062592052s_PROC @ TA @ TB @ ( proces988026546_ch2Of @ TA @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ D ) ) ) ) )
=> ( ! [D: proces554692349s_term @ TA @ TB,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ D @ E ) )
=> ( ( C = E )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ D @ E ) ) ) ) )
=> ~ ! [D: TA,E: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) )
=> ( ( C
= ( undefined @ ( proces554692349s_term @ TA @ TB ) ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces93903513H2_rel @ TB @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1454156180ss_ACT @ TA @ TB @ D @ E ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(211,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces401113213Choice @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_solution_Odisc__iff_I2_J) ).
thf(1459,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces401113213Choice @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_134_mk__disjoint__insert) ).
thf(482,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)],[48]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( ( proces1062592052s_PROC @ TA @ TB @ A )
= ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_process__term_Oinject_I2_J) ).
thf(688,plain,
! [TA: $tType,TB: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] :
( ( ( proces1062592052s_PROC @ TA @ TB @ A )
= ( proces1062592052s_PROC @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: proces554692349s_term @ TA @ TB,D: TA > $o,E: TB > $o] :
( ( proces2118920028s_term @ TA @ TB @ A @ B @ C )
=> ( ! [F: TA] :
( ( member @ TA @ F @ ( proces1264666542s_term @ TA @ TB @ C ) )
=> ( ( A @ F )
=> ( D @ F ) ) )
=> ( ! [F: TB] :
( ( member @ TB @ F @ ( proces1493547885s_term @ TA @ TB @ C ) )
=> ( ( B @ F )
=> ( E @ F ) ) )
=> ( proces2118920028s_term @ TA @ TB @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_process__term_Opred__mono__strong) ).
thf(368,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o,C: proces554692349s_term @ TA @ TB,D: TA > $o,E: TB > $o] :
( ( proces2118920028s_term @ TA @ TB @ A @ B @ C )
=> ( ! [F: TA] :
( ( member @ TA @ F @ ( proces1264666542s_term @ TA @ TB @ C ) )
=> ( ( A @ F )
=> ( D @ F ) ) )
=> ( ! [F: TB] :
( ( member @ TB @ F @ ( proces1493547885s_term @ TA @ TB @ C ) )
=> ( ( B @ F )
=> ( E @ F ) ) )
=> ( proces2118920028s_term @ TA @ TB @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces1062592052s_PROC @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_process__term_Oset__intros_I1_J) ).
thf(1276,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces634752977rocess @ TA] :
( ( member @ TA @ A @ ( proces1148692671rocess @ TA @ B ) )
=> ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ ( proces1062592052s_PROC @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB > $o,B: TC > TA > $o,C: proces634752977rocess @ TD,D: TA] :
~ ( proces2029722208s_term @ TD @ TB @ TC @ TA @ A @ B @ ( proces1062592052s_PROC @ TD @ TC @ C ) @ ( proces1627516585ss_VAR @ TA @ TB @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_process__term_Orel__distinct_I2_J) ).
thf(963,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB > $o,B: TC > TA > $o,C: proces634752977rocess @ TD,D: TA] :
~ ( proces2029722208s_term @ TD @ TB @ TC @ TA @ A @ B @ ( proces1062592052s_PROC @ TD @ TC @ C ) @ ( proces1627516585ss_VAR @ TA @ TB @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: TA,D: proces554692349s_term @ TA @ TB] :
( ( ( proces1454156180ss_ACT @ TA @ TB @ A @ B )
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_process__term_Oinject_I3_J) ).
thf(748,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: TA,D: proces554692349s_term @ TA @ TB] :
( ( ( proces1454156180ss_ACT @ TA @ TB @ A @ B )
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_102_process_Orel__cong) ).
thf(1062,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)],[143]) ).
thf(222,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( proces401113213Choice @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_process_Odisc_I4_J) ).
thf(1523,plain,
! [TA: $tType,A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( proces401113213Choice @ TA @ ( proces1915862579Choice @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD,C: TA,D: TC > TB > $o,E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TA @ TB] :
( ( A @ B @ C )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ D @ E @ F )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ D @ ( proces1454156180ss_ACT @ TD @ TC @ B @ E ) @ ( proces1454156180ss_ACT @ TA @ TB @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_process__term_Orel__intros_I3_J) ).
thf(378,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TD,C: TA,D: TC > TB > $o,E: proces554692349s_term @ TD @ TC,F: proces554692349s_term @ TA @ TB] :
( ( A @ B @ C )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ D @ E @ F )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ D @ ( proces1454156180ss_ACT @ TD @ TC @ B @ E ) @ ( proces1454156180ss_ACT @ TA @ TB @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TD @ TC,B: proces554692349s_term @ TD @ TC,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB,E: TD > TA > $o,F: TD > TA > $o,G: TC > TB > $o,H: TC > TB > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [I: TD,J: TA] :
( ( member @ TD @ I @ ( proces1264666542s_term @ TD @ TC @ B ) )
=> ( ( member @ TA @ J @ ( proces1264666542s_term @ TA @ TB @ D ) )
=> ( ( E @ I @ J )
= ( F @ I @ J ) ) ) )
=> ( ! [I: TC,J: TB] :
( ( member @ TC @ I @ ( proces1493547885s_term @ TD @ TC @ B ) )
=> ( ( member @ TB @ J @ ( proces1493547885s_term @ TA @ TB @ D ) )
=> ( ( G @ I @ J )
= ( H @ I @ J ) ) ) )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ E @ G @ A @ C )
= ( proces2029722208s_term @ TD @ TA @ TC @ TB @ F @ H @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_process__term_Orel__cong) ).
thf(246,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TD @ TC,B: proces554692349s_term @ TD @ TC,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB,E: TD > TA > $o,F: TD > TA > $o,G: TC > TB > $o,H: TC > TB > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [I: TD,J: TA] :
( ( member @ TD @ I @ ( proces1264666542s_term @ TD @ TC @ B ) )
=> ( ( member @ TA @ J @ ( proces1264666542s_term @ TA @ TB @ D ) )
=> ( ( E @ I @ J )
= ( F @ I @ J ) ) ) )
=> ( ! [I: TC,J: TB] :
( ( member @ TC @ I @ ( proces1493547885s_term @ TD @ TC @ B ) )
=> ( ( member @ TB @ J @ ( proces1493547885s_term @ TA @ TB @ D ) )
=> ( ( G @ I @ J )
= ( H @ I @ J ) ) ) )
=> ( ( proces2029722208s_term @ TD @ TA @ TC @ TB @ E @ G @ A @ C )
= ( proces2029722208s_term @ TD @ TA @ TC @ TB @ F @ H @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(146,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ C ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB] :
( B
!= ( proces1454156180ss_ACT @ TA @ TB @ A @ C ) )
=> ( ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ D ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB] :
( ? [D: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ C ) ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_process__term_Oset__cases_I1_J) ).
thf(1077,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB] :
( ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ~ ( member @ TA @ A @ ( proces1148692671rocess @ TA @ C ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB] :
( B
!= ( proces1454156180ss_ACT @ TA @ TB @ A @ C ) )
=> ( ! [C: TA,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ D ) ) )
=> ( ! [C: proces554692349s_term @ TA @ TB] :
( ? [D: proces554692349s_term @ TA @ TB] :
( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ C ) ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( member @ TA @ A @ ( proces1264666542s_term @ TA @ TB @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces1652378886lution @ TB @ TA @ A @ B )
= ( proces1525233512Action @ TA @ ( proces1708129104e_PREF @ TB @ TA @ TB @ A @ B ) @ ( proces1652378886lution @ TB @ TA @ A @ ( proces126235999e_CONT @ TB @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_solution_Octr_I1_J) ).
thf(763,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces1652378886lution @ TB @ TA @ A @ B )
= ( proces1525233512Action @ TA @ ( proces1708129104e_PREF @ TB @ TA @ TB @ A @ B ) @ ( proces1652378886lution @ TB @ TA @ A @ ( proces126235999e_CONT @ TB @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_12_process_Ocorec__disc_I1_J) ).
thf(1513,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)],[218]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: proces634752977rocess @ TD,C: proces634752977rocess @ TA,D: TC > TB > $o] :
( ( proces749077512rocess @ TD @ TA @ A @ B @ C )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ D @ ( proces1062592052s_PROC @ TD @ TC @ B ) @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_process__term_Orel__intros_I2_J) ).
thf(684,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: proces634752977rocess @ TD,C: proces634752977rocess @ TA,D: TC > TB > $o] :
( ( proces749077512rocess @ TD @ TA @ A @ B @ C )
=> ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ D @ ( proces1062592052s_PROC @ TD @ TC @ B ) @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',fact_57_process_Ocoinduct__strong) ).
thf(1309,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)],[193]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',fact_67_process_Osimps_I5_J) ).
thf(800,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)],[101]) ).
thf(210,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 ) )
& ( ( proces401113213Choice @ TA @ D )
= ( proces401113213Choice @ TA @ E ) ) ) )
=> ( ! [D: TA,E: TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1525233512Action @ TA @ D @ F ) @ ( proces1525233512Action @ TA @ E @ G ) )
=> ( ( D = E )
& ( ( A @ F @ G )
| ( F = G ) ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1915862579Choice @ TA @ D @ E ) @ ( proces1915862579Choice @ TA @ F @ G ) )
=> ( ( ( A @ D @ F )
| ( D = F ) )
& ( ( A @ E @ G )
| ( E = G ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_process__strong__coind) ).
thf(1440,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 ) )
& ( ( proces401113213Choice @ TA @ D )
= ( proces401113213Choice @ TA @ E ) ) ) )
=> ( ! [D: TA,E: TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1525233512Action @ TA @ D @ F ) @ ( proces1525233512Action @ TA @ E @ G ) )
=> ( ( D = E )
& ( ( A @ F @ G )
| ( F = G ) ) ) )
=> ( ! [D: proces634752977rocess @ TA,E: proces634752977rocess @ TA,F: proces634752977rocess @ TA,G: proces634752977rocess @ TA] :
( ( A @ ( proces1915862579Choice @ TA @ D @ E ) @ ( proces1915862579Choice @ TA @ F @ G ) )
=> ( ( ( A @ D @ F )
| ( D = F ) )
& ( ( A @ E @ G )
| ( E = G ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(129,axiom,
! [TA: $tType] :
( ( proces745025900prefOf @ TA )
= ( proces1406508781rocess @ TA @ TA
@ ^ [A: TA,B: proces634752977rocess @ TA] : A
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( undefined @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_prefOf__def) ).
thf(929,plain,
! [TA: $tType] :
( ( proces745025900prefOf @ TA )
= ( proces1406508781rocess @ TA @ TA
@ ^ [A: TA,B: proces634752977rocess @ TA] : A
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : ( undefined @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(196,axiom,
! [TA: $tType] :
( ( proces401113213Choice @ TA )
= ( proces1406508781rocess @ TA @ $o
@ ^ [A: TA,B: proces634752977rocess @ TA] : $false
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_process_Odisc__eq__case_I2_J) ).
thf(1348,plain,
! [TA: $tType] :
( ( proces401113213Choice @ TA )
= ( proces1406508781rocess @ TA @ $o
@ ^ [A: TA,B: proces634752977rocess @ TA] : $false
@ ^ [A: proces634752977rocess @ TA,B: proces634752977rocess @ TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',fact_75_process_Orel__sel) ).
thf(1546,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)],[228]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces1652378886lution @ TB @ TA @ A @ B )
= ( proces1915862579Choice @ TA @ ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275103le_CH1 @ TB @ TA @ A @ B ) ) @ ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275104le_CH2 @ TB @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_solution_Octr_I2_J) ).
thf(865,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces1652378886lution @ TB @ TA @ A @ B )
= ( proces1915862579Choice @ TA @ ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275103le_CH1 @ TB @ TA @ A @ B ) ) @ ( proces1652378886lution @ TB @ TA @ A @ ( proces1239275104le_CH2 @ TB @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( proces1454156180ss_ACT @ TA @ TB @ A @ B )
!= ( proces89589571ess_CH @ TA @ TB @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_process__term_Odistinct_I11_J) ).
thf(603,plain,
! [TA: $tType,TB: $tType,A: TA,B: proces554692349s_term @ TA @ TB,C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( proces1454156180ss_ACT @ TA @ TB @ A @ B )
!= ( proces89589571ess_CH @ TA @ TB @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( proces1121166967uarded @ TA @ TB @ TC )
= ( ^ [A: TA > ( proces554692349s_term @ TB @ TC )] :
! [B: TA,C: TC] :
( ( A @ B )
!= ( proces1627516585ss_VAR @ TC @ TB @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_guarded__def) ).
thf(918,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( proces1121166967uarded @ TA @ TB @ TC )
= ( ^ [A: TA > ( proces554692349s_term @ TB @ TC )] :
! [B: TA,C: TC] :
( ( A @ B )
!= ( proces1627516585ss_VAR @ TC @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',fact_113_process_Oset__induct) ).
thf(897,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)],[122]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_CONT_Ocases) ).
thf(960,plain,
! [TA: $tType,TB: $tType,A: product_prod @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB )] :
( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces634752977rocess @ TA] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: TA,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces1454156180ss_ACT @ TA @ TB @ C @ D ) ) )
=> ~ ! [B: TB > ( proces554692349s_term @ TA @ TB ),C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( A
!= ( product_Pair @ ( TB > ( proces554692349s_term @ TA @ TB ) ) @ ( proces554692349s_term @ TA @ TB ) @ B @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(189,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
| ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_isAction__isChoice) ).
thf(1288,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
| ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: TA > TC,C: TA > TC,D: TB > TD,E: TB > TD] :
( ! [F: TA] :
( ( member @ TA @ F @ ( proces1264666542s_term @ TA @ TB @ A ) )
=> ( ( B @ F )
= ( C @ F ) ) )
=> ( ! [F: TB] :
( ( member @ TB @ F @ ( proces1493547885s_term @ TA @ TB @ A ) )
=> ( ( D @ F )
= ( E @ F ) ) )
=> ( ( proces224683037s_term @ TA @ TC @ TB @ TD @ B @ D @ A )
= ( proces224683037s_term @ TA @ TC @ TB @ TD @ C @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_process__term_Omap__cong0) ).
thf(400,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: proces554692349s_term @ TA @ TB,B: TA > TC,C: TA > TC,D: TB > TD,E: TB > TD] :
( ! [F: TA] :
( ( member @ TA @ F @ ( proces1264666542s_term @ TA @ TB @ A ) )
=> ( ( B @ F )
= ( C @ F ) ) )
=> ( ! [F: TB] :
( ( member @ TB @ F @ ( proces1493547885s_term @ TA @ TB @ A ) )
=> ( ( D @ F )
= ( E @ F ) ) )
=> ( ( proces224683037s_term @ TA @ TC @ TB @ TD @ B @ D @ A )
= ( proces224683037s_term @ TA @ TC @ TB @ TD @ C @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB > $o,B: TC > TA > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: TA] :
~ ( proces2029722208s_term @ TD @ TB @ TC @ TA @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces1627516585ss_VAR @ TA @ TB @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_process__term_Orel__distinct_I6_J) ).
thf(1236,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB > $o,B: TC > TA > $o,C: proces554692349s_term @ TD @ TC,D: proces554692349s_term @ TD @ TC,E: TA] :
~ ( proces2029722208s_term @ TD @ TB @ TC @ TA @ A @ B @ ( proces89589571ess_CH @ TD @ TC @ C @ D ) @ ( proces1627516585ss_VAR @ TA @ TB @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces745025900prefOf @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1708129104e_PREF @ TB @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_solution_Osimps_I3_J) ).
thf(1261,plain,
! [TA: $tType,TB: $tType,A: TB > ( proces554692349s_term @ TA @ TB ),B: proces554692349s_term @ TA @ TB] :
( ( proces687458811_isACT @ TB @ TA @ TB @ TA @ A @ B )
=> ( ( proces745025900prefOf @ TA @ ( proces1652378886lution @ TB @ TA @ A @ B ) )
= ( proces1708129104e_PREF @ TB @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(225,axiom,
! [TA: $tType,A: proces634752977rocess @ TA,B: TA,C: proces634752977rocess @ TA] :
( ( A
= ( proces1525233512Action @ TA @ B @ C ) )
=> ( proces10484146Action @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_process_OdiscI_I1_J) ).
thf(1537,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)],[225]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( proces1627516585ss_VAR @ TA @ TB @ A )
= ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_process__term_Oinject_I1_J) ).
thf(528,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA] :
( ( ( proces1627516585ss_VAR @ TA @ TB @ A )
= ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: proces634752977rocess @ TA] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces1062592052s_PROC @ TA @ TB @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_process__term_Orel__distinct_I8_J) ).
thf(691,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: proces634752977rocess @ TA] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces1062592052s_PROC @ TA @ TB @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1121166967uarded @ TA @ TB @ TA @ A )
=> ( ( proces687458811_isACT @ TA @ TB @ TA @ TC @ A @ ( proces1627516585ss_VAR @ TA @ TC @ B ) )
= ( proces687458811_isACT @ TA @ TB @ TA @ TB @ A @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_isACT__VAR) ).
thf(871,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1121166967uarded @ TA @ TB @ TA @ A )
=> ( ( proces687458811_isACT @ TA @ TB @ TA @ TC @ A @ ( proces1627516585ss_VAR @ TA @ TC @ B ) )
= ( proces687458811_isACT @ TA @ TB @ TA @ TB @ A @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: ( proces634752977rocess @ TA ) > TC,C: TA > ( proces554692349s_term @ TA @ TB ) > TC,D: ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) > TC,E: TA,F: proces554692349s_term @ TA @ TB] :
( ( proces460752237s_term @ TB @ TC @ TA @ A @ B @ C @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
= ( C @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_process__term_Osimps_I19_J) ).
thf(501,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: ( proces634752977rocess @ TA ) > TC,C: TA > ( proces554692349s_term @ TA @ TB ) > TC,D: ( proces554692349s_term @ TA @ TB ) > ( proces554692349s_term @ TA @ TB ) > TC,E: TA,F: proces554692349s_term @ TA @ TB] :
( ( proces460752237s_term @ TB @ TC @ TA @ A @ B @ C @ D @ ( proces1454156180ss_ACT @ TA @ TB @ E @ F ) )
= ( C @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_process__term_Orel__distinct_I11_J) ).
thf(1093,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA > $o,B: TC > TB > $o,C: TD,D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TA @ TB,F: proces554692349s_term @ TA @ TB] :
~ ( proces2029722208s_term @ TD @ TA @ TC @ TB @ A @ B @ ( proces1454156180ss_ACT @ TD @ TC @ C @ D ) @ ( proces89589571ess_CH @ TA @ TB @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_78_process_Orel__inject_I1_J) ).
thf(624,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)],[77]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > $o,D: TA > $o,E: TB > $o,F: TB > $o] :
( ( A = B )
=> ( ! [G: TA] :
( ( member @ TA @ G @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ! [G: TB] :
( ( member @ TB @ G @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( proces2118920028s_term @ TA @ TB @ C @ E @ A )
= ( proces2118920028s_term @ TA @ TB @ D @ F @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_process__term_Opred__cong) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: proces554692349s_term @ TA @ TB,B: proces554692349s_term @ TA @ TB,C: TA > $o,D: TA > $o,E: TB > $o,F: TB > $o] :
( ( A = B )
=> ( ! [G: TA] :
( ( member @ TA @ G @ ( proces1264666542s_term @ TA @ TB @ B ) )
=> ( ( C @ G )
= ( D @ G ) ) )
=> ( ! [G: TB] :
( ( member @ TB @ G @ ( proces1493547885s_term @ TA @ TB @ B ) )
=> ( ( E @ G )
= ( F @ G ) ) )
=> ( ( proces2118920028s_term @ TA @ TB @ C @ E @ A )
= ( proces2118920028s_term @ TA @ TB @ D @ F @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1239275103le_CH1 @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces460752237s_term @ TA @ ( proces554692349s_term @ TB @ TA ) @ TB
@ ^ [C: TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces634752977rocess @ TB] : ( proces1062592052s_PROC @ TB @ TA @ ( proces979765041_ch1Of @ TB @ C ) )
@ ^ [C: TB,D: proces554692349s_term @ TB @ TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces554692349s_term @ TB @ TA,D: proces554692349s_term @ TB @ TA] : C
@ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_CH1_Osimps_I1_J) ).
thf(803,plain,
! [TA: $tType,TB: $tType,A: TA > ( proces554692349s_term @ TB @ TA ),B: TA] :
( ( proces1239275103le_CH1 @ TA @ TB @ A @ ( proces1627516585ss_VAR @ TA @ TB @ B ) )
= ( proces460752237s_term @ TA @ ( proces554692349s_term @ TB @ TA ) @ TB
@ ^ [C: TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces634752977rocess @ TB] : ( proces1062592052s_PROC @ TB @ TA @ ( proces979765041_ch1Of @ TB @ C ) )
@ ^ [C: TB,D: proces554692349s_term @ TB @ TA] : ( undefined @ ( proces554692349s_term @ TB @ TA ) )
@ ^ [C: proces554692349s_term @ TB @ TA,D: proces554692349s_term @ TB @ TA] : C
@ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(202,axiom,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ~ ( proces401113213Choice @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_process_Odistinct__disc_I1_J) ).
thf(1416,plain,
! [TA: $tType,A: proces634752977rocess @ TA] :
( ( proces10484146Action @ TA @ A )
=> ~ ( proces401113213Choice @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TA > $o,B: TC > TD > $o,C: proces634752977rocess @ TB,D: proces634752977rocess @ TA] :
( ( proces2029722208s_term @ TB @ TA @ TC @ TD @ A @ B @ ( proces1062592052s_PROC @ TB @ TC @ C ) @ ( proces1062592052s_PROC @ TA @ TD @ D ) )
= ( proces749077512rocess @ TB @ TA @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_process__term_Orel__inject_I2_J) ).
thf(676,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TA > $o,B: TC > TD > $o,C: proces634752977rocess @ TB,D: proces634752977rocess @ TA] :
( ( proces2029722208s_term @ TB @ TA @ TC @ TD @ A @ B @ ( proces1062592052s_PROC @ TB @ TC @ C ) @ ( proces1062592052s_PROC @ TA @ TD @ D ) )
= ( proces749077512rocess @ TB @ TA @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ B )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( proces460752237s_term @ TC @ $o @ TD
@ ^ [D: TC] : $false
@ ( proces10484146Action @ TD )
@ ^ [D: TD,E: proces554692349s_term @ TD @ TC] : $true
@ ^ [D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TD @ TC] : $false
@ ( A @ C ) ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( proces10484146Action @ TA @ C ) ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_isACT_Opelims_I3_J) ).
thf(1468,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > ( proces554692349s_term @ TD @ TC ),B: proces554692349s_term @ TA @ TB] :
( ~ ( proces687458811_isACT @ TB @ TD @ TC @ TA @ A @ B )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ B ) )
=> ( ! [C: TB] :
( ( B
= ( proces1627516585ss_VAR @ TB @ TA @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1627516585ss_VAR @ TB @ TA @ C ) ) )
=> ( proces460752237s_term @ TC @ $o @ TD
@ ^ [D: TC] : $false
@ ( proces10484146Action @ TD )
@ ^ [D: TD,E: proces554692349s_term @ TD @ TC] : $true
@ ^ [D: proces554692349s_term @ TD @ TC,E: proces554692349s_term @ TD @ TC] : $false
@ ( A @ C ) ) ) )
=> ( ! [C: proces634752977rocess @ TA] :
( ( B
= ( proces1062592052s_PROC @ TA @ TB @ C ) )
=> ( ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces1062592052s_PROC @ TA @ TB @ C ) ) )
=> ( proces10484146Action @ TA @ C ) ) )
=> ~ ! [C: proces554692349s_term @ TA @ TB,D: proces554692349s_term @ TA @ TB] :
( ( B
= ( proces89589571ess_CH @ TA @ TB @ C @ D ) )
=> ~ ( accp @ ( product_prod @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) ) @ ( proces896239806CT_rel @ TB @ TD @ TC @ TA ) @ ( product_Pair @ ( TB > ( proces554692349s_term @ TD @ TC ) ) @ ( proces554692349s_term @ TA @ TB ) @ A @ ( proces89589571ess_CH @ TA @ TB @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > ( proces554692349s_term @ TA @ TB ),B: TA,C: proces554692349s_term @ TA @ TC] :
( ( proces1708129104e_PREF @ TC @ TA @ TB @ A @ ( proces1454156180ss_ACT @ TA @ TC @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_PREF_Osimps_I3_J) ).
thf(454,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > ( proces554692349s_term @ TA @ TB ),B: TA,C: proces554692349s_term @ TA @ TC] :
( ( proces1708129104e_PREF @ TC @ TA @ TB @ A @ ( proces1454156180ss_ACT @ TA @ TC @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_83_process_Orel__intros_I2_J) ).
thf(882,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)],[117]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,A: TB,B: proces634752977rocess @ TA] :
( ( proces1627516585ss_VAR @ TB @ TA @ A )
!= ( proces1062592052s_PROC @ TA @ TB @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_process__term_Odistinct_I1_J) ).
thf(972,plain,
! [TA: $tType,TB: $tType,A: TB,B: proces634752977rocess @ TA] :
( ( proces1627516585ss_VAR @ TB @ TA @ A )
!= ( proces1062592052s_PROC @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1604,plain,
$false,
inference(e,[status(thm)],[892,365,760,1559,846,333,518,1549,1554,523,1290,1591,1269,614,1305,1486,1137,1233,814,913,1095,1243,1046,320,1518,504,1264,619,751,1462,460,817,606,325,289,448,1100,284,770,924,1465,1109,1418,514,806,353,480,1183,1283,766,877,1072,1119,396,1351,1345,243,1600,849,507,292,380,512,1438,798,1057,910,957,1255,862,693,1238,1423,916,879,583,889,757,1128,1281,1402,742,1541,874,1121,1425,356,499,328,884,339,679,686,1075,393,1588,1249,1266,1131,1552,457,1429,1246,1525,921,1054,1286,1515,773,586,412,965,1103,1483,1273,745,1595,1278,298,975,286,1520,281,1488,445,1271,1332,1258,1224,1356,350,274,1117,1574,509,1307,362,451,616,303,477,811,345,609,323,621,240,1556,330,932,1112,521,306,1000,1213,768,278,1528,868,1413,531,1420,1134,342,754,1049,617,516,525,1598,295,887,1252,739,409,1098,673,808,359,1218,544,1188,1186,1221,1052,1427,612,1240,1543,336,1353,600,627,1459,482,688,368,1276,963,748,1062,1523,378,246,1077,763,1513,684,1309,800,1440,929,1348,1546,865,603,918,897,960,1288,400,1236,1261,1537,528,691,871,501,1093,624,486,803,1416,676,1468,454,882,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PRO023^1 : TPTP v8.1.2. Released v7.0.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n027.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 15:56:39 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.01/1.17 % [INFO] Parsing done (290ms).
% 2.01/1.18 % [INFO] Running in sequential loop mode.
% 2.78/1.40 % [INFO] eprover registered as external prover.
% 2.78/1.40 % [INFO] cvc4 registered as external prover.
% 2.78/1.41 % [INFO] Scanning for conjecture ...
% 3.11/1.52 % [INFO] Found a conjecture and 258 axioms. Running axiom selection ...
% 3.32/1.63 % [INFO] Axiom selection finished. Selected 237 axioms (removed 21 axioms).
% 4.58/1.96 % [INFO] Problem is higher-order (TPTP THF).
% 4.84/1.99 % [INFO] Type checking passed.
% 4.84/1.99 % [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 ...
% 51.83/26.02 % External prover 'e' found a proof!
% 51.83/26.02 % [INFO] Killing All external provers ...
% 51.83/26.02 % Time passed: 25471ms (effective reasoning time: 24839ms)
% 51.83/26.02 % 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)>
% 51.83/26.02 % Axioms used in derivation (237): fact_94_prefOf__def, fact_30_process__strong__coind, fact_173_CONT_Oinduct, fact_148_isACT_Oelims_I3_J, fact_82_process_Orel__intros_I1_J, fact_150_CH1_Oelims, fact_119_process__term_Oinject_I1_J, fact_189_process__term_Orel__intros_I3_J, fact_60_process_Osel_I3_J, fact_86_solution_Ocode, fact_81_process_Orel__refl, fact_55_process_Oexpand, fact_140_insertI2, fact_23_process_Ocorec_I1_J, fact_70_solution_Osimps_I3_J, fact_84_process_Orel__map_I2_J, fact_52_process_Ocase__eq__if, fact_220_pred__equals__eq2, fact_143_guarded__def, fact_202_process__term_Orel__distinct_I8_J, fact_160_process__term_Odistinct_I9_J, fact_175_CH1_Osimps_I3_J, fact_174_CH2_Oinduct, fact_180_isACT_Oelims_I1_J, fact_163_process__term_Oset__intros_I4_J, fact_206_process__term_Orel__distinct_I4_J, fact_131_insert__iff, fact_147_isACT_Oelims_I2_J, fact_133_solution__VAR, fact_51_process_Osplit__sel, fact_34_process_Odisc_I1_J, fact_38_solution_Odisc_I1_J, fact_125_isACT_Osimps_I1_J, fact_83_process_Orel__intros_I2_J, fact_117_process__term_Osimps_I26_J, fact_18_process__term_Oinject_I2_J, fact_67_process_Osimps_I5_J, fact_96_process_Oset__sel_I4_J, fact_43_process_Omap__sel_I2_J, fact_6_process_Ocorec__disc__iff_I2_J, fact_98_process_Oset__sel_I2_J, fact_242_process__term_Omap__cong__pred, fact_101_process_Orel__mono__strong, fact_37_solution_Odisc_I2_J, fact_9_process_Omap__disc__iff_I2_J, fact_65_process_Ocorec__sel_I4_J, fact_211_CONT_Ocases, fact_188_process__term_Orel__intros_I4_J, fact_103_process_Oset__intros_I1_J, fact_192_process__term_Orel__refl, fact_239_process__term_Opred__inject_I4_J, fact_226_process__term_Osimps_I51_J, fact_181_PREF_Oelims, fact_77_CH2_Osimps_I2_J, fact_149_CH2_Oelims, fact_155_isACT_Osimps_I4_J, fact_25_process_Osimps_I15_J, fact_195_process__term_Orel__map_I2_J, fact_187_process__term_Orel__inject_I3_J, fact_100_process_Orel__refl__strong, fact_228_process__term_Orel__mono__strong, fact_128_CH2_Osimps_I1_J, fact_215_CONT_Opelims, fact_42_isACT_Osimps_I2_J, fact_7_process_Ocorec__disc__iff_I1_J, fact_112_ch2Of__def, fact_167_process__term_Osimps_I27_J, fact_170_process__term_Oinduct, fact_115_process__term_Osimps_I46_J, fact_85_process_Orel__map_I1_J, fact_22_process_Ocorec_I2_J, fact_127_CONT_Osimps_I1_J, fact_217_isACT_Opelims_I1_J, fact_36_solution_Odisc__iff_I1_J, fact_130_insertCI, fact_56_process_Ocoinduct, fact_14_process_Odisc_I3_J, fact_63_process_Ocorec__sel_I2_J, fact_108_process_Omap__cong0, fact_73_solution_Osimps_I4_J, fact_12_process_Ocorec__disc_I1_J, fact_201_process__term_Orel__distinct_I9_J, fact_223_process__term_Oset__intros_I7_J, fact_136_insert__eq__iff, fact_185_isACT_Ocases, fact_177_CONT_Osimps_I3_J, fact_196_process__term_Orel__intros_I2_J, fact_205_process__term_Orel__distinct_I5_J, fact_183_process__term_Orel__cases, help_If_1_1_T, fact_200_process__term_Orel__distinct_I10_J, fact_156_process__term_Osimps_I19_J, fact_231_process__term_Omap__cong0, fact_190_process__term_Orel__inject_I1_J, fact_154_process__term_Osimps_I20_J, fact_184_process__term_Orel__induct, fact_124_process__term_Odistinct_I1_J, fact_109_process_Omap__cong, fact_99_process_Oset__cases, fact_230_process__term_Omap__cong, fact_139_Set_Oset__insert, fact_49_process_Ocollapse_I1_J, fact_164_process__term_Oset__intros_I5_J, fact_153_process__term_Osimps_I47_J, fact_135_insert__commute, fact_11_process_Omap__disc__iff_I1_J, fact_44_process_Odisc__eq__case_I2_J, fact_80_process_Orel__eq, fact_71_solution_Osimps_I5_J, fact_102_process_Orel__cong, fact_176_CH2_Osimps_I3_J, fact_197_process__term_Orel__inject_I2_J, fact_40_process_Omap__sel_I3_J, fact_214_CH2_Opelims, fact_16_isChoice__def, fact_10_process_Ocorec__disc_I2_J, fact_182_CONT_Oelims, fact_13_process_Odisc_I4_J, fact_138_insert__ident, fact_32_isAction__def, fact_39_process_Omap__sel_I1_J, fact_123_process__term_Osimps_I17_J, fact_33_process_OdiscI_I1_J, fact_0__092_060open_062isAction_Ap_A_092_060or_062_AisChoice_Ap_092_060close_062, fact_222_process__term_Oset__intros_I6_J, fact_15_process_OdiscI_I2_J, fact_113_process_Oset__induct, fact_151_process__term_Oinject_I4_J, fact_212_PREF_Ocases, fact_21__092_060open_062q_A_061_Asolution_Asys_A_IPROC_Ap_J_092_060close_062, fact_219_isACT_Opelims_I2_J, fact_61_process_Osel_I4_J, fact_57_process_Ocoinduct__strong, fact_19_process_Oinject_I1_J, fact_221_process__term_Oset__cases_I2_J, fact_234_process__term_Opred__mono__strong, fact_105_process_Oset__intros_I3_J, fact_134_mk__disjoint__insert, fact_66_process_Ocorec__sel_I1_J, fact_90_solution_Octr_I1_J, fact_218_isACT_Opelims_I3_J, fact_92_CONT_Osimps_I2_J, help_If_3_1_T, fact_165_process__term_Odistinct_I3_J, help_If_2_1_T, fact_26_process_Odistinct_I1_J, fact_157_isACT_Osimps_I3_J, fact_232_process__term_Oinj__map__strong, fact_75_process_Orel__sel, fact_169_process__term_Oexhaust, fact_166_process__term_Odistinct_I5_J, fact_227_process__term_Orel__refl__strong, fact_2_process_Odistinct__disc_I1_J, fact_28_process_Ocorec__code, fact_78_process_Orel__inject_I1_J, fact_59_process_Osel_I2_J, fact_199_process__term_Orel__distinct_I1_J, fact_225_process__term_Oset__intros_I9_J, fact_50_process_Ocollapse_I2_J, fact_111_ch1Of__def, fact_203_process__term_Orel__distinct_I7_J, fact_95_process_Oset__sel_I3_J, fact_132_insert__absorb2, fact_122_process__term_Osimps_I25_J, fact_107_process_Oinj__map__strong, fact_72_solution_Osimps_I6_J, fact_208_process__term_Orel__distinct_I11_J, fact_24_process_Osimps_I16_J, fact_31_process__coind, fact_194_process__term_Orel__map_I1_J, fact_8_iss, fact_64_process_Ocorec__sel_I3_J, fact_129_CH1_Osimps_I1_J, fact_204_process__term_Orel__distinct_I6_J, fact_114_process_Osimps_I21_J, fact_29_process_Omap__ident, fact_191_process__term_Orel__intros_I1_J, fact_4_process_Oexhaust__disc, fact_210_CH2_Ocases, fact_172_PREF_Oinduct, fact_35_solution_Odisc__iff_I2_J, fact_224_process__term_Oset__intros_I8_J, fact_179_process__term_Oset__cases_I1_J, fact_87_process_Orel__distinct_I2_J, fact_89_process_Orel__cases, fact_68_process_Osimps_I6_J, fact_54_process_Oexhaust__sel, fact_110_contOf__def, fact_97_process_Oset__sel_I1_J, fact_93_CH1_Osimps_I2_J, fact_27_process_Oexhaust, fact_5_not__isAction__isChoice, fact_20_process_Oinject_I2_J, fact_121_process__term_Omap__ident, fact_76_PREF_Osimps_I2_J, fact_3_isAction__isChoice, fact_69_process_Odisc__eq__case_I1_J, fact_116_process__term_Oset__intros_I1_J, fact_142_insertE, fact_186_process__term_Orel__inject_I4_J, fact_161_process__term_Oset__intros_I2_J, fact_159_process__term_Odistinct_I7_J, fact_171_isACT_Oinduct, fact_74_process_Orel__coinduct, fact_152_process__term_Oinject_I3_J, fact_79_process_Orel__inject_I2_J, fact_58_process_Ocase__distrib, fact_17_process_Odisc_I2_J, fact_178_PREF_Osimps_I3_J, fact_1_process_Odistinct__disc_I2_J, fact_216_PREF_Opelims, fact_253_process__term_Opred__cong, fact_198_process__term_Orel__distinct_I2_J, fact_41_process_Omap__sel_I4_J, fact_141_insertI1, fact_146_isACT__VAR, fact_168_process__term_Osimps_I28_J, fact_246_process__term_Opred__True, fact_207_process__term_Orel__distinct_I3_J, fact_137_insert__absorb, fact_229_process__term_Orel__cong, fact_240_process__term_Opred__inject_I3_J, fact_162_process__term_Oset__intros_I3_J, fact_91_solution_Octr_I2_J, fact_193_process__term_Orel__eq, fact_118_PREF_Osimps_I1_J, fact_62_process_Osel_I1_J, fact_88_process_Orel__distinct_I1_J, fact_238_process__term_Opred__inject_I1_J, fact_213_CH1_Opelims, fact_209_process__term_Orel__distinct_I12_J, fact_106_process_Oset__intros_I4_J, fact_158_process__term_Odistinct_I11_J, fact_126_process__term_Osimps_I18_J, fact_104_process_Oset__intros_I2_J, fact_53_process_Osplit__sel__asm, fact_120_process__term_Ocase__distrib
% 51.83/26.02 % No. of inferences in proof: 478
% 51.83/26.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 25471 ms resp. 24839 ms w/o parsing
% 52.81/26.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.81/26.23 % [INFO] Killing All external provers ...
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