%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP127^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:51 AM UTC 2026
% Result : Theorem 191.36s 91.17s
% Output : Refutation 193.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 206
% Syntax : Number of formulae : 888 ( 357 unt; 0 typ; 22 def)
% Number of atoms : 2452 ( 994 equ; 35 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 8102 ( 814 ~; 564 |; 79 &;6143 @)
% ( 0 <=>; 502 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 372 ( 372 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 5 con; 0-4 aty)
% Number of variables : 2430 ( 346 ^;2022 !; 40 ?;2430 :)
% ( 0 !>; 0 ?*; 0 @-; 22 @+)
% 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_decl,type,
countable_Set_cin_c: c > countable_Set_cset_c > $o ).
thf(counta472291938sert_c_decl,type,
counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).
thf(comp_M1944986301tT_a_m_decl,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_decl,type,
comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).
thf(minus_1646763425cset_c_decl,type,
minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(if_Cou1542198912cset_c_decl,type,
if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(if_c_decl,type,
if_c: $o > c > c > c ).
thf(monomo2081011572_m_m_a_decl,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_decl,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_decl,type,
monomo412532791tT_m_a: m > monomo197243225tT_a_m ).
thf(monomo624345106et_a_m_decl,type,
monomo624345106et_a_m: monomo197243225tT_a_m > m ).
thf(bot_bo1320844070cset_c_decl,type,
bot_bo1320844070cset_c: countable_Set_cset_c ).
thf(ord_le1587667814cset_c_decl,type,
ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
thf(ord_le15364698cset_c_decl,type,
ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).
thf(order_1683649299cset_c_decl,type,
order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
thf(f_decl,type,
f: c > monomo197243225tT_a_m ).
thf(mergec_decl,type,
mergec: countable_Set_cset_c > ( c > m ) > m ).
thf(x_decl,type,
x: c ).
thf(sk1_decl,type,
sk1: countable_Set_cset_c > countable_Set_cset_c > c ).
thf(sk2_decl,type,
sk2: countable_Set_cset_c > countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk3_decl,type,
sk3: countable_Set_cset_c > countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk4_decl,type,
sk4: m > monomo197243225tT_a_m ).
thf(sk5_decl,type,
sk5: countable_Set_cset_c > countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk6_decl,type,
sk6: countable_Set_cset_c > countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk7_decl,type,
sk7: countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk8_decl,type,
sk8: countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk9_decl,type,
sk9: countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk10_decl,type,
sk10: countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk11_decl,type,
sk11: ( countable_Set_cset_c > $o ) > $o ).
thf(sk12_decl,type,
sk12: countable_Set_cset_c > ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
thf(sk13_decl,type,
sk13: ( countable_Set_cset_c > $o ) > countable_Set_cset_c > ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).
thf(sk14_decl,type,
sk14: countable_Set_cset_c > countable_Set_cset_c > c ).
thf(sk15_decl,type,
sk15: countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk16_decl,type,
sk16: countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk17_decl,type,
sk17: ( monomo197243225tT_a_m > $o ) > m ).
thf(sk18_decl,type,
sk18: countable_Set_cset_c > countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk19_decl,type,
sk19: countable_Set_cset_c > countable_Set_cset_c > ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c > countable_Set_cset_c ).
thf(sk31_decl,type,
sk31: monomo197243225tT_a_m > m ).
thf(sk35_decl,type,
sk35: countable_Set_cset_c > c > countable_Set_cset_c ).
thf(sk36_decl,type,
sk36: countable_Set_cset_c > c > countable_Set_cset_c ).
thf(sk37_decl,type,
sk37: countable_Set_cset_c > c ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
@+[C: c] :
( ( countable_Set_cin_c @ C @ B )
!= ( countable_Set_cin_c @ C @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ! [F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ( ( ord_le15364698cset_c @ ( sk2 @ A @ B @ C @ D ) @ E )
=> ( ord_le15364698cset_c @ ( C @ ( sk2 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: m > monomo197243225tT_a_m] :
! [B: monomo197243225tT_a_m] :
( ( A @ ( monomo624345106et_a_m @ B ) )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ! [F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ( ( ord_le15364698cset_c @ ( sk5 @ A @ B @ C @ D ) @ E )
=> ( ord_le15364698cset_c @ ( C @ ( sk5 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ! [F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ( ( ord_le15364698cset_c @ ( sk7 @ A @ B @ C @ D ) @ E )
=> ( ord_le15364698cset_c @ ( B @ ( sk7 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ! [F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ( ( ord_le15364698cset_c @ ( sk9 @ A @ B @ C @ D ) @ E )
=> ( ord_le15364698cset_c @ ( B @ ( sk9 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > $o] :
@+[C: countable_Set_cset_c] :
~ ( ( B @ C )
=> ( ord_le15364698cset_c @ C @ A ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: countable_Set_cset_c > $o,B: countable_Set_cset_c,C: countable_Set_cset_c > $o] :
@+[D: countable_Set_cset_c] :
~ ( ( C @ D )
=> ( ! [E: countable_Set_cset_c] :
( ( C @ E )
=> ( ord_le15364698cset_c @ E @ D ) )
=> ( A @ D ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
@+[C: c] :
~ ( ( countable_Set_cin_c @ C @ B )
=> ( countable_Set_cin_c @ C @ A ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ! [F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( B @ E ) @ ( B @ F ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ( ( ord_le15364698cset_c @ ( sk15 @ A @ B @ C @ D ) @ E )
=> ( ord_le15364698cset_c @ ( B @ ( sk15 @ A @ B @ C @ D ) ) @ ( B @ E ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: monomo197243225tT_a_m > $o] :
@+[B: m] :
~ ( A @ ( monomo412532791tT_m_a @ B ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ! [F: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ E @ F )
=> ( ord_le15364698cset_c @ ( C @ E ) @ ( C @ F ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
@+[E: countable_Set_cset_c] :
~ ( ( ord_le15364698cset_c @ ( sk18 @ A @ B @ C @ D ) @ E )
=> ( ord_le15364698cset_c @ ( C @ ( sk18 @ A @ B @ C @ D ) ) @ ( C @ E ) ) ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( ^ [A: monomo197243225tT_a_m] :
@+[B: m] :
( A
= ( monomo412532791tT_m_a @ B ) ) ) ) ).
thf(sk35_def,definition,
( sk35
= ( ^ [A: countable_Set_cset_c,B: c] :
@+[C: countable_Set_cset_c] :
~ ( ( A
= ( counta472291938sert_c @ B @ C ) )
=> ( countable_Set_cin_c @ B @ C ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [A: countable_Set_cset_c,B: c] :
@+[C: countable_Set_cset_c] :
( ( A
= ( counta472291938sert_c @ B @ C ) )
& ~ ( countable_Set_cin_c @ B @ C ) ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: countable_Set_cset_c] :
@+[B: c] : ( countable_Set_cin_c @ B @ A ) ) ) ).
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/sandbox/benchmark/theBenchmark.p',fact_295_dual__order_Ostrict__iff__order) ).
thf(269,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(270,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)],[269]) ).
thf(892,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A )
= ( ^ [B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( B != A ) ) ) ),
inference(func_ext,[status(esa)],[270]) ).
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/sandbox/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(829,plain,
! [B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( comp_M1944986301tT_a_m @ A @ B )
= ( ^ [C: monomo197243225tT_a_m] : ( A @ ( B @ C ) ) ) ),
inference(func_ext,[status(esa)],[189]) ).
thf(40,axiom,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nondetT_Osel) ).
thf(317,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(318,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(cnf,[status(esa)],[317]) ).
thf(319,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(lifteq,[status(thm)],[318]) ).
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/sandbox/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(1156,plain,
! [D: monomo197243225tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ B @ C @ D ) )
| ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
!= ( B @ ( C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[319,194]) ).
thf(1163,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[1156:[bind(A,$thf( A )),bind(B,$thf( monomo624345106et_a_m )),bind(C,$thf( ^ [E: monomo197243225tT_a_m] : E )),bind(D,$thf( monomo412532791tT_m_a @ A ))]]) ).
thf(1591,plain,
! [D: monomo197243225tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ B @ C @ D ) )
| ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [E: monomo197243225tT_a_m] : E
@ ( monomo412532791tT_m_a @ A ) )
!= ( B @ ( C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[1163,194]) ).
thf(1606,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B )
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[1591:[bind(A,$thf( A )),bind(B,$thf( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ ^ [E: monomo197243225tT_a_m] : E )),bind(C,$thf( ^ [E: monomo197243225tT_a_m] : E )),bind(D,$thf( monomo412532791tT_m_a @ A ))]]) ).
thf(77,axiom,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_nondetT_Ocollapse) ).
thf(453,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(454,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
= A ),
inference(cnf,[status(esa)],[453]) ).
thf(455,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
= A ),
inference(lifteq,[status(thm)],[454]) ).
thf(1589,plain,
! [B: m,A: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ A )
= B )
| ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
!= ( monomo412532791tT_m_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[455,1163]) ).
thf(1590,plain,
! [A: monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ A )
= ( monomo624345106et_a_m @ A ) ),
inference(pattern_uni,[status(thm)],[1589:[bind(A,$thf( C )),bind(B,$thf( monomo624345106et_a_m @ C ))]]) ).
thf(1613,plain,
! [A: monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ A )
= ( monomo624345106et_a_m @ A ) ),
inference(simp,[status(thm)],[1590]) ).
thf(2379,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(rewrite,[status(thm)],[1606,1613]) ).
thf(1162,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( B @ A )
= ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( B @ C ) )
@ A ) ),
inference(pre_uni,[status(thm)],[1156:[bind(A,$thf( G @ D )),bind(B,$thf( monomo624345106et_a_m )),bind(C,$thf( ^ [F: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( G @ F ) ) )),bind(D,$thf( D ))]]) ).
thf(1171,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( B @ A )
= ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( B @ C ) )
@ A ) ),
inference(simp,[status(thm)],[1162]) ).
thf(4209,plain,
! [C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( C @ D ) )
@ B ) )
| ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ A ) )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2379,1171]) ).
thf(4309,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[4209:[bind(A,$thf( A )),bind(B,$thf( monomo412532791tT_m_a @ A )),bind(C,$thf( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ ^ [D: monomo197243225tT_a_m] : D ))]]) ).
thf(4376,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(rewrite,[status(thm)],[4309,1613]) ).
thf(4386,plain,
! [C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( C @ D ) )
@ B ) )
| ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ D ) )
@ ( monomo412532791tT_m_a @ A ) )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4376,1171]) ).
thf(4403,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ C ) )
@ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[4386:[bind(A,$thf( A )),bind(B,$thf( monomo412532791tT_m_a @ A )),bind(C,$thf( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ ^ [D: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ D ) ) ))]]) ).
thf(5603,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(rewrite,[status(thm)],[4403,455]) ).
thf(5608,plain,
! [C: m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M1944986301tT_a_m @ ( comp_M1944986301tT_a_m @ A @ B )
@ ^ [D: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [E: monomo197243225tT_a_m] : E
@ D ) )
@ ( monomo412532791tT_m_a @ C ) )
= C )
| ( ( ^ [D: monomo197243225tT_a_m] : ( A @ ( B @ D ) ) )
!= monomo624345106et_a_m ) ),
inference(paramod_ordered,[status(thm)],[829,5603]) ).
thf(5635,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B )
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[5608:[bind(A,$thf( monomo624345106et_a_m )),bind(B,$thf( ^ [D: monomo197243225tT_a_m] : D )),bind(C,$thf( C ))]]) ).
thf(5647,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B )
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(simp,[status(thm)],[5635]) ).
thf(6231,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) )
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(rewrite,[status(thm)],[5647,1613]) ).
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/sandbox/benchmark/theBenchmark.p',fact_194_cset__eq__csubset) ).
thf(468,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(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/sandbox/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(232,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ ( B @ C ) )
=> ! [D: countable_Set_cset_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(miniscope,[status(thm)],[231]) ).
thf(233,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ~ ( ord_le15364698cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk2 @ D @ C @ B @ A ) @ ( sk3 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) )
& ( ~ ( ord_le15364698cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk2 @ D @ C @ B @ A ) ) @ ( B @ ( sk3 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(234,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk2 @ D @ C @ B @ A ) @ ( sk3 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
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/sandbox/benchmark/theBenchmark.p',fact_6_cinsert__commute) ).
thf(666,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(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/sandbox/benchmark/theBenchmark.p',fact_290_order_Ostrict__iff__order) ).
thf(481,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(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/sandbox/benchmark/theBenchmark.p',fact_211_cin__mono) ).
thf(628,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(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/sandbox/benchmark/theBenchmark.p',fact_259_ord__eq__less__trans) ).
thf(249,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(59,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_cDiff__csubset) ).
thf(387,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(388,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] : ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A ),
inference(cnf,[status(esa)],[387]) ).
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/sandbox/benchmark/theBenchmark.p',fact_292_dual__order_Ostrict__trans2) ).
thf(238,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(239,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
inference(miniscope,[status(thm)],[238]) ).
thf(240,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ C @ A )
| ( ord_le1587667814cset_c @ C @ B ) ),
inference(cnf,[status(esa)],[239]) ).
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/sandbox/benchmark/theBenchmark.p',fact_272_leD) ).
thf(532,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(533,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(cnf,[status(esa)],[532]) ).
thf(2943,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ $true
| ~ ( ord_le1587667814cset_c @ D @ C )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[388,533]) ).
thf(2944,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ D @ C )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ C @ D ) ) ),
inference(simp,[status(thm)],[2943]) ).
thf(2945,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ ( minus_1646763425cset_c @ A @ B ) ),
inference(pattern_uni,[status(thm)],[2944:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( minus_1646763425cset_c @ E @ F )),bind(D,$thf( E ))]]) ).
thf(2985,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ ( minus_1646763425cset_c @ A @ B ) ),
inference(simp,[status(thm)],[2945]) ).
thf(3250,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ C @ A )
| ~ $true
| ( ( ord_le1587667814cset_c @ C @ B )
!= ( ord_le1587667814cset_c @ D @ ( minus_1646763425cset_c @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[240,2985]) ).
thf(3251,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ C @ A )
| ( ( ord_le1587667814cset_c @ C @ B )
!= ( ord_le1587667814cset_c @ D @ ( minus_1646763425cset_c @ D @ E ) ) ) ),
inference(simp,[status(thm)],[3250]) ).
thf(3252,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
| ~ ( ord_le15364698cset_c @ B @ A ) ),
inference(pattern_uni,[status(thm)],[3251:[bind(A,$thf( A )),bind(B,$thf( minus_1646763425cset_c @ F @ G )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(3270,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
| ~ ( ord_le15364698cset_c @ B @ A ) ),
inference(simp,[status(thm)],[3252]) ).
thf(6749,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ~ $true
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[388,3270]) ).
thf(6750,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ D @ C ) ) ),
inference(simp,[status(thm)],[6749]) ).
thf(6751,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ B @ ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ B @ C ) @ A ) ),
inference(pattern_uni,[status(thm)],[6750:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( minus_1646763425cset_c @ F @ G ))]]) ).
thf(6813,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ B @ ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[6751]) ).
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/sandbox/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(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/sandbox/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(1051,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 @ B @ f )
!= ( f @ x ) )
| ( A
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[208,187]) ).
thf(1052,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
!= ( countable_Set_cin_c @ ( sk1 @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1051:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( B ))]]) ).
thf(1073,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
!= ( countable_Set_cin_c @ ( sk1 @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[1052]) ).
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/sandbox/benchmark/theBenchmark.p',fact_175_csubsetI) ).
thf(360,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(361,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk14 @ B @ A ) @ A )
| ( ord_le15364698cset_c @ A @ B ) )
& ( ~ ( countable_Set_cin_c @ ( sk14 @ B @ A ) @ B )
| ( ord_le15364698cset_c @ A @ B ) ) ),
inference(cnf,[status(esa)],[360]) ).
thf(362,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk14 @ B @ A ) @ A )
| ( ord_le15364698cset_c @ A @ B ) ),
inference(cnfConj,[status(thm)],[361]) ).
thf(169,axiom,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ A )
= bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_cDiff__cancel) ).
thf(766,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ A )
= bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(767,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ A )
= bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[766]) ).
thf(768,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ A )
= bot_bo1320844070cset_c ),
inference(lifteq,[status(thm)],[767]) ).
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/sandbox/benchmark/theBenchmark.p',fact_183_dual__order_Oantisym) ).
thf(354,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(355,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ A )
| ( B = A ) ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( B = A )
| ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ A ) ),
inference(lifteq,[status(thm)],[355]) ).
thf(19132,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ A )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ( B
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[356,187]) ).
thf(19133,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[19132:[bind(A,$thf( A )),bind(B,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c ))]]) ).
thf(20882,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ $true
| ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,19133]) ).
thf(20883,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ) ),
inference(simp,[status(thm)],[20882]) ).
thf(20884,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[20883:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( E )),bind(C,$thf( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ E ))]]) ).
thf(21058,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[20884]) ).
thf(25482,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ B ) )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( ( minus_1646763425cset_c @ A @ A )
!= ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[768,21058]) ).
thf(25483,plain,
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[25482:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c ))]]) ).
thf(26001,plain,
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(rewrite,[status(thm)],[25483,768]) ).
thf(26051,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk14 @ B @ A ) @ A )
| ~ $true
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ A @ B )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[362,26001]) ).
thf(26052,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk14 @ B @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ A @ B )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[26051]) ).
thf(26053,plain,
( ( countable_Set_cin_c @ ( sk14 @ bot_bo1320844070cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[26052:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( bot_bo1320844070cset_c ))]]) ).
thf(118,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_dual__order_Ostrict__implies__not__eq) ).
thf(597,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(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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_237_double__cDiff) ).
thf(273,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(274,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ B @ C )
=> ( ( minus_1646763425cset_c @ B @ ( minus_1646763425cset_c @ C @ A ) )
= A ) ) ),
inference(miniscope,[status(thm)],[273]) ).
thf(275,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: 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(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( minus_1646763425cset_c @ B @ ( minus_1646763425cset_c @ C @ A ) )
= A )
| ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C ) ),
inference(lifteq,[status(thm)],[275]) ).
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/sandbox/benchmark/theBenchmark.p',fact_277_order__less__le__subst1) ).
thf(437,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(438,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ ( B @ C ) )
=> ! [D: countable_Set_cset_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(miniscope,[status(thm)],[437]) ).
thf(439,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ~ ( ord_le1587667814cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk18 @ D @ C @ B @ A ) @ ( sk19 @ D @ C @ B @ A ) )
| ( ord_le1587667814cset_c @ A @ ( B @ D ) ) )
& ( ~ ( ord_le1587667814cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk18 @ D @ C @ B @ A ) ) @ ( B @ ( sk19 @ D @ C @ B @ A ) ) )
| ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[438]) ).
thf(440,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk18 @ D @ C @ B @ A ) @ ( sk19 @ D @ C @ B @ A ) )
| ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[439]) ).
thf(132,axiom,
! [A: c,B: c] :
( ( ( counta472291938sert_c @ A @ bot_bo1320844070cset_c )
= ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_csingleton__inject) ).
thf(655,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(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/sandbox/benchmark/theBenchmark.p',fact_248_ord__eq__less__subst) ).
thf(511,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(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/sandbox/benchmark/theBenchmark.p',fact_306_csubset__cpsubset__trans) ).
thf(384,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(177,axiom,
! [A: countable_Set_cset_c] :
( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A )
=> ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_equals__cemptyI) ).
thf(794,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(795,plain,
! [A: countable_Set_cset_c] :
( ~ ? [B: c] : ( countable_Set_cin_c @ B @ A )
=> ( A = bot_bo1320844070cset_c ) ),
inference(miniscope,[status(thm)],[794]) ).
thf(796,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( A = bot_bo1320844070cset_c ) ),
inference(cnf,[status(esa)],[795]) ).
thf(797,plain,
! [A: countable_Set_cset_c] :
( ( A = bot_bo1320844070cset_c )
| ( countable_Set_cin_c @ ( sk37 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[796]) ).
thf(162,axiom,
! [A: c,B: countable_Set_cset_c] : ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_cinsertI1) ).
thf(747,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(748,plain,
! [B: countable_Set_cset_c,A: c] : ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) ),
inference(cnf,[status(esa)],[747]) ).
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/sandbox/benchmark/theBenchmark.p',fact_220_mk__disjoint__cinsert) ).
thf(756,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(757,plain,
! [B: countable_Set_cset_c,A: c] :
( ( ~ ( countable_Set_cin_c @ A @ B )
| ( B
= ( counta472291938sert_c @ A @ ( sk36 @ B @ A ) ) ) )
& ( ~ ( countable_Set_cin_c @ A @ B )
| ~ ( countable_Set_cin_c @ A @ ( sk36 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[756]) ).
thf(759,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ~ ( countable_Set_cin_c @ A @ ( sk36 @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[757]) ).
thf(6339,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( ( countable_Set_cin_c @ A @ ( sk36 @ B @ A ) )
!= ( countable_Set_cin_c @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[759]) ).
thf(6343,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( A != A )
| ( ( sk36 @ B @ A )
!= B ) ),
inference(simp,[status(thm)],[6339]) ).
thf(6366,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( ( sk36 @ B @ A )
!= B ) ),
inference(simp,[status(thm)],[6343]) ).
thf(6709,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( sk36 @ D @ C )
!= D )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[748,6366]) ).
thf(6710,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( ( sk36 @ D @ C )
!= D )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(simp,[status(thm)],[6709]) ).
thf(6711,plain,
! [B: countable_Set_cset_c,A: c] :
( ( sk36 @ ( counta472291938sert_c @ A @ B ) @ A )
!= ( counta472291938sert_c @ A @ B ) ),
inference(pattern_uni,[status(thm)],[6710:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( counta472291938sert_c @ E @ F ))]]) ).
thf(6727,plain,
! [B: countable_Set_cset_c,A: c] :
( ( sk36 @ ( counta472291938sert_c @ A @ B ) @ A )
!= ( counta472291938sert_c @ A @ B ) ),
inference(simp,[status(thm)],[6711]) ).
thf(114,axiom,
! [A: monomo197243225tT_a_m] :
~ ! [B: m] :
( A
!= ( monomo412532791tT_m_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nondetT_Oexhaust) ).
thf(584,plain,
! [A: monomo197243225tT_a_m] :
~ ! [B: m] :
( A
!= ( monomo412532791tT_m_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(585,plain,
~ ~ ! [A: monomo197243225tT_a_m] :
? [B: m] :
( A
= ( monomo412532791tT_m_a @ B ) ),
inference(miniscope,[status(thm)],[584]) ).
thf(586,plain,
! [A: monomo197243225tT_a_m] :
( A
= ( monomo412532791tT_m_a @ ( sk31 @ A ) ) ),
inference(cnf,[status(esa)],[585]) ).
thf(587,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( sk31 @ A ) )
= A ),
inference(lifteq,[status(thm)],[586]) ).
thf(1277,plain,
! [D: monomo197243225tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( ( B @ A )
= ( comp_M1944986301tT_a_m @ B @ C @ D ) )
| ( ( monomo412532791tT_m_a @ ( sk31 @ A ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[587,194]) ).
thf(1284,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( B @ A )
= ( comp_M1944986301tT_a_m @ B
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ ( sk31 @ A ) ) ) ),
inference(pre_uni,[status(thm)],[1277:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: monomo197243225tT_a_m] : E )),bind(D,$thf( monomo412532791tT_m_a @ ( sk31 @ A ) ))]]) ).
thf(1279,plain,
! [B: m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
= B )
| ( ( monomo412532791tT_m_a @ ( sk31 @ A ) )
!= ( monomo412532791tT_m_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[587,319]) ).
thf(1280,plain,
! [A: monomo197243225tT_a_m] :
( ( sk31 @ A )
= ( monomo624345106et_a_m @ A ) ),
inference(pattern_uni,[status(thm)],[1279:[bind(A,$thf( C )),bind(B,$thf( sk31 @ C ))]]) ).
thf(1287,plain,
! [A: monomo197243225tT_a_m] :
( ( sk31 @ A )
= ( monomo624345106et_a_m @ A ) ),
inference(simp,[status(thm)],[1280]) ).
thf(14330,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( B @ A )
= ( comp_M1944986301tT_a_m @ B
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ),
inference(rewrite,[status(thm)],[1284,1287]) ).
thf(14433,plain,
! [C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ C
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) ) ) )
| ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[319,14330]) ).
thf(14499,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) )
= A ),
inference(pre_uni,[status(thm)],[14433:[bind(A,$thf( A )),bind(B,$thf( monomo412532791tT_m_a @ A )),bind(C,$thf( monomo624345106et_a_m ))]]) ).
thf(15457,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) )
= A ),
inference(rewrite,[status(thm)],[14499,1613]) ).
thf(15498,plain,
! [C: m,B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ B
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ) )
= C )
| ( ( B @ A )
!= ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[14330,15457]) ).
thf(15537,plain,
! [A: m] :
( ( monomo624345106et_a_m
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(pre_uni,[status(thm)],[15498:[bind(A,$thf( monomo412532791tT_m_a @ C )),bind(B,$thf( monomo624345106et_a_m )),bind(C,$thf( C ))]]) ).
thf(15582,plain,
! [A: m] :
( ( monomo624345106et_a_m
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[15537]) ).
thf(25799,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) )
= A ),
inference(rewrite,[status(thm)],[15582,319]) ).
thf(1178,plain,
! [D: monomo197243225tT_a_m,C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( ( B @ A )
= ( comp_M1944986301tT_a_m @ B @ C @ D ) )
| ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
!= ( C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[455,194]) ).
thf(1185,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( B @ A )
= ( comp_M1944986301tT_a_m @ B
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ),
inference(pre_uni,[status(thm)],[1178:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [E: monomo197243225tT_a_m] : E )),bind(D,$thf( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ))]]) ).
thf(11841,plain,
! [B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( B @ A )
= ( comp_M1944986301tT_a_m @ B
@ ^ [C: monomo197243225tT_a_m] : C
@ A ) ),
inference(rewrite,[status(thm)],[1185,455]) ).
thf(25824,plain,
! [C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ C
@ ^ [D: monomo197243225tT_a_m] : D
@ B ) )
| ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[25799,11841]) ).
thf(25889,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ^ [B: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) ) )
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[25824:[bind(A,$thf( A )),bind(B,$thf( monomo412532791tT_m_a @ A )),bind(C,$thf( ^ [D: monomo197243225tT_a_m] : ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ ^ [E: monomo197243225tT_a_m] : E @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ D ) ) ) ))]]) ).
thf(27178,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ^ [B: monomo197243225tT_a_m] : ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) ) )
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(rewrite,[status(thm)],[25889,1613]) ).
thf(27200,plain,
! [C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ C
@ ^ [D: monomo197243225tT_a_m] : D
@ B ) )
| ( ( comp_M1944986301tT_a_m
@ ^ [D: monomo197243225tT_a_m] : ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ D ) ) )
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ A ) )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27178,11841]) ).
thf(27260,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m
@ ^ [B: monomo197243225tT_a_m] : ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) ) )
@ ^ [B: monomo197243225tT_a_m] : B )
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(pre_uni,[status(thm)],[27200:[bind(A,$thf( A )),bind(B,$thf( monomo412532791tT_m_a @ A )),bind(C,$thf( comp_M1944986301tT_a_m @ ^ [D: monomo197243225tT_a_m] : ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ D ) ) ) @ ^ [D: monomo197243225tT_a_m] : D ))]]) ).
thf(15495,plain,
! [C: monomo197243225tT_a_m > m,B: monomo197243225tT_a_m,A: m] :
( ( A
= ( comp_M1944986301tT_a_m @ C
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) ) ) )
| ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) )
!= ( C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15457,14330]) ).
thf(15503,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(pre_uni,[status(thm)],[15495:[bind(A,$thf( A )),bind(B,$thf( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) )),bind(C,$thf( monomo624345106et_a_m ))]]) ).
thf(17903,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(rewrite,[status(thm)],[15503,1613]) ).
thf(17938,plain,
! [B: m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ) )
= B )
| ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
!= ( monomo412532791tT_m_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[455,17903]) ).
thf(17939,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ) )
= ( monomo624345106et_a_m @ A ) ),
inference(pattern_uni,[status(thm)],[17938:[bind(A,$thf( C )),bind(B,$thf( monomo624345106et_a_m @ C ))]]) ).
thf(18057,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ) )
= ( monomo624345106et_a_m @ A ) ),
inference(simp,[status(thm)],[17939]) ).
thf(18211,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) )
= ( monomo624345106et_a_m @ A ) ),
inference(rewrite,[status(thm)],[18057,319]) ).
thf(31171,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B )
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) )
= A ),
inference(rewrite,[status(thm)],[27260,18211]) ).
thf(136,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_cempty__fsubsetI) ).
thf(669,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(670,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
inference(cnf,[status(esa)],[669]) ).
thf(7404,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) )
| ( bot_bo1320844070cset_c != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[797,187]) ).
thf(7405,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[7404:[]]) ).
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/sandbox/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(221,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A = B )
| ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le1587667814cset_c @ A @ B ) ),
inference(cnf,[status(esa)],[220]) ).
thf(222,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A = B )
| ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le1587667814cset_c @ A @ B ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(1438,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le1587667814cset_c @ A @ B )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ( B
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[222,187]) ).
thf(1439,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ord_le1587667814cset_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1438:[bind(A,$thf( A )),bind(B,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c ))]]) ).
thf(3292,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ $true
| ( ord_le1587667814cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,1439]) ).
thf(3293,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ) ),
inference(simp,[status(thm)],[3292]) ).
thf(3294,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[3293:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( E )),bind(C,$thf( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ E ))]]) ).
thf(3332,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( minus_1646763425cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[3294]) ).
thf(73,axiom,
! [A: monomo197243225tT_a_m > $o,B: monomo197243225tT_a_m] :
( ! [C: m] : ( A @ ( monomo412532791tT_m_a @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nondetT_Oinduct) ).
thf(432,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(433,plain,
! [A: monomo197243225tT_a_m > $o] :
( ! [B: m] : ( A @ ( monomo412532791tT_m_a @ B ) )
=> ! [B: monomo197243225tT_a_m] : ( A @ B ) ),
inference(miniscope,[status(thm)],[432]) ).
thf(434,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m > $o] :
( ~ ( A @ ( monomo412532791tT_m_a @ ( sk17 @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[433]) ).
thf(435,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m > $o] :
( ( ( monomo412532791tT_m_a @ ( sk17 @ A ) )
!= ( monomo412532791tT_m_a @ ( sk17 @ ( (=) @ monomo197243225tT_a_m @ ( monomo412532791tT_m_a @ ( sk17 @ A ) ) ) ) ) )
| ( ( monomo412532791tT_m_a @ ( sk17 @ A ) )
= B ) ),
inference(replace_leibeq,[status(thm)],[434:[bind(A,$thf( (=) @ monomo197243225tT_a_m @ ( monomo412532791tT_m_a @ ( sk17 @ A ) ) ))]]) ).
thf(436,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m > $o] :
( ( ( monomo412532791tT_m_a @ ( sk17 @ A ) )
!= ( monomo412532791tT_m_a @ ( sk17 @ ( (=) @ monomo197243225tT_a_m @ ( monomo412532791tT_m_a @ ( sk17 @ A ) ) ) ) ) )
| ( ( monomo412532791tT_m_a @ ( sk17 @ A ) )
= B ) ),
inference(lifteq,[status(thm)],[435]) ).
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/sandbox/benchmark/theBenchmark.p',fact_246_GreatestI2__order) ).
thf(320,plain,
! [A: countable_Set_cset_c > $o,B: countable_Set_cset_c,C: countable_Set_cset_c > $o] :
( ( A @ B )
=> ( ! [D: countable_Set_cset_c] :
( ( A @ D )
=> ( ord_le15364698cset_c @ D @ B ) )
=> ( ! [D: countable_Set_cset_c] :
( ( A @ D )
=> ( ! [E: countable_Set_cset_c] :
( ( A @ E )
=> ( ord_le15364698cset_c @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1683649299cset_c @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(109,axiom,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_le__less) ).
thf(565,plain,
( ord_le15364698cset_c
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(60,axiom,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_eq__iff) ).
thf(389,plain,
( ( (=) @ countable_Set_cset_c )
= ( ^ [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7400,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( A
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[797,187]) ).
thf(7401,plain,
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[7400:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c ))]]) ).
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/sandbox/benchmark/theBenchmark.p',fact_281_antisym__conv2) ).
thf(381,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(382,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ( ~ ( ord_le1587667814cset_c @ A @ B ) )
= ( A = B ) ) ),
inference(cnf,[status(esa)],[381]) ).
thf(383,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( ~ ( ord_le1587667814cset_c @ A @ B ) )
= ( A = B ) )
| ~ ( ord_le15364698cset_c @ A @ B ) ),
inference(lifteq,[status(thm)],[382]) ).
thf(21914,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( ~ ( ord_le1587667814cset_c @ B @ C ) )
= ( B = C ) )
| ~ $true
| ( ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A )
!= ( ord_le15364698cset_c @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[670,383]) ).
thf(21915,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( ~ ( ord_le1587667814cset_c @ B @ C ) )
= ( B = C ) )
| ( ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A )
!= ( ord_le15364698cset_c @ B @ C ) ) ),
inference(simp,[status(thm)],[21914]) ).
thf(21916,plain,
! [A: countable_Set_cset_c] :
( ( ~ ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A ) )
= ( bot_bo1320844070cset_c = A ) ),
inference(pattern_uni,[status(thm)],[21915:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c )),bind(C,$thf( A ))]]) ).
thf(148,axiom,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
= ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_bot_Onot__eq__extremum) ).
thf(705,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(706,plain,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
= ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A ) ),
inference(cnf,[status(esa)],[705]) ).
thf(707,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A )
= ( A != bot_bo1320844070cset_c ) ),
inference(lifteq,[status(thm)],[706]) ).
thf(22003,plain,
! [A: countable_Set_cset_c] :
( ( ~ ( ( A != bot_bo1320844070cset_c ) ) )
= ( bot_bo1320844070cset_c = A ) ),
inference(rewrite,[status(thm)],[21916,707]) ).
thf(22004,plain,
! [A: countable_Set_cset_c] :
( ( A = bot_bo1320844070cset_c )
= ( bot_bo1320844070cset_c = A ) ),
inference(simp,[status(thm)],[22003]) ).
thf(33,axiom,
! [A: monomo197243225tT_a_m,B: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
= ( monomo624345106et_a_m @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_nondetT_Oexpand) ).
thf(282,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(283,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
!= ( monomo624345106et_a_m @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[282]) ).
thf(284,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m] :
( ( ( monomo624345106et_a_m @ A )
!= ( monomo624345106et_a_m @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(285,plain,
? [A: m > monomo197243225tT_a_m] :
! [B: monomo197243225tT_a_m] :
( ( A @ ( monomo624345106et_a_m @ B ) )
= B ),
inference(detectInverse,[status(thm)],[284]) ).
thf(286,plain,
! [A: monomo197243225tT_a_m] :
( ( sk4 @ ( monomo624345106et_a_m @ A ) )
= A ),
inference(cnf,[status(esa)],[285]) ).
thf(1565,plain,
! [A: monomo197243225tT_a_m] :
( ( sk4 @ ( monomo624345106et_a_m @ A ) )
= A ),
inference(lifteq,[status(thm)],[286]) ).
thf(1571,plain,
! [B: monomo197243225tT_a_m,A: m] :
( ( ( sk4 @ A )
= B )
| ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) )
!= ( monomo624345106et_a_m @ B ) ) ),
inference(paramod_ordered,[status(thm)],[319,1565]) ).
thf(1572,plain,
! [A: m] :
( ( sk4 @ A )
= ( monomo412532791tT_m_a @ A ) ),
inference(pattern_uni,[status(thm)],[1571:[bind(A,$thf( C )),bind(B,$thf( monomo412532791tT_m_a @ C ))]]) ).
thf(1577,plain,
! [A: m] :
( ( sk4 @ A )
= ( monomo412532791tT_m_a @ A ) ),
inference(simp,[status(thm)],[1572]) ).
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/sandbox/benchmark/theBenchmark.p',fact_195_order_Otrans) ).
thf(357,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(147,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ ( counta472291938sert_c @ A @ B ) )
= ( counta472291938sert_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cinsert__absorb2) ).
thf(702,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(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/sandbox/benchmark/theBenchmark.p',fact_19_cset__nondetM__base_Oaltc__nondet__def) ).
thf(751,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(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/sandbox/benchmark/theBenchmark.p',fact_231_cDiffD1) ).
thf(638,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(6330,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ~ ( countable_Set_cin_c @ C @ ( sk36 @ D @ C ) )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[748,759]) ).
thf(6331,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ C @ ( sk36 @ D @ C ) )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(simp,[status(thm)],[6330]) ).
thf(6332,plain,
! [B: countable_Set_cset_c,A: c] :
~ ( countable_Set_cin_c @ A @ ( sk36 @ ( counta472291938sert_c @ A @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[6331:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( counta472291938sert_c @ E @ F ))]]) ).
thf(6368,plain,
! [B: countable_Set_cset_c,A: c] :
~ ( countable_Set_cin_c @ A @ ( sk36 @ ( counta472291938sert_c @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[6332]) ).
thf(6380,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ ( sk36 @ ( counta472291938sert_c @ C @ D ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[748,6368]) ).
thf(6381,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ ( sk36 @ ( counta472291938sert_c @ C @ D ) @ C ) ) ),
inference(simp,[status(thm)],[6380]) ).
thf(6390,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( A != C )
| ( ( counta472291938sert_c @ A @ B )
!= ( sk36 @ ( counta472291938sert_c @ C @ D ) @ C ) ) ),
inference(simp,[status(thm)],[6381]) ).
thf(6396,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ( counta472291938sert_c @ B @ A )
!= ( sk36 @ ( counta472291938sert_c @ B @ C ) @ B ) ),
inference(simp,[status(thm)],[6390]) ).
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/sandbox/benchmark/theBenchmark.p',fact_288_order_Ostrict__trans2) ).
thf(421,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(321,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 ) )
=> ! [C: countable_Set_cset_c > $o] :
( ! [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(miniscope,[status(thm)],[320]) ).
thf(322,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > $o,B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ( ~ ( A @ B )
| ( A @ ( sk12 @ B @ A ) )
| ( sk11 @ A ) )
& ( ~ ( A @ B )
| ~ ( ord_le15364698cset_c @ ( sk12 @ B @ A ) @ B )
| ( sk11 @ A ) )
& ( ~ ( A @ B )
| ~ ( sk11 @ A )
| ( A @ ( sk13 @ C @ B @ A ) )
| ( C @ ( order_1683649299cset_c @ A ) ) )
& ( ~ ( A @ B )
| ~ ( sk11 @ A )
| ~ ( A @ D )
| ( ord_le15364698cset_c @ D @ ( sk13 @ C @ B @ A ) )
| ( C @ ( order_1683649299cset_c @ A ) ) )
& ( ~ ( A @ B )
| ~ ( sk11 @ A )
| ~ ( C @ ( sk13 @ C @ B @ A ) )
| ( C @ ( order_1683649299cset_c @ A ) ) ) ),
inference(cnf,[status(esa)],[321]) ).
thf(325,plain,
! [C: countable_Set_cset_c > $o,B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ~ ( A @ B )
| ~ ( sk11 @ A )
| ( A @ ( sk13 @ C @ B @ A ) )
| ( C @ ( order_1683649299cset_c @ A ) ) ),
inference(cnfConj,[status(thm)],[322]) ).
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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_161_cDiff__idemp) ).
thf(287,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(288,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B ) @ B )
= ( minus_1646763425cset_c @ A @ B ) ),
inference(cnf,[status(esa)],[287]) ).
thf(289,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ ( minus_1646763425cset_c @ A @ B ) @ B )
= ( minus_1646763425cset_c @ A @ B ) ),
inference(lifteq,[status(thm)],[288]) ).
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/sandbox/benchmark/theBenchmark.p',fact_276_order__le__less__subst2) ).
thf(312,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(313,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( 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(miniscope,[status(thm)],[312]) ).
thf(314,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ ( C @ B ) @ D )
| ( ord_le15364698cset_c @ ( sk9 @ D @ C @ B @ A ) @ ( sk10 @ D @ C @ B @ A ) )
| ( ord_le1587667814cset_c @ ( C @ A ) @ D ) )
& ( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ ( C @ B ) @ D )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk9 @ D @ C @ B @ A ) ) @ ( C @ ( sk10 @ D @ C @ B @ A ) ) )
| ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[313]) ).
thf(316,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ ( C @ B ) @ D )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk9 @ D @ C @ B @ A ) ) @ ( C @ ( sk10 @ D @ C @ B @ A ) ) )
| ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[314]) ).
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/sandbox/benchmark/theBenchmark.p',fact_286_less__le__not__le) ).
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(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(281,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)],[280]) ).
thf(924,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A )
= ( ^ [B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ~ ( ord_le15364698cset_c @ B @ A ) ) ) ),
inference(func_ext,[status(esa)],[281]) ).
thf(1440,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le1587667814cset_c @ A @ B )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) )
| ( B != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[222,187]) ).
thf(1441,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
| ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1440:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c ))]]) ).
thf(170,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_bot_Oextremum__strict) ).
thf(769,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(770,plain,
~ ? [A: countable_Set_cset_c] : ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(miniscope,[status(thm)],[769]) ).
thf(771,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[770]) ).
thf(175,axiom,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_csubset__cempty) ).
thf(787,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(788,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
inference(cnf,[status(esa)],[787]) ).
thf(789,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
inference(lifteq,[status(thm)],[788]) ).
thf(2467,plain,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| $false
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(rewrite,[status(thm)],[1441,771,789]) ).
thf(2468,plain,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[2467]) ).
thf(2469,plain,
! [A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(lifteq,[status(thm)],[2468]) ).
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/sandbox/benchmark/theBenchmark.p',fact_284_less__le__trans) ).
thf(348,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(116,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_dual__order_Orefl) ).
thf(591,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(146,axiom,
! [A: countable_Set_cset_c] :
( ( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_all__not__cin__conv) ).
thf(699,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(700,plain,
! [A: countable_Set_cset_c] :
( ( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( A = bot_bo1320844070cset_c ) ),
inference(cnf,[status(esa)],[699]) ).
thf(701,plain,
! [A: countable_Set_cset_c] :
( ( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( A = bot_bo1320844070cset_c ) ),
inference(lifteq,[status(thm)],[700]) ).
thf(22007,plain,
! [A: countable_Set_cset_c] :
( ( ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( bot_bo1320844070cset_c = A ) ),
inference(rewrite,[status(thm)],[701,22004]) ).
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/sandbox/benchmark/theBenchmark.p',fact_291_dual__order_Ostrict__trans1) ).
thf(264,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(265,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ C @ A )
=> ( ord_le1587667814cset_c @ C @ B ) ) ),
inference(miniscope,[status(thm)],[264]) ).
thf(266,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ C @ A )
| ( ord_le1587667814cset_c @ C @ B ) ),
inference(cnf,[status(esa)],[265]) ).
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/sandbox/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(226,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(miniscope,[status(thm)],[225]) ).
thf(227,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ( ord_le1587667814cset_c @ A @ C ) ),
inference(cnf,[status(esa)],[226]) ).
thf(1832,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ~ $true
| ( ( ord_le1587667814cset_c @ A @ C )
!= ( ord_le1587667814cset_c @ D @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[227,771]) ).
thf(1833,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ( ( ord_le1587667814cset_c @ A @ C )
!= ( ord_le1587667814cset_c @ D @ bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[1832]) ).
thf(1834,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ bot_bo1320844070cset_c ) ),
inference(pattern_uni,[status(thm)],[1833:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( bot_bo1320844070cset_c )),bind(D,$thf( A ))]]) ).
thf(2128,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ( B != bot_bo1320844070cset_c ) ),
inference(rewrite,[status(thm)],[1834,789]) ).
thf(2129,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( B != bot_bo1320844070cset_c )
| ~ ( ord_le1587667814cset_c @ A @ B ) ),
inference(lifteq,[status(thm)],[2128]) ).
thf(3588,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ C @ A )
| ( E != bot_bo1320844070cset_c )
| ~ $true
| ( ( ord_le1587667814cset_c @ C @ B )
!= ( ord_le1587667814cset_c @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[266,2129]) ).
thf(3589,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ C @ A )
| ( E != bot_bo1320844070cset_c )
| ( ( ord_le1587667814cset_c @ C @ B )
!= ( ord_le1587667814cset_c @ D @ E ) ) ),
inference(simp,[status(thm)],[3588]) ).
thf(3590,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ C @ A )
| ( B != bot_bo1320844070cset_c ) ),
inference(pattern_uni,[status(thm)],[3589:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( B ))]]) ).
thf(3628,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
| ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(simp,[status(thm)],[3590]) ).
thf(3669,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(rewrite,[status(thm)],[3628,789]) ).
thf(3670,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( ord_le1587667814cset_c @ B @ A ) ),
inference(lifteq,[status(thm)],[3669]) ).
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/sandbox/benchmark/theBenchmark.p',fact_196_eqcset__imp__iff) ).
thf(376,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(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/sandbox/benchmark/theBenchmark.p',fact_17_comp__apply) ).
thf(292,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(293,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)],[292]) ).
thf(1434,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le1587667814cset_c @ A @ B )
| ( ( monomo463139869_c_m_a @ mergec @ B @ f )
!= ( f @ x ) )
| ( A
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[222,187]) ).
thf(1435,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1434:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( B ))]]) ).
thf(1517,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[1435]) ).
thf(3718,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ $true
| ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[388,1517]) ).
thf(3719,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C ) ) ),
inference(simp,[status(thm)],[3718]) ).
thf(3743,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( minus_1646763425cset_c @ A @ B )
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( A != C ) ),
inference(simp,[status(thm)],[3719]) ).
thf(3756,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ B )
| ( ( monomo463139869_c_m_a @ mergec @ B @ f )
!= ( f @ x ) )
| ( ( minus_1646763425cset_c @ B @ A )
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[3743]) ).
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/sandbox/benchmark/theBenchmark.p',fact_209_csubsetD) ).
thf(241,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(242,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: c] :
( ( countable_Set_cin_c @ C @ A )
=> ( countable_Set_cin_c @ C @ B ) ) ),
inference(miniscope,[status(thm)],[241]) ).
thf(243,plain,
! [C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( countable_Set_cin_c @ C @ A )
| ( countable_Set_cin_c @ C @ B ) ),
inference(cnf,[status(esa)],[242]) ).
thf(5624,plain,
! [B: m,A: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : D
@ C ) )
@ A )
= B )
| ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
!= ( monomo412532791tT_m_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[455,5603]) ).
thf(5625,plain,
! [A: monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ B ) )
@ A )
= ( monomo624345106et_a_m @ A ) ),
inference(pattern_uni,[status(thm)],[5624:[bind(A,$thf( C )),bind(B,$thf( monomo624345106et_a_m @ C ))]]) ).
thf(5660,plain,
! [A: monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] :
( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [C: monomo197243225tT_a_m] : C
@ B ) )
@ A )
= ( monomo624345106et_a_m @ A ) ),
inference(simp,[status(thm)],[5625]) ).
thf(5665,plain,
! [A: monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ B ) )
@ A )
= ( monomo624345106et_a_m @ A ) ),
inference(rewrite,[status(thm)],[5660,1613]) ).
thf(1057,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) )
| ( B != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[208,187]) ).
thf(1058,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1057:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c ))]]) ).
thf(138,axiom,
! [A: countable_Set_cset_c,B: c] :
( ( A = bot_bo1320844070cset_c )
=> ~ ( countable_Set_cin_c @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_equals__cemptyD) ).
thf(674,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(675,plain,
! [A: countable_Set_cset_c] :
( ( A = bot_bo1320844070cset_c )
=> ~ ? [B: c] : ( countable_Set_cin_c @ B @ A ) ),
inference(miniscope,[status(thm)],[674]) ).
thf(676,plain,
! [B: c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(cnf,[status(esa)],[675]) ).
thf(677,plain,
! [B: c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(lifteq,[status(thm)],[676]) ).
thf(678,plain,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
inference(simp,[status(thm)],[677]) ).
thf(1119,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)],[1058,678]) ).
thf(171,axiom,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_cempty__cDiff) ).
thf(772,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(773,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[772]) ).
thf(774,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ bot_bo1320844070cset_c @ A )
= bot_bo1320844070cset_c ),
inference(lifteq,[status(thm)],[773]) ).
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/sandbox/benchmark/theBenchmark.p',fact_201_csubset__trans) ).
thf(396,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(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/sandbox/benchmark/theBenchmark.p',fact_223_set__cinsert) ).
thf(658,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(659,plain,
! [B: countable_Set_cset_c,A: c] :
( ( ~ ( countable_Set_cin_c @ A @ B )
| ( B
= ( counta472291938sert_c @ A @ ( sk35 @ B @ A ) ) ) )
& ( ~ ( countable_Set_cin_c @ A @ B )
| ~ ( countable_Set_cin_c @ A @ ( sk35 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[658]) ).
thf(661,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ~ ( countable_Set_cin_c @ A @ ( sk35 @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[659]) ).
thf(5232,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ~ ( countable_Set_cin_c @ C @ ( sk35 @ D @ C ) )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[748,661]) ).
thf(5233,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ C @ ( sk35 @ D @ C ) )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(simp,[status(thm)],[5232]) ).
thf(5234,plain,
! [B: countable_Set_cset_c,A: c] :
~ ( countable_Set_cin_c @ A @ ( sk35 @ ( counta472291938sert_c @ A @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[5233:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( counta472291938sert_c @ E @ F ))]]) ).
thf(5246,plain,
! [B: countable_Set_cset_c,A: c] :
~ ( countable_Set_cin_c @ A @ ( sk35 @ ( counta472291938sert_c @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[5234]) ).
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/sandbox/benchmark/theBenchmark.p',fact_285_le__imp__less__or__eq) ).
thf(527,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(163,axiom,
! [A: countable_Set_cset_c,B: c] : ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_csubset__cinsertI) ).
thf(749,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(750,plain,
! [B: c,A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) ),
inference(cnf,[status(esa)],[749]) ).
thf(3188,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ $true
| ~ ( ord_le1587667814cset_c @ D @ C )
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[750,533]) ).
thf(3189,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ D @ C )
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ C @ D ) ) ),
inference(simp,[status(thm)],[3188]) ).
thf(3190,plain,
! [B: countable_Set_cset_c,A: c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ A @ B ) @ B ),
inference(pattern_uni,[status(thm)],[3189:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( counta472291938sert_c @ E @ F ))]]) ).
thf(3234,plain,
! [B: countable_Set_cset_c,A: c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ A @ B ) @ B ),
inference(simp,[status(thm)],[3190]) ).
thf(3425,plain,
! [E: countable_Set_cset_c,D: c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ~ $true
| ( ( ord_le1587667814cset_c @ A @ C )
!= ( ord_le1587667814cset_c @ ( counta472291938sert_c @ D @ E ) @ E ) ) ),
inference(paramod_ordered,[status(thm)],[227,3234]) ).
thf(3426,plain,
! [E: countable_Set_cset_c,D: c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ( ( ord_le1587667814cset_c @ A @ C )
!= ( ord_le1587667814cset_c @ ( counta472291938sert_c @ D @ E ) @ E ) ) ),
inference(simp,[status(thm)],[3425]) ).
thf(3427,plain,
! [C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ C @ B ) @ A )
| ~ ( ord_le15364698cset_c @ A @ B ) ),
inference(pattern_uni,[status(thm)],[3426:[bind(A,$thf( counta472291938sert_c @ F @ C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( C ))]]) ).
thf(3433,plain,
! [C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ C @ B ) @ A )
| ~ ( ord_le15364698cset_c @ A @ B ) ),
inference(simp,[status(thm)],[3427]) ).
thf(9634,plain,
! [E: c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ E @ D ) @ C )
| ~ $true
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[750,3433]) ).
thf(9635,plain,
! [E: c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ E @ D ) @ C )
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ C @ D ) ) ),
inference(simp,[status(thm)],[9634]) ).
thf(9636,plain,
! [C: countable_Set_cset_c,B: c,A: c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ A @ ( counta472291938sert_c @ B @ C ) ) @ C ),
inference(pattern_uni,[status(thm)],[9635:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( counta472291938sert_c @ F @ G ))]]) ).
thf(9703,plain,
! [C: countable_Set_cset_c,B: c,A: c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ A @ ( counta472291938sert_c @ B @ C ) ) @ C ),
inference(simp,[status(thm)],[9636]) ).
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/sandbox/benchmark/theBenchmark.p',fact_308_csubset__iff__pfsubset__eq) ).
thf(546,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(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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_167_cDiff__single__cinsert) ).
thf(761,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(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/sandbox/benchmark/theBenchmark.p',fact_206_antisym) ).
thf(534,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(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/sandbox/benchmark/theBenchmark.p',fact_166_cDiff__cinsert2) ).
thf(714,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(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/sandbox/benchmark/theBenchmark.p',fact_243_cDiff__cinsert__absorb) ).
thf(798,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(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/sandbox/benchmark/theBenchmark.p',fact_179_cDiffI) ).
thf(364,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(365,plain,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ A @ C )
=> ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[364]) ).
thf(366,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( countable_Set_cin_c @ A @ C )
| ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) ) ),
inference(cnf,[status(esa)],[365]) ).
thf(323,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ~ ( A @ B )
| ( A @ ( sk12 @ B @ A ) )
| ( sk11 @ A ) ),
inference(cnfConj,[status(thm)],[322]) ).
thf(329,plain,
! [A: countable_Set_cset_c] :
( ( A != A )
| ( A
= ( sk12 @ A @ ( (=) @ countable_Set_cset_c @ A ) ) )
| ( sk11 @ ( (=) @ countable_Set_cset_c @ A ) ) ),
inference(replace_leibeq,[status(thm)],[323:[bind(A,$thf( (=) @ countable_Set_cset_c @ B ))]]) ).
thf(333,plain,
! [A: countable_Set_cset_c] :
( ( A != A )
| ( ( sk12 @ A @ ( (=) @ countable_Set_cset_c @ A ) )
= A )
| ( sk11 @ ( (=) @ countable_Set_cset_c @ A ) ) ),
inference(lifteq,[status(thm)],[329]) ).
thf(334,plain,
! [A: countable_Set_cset_c] :
( ( ( sk12 @ A @ ( (=) @ countable_Set_cset_c @ A ) )
= A )
| ( sk11 @ ( (=) @ countable_Set_cset_c @ A ) ) ),
inference(simp,[status(thm)],[333]) ).
thf(161,axiom,
monomo463139869_c_m_a = monomo463139869_c_m_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_cset__nondetM__base_Oaltc__nondet_Ocong) ).
thf(746,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(185,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_not__cpsubset__cempty) ).
thf(825,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
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/sandbox/benchmark/theBenchmark.p',fact_160_cinsert__cDiff__single) ).
thf(778,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(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/sandbox/benchmark/theBenchmark.p',fact_213_ord__eq__le__subst) ).
thf(294,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(295,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,C: countable_Set_cset_c] :
( ( A
= ( B @ C ) )
=> ! [D: countable_Set_cset_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(miniscope,[status(thm)],[294]) ).
thf(296,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( A
!= ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk5 @ D @ C @ B @ A ) @ ( sk6 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) )
& ( ( A
!= ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk5 @ D @ C @ B @ A ) ) @ ( B @ ( sk6 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ) ),
inference(cnf,[status(esa)],[295]) ).
thf(298,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A
!= ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk5 @ D @ C @ B @ A ) ) @ ( B @ ( sk6 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(301,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A
!= ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk5 @ D @ C @ B @ A ) ) @ ( B @ ( sk6 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ),
inference(lifteq,[status(thm)],[298]) ).
thf(302,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c > countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ B @ C )
| ~ ( ord_le15364698cset_c @ ( A @ ( sk5 @ C @ B @ A @ ( A @ B ) ) ) @ ( A @ ( sk6 @ C @ B @ A @ ( A @ B ) ) ) )
| ( ord_le15364698cset_c @ ( A @ B ) @ ( A @ C ) ) ),
inference(simp,[status(thm)],[301]) ).
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/sandbox/benchmark/theBenchmark.p',fact_252_order_Oasym) ).
thf(424,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(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/sandbox/benchmark/theBenchmark.p',fact_257_less__trans) ).
thf(429,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(156,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_cinsert__not__cempty) ).
thf(729,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(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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_275_order__le__less__subst1) ).
thf(522,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(752,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)],[751]) ).
thf(889,plain,
! [A: countable_Set_cset_c > ( c > m ) > m] :
( ( monomo463139869_c_m_a @ A )
= ( ^ [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(func_ext,[status(esa)],[752]) ).
thf(140,axiom,
! [A: countable_Set_cset_c] :
( ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) )
= ( A != bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_ex__cin__conv) ).
thf(682,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(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/sandbox/benchmark/theBenchmark.p',fact_280_antisym__conv1) ).
thf(551,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(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/sandbox/benchmark/theBenchmark.p',fact_207_cequalityE) ).
thf(456,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(324,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ~ ( A @ B )
| ~ ( ord_le15364698cset_c @ ( sk12 @ B @ A ) @ B )
| ( sk11 @ A ) ),
inference(cnfConj,[status(thm)],[322]) ).
thf(15,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_csubset__refl) ).
thf(223,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(224,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(cnf,[status(esa)],[223]) ).
thf(130,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_order_Ostrict__trans) ).
thf(650,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(17908,plain,
! [C: monomo197243225tT_a_m,B: monomo197243225tT_a_m,A: m] :
( ( A
!= ( monomo624345106et_a_m @ C ) )
| ( B = C )
| ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
!= ( monomo624345106et_a_m @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17903,284]) ).
thf(17909,plain,
! [B: m,A: monomo197243225tT_a_m] :
( ( B
!= ( monomo624345106et_a_m @ A ) )
| ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ B ) ) ) ) )
= A ) ),
inference(pattern_uni,[status(thm)],[17908:[bind(A,$thf( H )),bind(B,$thf( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ H ) ) ) ) )),bind(C,$thf( C ))]]) ).
thf(18115,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[17909]) ).
thf(17932,plain,
! [B: monomo197243225tT_a_m,A: m] :
( ( ( monomo412532791tT_m_a @ A )
= B )
| ( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
!= ( monomo624345106et_a_m @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17903,455]) ).
thf(17933,plain,
! [A: m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) )
= ( monomo412532791tT_m_a @ A ) ),
inference(pattern_uni,[status(thm)],[17932:[bind(A,$thf( G )),bind(B,$thf( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ G ) ) ) ) ))]]) ).
thf(18054,plain,
! [A: m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) )
= ( monomo412532791tT_m_a @ A ) ),
inference(simp,[status(thm)],[17933]) ).
thf(18128,plain,
! [A: m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) )
= ( monomo412532791tT_m_a @ A ) ),
inference(rewrite,[status(thm)],[18054,455]) ).
thf(20387,plain,
! [A: monomo197243225tT_a_m] :
( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ) )
= A ),
inference(rewrite,[status(thm)],[18115,18128]) ).
thf(358,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ B @ C )
=> ( ord_le15364698cset_c @ A @ C ) ) ),
inference(miniscope,[status(thm)],[357]) ).
thf(359,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ( ord_le15364698cset_c @ A @ C ) ),
inference(cnf,[status(esa)],[358]) ).
thf(26078,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ~ $true
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ A @ C )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[359,26001]) ).
thf(26079,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ B @ C )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ A @ C )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[26078]) ).
thf(26080,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ~ ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[26079:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( B )),bind(C,$thf( bot_bo1320844070cset_c ))]]) ).
thf(26164,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ~ ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[26080]) ).
thf(22006,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( bot_bo1320844070cset_c = A ) ),
inference(rewrite,[status(thm)],[789,22004]) ).
thf(27502,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( bot_bo1320844070cset_c != A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(rewrite,[status(thm)],[26164,22006]) ).
thf(27503,plain,
! [A: countable_Set_cset_c] :
( ( bot_bo1320844070cset_c != A )
| ~ ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(lifteq,[status(thm)],[27502]) ).
thf(117,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_eq__refl) ).
thf(593,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(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/sandbox/benchmark/theBenchmark.p',fact_46_comp__eq__elim) ).
thf(418,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(419,plain,
! [E: c,D: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
!= ( comp_M750374444_m_m_c @ C @ D ) )
| ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(cnf,[status(esa)],[418]) ).
thf(420,plain,
! [E: c,D: c > monomo197243225tT_a_m,C: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
!= ( comp_M750374444_m_m_c @ C @ D ) )
| ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(lifteq,[status(thm)],[419]) ).
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/sandbox/benchmark/theBenchmark.p',fact_294_dual__order_Oorder__iff__strict) ).
thf(653,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(654,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)],[653]) ).
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/sandbox/benchmark/theBenchmark.p',fact_289_order_Oorder__iff__strict) ).
thf(367,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(368,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)],[367]) ).
thf(857,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)],[654,368]) ).
thf(8338,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ( bot_bo1320844070cset_c != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[797,7401]) ).
thf(8339,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[8338:[]]) ).
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/sandbox/benchmark/theBenchmark.p',fact_230_cDiffD2) ).
thf(476,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(477,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
| ~ ( countable_Set_cin_c @ A @ C ) ),
inference(cnf,[status(esa)],[476]) ).
thf(3120,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ~ $true
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[748,477]) ).
thf(3121,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ E ) ) ),
inference(simp,[status(thm)],[3120]) ).
thf(3122,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
~ ( countable_Set_cin_c @ B @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) ) ),
inference(pattern_uni,[status(thm)],[3121:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( counta472291938sert_c @ F @ G ))]]) ).
thf(3161,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
~ ( countable_Set_cin_c @ B @ ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) ) ),
inference(simp,[status(thm)],[3122]) ).
thf(4461,plain,
! [E: countable_Set_cset_c,D: c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ D @ ( minus_1646763425cset_c @ C @ ( counta472291938sert_c @ D @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[748,3161]) ).
thf(4462,plain,
! [E: countable_Set_cset_c,D: c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ D @ ( minus_1646763425cset_c @ C @ ( counta472291938sert_c @ D @ E ) ) ) ),
inference(simp,[status(thm)],[4461]) ).
thf(4472,plain,
! [E: countable_Set_cset_c,D: c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ( A != D )
| ( ( counta472291938sert_c @ A @ B )
!= ( minus_1646763425cset_c @ C @ ( counta472291938sert_c @ D @ E ) ) ) ),
inference(simp,[status(thm)],[4462]) ).
thf(4486,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( counta472291938sert_c @ C @ A )
!= ( minus_1646763425cset_c @ B @ ( counta472291938sert_c @ C @ D ) ) ),
inference(simp,[status(thm)],[4472]) ).
thf(9926,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( countable_Set_cin_c @ ( sk37 @ B ) @ B )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( A
!= ( counta472291938sert_c @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[797,7405]) ).
thf(9927,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ A ) ) @ ( counta472291938sert_c @ x @ A ) )
| ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[9926:[bind(A,$thf( counta472291938sert_c @ x @ D )),bind(B,$thf( D ))]]) ).
thf(9936,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ A ) ) @ ( counta472291938sert_c @ x @ A ) )
| ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[9927]) ).
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/sandbox/benchmark/theBenchmark.p',fact_265_less__imp__triv) ).
thf(488,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(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/sandbox/benchmark/theBenchmark.p',fact_238_cminus__mono) ).
thf(339,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(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/sandbox/benchmark/theBenchmark.p',fact_36_comp__eq__dest) ).
thf(537,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(10,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_269_dual__order_Ostrict__trans) ).
thf(554,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(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/sandbox/benchmark/theBenchmark.p',fact_224_cinsertI2) ).
thf(753,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(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/sandbox/benchmark/theBenchmark.p',fact_10_cset__nondetM__base_Orun__altc__nondet) ).
thf(679,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(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/sandbox/benchmark/theBenchmark.p',fact_184_dual__order_Oeq__iff) ).
thf(290,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(291,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)],[290]) ).
thf(837,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 @ A ) ),
inference(func_ext,[status(esa)],[291]) ).
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/sandbox/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(219,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ( ord_le15364698cset_c @ A @ B ) ),
inference(cnf,[status(esa)],[218]) ).
thf(6758,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ~ $true
| ( ( ord_le15364698cset_c @ A @ B )
!= ( ord_le15364698cset_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[219,3270]) ).
thf(6759,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ( ( ord_le15364698cset_c @ A @ B )
!= ( ord_le15364698cset_c @ D @ C ) ) ),
inference(simp,[status(thm)],[6758]) ).
thf(6760,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ B @ ( minus_1646763425cset_c @ A @ C ) ) ),
inference(pattern_uni,[status(thm)],[6759:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(6816,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ B @ ( minus_1646763425cset_c @ A @ C ) ) ),
inference(simp,[status(thm)],[6760]) ).
thf(16789,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ( ( ord_le1587667814cset_c @ B @ ( minus_1646763425cset_c @ A @ C ) )
!= ( ord_le1587667814cset_c @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[6816]) ).
thf(16798,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ( B != A )
| ( ( minus_1646763425cset_c @ A @ C )
!= B ) ),
inference(simp,[status(thm)],[16789]) ).
thf(16822,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ A )
| ( ( minus_1646763425cset_c @ A @ B )
!= A ) ),
inference(simp,[status(thm)],[16798]) ).
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/sandbox/benchmark/theBenchmark.p',fact_302_cpsubset__eq) ).
thf(271,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(272,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)],[271]) ).
thf(910,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)],[272,270]) ).
thf(911,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)],[910:[]]) ).
thf(683,plain,
! [A: countable_Set_cset_c] :
( ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) )
= ( A != bot_bo1320844070cset_c ) ),
inference(cnf,[status(esa)],[682]) ).
thf(684,plain,
! [A: countable_Set_cset_c] :
( ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) )
= ( A != bot_bo1320844070cset_c ) ),
inference(lifteq,[status(thm)],[683]) ).
thf(2765,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( ~ ! [C: c] :
~ ( countable_Set_cin_c @ C @ A ) )
= ( ? [C: c] : ( countable_Set_cin_c @ C @ B ) ) )
| ( ( A = bot_bo1320844070cset_c )
!= ( B = bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[701,684]) ).
thf(2766,plain,
! [A: countable_Set_cset_c] :
( ( ~ ! [B: c] :
~ ( countable_Set_cin_c @ B @ A ) )
= ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[2765:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
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/sandbox/benchmark/theBenchmark.p',fact_188_order__class_Oorder_Oantisym) ).
thf(371,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(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/sandbox/benchmark/theBenchmark.p',fact_260_ord__less__eq__trans) ).
thf(244,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(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/sandbox/benchmark/theBenchmark.p',fact_212_ord__le__eq__subst) ).
thf(303,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(304,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_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(miniscope,[status(thm)],[303]) ).
thf(305,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ~ ( ord_le15364698cset_c @ A @ B )
| ( ( C @ B )
!= D )
| ( ord_le15364698cset_c @ ( sk7 @ D @ C @ B @ A ) @ ( sk8 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) )
& ( ~ ( ord_le15364698cset_c @ A @ B )
| ( ( C @ B )
!= D )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk7 @ D @ C @ B @ A ) ) @ ( C @ ( sk8 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[304]) ).
thf(307,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ( C @ B )
!= D )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk7 @ D @ C @ B @ A ) ) @ ( C @ ( sk8 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[305]) ).
thf(310,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( C @ B )
!= D )
| ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk7 @ D @ C @ B @ A ) ) @ ( C @ ( sk8 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(311,plain,
! [C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk7 @ ( C @ B ) @ C @ B @ A ) ) @ ( C @ ( sk8 @ ( C @ B ) @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ ( C @ B ) ) ),
inference(simp,[status(thm)],[310]) ).
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/sandbox/benchmark/theBenchmark.p',fact_293_order_Ostrict__implies__order) ).
thf(541,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(4243,plain,
! [E: monomo197243225tT_a_m > m,D: monomo197243225tT_a_m,C: monomo197243225tT_a_m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M1944986301tT_a_m @ A @ B @ C )
= ( E @ D ) )
| ( ( A @ ( B @ C ) )
!= ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [F: monomo197243225tT_a_m] : ( monomo412532791tT_m_a @ ( E @ F ) )
@ D ) ) ),
inference(paramod_ordered,[status(thm)],[194,1171]) ).
thf(4284,plain,
! [B: m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ B ) )
= B ),
inference(pre_uni,[status(thm)],[4243:[bind(A,$thf( ^ [G: monomo197243225tT_a_m] : ( comp_M1944986301tT_a_m @ monomo624345106et_a_m @ ^ [H: monomo197243225tT_a_m] : G @ ( H @ G ) ) )),bind(B,$thf( ^ [F: monomo197243225tT_a_m] : F )),bind(C,$thf( monomo412532791tT_m_a @ M )),bind(D,$thf( H @ ( monomo412532791tT_m_a @ M ) )),bind(E,$thf( ^ [G: monomo197243225tT_a_m] : M ))]]) ).
thf(4348,plain,
! [B: m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ B ) )
= B ),
inference(simp,[status(thm)],[4284]) ).
thf(5090,plain,
! [C: m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m
@ ^ [D: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [E: monomo197243225tT_a_m] : D
@ ( B @ D ) )
@ ^ [D: monomo197243225tT_a_m] : D
@ A )
= C )
| ( ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) )
!= ( monomo412532791tT_m_a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[455,4348]) ).
thf(5091,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ B )
= ( monomo624345106et_a_m @ B ) ),
inference(pattern_uni,[status(thm)],[5090:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( monomo624345106et_a_m @ D ))]]) ).
thf(5126,plain,
! [B: monomo197243225tT_a_m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ B )
= ( monomo624345106et_a_m @ B ) ),
inference(simp,[status(thm)],[5091]) ).
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/sandbox/benchmark/theBenchmark.p',fact_309_cpsubset__imp__ex__fmem) ).
thf(633,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(180,axiom,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_cempty__iff) ).
thf(805,plain,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
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/sandbox/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(22008,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A )
= ( bot_bo1320844070cset_c != A ) ),
inference(rewrite,[status(thm)],[707,22004]) ).
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/sandbox/benchmark/theBenchmark.p',fact_282_less__imp__le) ).
thf(530,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(184,axiom,
! [A: c,B: c > m] :
( ( mergec @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_mergec__single) ).
thf(822,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(823,plain,
! [B: c > m,A: c] :
( ( mergec @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) @ B )
= ( B @ A ) ),
inference(cnf,[status(esa)],[822]) ).
thf(824,plain,
! [B: c > m,A: c] :
( ( mergec @ ( counta472291938sert_c @ A @ bot_bo1320844070cset_c ) @ B )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[823]) ).
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/sandbox/benchmark/theBenchmark.p',fact_72_comp__apply__eq) ).
thf(277,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(278,plain,
! [E: c > monomo197243225tT_a_m,D: monomo197243225tT_a_m > m,C: c,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( A @ ( B @ C ) )
!= ( D @ ( E @ C ) ) )
| ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ C ) ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [E: c > monomo197243225tT_a_m,D: monomo197243225tT_a_m > m,C: c,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( A @ ( B @ C ) )
!= ( D @ ( E @ C ) ) )
| ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ C ) ) ),
inference(lifteq,[status(thm)],[278]) ).
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/sandbox/benchmark/theBenchmark.p',fact_199_if__split__cin1) ).
thf(444,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(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/sandbox/benchmark/theBenchmark.p',fact_181_cinsert__cDiff1) ).
thf(733,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(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/sandbox/benchmark/theBenchmark.p',fact_178_cDiff__iff) ).
thf(601,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(183,axiom,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
= ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_bot_Oextremum__unique) ).
thf(819,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(904,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A )
= ( ^ [B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
& ( A != B ) ) ) ),
inference(func_ext,[status(esa)],[272]) ).
thf(144,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_bot_Oextremum) ).
thf(694,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(64,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_cequalityD2) ).
thf(402,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(730,plain,
~ ? [A: c,B: countable_Set_cset_c] :
( ( counta472291938sert_c @ A @ B )
= bot_bo1320844070cset_c ),
inference(miniscope,[status(thm)],[729]) ).
thf(731,plain,
! [B: countable_Set_cset_c,A: c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
inference(cnf,[status(esa)],[730]) ).
thf(732,plain,
! [B: countable_Set_cset_c,A: c] :
( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ),
inference(lifteq,[status(thm)],[731]) ).
thf(843,plain,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A )
= ( ^ [B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
| ( A = B ) ) ) ),
inference(func_ext,[status(esa)],[368]) ).
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/sandbox/benchmark/theBenchmark.p',fact_173_cinsert__iff) ).
thf(743,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(150,axiom,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_cemptyE) ).
thf(711,plain,
! [A: c] :
~ ( countable_Set_cin_c @ A @ bot_bo1320844070cset_c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
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/sandbox/benchmark/theBenchmark.p',fact_71_comp__eq__dest__lhs) ).
thf(259,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(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/sandbox/benchmark/theBenchmark.p',fact_193_eqcelem__imp__iff) ).
thf(413,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(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/sandbox/benchmark/theBenchmark.p',fact_249_ord__less__eq__subst) ).
thf(641,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(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/sandbox/benchmark/theBenchmark.p',fact_214_order__subst2) ).
thf(391,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(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/sandbox/benchmark/theBenchmark.p',fact_192_antisym__conv) ).
thf(572,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(91,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( A = B )
=> ( ord_le15364698cset_c @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_cequalityD1) ).
thf(498,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(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/sandbox/benchmark/theBenchmark.p',fact_304_cpsubset__imp__fsubset) ).
thf(466,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(327,plain,
! [C: countable_Set_cset_c > $o,B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ~ ( A @ B )
| ~ ( sk11 @ A )
| ~ ( C @ ( sk13 @ C @ B @ A ) )
| ( C @ ( order_1683649299cset_c @ A ) ) ),
inference(cnfConj,[status(thm)],[322]) ).
thf(330,plain,
! [C: countable_Set_cset_c > $o,B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ~ ( A @ B )
| ~ ( sk11 @ A )
| ( ( sk13 @ C @ B @ A )
!= ( sk13 @ ( (=) @ countable_Set_cset_c @ ( sk13 @ C @ B @ A ) ) @ B @ A ) )
| ( ( sk13 @ C @ B @ A )
= ( order_1683649299cset_c @ A ) ) ),
inference(replace_leibeq,[status(thm)],[327:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ countable_Set_cset_c @ ( sk13 @ C @ B @ A ) ))]]) ).
thf(335,plain,
! [C: countable_Set_cset_c > $o,B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ( ( sk13 @ C @ B @ A )
!= ( sk13 @ ( (=) @ countable_Set_cset_c @ ( sk13 @ C @ B @ A ) ) @ B @ A ) )
| ( ( sk13 @ C @ B @ A )
= ( order_1683649299cset_c @ A ) )
| ~ ( A @ B )
| ~ ( sk11 @ A ) ),
inference(lifteq,[status(thm)],[330]) ).
thf(19,axiom,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_order__refl) ).
thf(236,plain,
! [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(120,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_cpsubset__trans) ).
thf(604,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c,C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1055,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ B @ A ) @ B ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ( B
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[208,187]) ).
thf(1056,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ A )
!= ( countable_Set_cin_c @ ( sk1 @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ A ) @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) )
| ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[1055:[bind(A,$thf( A )),bind(B,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c ))]]) ).
thf(1194,plain,
! [A: countable_Set_cset_c] :
( ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ( 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 ) ) ),
inference(bool_ext,[status(thm)],[1056]) ).
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/sandbox/benchmark/theBenchmark.p',fact_187_order__trans) ).
thf(406,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(831,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)],[293]) ).
thf(6755,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ~ $true
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[750,3270]) ).
thf(6756,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ C @ ( minus_1646763425cset_c @ D @ E ) )
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ D @ C ) ) ),
inference(simp,[status(thm)],[6755]) ).
thf(6757,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ B @ C ) @ ( minus_1646763425cset_c @ C @ A ) ),
inference(pattern_uni,[status(thm)],[6756:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( counta472291938sert_c @ F @ G )),bind(D,$thf( G ))]]) ).
thf(6815,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ B @ C ) @ ( minus_1646763425cset_c @ C @ A ) ),
inference(simp,[status(thm)],[6757]) ).
thf(229,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: $o,A: 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(cnf,[status(esa)],[228]) ).
thf(230,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: $o,A: 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(lifteq,[status(thm)],[229]) ).
thf(158,axiom,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_cDiff__cempty) ).
thf(737,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(5241,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( ( countable_Set_cin_c @ A @ ( sk35 @ B @ A ) )
!= ( countable_Set_cin_c @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[661]) ).
thf(5244,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( A != A )
| ( ( sk35 @ B @ A )
!= B ) ),
inference(simp,[status(thm)],[5241]) ).
thf(5267,plain,
! [B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ B )
| ( ( sk35 @ B @ A )
!= B ) ),
inference(simp,[status(thm)],[5244]) ).
thf(445,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( if_c @ $true @ A @ B ) @ C )
= ( ( $true
=> ( countable_Set_cin_c @ A @ C ) )
& ( ~ $true
=> ( countable_Set_cin_c @ B @ C ) ) ) ),
inference(instance,[status(thm)],[444]) ).
thf(446,plain,
! [A: c,B: c,C: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( if_c @ $true @ A @ B ) @ C )
= ( countable_Set_cin_c @ A @ C ) ),
inference(simp,[status(thm)],[445]) ).
thf(449,plain,
! [C: countable_Set_cset_c,B: c,A: c] :
( ( countable_Set_cin_c @ ( if_c @ $true @ A @ B ) @ C )
= ( countable_Set_cin_c @ A @ C ) ),
inference(cnf,[status(esa)],[446]) ).
thf(451,plain,
! [C: countable_Set_cset_c,B: c,A: c] :
( ( countable_Set_cin_c @ ( if_c @ $true @ A @ B ) @ C )
= ( countable_Set_cin_c @ A @ C ) ),
inference(lifteq,[status(thm)],[449]) ).
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/sandbox/benchmark/theBenchmark.p',fact_251_order__less__subst2) ).
thf(567,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(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/sandbox/benchmark/theBenchmark.p',fact_18_cset__nondetM__base_Oaltc__nondet__def) ).
thf(631,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(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/sandbox/benchmark/theBenchmark.p',fact_244_cpsubset__finsert__iff) ).
thf(816,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(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/sandbox/benchmark/theBenchmark.p',fact_303_less__cset__def) ).
thf(520,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(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/sandbox/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(3108,plain,
! [C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[748,678]) ).
thf(3109,plain,
! [C: c,B: countable_Set_cset_c,A: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ bot_bo1320844070cset_c ) ),
inference(simp,[status(thm)],[3108]) ).
thf(3140,plain,
! [C: c,B: countable_Set_cset_c,A: c] :
( ( A != C )
| ( ( counta472291938sert_c @ A @ B )
!= bot_bo1320844070cset_c ) ),
inference(simp,[status(thm)],[3109]) ).
thf(3150,plain,
! [B: c,A: countable_Set_cset_c] :
( ( counta472291938sert_c @ B @ A )
!= bot_bo1320844070cset_c ),
inference(simp,[status(thm)],[3140]) ).
thf(738,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
= A ),
inference(cnf,[status(esa)],[737]) ).
thf(739,plain,
! [A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
= A ),
inference(lifteq,[status(thm)],[738]) ).
thf(9154,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ C @ D ) @ A )
| ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
!= ( minus_1646763425cset_c @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[739,6815]) ).
thf(9155,plain,
! [B: c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ B @ A ) @ A ),
inference(pattern_uni,[status(thm)],[9154:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(9174,plain,
! [B: c,A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ ( counta472291938sert_c @ B @ A ) @ A ),
inference(simp,[status(thm)],[9155]) ).
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/sandbox/benchmark/theBenchmark.p',fact_232_cDiffE) ).
thf(609,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(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/sandbox/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(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/sandbox/benchmark/theBenchmark.p',fact_3_cdoubleton__eq__iff) ).
thf(726,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(20885,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ~ $true
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[388,19133]) ).
thf(20886,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ B ) @ A )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C ) ) ),
inference(simp,[status(thm)],[20885]) ).
thf(21006,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ C @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( minus_1646763425cset_c @ A @ B )
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( A != C ) ),
inference(simp,[status(thm)],[20886]) ).
thf(21052,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ B @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) )
| ( ( monomo463139869_c_m_a @ mergec @ B @ f )
!= ( f @ x ) )
| ( ( minus_1646763425cset_c @ B @ A )
!= ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[21006]) ).
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/sandbox/benchmark/theBenchmark.p',fact_190_ord__eq__le__trans) ).
thf(483,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(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/sandbox/benchmark/theBenchmark.p',fact_56_comp__cong) ).
thf(399,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(430,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(miniscope,[status(thm)],[429]) ).
thf(431,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ B @ C )
| ( ord_le1587667814cset_c @ A @ C ) ),
inference(cnf,[status(esa)],[430]) ).
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/sandbox/benchmark/theBenchmark.p',fact_242_csubset__csingletonD) ).
thf(685,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(392,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c > countable_Set_cset_c,D: countable_Set_cset_c] :
( ( 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(miniscope,[status(thm)],[391]) ).
thf(393,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ ( C @ B ) @ D )
| ( ord_le15364698cset_c @ ( sk15 @ D @ C @ B @ A ) @ ( sk16 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) )
& ( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ ( C @ B ) @ D )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk15 @ D @ C @ B @ A ) ) @ ( C @ ( sk16 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ) ),
inference(cnf,[status(esa)],[392]) ).
thf(394,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ ( C @ B ) @ D )
| ( ord_le15364698cset_c @ ( sk15 @ D @ C @ B @ A ) @ ( sk16 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[393]) ).
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/sandbox/benchmark/theBenchmark.p',fact_191_order__class_Oorder_Oeq__iff) ).
thf(267,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(1376,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( B = C )
| ~ $true
| ( ord_le1587667814cset_c @ B @ C )
| ( ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A )
!= ( ord_le15364698cset_c @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[670,222]) ).
thf(1377,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( B = C )
| ( ord_le1587667814cset_c @ B @ C )
| ( ( ord_le15364698cset_c @ bot_bo1320844070cset_c @ A )
!= ( ord_le15364698cset_c @ B @ C ) ) ),
inference(simp,[status(thm)],[1376]) ).
thf(1378,plain,
! [A: countable_Set_cset_c] :
( ( bot_bo1320844070cset_c = A )
| ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A ) ),
inference(pattern_uni,[status(thm)],[1377:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c )),bind(C,$thf( A ))]]) ).
thf(1635,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ A )
| ( bot_bo1320844070cset_c = B )
| ( A
!= ( minus_1646763425cset_c @ B @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[1378,739]) ).
thf(1636,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c ) )
| ( bot_bo1320844070cset_c = A ) ),
inference(pattern_uni,[status(thm)],[1635:[bind(A,$thf( minus_1646763425cset_c @ C @ bot_bo1320844070cset_c )),bind(B,$thf( C ))]]) ).
thf(1788,plain,
! [A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ bot_bo1320844070cset_c @ ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c ) )
| ( bot_bo1320844070cset_c = A ) ),
inference(simp,[status(thm)],[1636]) ).
thf(3510,plain,
! [A: countable_Set_cset_c] :
( ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
!= bot_bo1320844070cset_c )
| ( bot_bo1320844070cset_c = A ) ),
inference(rewrite,[status(thm)],[1788,707]) ).
thf(3511,plain,
! [A: countable_Set_cset_c] :
( ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
!= bot_bo1320844070cset_c )
| ( bot_bo1320844070cset_c = A ) ),
inference(simp,[status(thm)],[3510]) ).
thf(3512,plain,
! [A: countable_Set_cset_c] :
( ( ( minus_1646763425cset_c @ A @ bot_bo1320844070cset_c )
!= bot_bo1320844070cset_c )
| ( bot_bo1320844070cset_c = A ) ),
inference(lifteq,[status(thm)],[3511]) ).
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/sandbox/benchmark/theBenchmark.p',fact_300_cpsubsetD) ).
thf(473,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(8403,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ( B @ ( sk12 @ C @ B ) )
| ( sk11 @ B )
| ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[789,323]) ).
thf(8608,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ( B @ ( sk12 @ C @ B ) )
| ( sk11 @ B )
| ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
!= ( B @ C ) ) ),
inference(lifteq,[status(thm)],[8403]) ).
thf(8684,plain,
( ( sk11
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
| ( ord_le15364698cset_c
@ ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
@ bot_bo1320844070cset_c ) ),
inference(pre_uni,[status(thm)],[8608:[bind(A,$thf( bot_bo1320844070cset_c )),bind(B,$thf( ^ [D: countable_Set_cset_c] : ( ord_le15364698cset_c @ D @ bot_bo1320844070cset_c ) )),bind(C,$thf( bot_bo1320844070cset_c ))]]) ).
thf(9710,plain,
( ( sk11
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) )
| ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c ) ),
inference(rewrite,[status(thm)],[8684,789]) ).
thf(9711,plain,
( ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) ) ),
inference(lifteq,[status(thm)],[9710]) ).
thf(9721,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [B: countable_Set_cset_c] : ( ord_le15364698cset_c @ B @ bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11
@ ^ [B: countable_Set_cset_c] : ( B = bot_bo1320844070cset_c ) )
| ( A != bot_bo1320844070cset_c ) ),
inference(paramod_ordered,[status(thm)],[797,9711]) ).
thf(9722,plain,
( ( countable_Set_cin_c @ ( sk37 @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c )
| ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) ) ),
inference(pattern_uni,[status(thm)],[9721:[bind(A,$thf( bot_bo1320844070cset_c ))]]) ).
thf(15682,plain,
( $false
| ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) ) ),
inference(rewrite,[status(thm)],[9722,789,678]) ).
thf(15683,plain,
( ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11
@ ^ [A: countable_Set_cset_c] : ( A = bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[15682]) ).
thf(22005,plain,
( ( ( sk12 @ bot_bo1320844070cset_c @ ( (=) @ countable_Set_cset_c @ bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11 @ ( (=) @ countable_Set_cset_c @ bot_bo1320844070cset_c ) ) ),
inference(rewrite,[status(thm)],[15683,22004]) ).
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/sandbox/benchmark/theBenchmark.p',fact_279_le__neq__trans) ).
thf(426,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(44,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_less__imp__neq) ).
thf(342,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(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/sandbox/benchmark/theBenchmark.p',fact_233_csubset__cinsertI2) ).
thf(663,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(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/sandbox/benchmark/theBenchmark.p',fact_287_order_Ostrict__trans1) ).
thf(548,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(926,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 )
& ( A != B ) ) ) )
| ( ord_le1587667814cset_c != ord_le1587667814cset_c ) ),
inference(paramod_ordered,[status(thm)],[281,272]) ).
thf(927,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 )
& ( A != B ) ) ) ),
inference(pattern_uni,[status(thm)],[926:[]]) ).
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/sandbox/benchmark/theBenchmark.p',fact_25_comp__def) ).
thf(374,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(107,axiom,
! [A: m,B: m] :
( ( ( monomo412532791tT_m_a @ A )
= ( monomo412532791tT_m_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nondetT_Oinject) ).
thf(557,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(113,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_less__imp__not__eq) ).
thf(580,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(5078,plain,
! [D: m,C: monomo197243225tT_a_m > monomo197243225tT_a_m,B: monomo197243225tT_a_m > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M1944986301tT_a_m
@ ^ [E: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ ( comp_M1944986301tT_a_m @ A @ B )
@ ^ [F: monomo197243225tT_a_m] : E
@ ( C @ E ) )
@ ^ [E: monomo197243225tT_a_m] : E
@ ( monomo412532791tT_m_a @ D ) )
= D )
| ( ( ^ [E: monomo197243225tT_a_m] : ( A @ ( B @ E ) ) )
!= monomo624345106et_a_m ) ),
inference(paramod_ordered,[status(thm)],[829,4348]) ).
thf(5110,plain,
! [B: m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : D )
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ B ) )
= B ),
inference(pre_uni,[status(thm)],[5078:[bind(A,$thf( monomo624345106et_a_m )),bind(B,$thf( ^ [E: monomo197243225tT_a_m] : E )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(5139,plain,
! [B: m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : D )
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ B ) )
= B ),
inference(simp,[status(thm)],[5110]) ).
thf(8163,plain,
! [B: m,A: monomo197243225tT_a_m > monomo197243225tT_a_m] :
( ( comp_M1944986301tT_a_m
@ ^ [C: monomo197243225tT_a_m] :
( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : C
@ ( A @ C ) )
@ ^ [C: monomo197243225tT_a_m] : C
@ ( monomo412532791tT_m_a @ B ) )
= B ),
inference(rewrite,[status(thm)],[5139,1613]) ).
thf(66,axiom,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_less__imp__not__eq2) ).
thf(409,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(260,plain,
! [A: monomo197243225tT_a_m > m,B: c > monomo197243225tT_a_m,C: c > m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
= C )
=> ! [D: c] :
( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(miniscope,[status(thm)],[259]) ).
thf(261,plain,
! [D: c,C: c > m,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
!= C )
| ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(cnf,[status(esa)],[260]) ).
thf(262,plain,
! [D: c,C: c > m,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( comp_M750374444_m_m_c @ A @ B )
!= C )
| ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(lifteq,[status(thm)],[261]) ).
thf(263,plain,
! [C: c,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( A @ ( B @ C ) )
= ( comp_M750374444_m_m_c @ A @ B @ C ) ),
inference(simp,[status(thm)],[262]) ).
thf(3708,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ~ $true
| ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[750,1517]) ).
thf(3709,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C )
| ( ( monomo463139869_c_m_a @ mergec @ C @ f )
!= ( f @ x ) )
| ( ( ord_le15364698cset_c @ A @ ( counta472291938sert_c @ B @ A ) )
!= ( ord_le15364698cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ C ) ) ),
inference(simp,[status(thm)],[3708]) ).
thf(3710,plain,
! [A: c] :
( ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( counta472291938sert_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[3709:[bind(A,$thf( counta472291938sert_c @ x @ bot_bo1320844070cset_c )),bind(B,$thf( F )),bind(C,$thf( counta472291938sert_c @ F @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ))]]) ).
thf(3754,plain,
! [A: c] :
( ( ord_le1587667814cset_c @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) @ ( counta472291938sert_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ A @ ( counta472291938sert_c @ x @ bot_bo1320844070cset_c ) ) @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[3710]) ).
thf(5748,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ ( sk35 @ ( counta472291938sert_c @ C @ D ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[748,5246]) ).
thf(5749,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ ( sk35 @ ( counta472291938sert_c @ C @ D ) @ C ) ) ),
inference(simp,[status(thm)],[5748]) ).
thf(5758,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( A != C )
| ( ( counta472291938sert_c @ A @ B )
!= ( sk35 @ ( counta472291938sert_c @ C @ D ) @ C ) ) ),
inference(simp,[status(thm)],[5749]) ).
thf(5767,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ( counta472291938sert_c @ B @ A )
!= ( sk35 @ ( counta472291938sert_c @ B @ C ) @ B ) ),
inference(simp,[status(thm)],[5758]) ).
thf(441,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le1587667814cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk18 @ D @ C @ B @ A ) ) @ ( B @ ( sk19 @ D @ C @ B @ A ) ) )
| ( ord_le1587667814cset_c @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[439]) ).
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/sandbox/benchmark/theBenchmark.p',fact_226_cinsertE) ).
thf(717,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(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/sandbox/benchmark/theBenchmark.p',fact_245_Greatest__equality) ).
thf(502,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(21908,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ A @ B )
| ( A != B ) ),
inference(bool_ext,[status(thm)],[383]) ).
thf(21968,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A != B )
| ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ A @ B ) ),
inference(lifteq,[status(thm)],[21908]) ).
thf(21986,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A != B )
| ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ A @ B ) ),
inference(cnf,[status(esa)],[21968]) ).
thf(21987,plain,
! [A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ A )
| ~ ( ord_le1587667814cset_c @ A @ A ) ),
inference(simp,[status(thm)],[21986]) ).
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/sandbox/benchmark/theBenchmark.p',fact_283_le__less__trans) ).
thf(336,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(337,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c] :
( ( ord_le1587667814cset_c @ B @ C )
=> ( ord_le1587667814cset_c @ A @ C ) ) ),
inference(miniscope,[status(thm)],[336]) ).
thf(338,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ B @ C )
| ( ord_le1587667814cset_c @ A @ C ) ),
inference(cnf,[status(esa)],[337]) ).
thf(82,axiom,
! [A: monomo197243225tT_a_m] :
( A
= ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_nondetT_Oexhaust__sel) ).
thf(470,plain,
! [A: monomo197243225tT_a_m] :
( A
= ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
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/sandbox/benchmark/theBenchmark.p',fact_241_cinsert__cDiff__if) ).
thf(808,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(22251,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( bot_bo1320844070cset_c != A )
| ( B @ ( sk12 @ C @ B ) )
| ( sk11 @ B )
| ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
!= ( B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22006,323]) ).
thf(22393,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( bot_bo1320844070cset_c != A )
| ( B @ ( sk12 @ C @ B ) )
| ( sk11 @ B )
| ( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
!= ( B @ C ) ) ),
inference(lifteq,[status(thm)],[22251]) ).
thf(22434,plain,
( ( sk11
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
| ( ord_le15364698cset_c
@ ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
@ bot_bo1320844070cset_c ) ),
inference(pre_uni,[status(thm)],[22393:[bind(A,$thf( bot_bo1320844070cset_c )),bind(B,$thf( ^ [D: countable_Set_cset_c] : ( ord_le15364698cset_c @ D @ bot_bo1320844070cset_c ) )),bind(C,$thf( bot_bo1320844070cset_c ))]]) ).
thf(26174,plain,
( ( sk11 @ ( (=) @ countable_Set_cset_c @ bot_bo1320844070cset_c ) )
| ( bot_bo1320844070cset_c
= ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) ) ) ),
inference(rewrite,[status(thm)],[22434,22006]) ).
thf(26175,plain,
( ( ( sk12 @ bot_bo1320844070cset_c
@ ^ [A: countable_Set_cset_c] : ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c ) )
= bot_bo1320844070cset_c )
| ( sk11 @ ( (=) @ countable_Set_cset_c @ bot_bo1320844070cset_c ) ) ),
inference(lifteq,[status(thm)],[26174]) ).
thf(1053,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(1054,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)],[1053:[bind(A,$thf( bot_bo1320844070cset_c ))]]) ).
thf(1074,plain,
! [A: countable_Set_cset_c] :
( ( ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ bot_bo1320844070cset_c )
!= ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A ) )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[1054]) ).
thf(1126,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ ( counta472291938sert_c @ x @ A ) @ f )
!= ( f @ x ) ) ),
inference(rewrite,[status(thm)],[1074,678]) ).
thf(7493,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( countable_Set_cin_c @ ( sk1 @ B @ bot_bo1320844070cset_c ) @ B )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( A
!= ( counta472291938sert_c @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[797,1126]) ).
thf(7494,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ A ) ) @ ( counta472291938sert_c @ x @ A ) )
| ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[7493:[bind(A,$thf( counta472291938sert_c @ x @ D )),bind(B,$thf( D ))]]) ).
thf(7779,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ A ) ) @ ( counta472291938sert_c @ x @ A ) )
| ( countable_Set_cin_c @ ( sk1 @ A @ bot_bo1320844070cset_c ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[7494]) ).
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/sandbox/benchmark/theBenchmark.p',fact_205_cequalityCE) ).
thf(613,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(363,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( countable_Set_cin_c @ ( sk14 @ B @ A ) @ B )
| ( ord_le15364698cset_c @ A @ B ) ),
inference(cnfConj,[status(thm)],[361]) ).
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/sandbox/benchmark/theBenchmark.p',fact_180_cinsert__csubset) ).
thf(671,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(142,axiom,
! [A: c,B: countable_Set_cset_c] :
( ( countable_Set_cin_c @ A @ B )
=> ( ( counta472291938sert_c @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_cinsert__absorb) ).
thf(688,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(47,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_less__irrefl) ).
thf(351,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(632,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)],[631]) ).
thf(400,plain,
! [F: c,E: c > monomo197243225tT_a_m,D: monomo197243225tT_a_m > m,C: c,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( A @ ( B @ C ) )
!= ( D @ ( E @ F ) ) )
| ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ F ) ) ),
inference(cnf,[status(esa)],[399]) ).
thf(401,plain,
! [F: c,E: c > monomo197243225tT_a_m,D: monomo197243225tT_a_m > m,C: c,B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( ( A @ ( B @ C ) )
!= ( D @ ( E @ F ) ) )
| ( ( comp_M750374444_m_m_c @ A @ B @ C )
= ( comp_M750374444_m_m_c @ D @ E @ F ) ) ),
inference(lifteq,[status(thm)],[400]) ).
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/sandbox/benchmark/theBenchmark.p',fact_174_cinsertCI) ).
thf(781,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(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/sandbox/benchmark/theBenchmark.p',fact_185_dual__order_Otrans) ).
thf(588,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(235,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ~ ( ord_le15364698cset_c @ ( B @ ( sk2 @ D @ C @ B @ A ) ) @ ( B @ ( sk3 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(22009,plain,
! [A: countable_Set_cset_c] :
( ( ? [B: c] : ( countable_Set_cin_c @ B @ A ) )
= ( bot_bo1320844070cset_c != A ) ),
inference(rewrite,[status(thm)],[684,22004]) ).
thf(1193,plain,
! [A: countable_Set_cset_c] :
( ( ( monomo463139869_c_m_a @ mergec @ A @ f )
!= ( f @ x ) )
| ~ ( 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 ) ) ),
inference(bool_ext,[status(thm)],[1056]) ).
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/sandbox/benchmark/theBenchmark.p',fact_170_csubset__antisym) ).
thf(478,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(832,plain,
! [B: c > monomo197243225tT_a_m,A: monomo197243225tT_a_m > m] :
( ( comp_M750374444_m_m_c @ A @ B )
= ( ^ [C: c] : ( A @ ( B @ C ) ) ) ),
inference(func_ext,[status(esa)],[293]) ).
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/sandbox/benchmark/theBenchmark.p',fact_256_less__asym_H) ).
thf(346,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(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/sandbox/benchmark/theBenchmark.p',fact_11_altc__nondet__def) ).
thf(763,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(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(297,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A
!= ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk5 @ D @ C @ B @ A ) @ ( sk6 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ),
inference(cnfConj,[status(thm)],[296]) ).
thf(299,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c > countable_Set_cset_c,A: countable_Set_cset_c] :
( ( A
!= ( B @ C ) )
| ~ ( ord_le15364698cset_c @ C @ D )
| ( ord_le15364698cset_c @ ( sk5 @ D @ C @ B @ A ) @ ( sk6 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ A @ ( B @ D ) ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(300,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c > countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ B @ C )
| ( ord_le15364698cset_c @ ( sk5 @ C @ B @ A @ ( A @ B ) ) @ ( sk6 @ C @ B @ A @ ( A @ B ) ) )
| ( ord_le15364698cset_c @ ( A @ B ) @ ( A @ C ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(315,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le1587667814cset_c @ ( C @ B ) @ D )
| ( ord_le15364698cset_c @ ( sk9 @ D @ C @ B @ A ) @ ( sk10 @ D @ C @ B @ A ) )
| ( ord_le1587667814cset_c @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[314]) ).
thf(268,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)],[267]) ).
thf(835,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 @ A ) ),
inference(func_ext,[status(esa)],[268]) ).
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/sandbox/benchmark/theBenchmark.p',fact_182_csubset__cinsert) ).
thf(790,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(854,plain,
! [A: counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m] :
( ( monomo2081011572_m_m_a @ A )
= ( ^ [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(func_ext,[status(esa)],[632]) ).
thf(7342,plain,
! [B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ A ) @ A )
| ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ B ) @ B )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) )
| ( A
!= ( counta472291938sert_c @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[797,1119]) ).
thf(7343,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ A ) ) @ ( counta472291938sert_c @ x @ A ) )
| ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(pattern_uni,[status(thm)],[7342:[bind(A,$thf( counta472291938sert_c @ x @ D )),bind(B,$thf( D ))]]) ).
thf(7727,plain,
! [A: countable_Set_cset_c] :
( ( countable_Set_cin_c @ ( sk37 @ ( counta472291938sert_c @ x @ A ) ) @ ( counta472291938sert_c @ x @ A ) )
| ( countable_Set_cin_c @ ( sk1 @ bot_bo1320844070cset_c @ A ) @ A )
| ( ( monomo463139869_c_m_a @ mergec @ bot_bo1320844070cset_c @ f )
!= ( f @ x ) ) ),
inference(simp,[status(thm)],[7343]) ).
thf(326,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > $o,B: countable_Set_cset_c,A: countable_Set_cset_c > $o] :
( ~ ( A @ B )
| ~ ( sk11 @ A )
| ~ ( A @ D )
| ( ord_le15364698cset_c @ D @ ( sk13 @ C @ B @ A ) )
| ( C @ ( order_1683649299cset_c @ A ) ) ),
inference(cnfConj,[status(thm)],[322]) ).
thf(340,plain,
! [A: countable_Set_cset_c,B: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ B )
=> ! [C: countable_Set_cset_c,D: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ C @ D )
=> ( ord_le15364698cset_c @ ( minus_1646763425cset_c @ A @ D ) @ ( minus_1646763425cset_c @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[339]) ).
thf(341,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c,B: countable_Set_cset_c,A: 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(cnf,[status(esa)],[340]) ).
thf(828,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(127,axiom,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_dual__order_Oirrefl) ).
thf(635,plain,
! [A: countable_Set_cset_c] :
~ ( ord_le1587667814cset_c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
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/sandbox/benchmark/theBenchmark.p',fact_239_csubset__cinsert__iff) ).
thf(696,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(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/sandbox/benchmark/theBenchmark.p',fact_165_cDiff__cinsert) ).
thf(720,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(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/sandbox/benchmark/theBenchmark.p',fact_222_cinsert__ident) ).
thf(801,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(395,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( ord_le15364698cset_c @ ( C @ B ) @ D )
| ~ ( ord_le15364698cset_c @ ( C @ ( sk15 @ D @ C @ B @ A ) ) @ ( C @ ( sk16 @ D @ C @ B @ A ) ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[393]) ).
thf(159,axiom,
! [A: c,B: c] :
( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ B @ bot_bo1320844070cset_c ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_csingleton__iff) ).
thf(740,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(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/sandbox/benchmark/theBenchmark.p',fact_274_less__le) ).
thf(464,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(328,plain,
! [B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( A != A )
| ~ ( sk11 @ ( (=) @ countable_Set_cset_c @ A ) )
| ( A
= ( sk13 @ B @ A @ ( (=) @ countable_Set_cset_c @ A ) ) )
| ( B @ ( order_1683649299cset_c @ ( (=) @ countable_Set_cset_c @ A ) ) ) ),
inference(replace_leibeq,[status(thm)],[325:[bind(A,$thf( (=) @ countable_Set_cset_c @ B ))]]) ).
thf(331,plain,
! [B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( A != A )
| ( ( sk13 @ B @ A @ ( (=) @ countable_Set_cset_c @ A ) )
= A )
| ~ ( sk11 @ ( (=) @ countable_Set_cset_c @ A ) )
| ( B @ ( order_1683649299cset_c @ ( (=) @ countable_Set_cset_c @ A ) ) ) ),
inference(lifteq,[status(thm)],[328]) ).
thf(332,plain,
! [B: countable_Set_cset_c > $o,A: countable_Set_cset_c] :
( ( ( sk13 @ B @ A @ ( (=) @ countable_Set_cset_c @ A ) )
= A )
| ~ ( sk11 @ ( (=) @ countable_Set_cset_c @ A ) )
| ( B @ ( order_1683649299cset_c @ ( (=) @ countable_Set_cset_c @ A ) ) ) ),
inference(simp,[status(thm)],[331]) ).
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/sandbox/benchmark/theBenchmark.p',fact_189_ord__le__eq__trans) ).
thf(575,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(5787,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( sk35 @ D @ C )
!= D )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[748,5267]) ).
thf(5788,plain,
! [D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( ( sk35 @ D @ C )
!= D )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ D ) ) ),
inference(simp,[status(thm)],[5787]) ).
thf(5789,plain,
! [B: countable_Set_cset_c,A: c] :
( ( sk35 @ ( counta472291938sert_c @ A @ B ) @ A )
!= ( counta472291938sert_c @ A @ B ) ),
inference(pattern_uni,[status(thm)],[5788:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( counta472291938sert_c @ E @ F ))]]) ).
thf(5806,plain,
! [B: countable_Set_cset_c,A: c] :
( ( sk35 @ ( counta472291938sert_c @ A @ B ) @ A )
!= ( counta472291938sert_c @ A @ B ) ),
inference(simp,[status(thm)],[5789]) ).
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(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/sandbox/benchmark/theBenchmark.p',fact_263_less__not__sym) ).
thf(442,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(154,axiom,
! [A: countable_Set_cset_c] :
( ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
=> ( A = bot_bo1320844070cset_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_bot_Oextremum__uniqueI) ).
thf(723,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(15499,plain,
! [C: m,B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m @ B
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ A ) ) )
= C )
| ( ( B @ A )
!= ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14330,15457]) ).
thf(15506,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(pre_uni,[status(thm)],[15499:[bind(A,$thf( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ C ) ) )),bind(B,$thf( monomo624345106et_a_m )),bind(C,$thf( C ))]]) ).
thf(15558,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[15506]) ).
thf(21366,plain,
! [A: m] :
( ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ A ) ) ) ) ) )
= A ),
inference(rewrite,[status(thm)],[15558,1613]) ).
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/sandbox/benchmark/theBenchmark.p',fact_235_cinsert__mono) ).
thf(691,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(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/sandbox/benchmark/theBenchmark.p',fact_307_csubset__not__fsubset__eq) ).
thf(369,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(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/sandbox/benchmark/theBenchmark.p',fact_255_less__asym) ).
thf(607,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(2437,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ C )
| ( ( countable_Set_cin_c @ A @ ( minus_1646763425cset_c @ B @ C ) )
!= ( countable_Set_cin_c @ A @ C ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[477]) ).
thf(2440,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ C )
| ( A != A )
| ( ( minus_1646763425cset_c @ B @ C )
!= C ) ),
inference(simp,[status(thm)],[2437]) ).
thf(2453,plain,
! [C: countable_Set_cset_c,B: countable_Set_cset_c,A: c] :
( ~ ( countable_Set_cin_c @ A @ C )
| ( ( minus_1646763425cset_c @ B @ C )
!= C ) ),
inference(simp,[status(thm)],[2440]) ).
thf(4631,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ~ $true
| ( ( minus_1646763425cset_c @ D @ E )
!= E )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[748,2453]) ).
thf(4632,plain,
! [E: countable_Set_cset_c,D: countable_Set_cset_c,C: c,B: countable_Set_cset_c,A: c] :
( ( ( minus_1646763425cset_c @ D @ E )
!= E )
| ( ( countable_Set_cin_c @ A @ ( counta472291938sert_c @ A @ B ) )
!= ( countable_Set_cin_c @ C @ E ) ) ),
inference(simp,[status(thm)],[4631]) ).
thf(4633,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
!= ( counta472291938sert_c @ B @ C ) ),
inference(pattern_uni,[status(thm)],[4632:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( counta472291938sert_c @ F @ G ))]]) ).
thf(4655,plain,
! [C: countable_Set_cset_c,B: c,A: countable_Set_cset_c] :
( ( minus_1646763425cset_c @ A @ ( counta472291938sert_c @ B @ C ) )
!= ( counta472291938sert_c @ B @ C ) ),
inference(simp,[status(thm)],[4633]) ).
thf(306,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ( C @ B )
!= D )
| ( ord_le15364698cset_c @ ( sk7 @ D @ C @ B @ A ) @ ( sk8 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ),
inference(cnfConj,[status(thm)],[305]) ).
thf(308,plain,
! [D: countable_Set_cset_c,C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ( ( C @ B )
!= D )
| ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le15364698cset_c @ ( sk7 @ D @ C @ B @ A ) @ ( sk8 @ D @ C @ B @ A ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ D ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(309,plain,
! [C: countable_Set_cset_c > countable_Set_cset_c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ( ord_le15364698cset_c @ ( sk7 @ ( C @ B ) @ C @ B @ A ) @ ( sk8 @ ( C @ B ) @ C @ B @ A ) )
| ( ord_le15364698cset_c @ ( C @ A ) @ ( C @ B ) ) ),
inference(simp,[status(thm)],[308]) ).
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/sandbox/benchmark/theBenchmark.p',fact_153_function__factors__left) ).
thf(543,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(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/sandbox/benchmark/theBenchmark.p',fact_278_order__less__le__subst2) ).
thf(491,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(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/sandbox/benchmark/theBenchmark.p',fact_268_less__imp__not__less) ).
thf(496,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(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/sandbox/benchmark/theBenchmark.p',fact_168_cinsert__cDiff) ).
thf(708,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(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/sandbox/benchmark/theBenchmark.p',fact_200_eq__cmem__trans) ).
thf(254,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(3029,plain,
! [D: c,C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( countable_Set_cin_c @ C @ A )
| ~ $true
| ( ( countable_Set_cin_c @ C @ B )
!= ( countable_Set_cin_c @ D @ bot_bo1320844070cset_c ) ) ),
inference(paramod_ordered,[status(thm)],[243,678]) ).
thf(3030,plain,
! [D: c,C: c,B: countable_Set_cset_c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ B )
| ~ ( countable_Set_cin_c @ C @ A )
| ( ( countable_Set_cin_c @ C @ B )
!= ( countable_Set_cin_c @ D @ bot_bo1320844070cset_c ) ) ),
inference(simp,[status(thm)],[3029]) ).
thf(3031,plain,
! [B: c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(pattern_uni,[status(thm)],[3030:[bind(A,$thf( A )),bind(B,$thf( bot_bo1320844070cset_c )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(3098,plain,
! [B: c,A: countable_Set_cset_c] :
( ~ ( ord_le15364698cset_c @ A @ bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(simp,[status(thm)],[3031]) ).
thf(3473,plain,
! [B: c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(rewrite,[status(thm)],[3098,789]) ).
thf(3474,plain,
! [B: c,A: countable_Set_cset_c] :
( ( A != bot_bo1320844070cset_c )
| ~ ( countable_Set_cin_c @ B @ A ) ),
inference(lifteq,[status(thm)],[3473]) ).
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/sandbox/benchmark/theBenchmark.p',fact_7_run__altc__nondet) ).
thf(775,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(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/sandbox/benchmark/theBenchmark.p',fact_250_order__less__subst1) ).
thf(560,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(25827,plain,
! [C: m,B: monomo197243225tT_a_m > m,A: monomo197243225tT_a_m] :
( ( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [D: monomo197243225tT_a_m] : D
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ B
@ ^ [D: monomo197243225tT_a_m] : D
@ A ) ) )
= C )
| ( ( B @ A )
!= ( monomo624345106et_a_m @ ( monomo412532791tT_m_a @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[11841,25799]) ).
thf(25880,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) ) ) )
= A ),
inference(pre_uni,[status(thm)],[25827:[bind(A,$thf( monomo412532791tT_m_a @ C )),bind(B,$thf( monomo624345106et_a_m )),bind(C,$thf( C ))]]) ).
thf(25943,plain,
! [A: m] :
( ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) ) ) )
= A ),
inference(simp,[status(thm)],[25880]) ).
thf(27961,plain,
! [A: m] :
( ( monomo624345106et_a_m
@ ( monomo412532791tT_m_a
@ ( comp_M1944986301tT_a_m @ monomo624345106et_a_m
@ ^ [B: monomo197243225tT_a_m] : B
@ ( monomo412532791tT_m_a @ A ) ) ) )
= A ),
inference(rewrite,[status(thm)],[25943,1613]) ).
thf(31865,plain,
$false,
inference(e,[status(thm)],[892,6231,468,234,666,481,628,249,6813,1073,26053,269,597,217,276,440,655,511,384,533,797,6727,747,31171,670,7405,3332,829,2985,1613,436,320,565,389,1287,7401,22004,1577,357,702,751,638,189,6396,421,284,325,228,289,316,924,756,2469,238,348,591,22007,3670,376,766,280,293,453,3756,243,5665,206,1119,774,396,5246,527,312,9703,292,678,270,661,546,201,761,381,534,714,798,220,366,334,746,825,778,302,424,429,729,197,522,889,682,551,456,324,224,317,650,20387,27503,388,356,593,420,857,8339,4486,188,9936,488,225,339,537,669,476,212,554,753,27178,679,837,16822,911,2766,5603,371,244,266,311,541,674,5126,794,633,360,805,205,22008,530,6368,750,824,264,279,444,733,601,584,819,904,694,402,3234,732,843,772,743,711,259,413,641,391,572,787,498,466,335,236,11841,604,1194,187,406,831,219,6815,3270,230,737,434,303,1439,5267,362,451,567,271,208,477,387,631,367,2129,816,323,520,240,22006,769,198,3150,9174,609,213,726,21052,483,399,768,455,223,431,658,685,1171,6816,394,267,3512,241,653,473,22005,426,3161,209,749,342,194,663,548,927,374,557,580,8163,739,409,263,705,282,327,3754,5767,21058,441,717,502,21987,18128,338,470,808,359,26175,7779,2379,613,18211,19133,336,231,3433,363,203,671,688,1517,759,26001,771,218,1126,319,748,351,186,632,401,418,781,588,699,290,235,22009,1193,478,383,832,346,763,272,214,287,300,752,315,432,835,790,273,6366,854,190,7727,326,341,195,437,1056,828,635,532,696,720,294,801,395,740,464,332,575,5806,822,200,14330,442,723,21366,277,691,369,607,4655,354,309,543,25799,215,2453,491,496,364,708,254,227,3474,775,560,222,27961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP127^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.22 % Computer : n018.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 19:59:41 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.65/1.39 % [INFO] Parsing done (581ms).
% 3.12/1.41 % [INFO] Running in sequential loop mode.
% 4.79/1.89 % [INFO] eprover registered as external prover.
% 5.21/1.90 % [INFO] Scanning for conjecture ...
% 5.21/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 315 axioms. Running axiom selection ...
% 5.88/2.14 % [INFO] Axiom selection finished. Selected 183 axioms (removed 132 axioms).
% 6.46/2.36 % [INFO] Problem is higher-order (TPTP THF).
% 6.46/2.39 % [INFO] Type checking passed.
% 6.46/2.39 % [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 ...
% 191.36/91.17 % External prover 'e' found a proof!
% 191.36/91.17 % [INFO] Killing All external provers ...
% 191.36/91.17 % Time passed: 90811ms (effective reasoning time: 89748ms)
% 191.36/91.17 % 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)>
% 191.36/91.17 % 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
% 191.36/91.17 % No. of inferences in proof: 866
% 191.36/91.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 90811 ms resp. 89748 ms w/o parsing
% 193.14/91.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 193.14/91.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------