TSTP Solution File: ITP127^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP127^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Mon May 20 22:23:10 EDT 2024
% Result : Theorem 68.72s 26.98s
% Output : Refutation 69.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 210
% Syntax : Number of formulae : 459 ( 192 unt; 25 typ; 0 def)
% Number of atoms : 1156 ( 450 equ; 10 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 3041 ( 179 ~; 45 |; 57 &;2336 @)
% ( 0 <=>; 424 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 258 ( 258 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 1148 ( 146 ^ 970 !; 32 ?;1148 :)
% Comments :
%------------------------------------------------------------------------------
thf(counta191869203tT_a_m_type,type,
counta191869203tT_a_m: $tType ).
thf(monomo197243225tT_a_m_type,type,
monomo197243225tT_a_m: $tType ).
thf(countable_Set_cset_c_type,type,
countable_Set_cset_c: $tType ).
thf(m_type,type,
m: $tType ).
thf(c_type,type,
c: $tType ).
thf(countable_Set_cin_c_type,type,
countable_Set_cin_c: c > countable_Set_cset_c > $o ).
thf(counta472291938sert_c_type,type,
counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).
thf(comp_M1944986301tT_a_m_type,type,
comp_M1944986301tT_a_m: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).
thf(comp_M750374444_m_m_c_type,type,
comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).
thf(minus_1646763425cset_c_type,type,
minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(if_Cou1542198912cset_c_type,type,
if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(if_c_type,type,
if_c: $o > c > c > c ).
thf(monomo2081011572_m_m_a_type,type,
monomo2081011572_m_m_a: ( counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m ) > counta191869203tT_a_m > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
thf(monomo463139869_c_m_a_type,type,
monomo463139869_c_m_a: ( countable_Set_cset_c > ( c > m ) > m ) > countable_Set_cset_c > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).
thf(monomo412532791tT_m_a_type,type,
monomo412532791tT_m_a: m > monomo197243225tT_a_m ).
thf(monomo624345106et_a_m_type,type,
monomo624345106et_a_m: monomo197243225tT_a_m > m ).
thf(bot_bo1320844070cset_c_type,type,
bot_bo1320844070cset_c: countable_Set_cset_c ).
thf(ord_le1587667814cset_c_type,type,
ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
thf(ord_le15364698cset_c_type,type,
ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
thf(order_1683649299cset_c_type,type,
order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
thf(f_type,type,
f: c > monomo197243225tT_a_m ).
thf(mergec_type,type,
mergec: countable_Set_cset_c > ( c > m ) > m ).
thf(x_type,type,
x: c ).
thf(sk1_type,type,
sk1: countable_Set_cset_c > countable_Set_cset_c > c ).
thf(sk4_type,type,
sk4: m > monomo197243225tT_a_m ).
thf(35,axiom,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ B @ A )
& ( ord_le15364698cset_c @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_dual__order_Oeq__iff) ).
thf(288,plain,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ B @ A )
& ( ord_le15364698cset_c @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(138,axiom,
! [A: countable_Set_cset_c,B: c] :
( ( A = bot_bo1320844070cset_c )
=> ~ ( countable_Set_cin_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_equals__cemptyD) ).
thf(641,plain,
! [A: countable_Set_cset_c,B: c] :
( ( A = bot_bo1320844070cset_c )
=> ~ ( countable_Set_cin_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(642,plain,
! [A: countable_Set_cset_c] :
( ( A = bot_bo1320844070cset_c )
=> ~ ? [B: c] : ( countable_Set_cin_c @ B @ A ) ),
inference(miniscope,[status(thm)],[641]) ).
thf(643,plain,
! [B: c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(cnf,[status(esa)],[642]) ).
thf(644,plain,
! [B: c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(lifteq,[status(thm)],[643]) ).
thf(645,plain,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
inference(simp,[status(thm)],[644]) ).
thf(88,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: $o] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ A )
=> C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_less__imp__triv) ).
thf(468,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: $o] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ A )
=> C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(114,axiom,
! [A: monomo197243225tT_a_m] :
~ ! [B: m] :
( A
!= ( monomo412532791tT_m_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_nondetT_Oexhaust) ).
thf(555,plain,
! [A: monomo197243225tT_a_m] :
~ ! [B: m] :
( A
!= ( monomo412532791tT_m_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(146,axiom,
! [A: countable_Set_cset_c] :
( ( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_all__not__cin__conv) ).
thf(666,plain,
! [A: countable_Set_cset_c] :
( ( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( A = bot_bo1320844070cset_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(92,axiom,
! [A: countable_Set_cset_c > $o,B: countable_Set_cset_c] :
( ( A @ B )
=> ( ! [C: countable_Set_cset_c] :
( ( A @ C )
=> ( ord_le15364698cset_c @ C @ B ) )
=> ( ( order_1683649299cset_c @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Greatest__equality) ).
thf(481,plain,
! [A: countable_Set_cset_c > $o,B: countable_Set_cset_c] :
( ( A @ B )
=> ( ! [C: countable_Set_cset_c] :
( ( A @ C )
=> ( ord_le15364698cset_c @ C @ B ) )
=> ( ( order_1683649299cset_c @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(52,axiom,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_order_Oorder__iff__strict) ).
thf(352,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(70,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_order_Oasym) ).
thf(408,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(39,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_order__le__less__subst2) ).
thf(308,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(172,axiom,
! [A: countable_Set_cset_c,B: c > monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ mergec @ A @ B ) )
= ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_run__altc__nondet) ).
thf(741,plain,
! [A: countable_Set_cset_c,B: c > monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ mergec @ A @ B ) )
= ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(142,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( counta472291938sert_c @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_cinsert__absorb) ).
thf(655,plain,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( counta472291938sert_c @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(28,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_dual__order_Ostrict__iff__order) ).
thf(268,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(269,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(124,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_cin__mono) ).
thf(597,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(12,axiom,
! [A: monomo197243225tT_a_m > m,B: c > m] :
( ( ! [C: c] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: c > monomo197243225tT_a_m] :
( B
= ( comp_M750374444_m_m_c @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_function__factors__right) ).
thf(215,plain,
! [A: monomo197243225tT_a_m > m,B: c > m] :
( ( ! [C: c] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: c > monomo197243225tT_a_m] :
( B
= ( comp_M750374444_m_m_c @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(216,plain,
! [B: c > m,A: monomo197243225tT_a_m > m] :
( ( ! [C: c] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: c > monomo197243225tT_a_m] :
( B
= ( comp_M750374444_m_m_c @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(217,plain,
! [B: c > m,A: monomo197243225tT_a_m > m] :
( ( ! [C: c] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: c > monomo197243225tT_a_m] :
( B
= ( comp_M750374444_m_m_c @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(31,axiom,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c,D: monomo197243225tT_a_m > m,E: c > monomo197243225tT_a_m] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_comp__apply__eq) ).
thf(276,plain,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c,D: monomo197243225tT_a_m > m,E: c > monomo197243225tT_a_m] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ C ) ) )
=> ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(108,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( B @ C ) )
=> ( ( ord_le1587667814cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_order__less__subst1) ).
thf(533,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( B @ C ) )
=> ( ( ord_le1587667814cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(96,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_le__imp__less__or__eq) ).
thf(500,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(174,axiom,
! [A: c,B: countable_Set_cset_c,C: c] :
( ( ~ ( countable_Set_cin_c @ A @ B )
=> ( A = C ) )
=> ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_cinsertCI) ).
thf(747,plain,
! [A: c,B: countable_Set_cset_c,C: c] :
( ( ~ ( countable_Set_cin_c @ A @ B )
=> ( A = C ) )
=> ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(48,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_dual__order_Oantisym) ).
thf(340,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(164,axiom,
( monomo463139869_c_m_a
= ( ^ [A: countable_Set_cset_c > ( c > m ) > m,B: countable_Set_cset_c,C: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( A @ B @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_cset__nondetM__base_Oaltc__nondet__def) ).
thf(718,plain,
( monomo463139869_c_m_a
= ( ^ [A: countable_Set_cset_c > ( c > m ) > m,B: countable_Set_cset_c,C: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( A @ B @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(719,plain,
( monomo463139869_c_m_a
= ( ^ [A: countable_Set_cset_c > ( c > m ) > m,B: countable_Set_cset_c,C: c > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( A @ B @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[718]) ).
thf(59,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_cDiff__csubset) ).
thf(372,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(115,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ C @ A )
=> ( ord_le15364698cset_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_dual__order_Otrans) ).
thf(559,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ C @ A )
=> ( ord_le15364698cset_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(137,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ ( counta472291938sert_c @ A @ B ) @ C )
= ( ( countable_Set_cin_c @ A @ C )
& ( ord_le15364698cset_c @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_cinsert__csubset) ).
thf(638,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ ( counta472291938sert_c @ A @ B ) @ C )
= ( ( countable_Set_cin_c @ A @ C )
& ( ord_le15364698cset_c @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(3,axiom,
( comp_M1944986301tT_a_m
= ( ^ [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_comp__apply) ).
thf(188,plain,
( comp_M1944986301tT_a_m
= ( ^ [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(189,plain,
( comp_M1944986301tT_a_m
= ( ^ [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(73,axiom,
! [A: monomo197243225tT_a_m > $o,B: monomo197243225tT_a_m] :
( ! [C: m] : ( A @ ( monomo412532791tT_m_a @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_nondetT_Oinduct) ).
thf(416,plain,
! [A: monomo197243225tT_a_m > $o,B: monomo197243225tT_a_m] :
( ! [C: m] : ( A @ ( monomo412532791tT_m_a @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(43,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ D ) @ ( minus_1646763425cset_c @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_cminus__mono) ).
thf(325,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ D ) @ ( minus_1646763425cset_c @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(17,axiom,
! [A: c,B: $o,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( if_Cou1542198912cset_c @ B @ C @ D ) )
= ( ( B
=> ( countable_Set_cin_c @ A @ C ) )
& ( ~ B
=> ( countable_Set_cin_c @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_if__split__cin2) ).
thf(228,plain,
! [A: c,B: $o,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( if_Cou1542198912cset_c @ B @ C @ D ) )
= ( ( B
=> ( countable_Set_cin_c @ A @ C ) )
& ( ~ B
=> ( countable_Set_cin_c @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(289,plain,
( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ B @ A )
& ( ord_le15364698cset_c @ A @ B ) ) )
= ( (=) @ countable_Set_cset_c ) ),
inference(lifteq,[status(thm)],[288]) ).
thf(81,axiom,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_cset__eq__csubset) ).
thf(448,plain,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(33,axiom,
! [A: monomo197243225tT_a_m,B: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
= ( monomo624345106et_a_m @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_nondetT_Oexpand) ).
thf(281,plain,
! [A: monomo197243225tT_a_m,B: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
= ( monomo624345106et_a_m @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(282,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
!= ( monomo624345106et_a_m @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
!= ( monomo624345106et_a_m @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(284,plain,
! [A: monomo197243225tT_a_m] :
( ( sk4 @ ( monomo624345106et_a_m @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(monomo624345106et_a_m),[sk4])]) ).
thf(180,axiom,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_cempty__iff) ).
thf(770,plain,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(90,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_less__imp__not__less) ).
thf(475,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(185,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_not__cpsubset__cempty) ).
thf(789,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(61,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le15364698cset_c @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_order__subst2) ).
thf(376,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le15364698cset_c @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(132,axiom,
! [A: c,B: c] :
( ( ( counta472291938sert_c @ A @ bot_bo1320844070cset_c )
= ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_csingleton__inject) ).
thf(623,plain,
! [A: c,B: c] :
( ( ( counta472291938sert_c @ A @ bot_bo1320844070cset_c )
= ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(101,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_order_Ostrict__implies__order) ).
thf(514,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(353,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[352]) ).
thf(139,axiom,
! [A: countable_Set_cset_c > ( c > m ) > m,B: countable_Set_cset_c,C: c > monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ A @ B @ C ) )
= ( A @ B @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_cset__nondetM__base_Orun__altc__nondet) ).
thf(646,plain,
! [A: countable_Set_cset_c > ( c > m ) > m,B: countable_Set_cset_c,C: c > monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo463139869_c_m_a @ A @ B @ C ) )
= ( A @ B @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(24,axiom,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( countable_Set_cin_c @ B @ C )
=> ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_eq__cmem__trans) ).
thf(253,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( countable_Set_cin_c @ B @ C )
=> ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(22,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( B = C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_ord__less__eq__trans) ).
thf(243,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( B = C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(99,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_antisym) ).
thf(507,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(9,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ! [C: c] :
( ( countable_Set_cin_c @ C @ A )
= ( countable_Set_cin_c @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_cset__eqI) ).
thf(206,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ! [C: c] :
( ( countable_Set_cin_c @ C @ A )
= ( countable_Set_cin_c @ C @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(126,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ? [C: c] : ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_cpsubset__imp__ex__fmem) ).
thf(602,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ? [C: c] : ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(179,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ B )
=> ( ~ ( countable_Set_cin_c @ A @ C )
=> ( ( ( counta472291938sert_c @ A @ B )
= ( counta472291938sert_c @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_cinsert__ident) ).
thf(766,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ B )
=> ( ~ ( countable_Set_cin_c @ A @ C )
=> ( ( ( counta472291938sert_c @ A @ B )
= ( counta472291938sert_c @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(67,axiom,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( countable_Set_cin_c @ A @ C )
= ( countable_Set_cin_c @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_eqcelem__imp__iff) ).
thf(397,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( countable_Set_cin_c @ A @ C )
= ( countable_Set_cin_c @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(153,axiom,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ C ) @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_cDiff__cinsert) ).
thf(687,plain,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ C ) @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(207,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[206]) ).
thf(208,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(1,conjecture,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
= ( f @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
!= ( f @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(186,plain,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
!= ( f @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(187,plain,
( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ f )
!= ( f @ x ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(1004,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) )
| ( B != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[208,187]) ).
thf(1005,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1004:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c ))]]) ).
thf(1072,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(rewrite,[status(thm)],[1005,645]) ).
thf(83,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_cpsubsetD) ).
thf(453,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(106,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_dual__order_Ostrict__trans) ).
thf(527,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(40,axiom,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_nondetT_Osel) ).
thf(312,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(37,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( A
= ( B @ C ) )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le15364698cset_c @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_ord__eq__le__subst) ).
thf(292,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( A
= ( B @ C ) )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le15364698cset_c @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(23,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_ord__eq__less__trans) ).
thf(248,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(62,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_csubset__trans) ).
thf(380,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(150,axiom,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_cemptyE) ).
thf(678,plain,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(29,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_cpsubset__eq) ).
thf(270,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(144,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_bot_Oextremum) ).
thf(661,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(112,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( B = C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_ord__le__eq__trans) ).
thf(546,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( B = C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(7,axiom,
( comp_M1944986301tT_a_m
= ( ^ [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_comp__def) ).
thf(201,plain,
( comp_M1944986301tT_a_m
= ( ^ [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(162,axiom,
! [A: c,B: countable_Set_cset_c] : ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_cinsertI1) ).
thf(714,plain,
! [A: c,B: countable_Set_cset_c] : ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(14,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A != B )
=> ( ( ord_le15364698cset_c @ A @ B )
=> ( ord_le1587667814cset_c @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_order_Onot__eq__order__implies__strict) ).
thf(220,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A != B )
=> ( ( ord_le15364698cset_c @ A @ B )
=> ( ord_le1587667814cset_c @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(57,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ~ ( ord_le1587667814cset_c @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_antisym__conv2) ).
thf(366,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ~ ( ord_le1587667814cset_c @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(46,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_less__le__trans) ).
thf(334,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(51,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ~ ( countable_Set_cin_c @ A @ C )
=> ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_cDiffI) ).
thf(349,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ~ ( countable_Set_cin_c @ A @ C )
=> ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(168,axiom,
! [A: countable_Set_cset_c,B: c > monomo197243225tT_a_m] :
( ( monomo463139869_c_m_a @ mergec @ A @ B )
= ( monomo412532791tT_m_a @ ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_altc__nondet__def) ).
thf(729,plain,
! [A: countable_Set_cset_c,B: c > monomo197243225tT_a_m] :
( ( monomo463139869_c_m_a @ mergec @ A @ B )
= ( monomo412532791tT_m_a @ ( mergec @ A @ ( comp_M750374444_m_m_c @ monomo624345106et_a_m @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(155,axiom,
! [A: c,B: c,C: c,D: c] :
( ( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
= ( counta472291938sert_c @ C @ ( counta472291938sert_c @ D @ bot_bo1320844070cset_c ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_cdoubleton__eq__iff) ).
thf(693,plain,
! [A: c,B: c,C: c,D: c] :
( ( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
= ( counta472291938sert_c @ C @ ( counta472291938sert_c @ D @ bot_bo1320844070cset_c ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(134,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_csubset__cinsertI2) ).
thf(630,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(5,axiom,
! [A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,B: counta191869203tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ A @ B @ C ) )
= ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_cset__nondetM__base_Orun__altc__nondet) ).
thf(195,plain,
! [A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,B: counta191869203tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ A @ B @ C ) )
= ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(196,plain,
! [C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: counta191869203tT_a_m,A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m] :
( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ A @ B @ C ) )
= ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: counta191869203tT_a_m,A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m] :
( ( monomo624345106et_a_m @ ( monomo2081011572_m_m_a @ A @ B @ C ) )
= ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(56,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( A = B )
=> ( ( countable_Set_cin_c @ C @ A )
= ( countable_Set_cin_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_eqcset__imp__iff) ).
thf(361,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( A = B )
=> ( ( countable_Set_cin_c @ C @ A )
= ( countable_Set_cin_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(123,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( A = B )
=> ( ( ( countable_Set_cin_c @ C @ A )
=> ~ ( countable_Set_cin_c @ C @ B ) )
=> ~ ( ~ ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_cequalityCE) ).
thf(583,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( A = B )
=> ( ( ( countable_Set_cin_c @ C @ A )
=> ~ ( countable_Set_cin_c @ C @ B ) )
=> ~ ( ~ ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(86,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_order_Ostrict__iff__order) ).
thf(461,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1000,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ B ) @ f )
!= ( f @ x ) )
| ( A != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[208,187]) ).
thf(1001,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c )
!= ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1000:[bind(A,$thf( bot_bo1320844070cset_c ))]]) ).
thf(1022,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c )
!= ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1079,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(rewrite,[status(thm)],[1022,645]) ).
thf(113,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_less__imp__not__eq) ).
thf(551,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(160,axiom,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( ( A = B )
| ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_cinsert__iff) ).
thf(710,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( ( A = B )
| ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(84,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
=> ~ ( countable_Set_cin_c @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_cDiffD2) ).
thf(456,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
=> ~ ( countable_Set_cin_c @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(34,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B ) @ B )
= ( minus_1646763425cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_cDiff__idemp) ).
thf(285,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B ) @ B )
= ( minus_1646763425cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_csubset__refl) ).
thf(223,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(224,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(cnf,[status(esa)],[223]) ).
thf(54,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_order__class_Oorder_Oantisym) ).
thf(356,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(271,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(868,plain,
( ( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) )
| ( ord_le1587667814cset_c != ord_le1587667814cset_c ) ),
inference(paramod_ordered,[status(thm)],[271,269]) ).
thf(869,plain,
( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) ),
inference(pattern_uni,[status(thm)],[868:[]]) ).
thf(129,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_ord__less__eq__subst) ).
thf(610,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(183,axiom,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_bot_Oextremum__unique) ).
thf(783,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(103,axiom,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_csubset__iff__pfsubset__eq) ).
thf(519,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(121,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_less__asym) ).
thf(578,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(16,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_cpsubset__csubset__trans) ).
thf(225,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(109,axiom,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_le__less) ).
thf(537,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(147,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ A @ B ) )
= ( counta472291938sert_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cinsert__absorb2) ).
thf(669,plain,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ A @ B ) )
= ( counta472291938sert_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(136,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_cempty__fsubsetI) ).
thf(636,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(637,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
inference(cnf,[status(esa)],[636]) ).
thf(10,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_order_Ostrict__implies__not__eq) ).
thf(209,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(210,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A != B )
| ~ ( ord_le1587667814cset_c @ A @ B ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(212,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
inference(simp,[status(thm)],[211]) ).
thf(44,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_less__imp__neq) ).
thf(328,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(89,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_order__less__le__subst2) ).
thf(471,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(66,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_less__imp__not__eq2) ).
thf(393,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(171,axiom,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_cempty__cDiff) ).
thf(738,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(97,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_less__imp__le) ).
thf(503,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(792,plain,
! [A: monomo197243225tT_a_m > m] :
( ( comp_M1944986301tT_a_m @ A )
= ( ^ [B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
inference(func_ext,[status(esa)],[189]) ).
thf(27,axiom,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_order__class_Oorder_Oeq__iff) ).
thf(266,plain,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(135,axiom,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( counta472291938sert_c @ B @ ( counta472291938sert_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_cinsert__commute) ).
thf(633,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( counta472291938sert_c @ B @ ( counta472291938sert_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(8,axiom,
! [A: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > m] :
( ( ! [C: monomo197243225tT_a_m,D: monomo197243225tT_a_m] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: monomo197243225tT_a_m > m] :
( B
= ( comp_M1944986301tT_a_m @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_function__factors__left) ).
thf(203,plain,
! [A: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > m] :
( ( ! [C: monomo197243225tT_a_m,D: monomo197243225tT_a_m] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: monomo197243225tT_a_m > m] :
( B
= ( comp_M1944986301tT_a_m @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(204,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( ! [C: monomo197243225tT_a_m,D: monomo197243225tT_a_m] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: monomo197243225tT_a_m > m] :
( B
= ( comp_M1944986301tT_a_m @ C @ A ) ) ) ),
inference(cnf,[status(esa)],[203]) ).
thf(205,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( ! [C: monomo197243225tT_a_m,D: monomo197243225tT_a_m] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: monomo197243225tT_a_m > m] :
( B
= ( comp_M1944986301tT_a_m @ C @ A ) ) ) ),
inference(lifteq,[status(thm)],[204]) ).
thf(107,axiom,
! [A: m,B: m] :
( ( ( monomo412532791tT_m_a @ A )
= ( monomo412532791tT_m_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nondetT_Oinject) ).
thf(530,plain,
! [A: m,B: m] :
( ( ( monomo412532791tT_m_a @ A )
= ( monomo412532791tT_m_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(181,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ C ) @ B )
= ( minus_1646763425cset_c @ C @ B ) ) )
& ( ~ ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ C ) @ B )
= ( counta472291938sert_c @ A @ ( minus_1646763425cset_c @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_cinsert__cDiff__if) ).
thf(773,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ C ) @ B )
= ( minus_1646763425cset_c @ C @ B ) ) )
& ( ~ ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ C ) @ B )
= ( counta472291938sert_c @ A @ ( minus_1646763425cset_c @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(49,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_order_Otrans) ).
thf(343,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(20,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_dual__order_Ostrict__trans2) ).
thf(237,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(130,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_order_Ostrict__trans) ).
thf(618,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(76,axiom,
! [A: $o,B: c,C: c,D: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( if_c @ A @ B @ C ) @ D )
= ( ( A
=> ( countable_Set_cin_c @ B @ D ) )
& ( ~ A
=> ( countable_Set_cin_c @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_if__split__cin1) ).
thf(425,plain,
! [A: $o,B: c,C: c,D: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( if_c @ A @ B @ C ) @ D )
= ( ( A
=> ( countable_Set_cin_c @ B @ D ) )
& ( ~ A
=> ( countable_Set_cin_c @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(32,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_less__le__not__le) ).
thf(279,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(79,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_less__le) ).
thf(444,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(125,axiom,
( monomo2081011572_m_m_a
= ( ^ [A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,B: counta191869203tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_cset__nondetM__base_Oaltc__nondet__def) ).
thf(600,plain,
( monomo2081011572_m_m_a
= ( ^ [A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,B: counta191869203tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(601,plain,
( monomo2081011572_m_m_a
= ( ^ [A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m,B: counta191869203tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( A @ B @ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ C ) ) ) ) ),
inference(lifteq,[status(thm)],[600]) ).
thf(116,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_dual__order_Orefl) ).
thf(562,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(75,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_less__not__sym) ).
thf(423,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(68,axiom,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= ( comp_M750374444_m_m_c @ C @ D ) )
=> ! [E: c] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_comp__eq__elim) ).
thf(402,plain,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= ( comp_M750374444_m_m_c @ C @ D ) )
=> ! [E: c] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(169,axiom,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ A )
= bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_cDiff__cancel) ).
thf(732,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ A )
= bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(36,axiom,
( comp_M750374444_m_m_c
= ( ^ [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_comp__apply) ).
thf(290,plain,
( comp_M750374444_m_m_c
= ( ^ [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(291,plain,
( comp_M750374444_m_m_c
= ( ^ [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c] : ( A @ ( B @ C ) ) ) ),
inference(lifteq,[status(thm)],[290]) ).
thf(72,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_less__trans) ).
thf(413,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(119,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
= ( ( countable_Set_cin_c @ A @ B )
& ~ ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_cDiff__iff) ).
thf(572,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
= ( ( countable_Set_cin_c @ A @ B )
& ~ ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(161,axiom,
monomo463139869_c_m_a = monomo463139869_c_m_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_cset__nondetM__base_Oaltc__nondet_Ocong) ).
thf(713,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(158,axiom,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_cDiff__cempty) ).
thf(704,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(148,axiom,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
= ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_bot_Onot__eq__extremum) ).
thf(672,plain,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
= ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(127,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_dual__order_Oirrefl) ).
thf(604,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(151,axiom,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_cDiff__cinsert2) ).
thf(681,plain,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(74,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( B @ C ) )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_order__less__le__subst1) ).
thf(419,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( B @ C ) )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(170,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_bot_Oextremum__strict) ).
thf(735,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(736,plain,
~ ? [A: countable_Set_cset_c] : ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(miniscope,[status(thm)],[735]) ).
thf(737,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[736]) ).
thf(140,axiom,
! [A: countable_Set_cset_c] :
( ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) )
= ( A != bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_ex__cin__conv) ).
thf(649,plain,
! [A: countable_Set_cset_c] :
( ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) )
= ( A != bot_bo1320844070cset_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(77,axiom,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_nondetT_Ocollapse) ).
thf(434,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(91,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_cequalityD1) ).
thf(477,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(94,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_less__cset__def) ).
thf(494,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(11,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_dual__order_Oasym) ).
thf(213,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(131,axiom,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_dual__order_Oorder__iff__strict) ).
thf(621,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(157,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ C ) @ B )
= ( minus_1646763425cset_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_cinsert__cDiff1) ).
thf(700,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ C ) @ B )
= ( minus_1646763425cset_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(21,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_csubsetD) ).
thf(240,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(133,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ~ ! [C: countable_Set_cset_c] :
( ( B
= ( counta472291938sert_c @ A @ C ) )
=> ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_set__cinsert) ).
thf(626,plain,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ~ ! [C: countable_Set_cset_c] :
( ( B
= ( counta472291938sert_c @ A @ C ) )
=> ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(6,axiom,
! [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > m] :
( ( ! [C: monomo197243225tT_a_m] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( B
= ( comp_M1944986301tT_a_m @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_function__factors__right) ).
thf(198,plain,
! [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > m] :
( ( ! [C: monomo197243225tT_a_m] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( B
= ( comp_M1944986301tT_a_m @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(104,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_order_Ostrict__trans1) ).
thf(521,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(182,axiom,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( ( ( countable_Set_cin_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) )
& ( ~ ( countable_Set_cin_c @ B @ C )
=> ( ( ( countable_Set_cin_c @ B @ A )
=> ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C ) )
& ( ~ ( countable_Set_cin_c @ B @ A )
=> ( ord_le15364698cset_c @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_cpsubset__finsert__iff) ).
thf(780,plain,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( ( ( countable_Set_cin_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) )
& ( ~ ( countable_Set_cin_c @ B @ C )
=> ( ( ( countable_Set_cin_c @ B @ A )
=> ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C ) )
& ( ~ ( countable_Set_cin_c @ B @ A )
=> ( ord_le15364698cset_c @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(98,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_leD) ).
thf(505,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(143,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ord_le15364698cset_c @ ( counta472291938sert_c @ C @ A ) @ ( counta472291938sert_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_cinsert__mono) ).
thf(658,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ord_le15364698cset_c @ ( counta472291938sert_c @ C @ A ) @ ( counta472291938sert_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(267,plain,
( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) )
= ( (=) @ countable_Set_cset_c ) ),
inference(lifteq,[status(thm)],[266]) ).
thf(622,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( B = A ) ) ) ),
inference(lifteq,[status(thm)],[621]) ).
thf(851,plain,
( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( B = A ) ) ) ),
inference(rewrite,[status(thm)],[622,353]) ).
thf(149,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( counta472291938sert_c @ A @ ( minus_1646763425cset_c @ B @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_cinsert__cDiff) ).
thf(675,plain,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( counta472291938sert_c @ A @ ( minus_1646763425cset_c @ B @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(795,plain,
! [A: monomo197243225tT_a_m > m] :
( ( comp_M750374444_m_m_c @ A )
= ( ^ [B: c > monomo197243225tT_a_m,C: c] : ( A @ ( B @ C ) ) ) ),
inference(func_ext,[status(esa)],[291]) ).
thf(145,axiom,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( ( ( countable_Set_cin_c @ B @ A )
=> ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C ) )
& ( ~ ( countable_Set_cin_c @ B @ A )
=> ( ord_le15364698cset_c @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_csubset__cinsert__iff) ).
thf(663,plain,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
= ( ( ( countable_Set_cin_c @ B @ A )
=> ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C ) )
& ( ~ ( countable_Set_cin_c @ B @ A )
=> ( ord_le15364698cset_c @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(60,axiom,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_eq__iff) ).
thf(374,plain,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(102,axiom,
! [A: c > monomo197243225tT_a_m,B: c > m] :
( ( ! [C: c,D: c] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: monomo197243225tT_a_m > m] :
( B
= ( comp_M750374444_m_m_c @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_function__factors__left) ).
thf(516,plain,
! [A: c > monomo197243225tT_a_m,B: c > m] :
( ( ! [C: c,D: c] :
( ( ( A @ C )
= ( A @ D ) )
=> ( ( B @ C )
= ( B @ D ) ) ) )
= ( ? [C: monomo197243225tT_a_m > m] :
( B
= ( comp_M750374444_m_m_c @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(85,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_csubset__antisym) ).
thf(458,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(4,axiom,
! [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_comp__eq__dest__lhs) ).
thf(190,plain,
! [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(191,plain,
! [A: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m] :
( ( ( comp_M1944986301tT_a_m @ A @ B )
= C )
=> ! [D: monomo197243225tT_a_m] :
( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(miniscope,[status(thm)],[190]) ).
thf(192,plain,
! [D: monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M1944986301tT_a_m @ A @ B )
!= C )
| ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
! [D: monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M1944986301tT_a_m @ A @ B )
!= C )
| ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(194,plain,
! [C: monomo197243225tT_a_m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( A @ ( B @ C ) )
= ( comp_M1944986301tT_a_m @ A @ B @ C ) ),
inference(simp,[status(thm)],[193]) ).
thf(1002,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ( B
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[208,187]) ).
thf(1003,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1002:[bind(A,$thf( A )),bind(B,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c ))]]) ).
thf(122,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
=> ~ ( ( countable_Set_cin_c @ A @ B )
=> ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_cDiffE) ).
thf(580,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
=> ~ ( ( countable_Set_cin_c @ A @ B )
=> ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(154,axiom,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
=> ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_bot_Oextremum__uniqueI) ).
thf(690,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
=> ( A = bot_bo1320844070cset_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(159,axiom,
! [A: c,B: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_csingleton__iff) ).
thf(707,plain,
! [A: c,B: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(280,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(886,plain,
( ( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) )
| ( ord_le1587667814cset_c != ord_le1587667814cset_c ) ),
inference(paramod_ordered,[status(thm)],[280,269]) ).
thf(887,plain,
( ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) ),
inference(pattern_uni,[status(thm)],[886:[]]) ).
thf(26,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_dual__order_Ostrict__trans1) ).
thf(263,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(87,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_ord__eq__le__trans) ).
thf(463,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( A = B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(55,axiom,
( comp_M750374444_m_m_c
= ( ^ [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_comp__def) ).
thf(359,plain,
( comp_M750374444_m_m_c
= ( ^ [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(173,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( minus_1646763425cset_c @ B @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) ) )
= ( counta472291938sert_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_cinsert__cDiff__single) ).
thf(744,plain,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( minus_1646763425cset_c @ B @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) ) )
= ( counta472291938sert_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(167,axiom,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C )
=> ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_cDiff__single__cinsert) ).
thf(727,plain,
! [A: countable_Set_cset_c,B: c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) @ C )
=> ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(64,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_cequalityD2) ).
thf(386,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(313,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(cnf,[status(esa)],[312]) ).
thf(314,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(lifteq,[status(thm)],[313]) ).
thf(80,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_cpsubset__imp__fsubset) ).
thf(446,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(18,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( B @ C ) )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le15364698cset_c @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_order__subst1) ).
thf(231,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( B @ C ) )
=> ( ( ord_le15364698cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le15364698cset_c @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(82,axiom,
! [A: monomo197243225tT_a_m] :
( A
= ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_nondetT_Oexhaust__sel) ).
thf(450,plain,
! [A: monomo197243225tT_a_m] :
( A
= ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(110,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_order__less__subst2) ).
thf(539,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ ( C @ B ) @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(105,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_antisym__conv1) ).
thf(524,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(177,axiom,
! [A: countable_Set_cset_c] :
( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A )
=> ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_equals__cemptyI) ).
thf(759,plain,
! [A: countable_Set_cset_c] :
( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A )
=> ( A = bot_bo1320844070cset_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(13,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_dual__order_Ostrict__implies__order) ).
thf(218,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(156,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_cinsert__not__cempty) ).
thf(696,plain,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(697,plain,
~ ? [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ B )
= bot_bo1320844070cset_c ),
inference(miniscope,[status(thm)],[696]) ).
thf(698,plain,
! [B: countable_Set_cset_c,A: c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[697]) ).
thf(699,plain,
! [B: countable_Set_cset_c,A: c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
inference(lifteq,[status(thm)],[698]) ).
thf(25,axiom,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comp__eq__dest__lhs) ).
thf(258,plain,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m,D: c] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(141,axiom,
! [A: countable_Set_cset_c,B: c] :
( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
=> ( ( A = bot_bo1320844070cset_c )
| ( A
= ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_csubset__csingletonD) ).
thf(652,plain,
! [A: countable_Set_cset_c,B: c] :
( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
=> ( ( A = bot_bo1320844070cset_c )
| ( A
= ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(65,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order__trans) ).
thf(390,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(184,axiom,
! [A: c,B: c > m] :
( ( mergec @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_mergec__single) ).
thf(786,plain,
! [A: c,B: c > m] :
( ( mergec @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(118,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_dual__order_Ostrict__implies__not__eq) ).
thf(568,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(19,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_order__refl) ).
thf(235,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(100,axiom,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,E: c] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= ( comp_M750374444_m_m_c @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_comp__eq__dest) ).
thf(510,plain,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,D: c > monomo197243225tT_a_m,E: c] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= ( comp_M750374444_m_m_c @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(63,axiom,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c,D: monomo197243225tT_a_m > m,E: c > monomo197243225tT_a_m,F: c] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_comp__cong) ).
thf(383,plain,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c,D: monomo197243225tT_a_m > m,E: c > monomo197243225tT_a_m,F: c] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(152,axiom,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ C ) )
=> ( ( A != B )
=> ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_cinsertE) ).
thf(684,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ C ) )
=> ( ( A != B )
=> ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(50,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ! [C: c] :
( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_csubsetI) ).
thf(346,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ! [C: c] :
( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(178,axiom,
! [A: c,B: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ B ) @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_cDiff__cinsert__absorb) ).
thf(763,plain,
! [A: c,B: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ B )
=> ( ( minus_1646763425cset_c @ ( counta472291938sert_c @ A @ B ) @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(30,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ( minus_1646763425cset_c @ B @ ( minus_1646763425cset_c @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_double__cDiff) ).
thf(272,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ( minus_1646763425cset_c @ B @ ( minus_1646763425cset_c @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(163,axiom,
! [A: countable_Set_cset_c,B: c] : ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_csubset__cinsertI) ).
thf(716,plain,
! [A: countable_Set_cset_c,B: c] : ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(214,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(cnf,[status(esa)],[213]) ).
thf(38,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le15364698cset_c @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_ord__le__eq__subst) ).
thf(300,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le15364698cset_c @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(175,axiom,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_csubset__cempty) ).
thf(752,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(41,axiom,
! [A: countable_Set_cset_c > $o,B: countable_Set_cset_c,C: countable_Set_cset_c > $o] :
( ( A @ B )
=> ( ! [D: countable_Set_cset_c] :
( ( A @ D )
=> ( ord_le15364698cset_c @ D @ B ) )
=> ( ! [D: countable_Set_cset_c] :
( ( A @ D )
=> ( ! [E: countable_Set_cset_c] :
( ( A @ E )
=> ( ord_le15364698cset_c @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1683649299cset_c @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_GreatestI2__order) ).
thf(315,plain,
! [A: countable_Set_cset_c > $o,B: countable_Set_cset_c,C: countable_Set_cset_c > $o] :
( ( A @ B )
=> ( ! [D: countable_Set_cset_c] :
( ( A @ D )
=> ( ord_le15364698cset_c @ D @ B ) )
=> ( ! [D: countable_Set_cset_c] :
( ( A @ D )
=> ( ! [E: countable_Set_cset_c] :
( ( A @ E )
=> ( ord_le15364698cset_c @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1683649299cset_c @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(71,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( A != B )
=> ( ord_le1587667814cset_c @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_le__neq__trans) ).
thf(410,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( A != B )
=> ( ord_le1587667814cset_c @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(69,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_order_Ostrict__trans2) ).
thf(405,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(117,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_eq__refl) ).
thf(564,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(78,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ~ ( ( ord_le15364698cset_c @ A @ B )
=> ~ ( ord_le15364698cset_c @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_cequalityE) ).
thf(437,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ~ ( ( ord_le15364698cset_c @ A @ B )
=> ~ ( ord_le15364698cset_c @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(165,axiom,
! [A: c,B: countable_Set_cset_c,C: c] :
( ( countable_Set_cin_c @ A @ B )
=> ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_cinsertI2) ).
thf(720,plain,
! [A: c,B: countable_Set_cset_c,C: c] :
( ( countable_Set_cin_c @ A @ B )
=> ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(739,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[738]) ).
thf(740,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
inference(lifteq,[status(thm)],[739]) ).
thf(45,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_less__asym_H) ).
thf(332,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(120,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_cpsubset__trans) ).
thf(575,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(166,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ? [C: countable_Set_cset_c] :
( ( B
= ( counta472291938sert_c @ A @ C ) )
& ~ ( countable_Set_cin_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_mk__disjoint__cinsert) ).
thf(723,plain,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ? [C: countable_Set_cset_c] :
( ( B
= ( counta472291938sert_c @ A @ C ) )
& ~ ( countable_Set_cin_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(199,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m > m] :
( ( ! [C: monomo197243225tT_a_m] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( B
= ( comp_M1944986301tT_a_m @ A @ C ) ) ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m > m] :
( ( ! [C: monomo197243225tT_a_m] :
? [D: monomo197243225tT_a_m] :
( ( A @ D )
= ( B @ C ) ) )
= ( ? [C: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( B
= ( comp_M1944986301tT_a_m @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(58,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_csubset__cpsubset__trans) ).
thf(369,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(128,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
=> ( countable_Set_cin_c @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_cDiffD1) ).
thf(607,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
=> ( countable_Set_cin_c @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(42,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_le__less__trans) ).
thf(322,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(93,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1587667814cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ord__eq__less__subst) ).
thf(486,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1587667814cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(47,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_less__irrefl) ).
thf(337,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(53,axiom,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_csubset__not__fsubset__eq) ).
thf(354,plain,
( ord_le1587667814cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(111,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_antisym__conv) ).
thf(543,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(176,axiom,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ ( counta472291938sert_c @ A @ C ) )
= ( ord_le15364698cset_c @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_csubset__cinsert) ).
thf(755,plain,
! [A: c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ B )
=> ( ( ord_le15364698cset_c @ B @ ( counta472291938sert_c @ A @ C ) )
= ( ord_le15364698cset_c @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(95,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( B @ C ) )
=> ( ( ord_le1587667814cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_order__le__less__subst1) ).
thf(496,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( B @ C ) )
=> ( ( ord_le1587667814cset_c @ C @ D )
=> ( ! [E: countable_Set_cset_c,F: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ E @ F )
=> ( ord_le1587667814cset_c @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(12548,plain,
$false,
inference(cvc4,[status(thm)],[288,645,468,555,666,481,352,408,308,741,655,269,597,217,276,533,500,747,340,719,372,559,638,189,416,325,228,289,448,284,770,475,789,376,623,514,353,646,253,243,507,206,602,766,397,687,1072,453,527,312,292,248,380,678,270,661,546,201,714,220,366,334,349,729,693,630,197,361,583,461,1079,551,710,456,285,224,188,356,869,610,783,519,578,225,537,669,637,212,328,471,393,738,503,792,266,633,205,530,773,718,343,237,618,425,279,444,601,562,423,402,732,291,281,413,641,572,713,704,672,604,187,681,419,737,649,434,271,208,477,494,213,621,700,240,626,198,521,636,780,223,505,658,267,851,675,795,663,374,209,516,458,194,1003,580,690,707,887,263,463,359,744,600,727,386,314,446,231,450,539,203,524,759,218,699,258,652,390,186,786,568,290,235,510,383,684,346,763,272,716,214,300,752,315,410,405,190,735,564,268,195,437,696,720,740,332,575,723,200,369,607,322,486,337,354,543,215,755,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : ITP127^1 : TPTP v8.2.0. Released v7.5.0.
% 0.09/0.13 % Command : run_Leo-III %s %d
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat May 18 18:07:24 EDT 2024
% 0.13/0.33 % CPUTime :
% 1.00/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.88/1.28 % [INFO] Parsing done (339ms).
% 1.88/1.29 % [INFO] Running in sequential loop mode.
% 3.11/1.66 % [INFO] eprover registered as external prover.
% 3.11/1.66 % [INFO] cvc4 registered as external prover.
% 3.11/1.67 % [INFO] Scanning for conjecture ...
% 3.47/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 315 axioms. Running axiom selection ...
% 3.62/1.86 % [INFO] Axiom selection finished. Selected 183 axioms (removed 132 axioms).
% 4.17/2.00 % [INFO] Problem is higher-order (TPTP THF).
% 4.17/2.02 % [INFO] Type checking passed.
% 4.17/2.02 % [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 ...
% 68.72/26.98 % External prover 'cvc4' found a proof!
% 68.72/26.98 % [INFO] Killing All external provers ...
% 68.72/26.98 % Time passed: 26492ms (effective reasoning time: 25679ms)
% 68.72/26.98 % 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)>
% 68.72/26.98 % Axioms used in derivation (183): fact_229_bot_Oextremum, fact_87_nondetT_Osel, fact_25_comp__def, fact_219_cemptyE, fact_172_cempty__iff, fact_296_dual__order_Ostrict__implies__order, fact_148_function__factors__left, fact_36_comp__eq__dest, fact_303_less__cset__def, fact_294_dual__order_Oorder__iff__strict, fact_204_cequalityD1, fact_56_comp__cong, fact_8_nondetT_Oexpand, fact_180_cinsert__csubset, fact_196_eqcset__imp__iff, fact_72_comp__apply__eq, fact_213_ord__eq__le__subst, fact_243_cDiff__cinsert__absorb, fact_220_mk__disjoint__cinsert, fact_288_order_Ostrict__trans2, fact_275_order__le__less__subst1, fact_3_cdoubleton__eq__iff, fact_282_less__imp__le, fact_7_run__altc__nondet, fact_304_cpsubset__imp__fsubset, fact_194_cset__eq__csubset, fact_307_csubset__not__fsubset__eq, fact_187_order__trans, fact_241_cinsert__cDiff__if, fact_238_cminus__mono, fact_161_cDiff__idemp, fact_198_if__split__cin2, fact_268_less__imp__not__less, fact_222_cinsert__ident, fact_278_order__less__le__subst2, fact_193_eqcelem__imp__iff, fact_290_order_Ostrict__iff__order, fact_178_cDiff__iff, fact_227_bot_Oextremum__uniqueI, fact_174_cinsertCI, fact_173_cinsert__iff, fact_179_cDiffI, fact_302_cpsubset__eq, fact_171_all__not__cin__conv, fact_292_dual__order_Ostrict__trans2, fact_201_csubset__trans, fact_233_csubset__cinsertI2, fact_9_cset__nondetM__base_Orun__altc__nondet, fact_239_csubset__cinsert__iff, fact_185_dual__order_Otrans, fact_5_cinsert__not__cempty, fact_175_csubsetI, fact_46_comp__eq__elim, fact_170_csubset__antisym, fact_293_order_Ostrict__implies__order, fact_299_bot_Onot__eq__extremum, fact_237_double__cDiff, fact_4_csingleton__inject, fact_182_csubset__cinsert, fact_199_if__split__cin1, fact_186_dual__order_Orefl, fact_261_dual__order_Oasym, fact_231_cDiffD1, fact_2_cinsert__absorb2, fact_176_cempty__fsubsetI, fact_306_csubset__cpsubset__trans, fact_281_antisym__conv2, fact_256_less__asym_H, fact_211_cin__mono, fact_280_antisym__conv1, fact_267_order_Ostrict__trans, fact_159_function__factors__right, fact_266_dual__order_Oirrefl, fact_242_csubset__csingletonD, fact_163_cDiff__cempty, fact_191_order__class_Oorder_Oeq__iff, fact_162_cDiff__cancel, fact_206_antisym, fact_270_order_Ostrict__implies__not__eq, fact_71_comp__eq__dest__lhs, fact_224_cinsertI2, fact_246_GreatestI2__order, fact_272_leD, fact_183_dual__order_Oantisym, fact_244_cpsubset__finsert__iff, fact_259_ord__eq__less__trans, fact_295_dual__order_Ostrict__iff__order, fact_0_mergec__single, fact_18_cset__nondetM__base_Oaltc__nondet__def, fact_215_order__subst1, fact_305_cpsubset__csubset__trans, fact_202_csubset__refl, fact_309_cpsubset__imp__ex__fmem, fact_277_order__less__le__subst1, fact_226_cinsertE, fact_300_cpsubsetD, fact_86_nondetT_Oexhaust__sel, fact_269_dual__order_Ostrict__trans, fact_273_le__less, fact_184_dual__order_Oeq__iff, fact_166_cDiff__cinsert2, fact_154_function__factors__right, fact_258_less__irrefl, fact_260_ord__less__eq__trans, fact_297_order_Onot__eq__order__implies__strict, fact_264_less__imp__not__eq2, fact_209_csubsetD, fact_284_less__le__trans, fact_205_cequalityCE, fact_10_cset__nondetM__base_Orun__altc__nondet, fact_83_nondetT_Ocollapse, fact_271_dual__order_Ostrict__implies__not__eq, fact_11_altc__nondet__def, fact_12_comp__apply, fact_249_ord__less__eq__subst, fact_189_ord__le__eq__trans, fact_252_order_Oasym, fact_84_nondetT_Oexhaust, fact_160_cinsert__cDiff__single, fact_228_bot_Oextremum__unique, fact_298_bot_Oextremum__strict, fact_207_cequalityE, fact_234_csubset__cinsertI, fact_230_cDiffD2, fact_289_order_Oorder__iff__strict, fact_181_cinsert__cDiff1, fact_263_less__not__sym, fact_308_csubset__iff__pfsubset__eq, fact_262_less__imp__not__eq, fact_66_comp__eq__dest__lhs, fact_82_nondetT_Oinject, fact_301_not__cpsubset__cempty, fact_291_dual__order_Ostrict__trans1, fact_192_antisym__conv, fact_254_less__imp__neq, fact_240_csingleton__iff, fact_248_ord__eq__less__subst, fact_221_cinsert__absorb, fact_169_order__refl, fact_168_cinsert__cDiff, fact_250_order__less__subst1, fact_208_eq__iff, fact_165_cDiff__cinsert, fact_6_cinsert__commute, fact_214_order__subst2, fact_218_ex__cin__conv, fact_223_set__cinsert, fact_85_nondetT_Oinduct, fact_1_cset__nondetM__base_Oaltc__nondet_Ocong, fact_285_le__imp__less__or__eq, fact_232_cDiffE, fact_235_cinsert__mono, fact_253_cpsubset__trans, fact_216_equals__cemptyI, fact_164_cempty__cDiff, fact_195_order_Otrans, fact_217_equals__cemptyD, fact_276_order__le__less__subst2, fact_274_less__le, fact_210_cset__eqI, fact_190_ord__eq__le__trans, fact_287_order_Ostrict__trans1, fact_283_le__less__trans, fact_167_cDiff__single__cinsert, fact_17_comp__apply, fact_251_order__less__subst2, fact_177_csubset__cempty, fact_279_le__neq__trans, fact_236_cDiff__csubset, fact_200_eq__cmem__trans, fact_19_cset__nondetM__base_Oaltc__nondet__def, fact_212_ord__le__eq__subst, fact_255_less__asym, fact_153_function__factors__left, fact_203_cequalityD2, fact_197_eq__refl, fact_265_less__imp__triv, fact_225_cinsertI1, fact_257_less__trans, fact_286_less__le__not__le, fact_245_Greatest__equality, fact_20_comp__def, fact_188_order__class_Oorder_Oantisym
% 68.72/26.98 % No. of inferences in proof: 434
% 68.72/26.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 26492 ms resp. 25679 ms w/o parsing
% 69.22/27.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.22/27.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------