%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ITP128^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 Oct 7 10:24:13 AM UTC 2026
% Result : Theorem 5.60s 1.23s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 456 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 4198 (1580 equ; 0 cnn)
% Maximal formula atoms : 4 ( 9 avg)
% Number of connectives : 3541 ( 583 ~;1121 |; 0 &;1798 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 355 ( 355 >; 0 *; 0 +; 0 <<)
% Number of symbols : 370 ( 367 usr; 2 con; 0-7 aty)
% Number of variables : 644 ( 4 ^; 640 !; 0 ?; 644 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_b,type,
b: $tType ).
thf(tp_c,type,
c: $tType ).
thf(tp_d,type,
d: $tType ).
thf(tp_fset_a,type,
fset_a: $tType ).
thf(tp_fset_b,type,
fset_b: $tType ).
thf(tp_multiset_a,type,
multiset_a: $tType ).
thf(tp_multiset_b,type,
multiset_b: $tType ).
thf(tp_set_a,type,
set_a: $tType ).
thf(tp_set_b,type,
set_b: $tType ).
thf(tp_set_c,type,
set_c: $tType ).
thf(tp_set_d,type,
set_d: $tType ).
thf(tp_a2,type,
a2: a > b > $o ).
thf(tp_b2,type,
b2: c > d > $o ).
thf(tp_bNF_re1062117919_b_d_d,type,
bNF_re1062117919_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( b > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > $o ).
thf(tp_bNF_re1071888283_a_b_o,type,
bNF_re1071888283_a_b_o: ( ( a > a > $o ) > ( b > b > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > b ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( b > b > $o ) > ( a > b ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1088547499_b_o_o,type,
bNF_re1088547499_b_o_o: ( ( a > b ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > b ) > $o ) > ( ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1093913501_a_b_b,type,
bNF_re1093913501_a_b_b: ( a > a > $o ) > ( ( ( a > a ) > a ) > ( ( a > b ) > b ) > $o ) > ( a > ( a > a ) > a ) > ( a > ( a > b ) > b ) > $o ).
thf(tp_bNF_re1133483099_a_b_o,type,
bNF_re1133483099_a_b_o: ( ( ( c > c ) > ( d > d ) > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1138812345_b_b_b,type,
bNF_re1138812345_b_b_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( ( ( d > d ) > b ) > ( d > d ) > b ) > ( ( b > b ) > b > b ) > $o ) > ( ( b > b ) > ( ( d > d ) > b ) > ( d > d ) > b ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re1143700905_c_c_c,type,
bNF_re1143700905_c_c_c: ( a > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ).
thf(tp_bNF_re1145286186_b_d_d,type,
bNF_re1145286186_b_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( c > c ) > a > c > c ) > ( ( d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re1160226589_b_d_d,type,
bNF_re1160226589_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( b > a ) > b > c > c ) > ( ( b > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > $o ).
thf(tp_bNF_re1164948833_d_d_d,type,
bNF_re1164948833_d_d_d: ( ( c > a ) > ( d > b ) > $o ) > ( ( ( ( c > c ) > c ) > ( a > c > c ) > c > c ) > ( ( ( d > d ) > d ) > ( b > d > d ) > d > d ) > $o ) > ( ( c > a ) > ( ( c > c ) > c ) > ( a > c > c ) > c > c ) > ( ( d > b ) > ( ( d > d ) > d ) > ( b > d > d ) > d > d ) > $o ).
thf(tp_bNF_re1165460699_a_b_o,type,
bNF_re1165460699_a_b_o: ( ( a > a > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1177671453_a_a_a,type,
bNF_re1177671453_a_a_a: ( ( ( c > c ) > a ) > ( a > a ) > $o ) > ( ( ( c > c ) > a ) > ( a > a ) > $o ) > ( ( ( c > c ) > a ) > ( c > c ) > a ) > ( ( a > a ) > a > a ) > $o ).
thf(tp_bNF_re1209333166_c_b_d,type,
bNF_re1209333166_c_b_d: ( ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ) > ( ( a > c ) > ( b > d ) > $o ) > ( ( ( c > c ) > c ) > a > c ) > ( ( ( d > d ) > d ) > b > d ) > $o ).
thf(tp_bNF_re1217999849_a_b_o,type,
bNF_re1217999849_a_b_o: ( ( a > a ) > ( a > b ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1222471293_b_b_b,type,
bNF_re1222471293_b_b_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( ( b > b ) > b > b ) > ( ( b > b ) > b > b ) > $o ) > ( ( b > b ) > ( b > b ) > b > b ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re1238578079_d_d_d,type,
bNF_re1238578079_d_d_d: ( ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( b > d > d ) > d > d ) > $o ) > ( ( ( c > c ) > c ) > ( a > c > c ) > c > c ) > ( ( ( d > d ) > d ) > ( b > d > d ) > d > d ) > $o ).
thf(tp_bNF_re1256092317_b_o_o,type,
bNF_re1256092317_b_o_o: ( ( a > c > c ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > c > c ) > $o ) > ( ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1258259453_a_a_a,type,
bNF_re1258259453_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > a ) > a > a ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( a > a ) > ( a > a ) > a > a ) > $o ).
thf(tp_bNF_re1303182826_d_c_d,type,
bNF_re1303182826_d_c_d: ( ( c > c ) > ( d > d ) > $o ) > ( c > d > $o ) > ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ).
thf(tp_bNF_re1306877487_o_a_o,type,
bNF_re1306877487_o_a_o: ( ( c > c ) > a > $o ) > ( ( ( d > d ) > $o ) > ( a > $o ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > a > $o ) > $o ).
thf(tp_bNF_re1307884917_a_b_b,type,
bNF_re1307884917_a_b_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( a > a ) > ( b > b ) > $o ) > ( ( a > a ) > a > a ) > ( ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re131001756_o_b_o,type,
bNF_re131001756_o_b_o: ( a > a > $o ) > ( ( a > $o ) > ( b > $o ) > $o ) > ( a > a > $o ) > ( a > b > $o ) > $o ).
thf(tp_bNF_re1310167325_a_a_o,type,
bNF_re1310167325_a_a_o: ( ( a > a > $o ) > ( b > a > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > a ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( b > a > $o ) > ( a > b ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1311853791_b_c_c,type,
bNF_re1311853791_b_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( b > a ) > b > c > c ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > $o ).
thf(tp_bNF_re1313098655_d_d_d,type,
bNF_re1313098655_d_d_d: ( c > d > $o ) > ( ( ( c > c ) > c ) > ( ( d > d ) > d ) > $o ) > ( c > ( c > c ) > c ) > ( d > ( d > d ) > d ) > $o ).
thf(tp_bNF_re1327926367_d_d_d,type,
bNF_re1327926367_d_d_d: ( a > b > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( b > d > d ) > d > d ) > $o ) > ( a > ( a > c > c ) > c > c ) > ( b > ( b > d > d ) > d > d ) > $o ).
thf(tp_bNF_re1342462312_a_c_c,type,
bNF_re1342462312_a_c_c: ( ( b > b ) > ( a > a ) > $o ) > ( ( b > d > d ) > ( a > c > c ) > $o ) > ( ( b > b ) > b > d > d ) > ( ( a > a ) > a > c > c ) > $o ).
thf(tp_bNF_re134330537_a_o_o,type,
bNF_re134330537_a_o_o: ( ( a > a ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1391160029_d_d_d,type,
bNF_re1391160029_d_d_d: ( a > a > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( a > d > d ) > d > d ) > $o ) > ( a > ( a > c > c ) > c > c ) > ( a > ( a > d > d ) > d > d ) > $o ).
thf(tp_bNF_re1403739741_a_a_o,type,
bNF_re1403739741_a_a_o: ( ( a > a > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1409962461_b_c_c,type,
bNF_re1409962461_b_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( b > a ) > b > c > c ) > ( ( b > a ) > b > c > c ) > $o ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > $o ).
thf(tp_bNF_re1412708073_b_d_d,type,
bNF_re1412708073_b_d_d: ( ( b > b ) > ( b > b ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > ( ( b > b ) > b > d > d ) > ( ( b > b ) > b > d > d ) > $o ).
thf(tp_bNF_re141854397_b_d_d,type,
bNF_re141854397_b_d_d: ( ( ( c > c ) > c > c ) > ( ( d > d ) > d > d ) > $o ) > ( ( ( a > c > c ) > a > c > c ) > ( ( b > d > d ) > b > d > d ) > $o ) > ( ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ) > ( ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re1424479610_b_d_d,type,
bNF_re1424479610_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > ( c > c ) > a > c > c ) > ( b > ( d > d ) > b > d > d ) > $o ) > ( ( a > c > c ) > a > ( c > c ) > a > c > c ) > ( ( b > d > d ) > b > ( d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re1424579386_a_a_a,type,
bNF_re1424579386_a_a_a: ( ( c > c ) > a > $o ) > ( a > a > $o ) > ( ( c > c ) > a ) > ( a > a ) > $o ).
thf(tp_bNF_re1450278895_o_a_o,type,
bNF_re1450278895_o_a_o: ( ( c > c ) > a > $o ) > ( ( ( c > c ) > $o ) > ( a > $o ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > a > $o ) > $o ).
thf(tp_bNF_re145798749_a_a_o,type,
bNF_re145798749_a_a_o: ( ( ( c > c ) > ( d > d ) > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1463366826_b_o_o,type,
bNF_re1463366826_b_o_o: ( ( a > a ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > a ) > $o ) > ( ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1482032989_c_c_c,type,
bNF_re1482032989_c_c_c: ( a > a > $o ) > ( ( ( a > c > c ) > c > c ) > ( ( a > c > c ) > c > c ) > $o ) > ( a > ( a > c > c ) > c > c ) > ( a > ( a > c > c ) > c > c ) > $o ).
thf(tp_bNF_re1501709470_d_o_o,type,
bNF_re1501709470_d_o_o: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( $o > $o > $o ) > ( ( a > c > c ) > $o ) > ( ( b > d > d ) > $o ) > $o ).
thf(tp_bNF_re1503602041_a_a_a,type,
bNF_re1503602041_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( ( c > c ) > a ) > ( c > c ) > a ) > ( ( a > a ) > a > a ) > $o ) > ( ( a > a ) > ( ( c > c ) > a ) > ( c > c ) > a ) > ( ( a > a ) > ( a > a ) > a > a ) > $o ).
thf(tp_bNF_re1507718559_b_d_d,type,
bNF_re1507718559_b_d_d: ( ( c > c > c ) > ( d > d > d ) > $o ) > ( ( ( c > c ) > a > c > c ) > ( ( d > d ) > b > d > d ) > $o ) > ( ( c > c > c ) > ( c > c ) > a > c > c ) > ( ( d > d > d ) > ( d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re1509948838_d_d_d,type,
bNF_re1509948838_d_d_d: ( ( c > a ) > ( d > b ) > $o ) > ( ( c > c > c ) > ( d > d > d ) > $o ) > ( ( c > a ) > c > c > c ) > ( ( d > b ) > d > d > d ) > $o ).
thf(tp_bNF_re1514436479_a_a_b,type,
bNF_re1514436479_a_a_b: ( ( a > a ) > ( a > b ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > a ) > a > b ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( a > b ) > ( a > a ) > a > b ) > $o ).
thf(tp_bNF_re1565463783_b_c_c,type,
bNF_re1565463783_b_c_c: ( ( b > a ) > ( b > a ) > $o ) > ( ( b > c > c ) > ( b > c > c ) > $o ) > ( ( b > a ) > b > c > c ) > ( ( b > a ) > b > c > c ) > $o ).
thf(tp_bNF_re1573506119_d_b_b,type,
bNF_re1573506119_d_b_b: ( b > ( d > d ) > $o ) > ( b > b > $o ) > ( b > b ) > ( ( d > d ) > b ) > $o ).
thf(tp_bNF_re1573878111_b_d_d,type,
bNF_re1573878111_b_d_d: ( a > b > $o ) > ( ( ( c > c ) > a > c > c ) > ( ( d > d ) > b > d > d ) > $o ) > ( a > ( c > c ) > a > c > c ) > ( b > ( d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re1591514407_a_c_c,type,
bNF_re1591514407_a_c_c: ( ( b > a ) > ( a > a ) > $o ) > ( ( b > c > c ) > ( a > c > c ) > $o ) > ( ( b > a ) > b > c > c ) > ( ( a > a ) > a > c > c ) > $o ).
thf(tp_bNF_re1606289753_b_d_d,type,
bNF_re1606289753_b_d_d: ( ( a > c ) > ( b > d ) > $o ) > ( ( ( c > c > c ) > ( c > c ) > a > c > c ) > ( ( d > d > d ) > ( d > d ) > b > d > d ) > $o ) > ( ( a > c ) > ( c > c > c ) > ( c > c ) > a > c > c ) > ( ( b > d ) > ( d > d > d ) > ( d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re1620723804_a_o_o,type,
bNF_re1620723804_a_o_o: ( ( a > d > d ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > d > d ) > $o ) > ( ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1645058365_a_a_a,type,
bNF_re1645058365_a_a_a: ( ( b > b ) > ( a > a ) > $o ) > ( ( ( b > b ) > b > b ) > ( ( a > a ) > a > a ) > $o ) > ( ( b > b ) > ( b > b ) > b > b ) > ( ( a > a ) > ( a > a ) > a > a ) > $o ).
thf(tp_bNF_re1652452067_a_a_o,type,
bNF_re1652452067_a_a_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > d > d ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1661760168_b_d_d,type,
bNF_re1661760168_b_d_d: ( ( b > a ) > ( b > b ) > $o ) > ( ( b > c > c ) > ( b > d > d ) > $o ) > ( ( b > a ) > b > c > c ) > ( ( b > b ) > b > d > d ) > $o ).
thf(tp_bNF_re1665173865_b_c_c,type,
bNF_re1665173865_b_c_c: ( ( a > a ) > ( b > a ) > $o ) > ( ( a > c > c ) > ( b > c > c ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( b > a ) > b > c > c ) > $o ).
thf(tp_bNF_re1684125987_a_a_o,type,
bNF_re1684125987_a_a_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1690123229_o_a_o,type,
bNF_re1690123229_o_a_o: ( a > a > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(tp_bNF_re1690311157_a_a_a,type,
bNF_re1690311157_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > a ) > a > a ) > $o ).
thf(tp_bNF_re1691224489_a_c_c,type,
bNF_re1691224489_a_c_c: ( ( a > a ) > ( a > a ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( a > a ) > a > c > c ) > $o ).
thf(tp_bNF_re1698572662_a_a_b,type,
bNF_re1698572662_a_a_b: ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > a ) > a > b ) > $o ).
thf(tp_bNF_re1703323451_b_b_b,type,
bNF_re1703323451_b_b_b: ( ( d > d ) > b > $o ) > ( b > b > $o ) > ( ( d > d ) > b ) > ( b > b ) > $o ).
thf(tp_bNF_re1705765981_a_a_a,type,
bNF_re1705765981_a_a_a: ( $o > $o > $o ) > ( ( a > a > a ) > ( a > a > a ) > $o ) > ( $o > a > a > a ) > ( $o > a > a > a ) > $o ).
thf(tp_bNF_re1709888353_d_d_d,type,
bNF_re1709888353_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( a > c > c ) > ( c > a ) > c > c > c ) > ( ( b > d > d ) > ( d > b ) > d > d > d ) > $o ) > ( ( c > c ) > ( a > c > c ) > ( c > a ) > c > c > c ) > ( ( d > d ) > ( b > d > d ) > ( d > b ) > d > d > d ) > $o ).
thf(tp_bNF_re1728528361_c_c_c,type,
bNF_re1728528361_c_c_c: ( b > b > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( b > c > c ) > ( b > c > c ) > $o ).
thf(tp_bNF_re1730737055_b_b_b,type,
bNF_re1730737055_b_b_b: ( a > b > $o ) > ( ( ( a > a ) > a ) > ( ( b > b ) > b ) > $o ) > ( a > ( a > a ) > a ) > ( b > ( b > b ) > b ) > $o ).
thf(tp_bNF_re1761470250_b_d_d,type,
bNF_re1761470250_b_d_d: ( ( a > a ) > ( b > b ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( b > b ) > b > d > d ) > $o ).
thf(tp_bNF_re1787520874_a_d_d,type,
bNF_re1787520874_a_d_d: ( ( a > a ) > ( a > b ) > $o ) > ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > a > c > c ) > ( ( a > b ) > a > d > d ) > $o ).
thf(tp_bNF_re1794062813_d_d_b,type,
bNF_re1794062813_d_d_b: ( ( b > b ) > ( ( d > d ) > b ) > $o ) > ( ( b > b ) > ( ( d > d ) > b ) > $o ) > ( ( b > b ) > b > b ) > ( ( ( d > d ) > b ) > ( d > d ) > b ) > $o ).
thf(tp_bNF_re1795127658_d_a_b,type,
bNF_re1795127658_d_a_b: ( ( c > c ) > ( d > d ) > $o ) > ( a > b > $o ) > ( ( c > c ) > a ) > ( ( d > d ) > b ) > $o ).
thf(tp_bNF_re1809376028_o_a_o,type,
bNF_re1809376028_o_a_o: ( a > a > $o ) > ( ( b > $o ) > ( a > $o ) > $o ) > ( a > b > $o ) > ( a > a > $o ) > $o ).
thf(tp_bNF_re1812319081_a_b_o,type,
bNF_re1812319081_a_b_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > b ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re1844863849_d_d_d,type,
bNF_re1844863849_d_d_d: ( b > b > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > ( b > d > d ) > $o ).
thf(tp_bNF_re1855937521_d_d_o,type,
bNF_re1855937521_d_d_o: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( b > d > d ) > $o ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > $o ).
thf(tp_bNF_re1867846365_a_a_o,type,
bNF_re1867846365_a_a_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1895239662_o_b_o,type,
bNF_re1895239662_o_b_o: ( ( c > c ) > a > $o ) > ( ( ( d > d ) > $o ) > ( b > $o ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > b > $o ) > $o ).
thf(tp_bNF_re1900831913_a_a_o,type,
bNF_re1900831913_a_a_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re1906994858_a_o_o,type,
bNF_re1906994858_a_o_o: ( ( a > b ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > b ) > $o ) > ( ( a > a ) > $o ) > $o ).
thf(tp_bNF_re19414301_d_d_o,type,
bNF_re19414301_d_d_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ) > ( ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > ( b > d > d ) > $o ) > $o ).
thf(tp_bNF_re1941803873_d_d_d,type,
bNF_re1941803873_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c > c > c ) > ( d > d > d > d ) > $o ) > ( ( c > c ) > c > c > c > c ) > ( ( d > d ) > d > d > d > d ) > $o ).
thf(tp_bNF_re1955249705_c_d_d,type,
bNF_re1955249705_c_d_d: ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( ( a > c > c ) > c > c ) > ( ( a > d > d ) > d > d ) > $o ).
thf(tp_bNF_re1972258794_c_d_d,type,
bNF_re1972258794_c_d_d: ( c > d > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( c > c > c ) > ( d > d > d ) > $o ).
thf(tp_bNF_re1977372894_o_a_o,type,
bNF_re1977372894_o_a_o: ( a > b > $o ) > ( ( a > $o ) > ( a > $o ) > $o ) > ( a > a > $o ) > ( b > a > $o ) > $o ).
thf(tp_bNF_re1979731817_c_d_d,type,
bNF_re1979731817_c_d_d: ( a > a > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( a > d > d ) > $o ).
thf(tp_bNF_re199323387_b_o_o,type,
bNF_re199323387_b_o_o: ( ( d > d ) > b > $o ) > ( $o > $o > $o ) > ( ( d > d ) > $o ) > ( b > $o ) > $o ).
thf(tp_bNF_re2038021754_d_d_a,type,
bNF_re2038021754_d_d_a: ( a > a > $o ) > ( ( d > d ) > a > $o ) > ( a > d > d ) > ( a > a ) > $o ).
thf(tp_bNF_re2038021755_d_d_b,type,
bNF_re2038021755_d_d_b: ( a > a > $o ) > ( ( d > d ) > b > $o ) > ( a > d > d ) > ( a > b ) > $o ).
thf(tp_bNF_re2038641070_o_b_o,type,
bNF_re2038641070_o_b_o: ( ( c > c ) > a > $o ) > ( ( ( c > c ) > $o ) > ( b > $o ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > b > $o ) > $o ).
thf(tp_bNF_re2074539676_a_o_o,type,
bNF_re2074539676_a_o_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( $o > $o > $o ) > ( ( a > c > c ) > $o ) > ( ( a > a ) > $o ) > $o ).
thf(tp_bNF_re2075418869_b_b_b,type,
bNF_re2075418869_b_b_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( b > b ) > ( b > b ) > $o ) > ( ( b > b ) > b > b ) > ( ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re2078100341_c_d_d,type,
bNF_re2078100341_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c ) > c > c ) > ( ( d > d ) > d > d ) > $o ).
thf(tp_bNF_re2087760490_b_a_b,type,
bNF_re2087760490_b_a_b: ( ( a > a ) > ( b > b ) > $o ) > ( a > b > $o ) > ( ( a > a ) > a ) > ( ( b > b ) > b ) > $o ).
thf(tp_bNF_re2114056618_c_c_c,type,
bNF_re2114056618_c_c_c: ( a > b > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( b > c > c ) > $o ).
thf(tp_bNF_re2120361759_d_d_d,type,
bNF_re2120361759_d_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( c > a ) > c > c > c ) > ( ( d > b ) > d > d > d ) > $o ) > ( ( a > c > c ) > ( c > a ) > c > c > c ) > ( ( b > d > d ) > ( d > b ) > d > d > d ) > $o ).
thf(tp_bNF_re2129955100_d_d_o,type,
bNF_re2129955100_d_d_o: ( ( a > a > $o ) > ( b > b > $o ) > $o ) > ( ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ) > ( ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ) > $o ) > ( ( a > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ) > ( ( b > b > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ) > $o ).
thf(tp_bNF_re2141181021_a_b_o,type,
bNF_re2141181021_a_b_o: ( ( a > b > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re231976415_a_a_o,type,
bNF_re231976415_a_a_o: ( ( a > b > $o ) > ( a > a > $o ) > $o ) > ( ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > ( ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re250254555_o_b_o,type,
bNF_re250254555_o_b_o: ( a > a > $o ) > ( ( b > $o ) > ( b > $o ) > $o ) > ( a > b > $o ) > ( a > b > $o ) > $o ).
thf(tp_bNF_re27458217_c_c_c,type,
bNF_re27458217_c_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( ( a > c > c ) > c > c ) > ( ( a > c > c ) > c > c ) > $o ).
thf(tp_bNF_re27482973_d_d_o,type,
bNF_re27482973_d_d_o: ( ( c > c > $o ) > ( d > d > $o ) > $o ) > ( ( ( c > c ) > $o ) > ( ( d > d ) > $o ) > $o ) > ( ( c > c > $o ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d ) > $o ) > $o ).
thf(tp_bNF_re310361461_b_a_a,type,
bNF_re310361461_b_a_a: ( ( b > b ) > ( a > a ) > $o ) > ( ( b > b ) > ( a > a ) > $o ) > ( ( b > b ) > b > b ) > ( ( a > a ) > a > a ) > $o ).
thf(tp_bNF_re323253981_b_b_b,type,
bNF_re323253981_b_b_b: ( ( ( d > d ) > b ) > ( b > b ) > $o ) > ( ( ( d > d ) > b ) > ( b > b ) > $o ) > ( ( ( d > d ) > b ) > ( d > d ) > b ) > ( ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re332737826_a_b_o,type,
bNF_re332737826_a_b_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > d > d ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > c > c ) > ( a > d > d ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re335372010_d_b_d,type,
bNF_re335372010_d_b_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( ( c > c ) > c ) > a > c ) > ( ( ( d > d ) > d ) > b > d ) > $o ) > ( ( c > c ) > ( ( c > c ) > c ) > a > c ) > ( ( d > d ) > ( ( d > d ) > d ) > b > d ) > $o ).
thf(tp_bNF_re35019871_b_d_d,type,
bNF_re35019871_b_d_d: ( ( ( c > c ) > a ) > ( ( d > d ) > b ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( c > c ) > a ) > a > c > c ) > ( ( ( d > d ) > b ) > b > d > d ) > $o ).
thf(tp_bNF_re364411746_a_b_o,type,
bNF_re364411746_a_b_o: ( ( a > c > c ) > ( a > a ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re364486559_b_d_d,type,
bNF_re364486559_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ) > ( ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ) > ( ( b > d > d ) > ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ) > $o ).
thf(tp_bNF_re38477224_d_c_c,type,
bNF_re38477224_d_c_c: ( b > a > $o ) > ( ( d > d ) > ( c > c ) > $o ) > ( b > d > d ) > ( a > c > c ) > $o ).
thf(tp_bNF_re387831090_b_d_d,type,
bNF_re387831090_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( ( c > c ) > a ) > a > c > c ) > ( ( ( d > d ) > b ) > b > d > d ) > $o ) > ( ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ) > ( ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ) > $o ).
thf(tp_bNF_re390230442_a_a_o,type,
bNF_re390230442_a_a_o: ( ( a > a ) > ( a > b ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > b ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re391428377_o_d_o,type,
bNF_re391428377_o_d_o: ( c > d > $o ) > ( ( c > $o ) > ( d > $o ) > $o ) > ( c > c > $o ) > ( d > d > $o ) > $o ).
thf(tp_bNF_re417075625_c_d_d,type,
bNF_re417075625_c_d_d: ( b > b > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( b > c > c ) > ( b > d > d ) > $o ).
thf(tp_bNF_re418251421_o_b_o,type,
bNF_re418251421_o_b_o: ( a > b > $o ) > ( ( a > $o ) > ( b > $o ) > $o ) > ( a > a > $o ) > ( b > b > $o ) > $o ).
thf(tp_bNF_re473406379_b_a_b,type,
bNF_re473406379_b_a_b: ( ( a > a ) > ( a > b ) > $o ) > ( a > b > $o ) > ( ( a > a ) > a ) > ( ( a > b ) > b ) > $o ).
thf(tp_bNF_re539937469_b_a_a,type,
bNF_re539937469_b_a_a: ( ( a > a ) > ( b > a ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > b ) > a > a ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( b > a ) > ( a > b ) > a > a ) > $o ).
thf(tp_bNF_re561231771_a_c_c,type,
bNF_re561231771_a_c_c: ( ( b > d > d ) > ( a > c > c ) > $o ) > ( ( ( b > b ) > b > d > d ) > ( ( a > a ) > a > c > c ) > $o ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > $o ).
thf(tp_bNF_re569932906_a_b_b,type,
bNF_re569932906_a_b_b: ( a > b > $o ) > ( ( a > a ) > ( b > b ) > $o ) > ( a > a > a ) > ( b > b > b ) > $o ).
thf(tp_bNF_re571457705_a_a_a,type,
bNF_re571457705_a_a_a: ( ( a > a ) > ( a > a ) > $o ) > ( a > a > $o ) > ( ( a > a ) > a ) > ( ( a > a ) > a ) > $o ).
thf(tp_bNF_re581117672_a_b_o,type,
bNF_re581117672_a_b_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > a ) > $o ) > ( ( a > b ) > $o ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re588060702_b_b_b,type,
bNF_re588060702_b_b_b: ( $o > $o > $o ) > ( ( a > a > a ) > ( b > b > b ) > $o ) > ( $o > a > a > a ) > ( $o > b > b > b ) > $o ).
thf(tp_bNF_re631104669_a_d_d,type,
bNF_re631104669_a_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( a > b ) > a > d > d ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( b > d > d ) > ( a > b ) > a > d > d ) > $o ).
thf(tp_bNF_re647211934_d_d_d,type,
bNF_re647211934_d_d_d: ( $o > $o > $o ) > ( ( c > c > c ) > ( d > d > d ) > $o ) > ( $o > c > c > c ) > ( $o > d > d > d ) > $o ).
thf(tp_bNF_re668686835_a_b_b,type,
bNF_re668686835_a_b_b: ( ( b > a ) > ( b > b ) > $o ) > ( ( b > a ) > ( b > b ) > $o ) > ( ( b > a ) > b > a ) > ( ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re674980784_d_d_o,type,
bNF_re674980784_d_d_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ) > ( ( ( a > c > c ) > $o ) > ( ( b > d > d ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ) > ( ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ) > $o ).
thf(tp_bNF_re692482399_b_d_d,type,
bNF_re692482399_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > c > c ) > a > c > c ) > ( ( b > d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re708047067_a_b_o,type,
bNF_re708047067_a_b_o: ( ( ( c > c ) > ( c > c ) > $o ) > ( a > b > $o ) > $o ) > ( ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ) > $o ).
thf(tp_bNF_re727696351_d_b_d,type,
bNF_re727696351_d_b_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( ( c > c ) > ( ( c > c ) > c ) > a > c ) > ( ( d > d ) > ( ( d > d ) > d ) > b > d ) > $o ) > ( ( a > c > c ) > ( c > c ) > ( ( c > c ) > c ) > a > c ) > ( ( b > d > d ) > ( d > d ) > ( ( d > d ) > d ) > b > d ) > $o ).
thf(tp_bNF_re742509149_b_d_d,type,
bNF_re742509149_b_d_d: ( ( b > d > d ) > ( b > d > d ) > $o ) > ( ( ( b > b ) > b > d > d ) > ( ( b > b ) > b > d > d ) > $o ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > $o ).
thf(tp_bNF_re758172648_c_c_c,type,
bNF_re758172648_c_c_c: ( b > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( b > c > c ) > ( a > c > c ) > $o ).
thf(tp_bNF_re764096061_d_d_d,type,
bNF_re764096061_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( c > c ) > c > c ) > ( ( d > d ) > d > d ) > $o ) > ( ( c > c ) > ( c > c ) > c > c ) > ( ( d > d ) > ( d > d ) > d > d ) > $o ).
thf(tp_bNF_re764708765_d_d_o,type,
bNF_re764708765_d_d_o: ( ( c > c > $o ) > ( d > d > $o ) > $o ) > ( ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ) > ( ( c > c > $o ) > ( c > c ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d ) > ( d > d ) > $o ) > $o ).
thf(tp_bNF_re774352699_b_b_b,type,
bNF_re774352699_b_b_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( b > a ) > b > a ) > ( ( b > b ) > b > b ) > $o ) > ( ( a > a ) > ( b > a ) > b > a ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re781155241_d_d_o,type,
bNF_re781155241_d_d_o: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( c > c ) > $o ) > ( ( d > d ) > $o ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > $o ).
thf(tp_bNF_re796114495_b_a_b,type,
bNF_re796114495_b_a_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( a > b ) > a > b ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( b > b ) > ( a > b ) > a > b ) > $o ).
thf(tp_bNF_re802276445_b_o_o,type,
bNF_re802276445_b_o_o: ( ( a > d > d ) > ( a > b ) > $o ) > ( $o > $o > $o ) > ( ( a > d > d ) > $o ) > ( ( a > b ) > $o ) > $o ).
thf(tp_bNF_re802603882_c_d_d,type,
bNF_re802603882_c_d_d: ( a > b > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( a > c > c ) > ( b > d > d ) > $o ).
thf(tp_bNF_re822780063_d_d_d,type,
bNF_re822780063_d_d_d: ( c > d > $o ) > ( ( c > c > c ) > ( d > d > d ) > $o ) > ( c > c > c > c ) > ( d > d > d > d ) > $o ).
thf(tp_bNF_re835672381_b_b_b,type,
bNF_re835672381_b_b_b: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( a > a ) > a > a ) > ( ( b > b ) > b > b ) > $o ) > ( ( a > a ) > ( a > a ) > a > a ) > ( ( b > b ) > ( b > b ) > b > b ) > $o ).
thf(tp_bNF_re84044842_c_d_d,type,
bNF_re84044842_c_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( ( a > c > c ) > c > c ) > ( ( b > d > d ) > d > d ) > $o ).
thf(tp_bNF_re857382262_a_a_a,type,
bNF_re857382262_a_a_a: ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > b ) > a > a ) > $o ).
thf(tp_bNF_re857878889_d_o_o,type,
bNF_re857878889_d_o_o: ( ( c > c ) > ( d > d ) > $o ) > ( $o > $o > $o ) > ( ( c > c ) > $o ) > ( ( d > d ) > $o ) > $o ).
thf(tp_bNF_re865643767_a_a_b,type,
bNF_re865643767_a_a_b: ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > a > a ) > ( ( a > b ) > a > b ) > $o ).
thf(tp_bNF_re865741149_a_a_a,type,
bNF_re865741149_a_a_a: ( a > a > $o ) > ( ( ( a > a ) > a ) > ( ( a > a ) > a ) > $o ) > ( a > ( a > a ) > a ) > ( a > ( a > a ) > a ) > $o ).
thf(tp_bNF_re880840541_a_c_c,type,
bNF_re880840541_a_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( a > a ) > a > c > c ) > ( ( a > a ) > a > c > c ) > $o ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > $o ).
thf(tp_bNF_re883196986_a_o_o,type,
bNF_re883196986_a_o_o: ( ( c > c ) > a > $o ) > ( $o > $o > $o ) > ( ( c > c ) > $o ) > ( a > $o ) > $o ).
thf(tp_bNF_re888371717_d_d_d,type,
bNF_re888371717_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( ( c > c ) > ( c > c ) > c > c ) > ( ( d > d ) > ( d > d ) > d > d ) > $o ) > ( ( c > c ) > ( c > c ) > ( c > c ) > c > c ) > ( ( d > d ) > ( d > d ) > ( d > d ) > d > d ) > $o ).
thf(tp_bNF_re90976443_b_o_o,type,
bNF_re90976443_b_o_o: ( ( c > c ) > b > $o ) > ( $o > $o > $o ) > ( ( c > c ) > $o ) > ( b > $o ) > $o ).
thf(tp_bNF_re911029929_a_a_a,type,
bNF_re911029929_a_a_a: ( a > a > $o ) > ( ( a > a ) > ( a > a ) > $o ) > ( a > a > a ) > ( a > a > a ) > $o ).
thf(tp_bNF_re921674337_d_d_o,type,
bNF_re921674337_d_d_o: ( ( c > c > $o ) > ( d > d > $o ) > $o ) > ( ( ( c > c > $o ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d ) > $o ) > $o ) > ( ( c > c > $o ) > ( c > c > $o ) > ( c > c ) > $o ) > ( ( d > d > $o ) > ( d > d > $o ) > ( d > d ) > $o ) > $o ).
thf(tp_bNF_re932551557_b_d_d,type,
bNF_re932551557_b_d_d: ( ( a > a ) > ( b > b ) > $o ) > ( ( ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ) > ( ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ) > $o ) > ( ( a > a ) > ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ) > ( ( b > b ) > ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ) > $o ).
thf(tp_bNF_re950444090_c_c_a,type,
bNF_re950444090_c_c_a: ( a > a > $o ) > ( ( c > c ) > a > $o ) > ( a > c > c ) > ( a > a ) > $o ).
thf(tp_bNF_re950444091_c_c_b,type,
bNF_re950444091_c_c_b: ( a > a > $o ) > ( ( c > c ) > b > $o ) > ( a > c > c ) > ( a > b ) > $o ).
thf(tp_bNF_re961930425_d_d_b,type,
bNF_re961930425_d_d_b: ( ( b > b ) > ( b > b ) > $o ) > ( ( ( b > b ) > b > b ) > ( ( ( d > d ) > b ) > ( d > d ) > b ) > $o ) > ( ( b > b ) > ( b > b ) > b > b ) > ( ( b > b ) > ( ( d > d ) > b ) > ( d > d ) > b ) > $o ).
thf(tp_bNF_re978949211_a_c_c,type,
bNF_re978949211_a_c_c: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( ( b > a ) > b > c > c ) > ( ( a > a ) > a > c > c ) > $o ) > ( ( a > c > c ) > ( b > a ) > b > c > c ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > $o ).
thf(tp_bNF_re984549674_a_a_o,type,
bNF_re984549674_a_a_o: ( ( a > a ) > ( a > a ) > $o ) > ( ( ( a > b ) > $o ) > ( ( a > a ) > $o ) > $o ) > ( ( a > a ) > ( a > b ) > $o ) > ( ( a > a ) > ( a > a ) > $o ) > $o ).
thf(tp_bNF_re991543930_a_o_o,type,
bNF_re991543930_a_o_o: ( ( d > d ) > a > $o ) > ( $o > $o > $o ) > ( ( d > d ) > $o ) > ( a > $o ) > $o ).
thf(tp_bNF_rel_fun_a_a_a_a,type,
bNF_rel_fun_a_a_a_a: ( a > a > $o ) > ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ).
thf(tp_bNF_rel_fun_a_a_a_b,type,
bNF_rel_fun_a_a_a_b: ( a > a > $o ) > ( a > b > $o ) > ( a > a ) > ( a > b ) > $o ).
thf(tp_bNF_rel_fun_a_a_b_a,type,
bNF_rel_fun_a_a_b_a: ( a > a > $o ) > ( b > a > $o ) > ( a > b ) > ( a > a ) > $o ).
thf(tp_bNF_rel_fun_a_a_b_b,type,
bNF_rel_fun_a_a_b_b: ( a > a > $o ) > ( b > b > $o ) > ( a > b ) > ( a > b ) > $o ).
thf(tp_bNF_rel_fun_a_a_o_o,type,
bNF_rel_fun_a_a_o_o: ( a > a > $o ) > ( $o > $o > $o ) > ( a > $o ) > ( a > $o ) > $o ).
thf(tp_bNF_rel_fun_a_b_a_a,type,
bNF_rel_fun_a_b_a_a: ( a > b > $o ) > ( a > a > $o ) > ( a > a ) > ( b > a ) > $o ).
thf(tp_bNF_rel_fun_a_b_a_b,type,
bNF_rel_fun_a_b_a_b: ( a > b > $o ) > ( a > b > $o ) > ( a > a ) > ( b > b ) > $o ).
thf(tp_bNF_rel_fun_a_b_c_d,type,
bNF_rel_fun_a_b_c_d: ( a > b > $o ) > ( c > d > $o ) > ( a > c ) > ( b > d ) > $o ).
thf(tp_bNF_rel_fun_a_b_o_o,type,
bNF_rel_fun_a_b_o_o: ( a > b > $o ) > ( $o > $o > $o ) > ( a > $o ) > ( b > $o ) > $o ).
thf(tp_bNF_rel_fun_b_a_a_a,type,
bNF_rel_fun_b_a_a_a: ( b > a > $o ) > ( a > a > $o ) > ( b > a ) > ( a > a ) > $o ).
thf(tp_bNF_rel_fun_b_a_b_a,type,
bNF_rel_fun_b_a_b_a: ( b > a > $o ) > ( b > a > $o ) > ( b > b ) > ( a > a ) > $o ).
thf(tp_bNF_rel_fun_b_a_o_o,type,
bNF_rel_fun_b_a_o_o: ( b > a > $o ) > ( $o > $o > $o ) > ( b > $o ) > ( a > $o ) > $o ).
thf(tp_bNF_rel_fun_b_b_a_a,type,
bNF_rel_fun_b_b_a_a: ( b > b > $o ) > ( a > a > $o ) > ( b > a ) > ( b > a ) > $o ).
thf(tp_bNF_rel_fun_b_b_a_b,type,
bNF_rel_fun_b_b_a_b: ( b > b > $o ) > ( a > b > $o ) > ( b > a ) > ( b > b ) > $o ).
thf(tp_bNF_rel_fun_b_b_b_b,type,
bNF_rel_fun_b_b_b_b: ( b > b > $o ) > ( b > b > $o ) > ( b > b ) > ( b > b ) > $o ).
thf(tp_bNF_rel_fun_b_b_o_o,type,
bNF_rel_fun_b_b_o_o: ( b > b > $o ) > ( $o > $o > $o ) > ( b > $o ) > ( b > $o ) > $o ).
thf(tp_bNF_rel_fun_c_c_c_c,type,
bNF_rel_fun_c_c_c_c: ( c > c > $o ) > ( c > c > $o ) > ( c > c ) > ( c > c ) > $o ).
thf(tp_bNF_rel_fun_c_d_a_b,type,
bNF_rel_fun_c_d_a_b: ( c > d > $o ) > ( a > b > $o ) > ( c > a ) > ( d > b ) > $o ).
thf(tp_bNF_rel_fun_c_d_c_d,type,
bNF_rel_fun_c_d_c_d: ( c > d > $o ) > ( c > d > $o ) > ( c > c ) > ( d > d ) > $o ).
thf(tp_bNF_rel_fun_c_d_o_o,type,
bNF_rel_fun_c_d_o_o: ( c > d > $o ) > ( $o > $o > $o ) > ( c > $o ) > ( d > $o ) > $o ).
thf(tp_bNF_rel_fun_d_d_d_d,type,
bNF_rel_fun_d_d_d_d: ( d > d > $o ) > ( d > d > $o ) > ( d > d ) > ( d > d ) > $o ).
thf(tp_bi_total_a_b,type,
bi_total_a_b: ( a > b > $o ) > $o ).
thf(tp_bi_total_a_c_c_b_d_d,type,
bi_total_a_c_c_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_bi_total_c_c_d_d,type,
bi_total_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_bi_total_c_d,type,
bi_total_c_d: ( c > d > $o ) > $o ).
thf(tp_bi_uni844770768_b_d_d,type,
bi_uni844770768_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_bi_unique_a_b,type,
bi_unique_a_b: ( a > b > $o ) > $o ).
thf(tp_bi_unique_c_c_d_d,type,
bi_unique_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_bi_unique_c_d,type,
bi_unique_c_d: ( c > d > $o ) > $o ).
thf(tp_collect_a,type,
collect_a: ( a > $o ) > set_a ).
thf(tp_collect_b,type,
collect_b: ( b > $o ) > set_b ).
thf(tp_collect_c,type,
collect_c: ( c > $o ) > set_c ).
thf(tp_collect_d,type,
collect_d: ( d > $o ) > set_d ).
thf(tp_comp_a_a_a,type,
comp_a_a_a: ( a > a ) > ( a > a ) > a > a ).
thf(tp_comp_a_a_a_c_c_c_c_a,type,
comp_a_a_a_c_c_c_c_a: ( ( a > a ) > a > c > c ) > ( ( ( c > c ) > a ) > a > a ) > ( ( c > c ) > a ) > a > c > c ).
thf(tp_comp_a_a_b,type,
comp_a_a_b: ( a > a ) > ( b > a ) > b > a ).
thf(tp_comp_a_a_c_c,type,
comp_a_a_c_c: ( a > a ) > ( ( c > c ) > a ) > ( c > c ) > a ).
thf(tp_comp_a_b_a,type,
comp_a_b_a: ( a > b ) > ( a > a ) > a > b ).
thf(tp_comp_a_b_a_d_d_c_c_b,type,
comp_a_b_a_d_d_c_c_b: ( ( a > b ) > a > d > d ) > ( ( ( c > c ) > b ) > a > b ) > ( ( c > c ) > b ) > a > d > d ).
thf(tp_comp_a_b_b,type,
comp_a_b_b: ( a > b ) > ( b > a ) > b > b ).
thf(tp_comp_a_c_c_a,type,
comp_a_c_c_a: ( a > c > c ) > ( a > a ) > a > c > c ).
thf(tp_comp_a_c_c_b,type,
comp_a_c_c_b: ( a > c > c ) > ( b > a ) > b > c > c ).
thf(tp_comp_b_a_a,type,
comp_b_a_a: ( b > a ) > ( a > b ) > a > a ).
thf(tp_comp_b_a_b,type,
comp_b_a_b: ( b > a ) > ( b > b ) > b > a ).
thf(tp_comp_b_a_b_c_c_d_d_a,type,
comp_b_a_b_c_c_d_d_a: ( ( b > a ) > b > c > c ) > ( ( ( d > d ) > a ) > b > a ) > ( ( d > d ) > a ) > b > c > c ).
thf(tp_comp_b_b_a,type,
comp_b_b_a: ( b > b ) > ( a > b ) > a > b ).
thf(tp_comp_b_b_b,type,
comp_b_b_b: ( b > b ) > ( b > b ) > b > b ).
thf(tp_comp_b_b_b_d_d_d_d_b,type,
comp_b_b_b_d_d_d_d_b: ( ( b > b ) > b > d > d ) > ( ( ( d > d ) > b ) > b > b ) > ( ( d > d ) > b ) > b > d > d ).
thf(tp_comp_b_b_d_d,type,
comp_b_b_d_d: ( b > b ) > ( ( d > d ) > b ) > ( d > d ) > b ).
thf(tp_comp_b_c_c_a,type,
comp_b_c_c_a: ( b > c > c ) > ( a > b ) > a > c > c ).
thf(tp_comp_b_c_c_b,type,
comp_b_c_c_b: ( b > c > c ) > ( b > b ) > b > c > c ).
thf(tp_comp_b_d_d_a,type,
comp_b_d_d_a: ( b > d > d ) > ( a > b ) > a > d > d ).
thf(tp_comp_b_d_d_b,type,
comp_b_d_d_b: ( b > d > d ) > ( b > b ) > b > d > d ).
thf(tp_comp_c_c_a_a,type,
comp_c_c_a_a: ( ( c > c ) > a ) > ( a > c > c ) > a > a ).
thf(tp_comp_c_c_a_c_c,type,
comp_c_c_a_c_c: ( ( c > c ) > a ) > ( ( c > c ) > c > c ) > ( c > c ) > a ).
thf(tp_comp_c_c_b_a,type,
comp_c_c_b_a: ( ( c > c ) > b ) > ( a > c > c ) > a > b ).
thf(tp_comp_c_c_b_b,type,
comp_c_c_b_b: ( ( c > c ) > b ) > ( b > c > c ) > b > b ).
thf(tp_comp_c_c_c,type,
comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).
thf(tp_comp_c_c_c_c_a,type,
comp_c_c_c_c_a: ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ).
thf(tp_comp_d_d_b_b,type,
comp_d_d_b_b: ( ( d > d ) > b ) > ( b > d > d ) > b > b ).
thf(tp_comp_d_d_d,type,
comp_d_d_d: ( d > d ) > ( d > d ) > d > d ).
thf(tp_comp_d_d_d_d_b,type,
comp_d_d_d_d_b: ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ).
thf(tp_comple1615148455ne_d_d,type,
comple1615148455ne_d_d: ( d > d > $o ) > ( d > d > $o ) > ( d > d ) > $o ).
thf(tp_comple1702356924_a_c_c,type,
comple1702356924_a_c_c: ( a > a > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > $o ).
thf(tp_comple61207421_b_d_d,type,
comple61207421_b_d_d: ( b > b > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > $o ).
thf(tp_comple787379047ne_c_c,type,
comple787379047ne_c_c: ( c > c > $o ) > ( c > c > $o ) > ( c > c ) > $o ).
thf(tp_f1,type,
f1: a > c > c ).
thf(tp_f2,type,
f2: b > d > d ).
thf(tp_ffold_a_c,type,
ffold_a_c: ( a > c > c ) > c > fset_a > c ).
thf(tp_ffold_b_d,type,
ffold_b_d: ( b > d > d ) > d > fset_b > d ).
thf(tp_finite1019684932ph_c_a,type,
finite1019684932ph_c_a: ( c > a > a ) > a > set_c > a > $o ).
thf(tp_finite1019684933ph_c_b,type,
finite1019684933ph_c_b: ( c > b > b ) > b > set_c > b > $o ).
thf(tp_finite1019684934ph_c_c,type,
finite1019684934ph_c_c: ( c > c > c ) > c > set_c > c > $o ).
thf(tp_finite1019684935ph_c_d,type,
finite1019684935ph_c_d: ( c > d > d ) > d > set_c > d > $o ).
thf(tp_finite1511629766ph_a_a,type,
finite1511629766ph_a_a: ( a > a > a ) > a > set_a > a > $o ).
thf(tp_finite1511629767ph_a_b,type,
finite1511629767ph_a_b: ( a > b > b ) > b > set_a > b > $o ).
thf(tp_finite1511629768ph_a_c,type,
finite1511629768ph_a_c: ( a > c > c ) > c > set_a > c > $o ).
thf(tp_finite1511629769ph_a_d,type,
finite1511629769ph_a_d: ( a > d > d ) > d > set_a > d > $o ).
thf(tp_finite1574384658te_b_c,type,
finite1574384658te_b_c: ( b > c > c ) > $o ).
thf(tp_finite1574384659te_b_d,type,
finite1574384659te_b_d: ( b > d > d ) > $o ).
thf(tp_finite191915525ph_b_a,type,
finite191915525ph_b_a: ( b > a > a ) > a > set_b > a > $o ).
thf(tp_finite191915528ph_b_d,type,
finite191915528ph_b_d: ( b > d > d ) > d > set_b > d > $o ).
thf(tp_finite19304177ms_a_c,type,
finite19304177ms_a_c: ( a > c > c ) > $o ).
thf(tp_finite40241358em_a_c,type,
finite40241358em_a_c: ( a > c > c ) > $o ).
thf(tp_finite746615251te_a_c,type,
finite746615251te_a_c: ( a > c > c ) > $o ).
thf(tp_finite847073585ms_b_d,type,
finite847073585ms_b_d: ( b > d > d ) > $o ).
thf(tp_finite868010765em_b_c,type,
finite868010765em_b_c: ( b > c > c ) > $o ).
thf(tp_finite868010766em_b_d,type,
finite868010766em_b_d: ( b > d > d ) > $o ).
thf(tp_fold_mset_a_c,type,
fold_mset_a_c: ( a > c > c ) > c > multiset_a > c ).
thf(tp_fold_mset_b_d,type,
fold_mset_b_d: ( b > d > d ) > d > multiset_b > d ).
thf(tp_fun_upd_a_c_c,type,
fun_upd_a_c_c: ( a > c > c ) > a > ( c > c ) > a > c > c ).
thf(tp_fun_upd_b_d_d,type,
fun_upd_b_d_d: ( b > d > d ) > b > ( d > d ) > b > d > d ).
thf(tp_fun_upd_c_c,type,
fun_upd_c_c: ( c > c ) > c > c > c > c ).
thf(tp_fun_upd_d_d,type,
fun_upd_d_d: ( d > d ) > d > d > d > d ).
thf(tp_if_a,type,
if_a: $o > a > a > a ).
thf(tp_if_b,type,
if_b: $o > b > b > b ).
thf(tp_if_c,type,
if_c: $o > c > c > c ).
thf(tp_if_d,type,
if_d: $o > d > d > d ).
thf(tp_left_t1993719015_b_d_d,type,
left_t1993719015_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_left_total_a_b,type,
left_total_a_b: ( a > b > $o ) > $o ).
thf(tp_left_total_b_b,type,
left_total_b_b: ( b > b > $o ) > $o ).
thf(tp_left_total_c_c_d_d,type,
left_total_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_left_total_c_d,type,
left_total_c_d: ( c > d > $o ) > $o ).
thf(tp_left_total_d_d,type,
left_total_d_d: ( d > d > $o ) > $o ).
thf(tp_left_u1654071760_b_d_d,type,
left_u1654071760_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_left_unique_a_a,type,
left_unique_a_a: ( a > a > $o ) > $o ).
thf(tp_left_unique_a_b,type,
left_unique_a_b: ( a > b > $o ) > $o ).
thf(tp_left_unique_c_c,type,
left_unique_c_c: ( c > c > $o ) > $o ).
thf(tp_left_unique_c_c_d_d,type,
left_unique_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_left_unique_c_d,type,
left_unique_c_d: ( c > d > $o ) > $o ).
thf(tp_left_unique_d_d,type,
left_unique_d_d: ( d > d > $o ) > $o ).
thf(tp_left_unique_d_d_d_d,type,
left_unique_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > $o ).
thf(tp_map_fu1569200227_b_d_d,type,
map_fu1569200227_b_d_d: ( ( b > b ) > a > a ) > ( ( a > c > c ) > b > d > d ) > ( ( a > a ) > a > c > c ) > ( b > b ) > b > d > d ).
thf(tp_map_fu232832790_a_c_c,type,
map_fu232832790_a_c_c: ( ( a > c > c ) > b > d > d ) > ( ( ( b > b ) > b > d > d ) > ( a > a ) > a > c > c ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( a > c > c ) > ( a > a ) > a > c > c ).
thf(tp_map_fu538233110_b_d_d,type,
map_fu538233110_b_d_d: ( ( b > d > d ) > b > d > d ) > ( ( ( b > b ) > b > d > d ) > ( b > b ) > b > d > d ) > ( ( b > d > d ) > ( b > b ) > b > d > d ) > ( b > d > d ) > ( b > b ) > b > d > d ).
thf(tp_map_fu676564502_a_c_c,type,
map_fu676564502_a_c_c: ( ( a > c > c ) > a > c > c ) > ( ( ( a > a ) > a > c > c ) > ( a > a ) > a > c > c ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( a > c > c ) > ( a > a ) > a > c > c ).
thf(tp_map_fu683206690_b_d_d,type,
map_fu683206690_b_d_d: ( ( b > b ) > b > b ) > ( ( b > d > d ) > b > d > d ) > ( ( b > b ) > b > d > d ) > ( b > b ) > b > d > d ).
thf(tp_map_fu75729569_a_c_c,type,
map_fu75729569_a_c_c: ( ( a > a ) > b > b ) > ( ( b > d > d ) > a > c > c ) > ( ( b > b ) > b > d > d ) > ( a > a ) > a > c > c ).
thf(tp_map_fu961723106_a_c_c,type,
map_fu961723106_a_c_c: ( ( a > a ) > a > a ) > ( ( a > c > c ) > a > c > c ) > ( ( a > a ) > a > c > c ) > ( a > a ) > a > c > c ).
thf(tp_map_fu981964822_b_d_d,type,
map_fu981964822_b_d_d: ( ( b > d > d ) > a > c > c ) > ( ( ( a > a ) > a > c > c ) > ( b > b ) > b > d > d ) > ( ( a > c > c ) > ( a > a ) > a > c > c ) > ( b > d > d ) > ( b > b ) > b > d > d ).
thf(tp_map_fun_a_a_a_a,type,
map_fun_a_a_a_a: ( a > a ) > ( a > a ) > ( a > a ) > a > a ).
thf(tp_map_fun_a_a_a_c_c,type,
map_fun_a_a_a_c_c: ( a > a ) > ( a > c > c ) > ( a > a ) > a > c > c ).
thf(tp_map_fun_a_a_b_d_d,type,
map_fun_a_a_b_d_d: ( a > a ) > ( b > d > d ) > ( a > b ) > a > d > d ).
thf(tp_map_fun_a_a_c_c_c_c,type,
map_fun_a_a_c_c_c_c: ( a > a ) > ( ( c > c ) > c > c ) > ( a > c > c ) > a > c > c ).
thf(tp_map_fun_a_b_b_a,type,
map_fun_a_b_b_a: ( a > b ) > ( b > a ) > ( b > b ) > a > a ).
thf(tp_map_fun_a_b_d_d_c_c,type,
map_fun_a_b_d_d_c_c: ( a > b ) > ( ( d > d ) > c > c ) > ( b > d > d ) > a > c > c ).
thf(tp_map_fun_a_c_c_a_a,type,
map_fun_a_c_c_a_a: ( a > c > c ) > ( a > a ) > ( ( c > c ) > a ) > a > a ).
thf(tp_map_fun_a_c_c_a_c_c,type,
map_fun_a_c_c_a_c_c: ( a > c > c ) > ( a > c > c ) > ( ( c > c ) > a ) > a > c > c ).
thf(tp_map_fun_a_c_c_b_b,type,
map_fun_a_c_c_b_b: ( a > c > c ) > ( b > b ) > ( ( c > c ) > b ) > a > b ).
thf(tp_map_fun_a_c_c_b_d_d,type,
map_fun_a_c_c_b_d_d: ( a > c > c ) > ( b > d > d ) > ( ( c > c ) > b ) > a > d > d ).
thf(tp_map_fun_a_c_c_c_c,type,
map_fun_a_c_c_c_c: ( a > c > c ) > ( c > c ) > ( ( c > c ) > c ) > a > c ).
thf(tp_map_fun_a_c_c_c_c2,type,
map_fun_a_c_c_c_c2: ( a > c ) > ( c > c > c ) > ( c > c ) > a > c > c ).
thf(tp_map_fun_b_a_a_b,type,
map_fun_b_a_a_b: ( b > a ) > ( a > b ) > ( a > a ) > b > b ).
thf(tp_map_fun_b_a_c_c_d_d,type,
map_fun_b_a_c_c_d_d: ( b > a ) > ( ( c > c ) > d > d ) > ( a > c > c ) > b > d > d ).
thf(tp_map_fun_b_b_a_c_c,type,
map_fun_b_b_a_c_c: ( b > b ) > ( a > c > c ) > ( b > a ) > b > c > c ).
thf(tp_map_fun_b_b_b_b,type,
map_fun_b_b_b_b: ( b > b ) > ( b > b ) > ( b > b ) > b > b ).
thf(tp_map_fun_b_b_b_d_d,type,
map_fun_b_b_b_d_d: ( b > b ) > ( b > d > d ) > ( b > b ) > b > d > d ).
thf(tp_map_fun_b_b_d_d_d_d,type,
map_fun_b_b_d_d_d_d: ( b > b ) > ( ( d > d ) > d > d ) > ( b > d > d ) > b > d > d ).
thf(tp_map_fun_b_d_d_a_a,type,
map_fun_b_d_d_a_a: ( b > d > d ) > ( a > a ) > ( ( d > d ) > a ) > b > a ).
thf(tp_map_fun_b_d_d_a_c_c,type,
map_fun_b_d_d_a_c_c: ( b > d > d ) > ( a > c > c ) > ( ( d > d ) > a ) > b > c > c ).
thf(tp_map_fun_b_d_d_b_b,type,
map_fun_b_d_d_b_b: ( b > d > d ) > ( b > b ) > ( ( d > d ) > b ) > b > b ).
thf(tp_map_fun_b_d_d_b_d_d,type,
map_fun_b_d_d_b_d_d: ( b > d > d ) > ( b > d > d ) > ( ( d > d ) > b ) > b > d > d ).
thf(tp_map_fun_b_d_d_d_d,type,
map_fun_b_d_d_d_d: ( b > d > d ) > ( d > d ) > ( ( d > d ) > d ) > b > d ).
thf(tp_map_fun_b_d_d_d_d2,type,
map_fun_b_d_d_d_d2: ( b > d ) > ( d > d > d ) > ( d > d ) > b > d > d ).
thf(tp_map_fun_c_a_c_c_c,type,
map_fun_c_a_c_c_c: ( c > a ) > ( ( c > c ) > c ) > ( a > c > c ) > c > c ).
thf(tp_map_fun_c_c_a_c_c,type,
map_fun_c_c_a_c_c: ( c > c ) > ( a > c > c ) > ( c > a ) > c > c > c ).
thf(tp_map_fun_c_c_c_c,type,
map_fun_c_c_c_c: ( c > c ) > ( c > c ) > ( c > c ) > c > c ).
thf(tp_map_fun_d_b_d_d_d,type,
map_fun_d_b_d_d_d: ( d > b ) > ( ( d > d ) > d ) > ( b > d > d ) > d > d ).
thf(tp_map_fun_d_d_b_d_d,type,
map_fun_d_d_b_d_d: ( d > d ) > ( b > d > d ) > ( d > b ) > d > d > d ).
thf(tp_map_fun_d_d_d_d,type,
map_fun_d_d_d_d: ( d > d ) > ( d > d ) > ( d > d ) > d > d ).
thf(tp_member_a,type,
member_a: a > set_a > $o ).
thf(tp_member_b,type,
member_b: b > set_b > $o ).
thf(tp_member_c,type,
member_c: c > set_c > $o ).
thf(tp_member_d,type,
member_d: d > set_d > $o ).
thf(tp_ord_le1338099484_d_d_o,type,
ord_le1338099484_d_d_o: ( ( c > c ) > ( d > d ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_ord_le469275661_d_d_o,type,
ord_le469275661_d_d_o: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_ord_less_eq_a_b_o,type,
ord_less_eq_a_b_o: ( a > b > $o ) > ( a > b > $o ) > $o ).
thf(tp_ord_less_eq_c_d_o,type,
ord_less_eq_c_d_o: ( c > d > $o ) > ( c > d > $o ) > $o ).
thf(tp_partia1041982257_d_d_d,type,
partia1041982257_d_d_d: ( d > d > $o ) > ( d > d ) > ( d > d ) > $o ).
thf(tp_partia1494029680_c_c_c,type,
partia1494029680_c_c_c: ( c > c > $o ) > ( c > c ) > ( c > c ) > $o ).
thf(tp_partia1709452835_d_d_b,type,
partia1709452835_d_d_b: ( ( d > d ) > ( d > d ) > $o ) > ( b > d > d ) > ( b > d > d ) > $o ).
thf(tp_partia186872226_c_c_a,type,
partia186872226_c_c_a: ( ( c > c ) > ( c > c ) > $o ) > ( a > c > c ) > ( a > c > c ) > $o ).
thf(tp_plus_plus_multiset_a,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(tp_plus_plus_multiset_b,type,
plus_plus_multiset_b: multiset_b > multiset_b > multiset_b ).
thf(tp_quotient3_a_a,type,
quotient3_a_a: ( a > a > $o ) > ( a > a ) > ( a > a ) > $o ).
thf(tp_quotient3_a_b,type,
quotient3_a_b: ( a > a > $o ) > ( a > b ) > ( b > a ) > $o ).
thf(tp_quotient3_a_c_c,type,
quotient3_a_c_c: ( a > a > $o ) > ( a > c > c ) > ( ( c > c ) > a ) > $o ).
thf(tp_quotient3_b_a,type,
quotient3_b_a: ( b > b > $o ) > ( b > a ) > ( a > b ) > $o ).
thf(tp_quotient3_b_b,type,
quotient3_b_b: ( b > b > $o ) > ( b > b ) > ( b > b ) > $o ).
thf(tp_quotient3_b_d_d,type,
quotient3_b_d_d: ( b > b > $o ) > ( b > d > d ) > ( ( d > d ) > b ) > $o ).
thf(tp_quotient3_c_c_a,type,
quotient3_c_c_a: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > a ) > ( a > c > c ) > $o ).
thf(tp_quotient3_c_c_c_c,type,
quotient3_c_c_c_c: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > c > c ) > ( ( c > c ) > c > c ) > $o ).
thf(tp_quotient3_c_c_d_d,type,
quotient3_c_c_d_d: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > d > d ) > ( ( d > d ) > c > c ) > $o ).
thf(tp_quotient3_d_d_b,type,
quotient3_d_d_b: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > b ) > ( b > d > d ) > $o ).
thf(tp_quotient3_d_d_c_c,type,
quotient3_d_d_c_c: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > c > c ) > ( ( c > c ) > d > d ) > $o ).
thf(tp_quotient3_d_d_d_d,type,
quotient3_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > d > d ) > ( ( d > d ) > d > d ) > $o ).
thf(tp_relcom1813708708_b_d_d,type,
relcom1813708708_b_d_d: ( ( a > c > c ) > ( a > c > c ) > $o ) > ( ( a > c > c ) > ( b > d > d ) > $o ) > ( a > c > c ) > ( b > d > d ) > $o ).
thf(tp_relcom1887247779_b_d_d,type,
relcom1887247779_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > ( ( b > d > d ) > ( b > d > d ) > $o ) > ( a > c > c ) > ( b > d > d ) > $o ).
thf(tp_relcompp_a_a_a,type,
relcompp_a_a_a: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
thf(tp_relcompp_a_a_b,type,
relcompp_a_a_b: ( a > a > $o ) > ( a > b > $o ) > a > b > $o ).
thf(tp_relcompp_a_b_b,type,
relcompp_a_b_b: ( a > b > $o ) > ( b > b > $o ) > a > b > $o ).
thf(tp_relcompp_b_b_b,type,
relcompp_b_b_b: ( b > b > $o ) > ( b > b > $o ) > b > b > $o ).
thf(tp_relcompp_c_c_c_c_c_c,type,
relcompp_c_c_c_c_c_c: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > ( c > c ) > $o ) > ( c > c ) > ( c > c ) > $o ).
thf(tp_relcompp_c_c_c_c_d_d,type,
relcompp_c_c_c_c_d_d: ( ( c > c ) > ( c > c ) > $o ) > ( ( c > c ) > ( d > d ) > $o ) > ( c > c ) > ( d > d ) > $o ).
thf(tp_relcompp_c_c_d,type,
relcompp_c_c_d: ( c > c > $o ) > ( c > d > $o ) > c > d > $o ).
thf(tp_relcompp_c_c_d_d_d_d,type,
relcompp_c_c_d_d_d_d: ( ( c > c ) > ( d > d ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( c > c ) > ( d > d ) > $o ).
thf(tp_relcompp_c_d_d,type,
relcompp_c_d_d: ( c > d > $o ) > ( d > d > $o ) > c > d > $o ).
thf(tp_relcompp_d_d_d_d_d_d,type,
relcompp_d_d_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > ( ( d > d ) > ( d > d ) > $o ) > ( d > d ) > ( d > d ) > $o ).
thf(tp_rev_implies,type,
rev_implies: $o > $o > $o ).
thf(tp_right_2142487_b_d_d,type,
right_2142487_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_right_386984928_b_d_d,type,
right_386984928_b_d_d: ( ( a > c > c ) > ( b > d > d ) > $o ) > $o ).
thf(tp_right_total_a_a,type,
right_total_a_a: ( a > a > $o ) > $o ).
thf(tp_right_total_a_b,type,
right_total_a_b: ( a > b > $o ) > $o ).
thf(tp_right_total_c_c,type,
right_total_c_c: ( c > c > $o ) > $o ).
thf(tp_right_total_c_c_d_d,type,
right_total_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_right_total_c_d,type,
right_total_c_d: ( c > d > $o ) > $o ).
thf(tp_right_total_d_d,type,
right_total_d_d: ( d > d > $o ) > $o ).
thf(tp_right_total_d_d_d_d,type,
right_total_d_d_d_d: ( ( d > d ) > ( d > d ) > $o ) > $o ).
thf(tp_right_unique_a_b,type,
right_unique_a_b: ( a > b > $o ) > $o ).
thf(tp_right_unique_b_b,type,
right_unique_b_b: ( b > b > $o ) > $o ).
thf(tp_right_unique_c_c_d_d,type,
right_unique_c_c_d_d: ( ( c > c ) > ( d > d ) > $o ) > $o ).
thf(tp_right_unique_c_d,type,
right_unique_c_d: ( c > d > $o ) > $o ).
thf(tp_right_unique_d_d,type,
right_unique_d_d: ( d > d > $o ) > $o ).
thf(tp_sK1_SY51,type,
sK1_SY51: ( a > c > c ) > a ).
thf(tp_sK2_SY92,type,
sK2_SY92: ( a > c > c ) > a ).
thf(tp_sK3_SY63,type,
sK3_SY63: ( a > c > c ) > a ).
thf(tp_sK4_SV34,type,
sK4_SV34: ( a > c > c ) > c ).
thf(tp_sK5_SY96,type,
sK5_SY96: ( a > c > c ) > a ).
thf(tp_sK6_SV36,type,
sK6_SV36: ( a > c > c ) > c ).
thf(tp_sK7_SY83,type,
sK7_SY83: multiset_a > c > ( a > c > c ) > ( a > c > c ) > ( c > c ) > a ).
thf(tp_sK8_SY98,type,
sK8_SY98: ( a > c > c ) > c > multiset_a > ( a > c > c ) > ( c > c ) > c ).
thf(3,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001tf__d_T) ).
thf(341,axiom,
! [F: a > c > c,Y: a,X: a] :
( ( finite746615251te_a_c @ F )
=> ( ( comp_c_c_c @ ( F @ Y ) @ ( F @ X ) )
= ( comp_c_c_c @ ( F @ X ) @ ( F @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_comp__fun__commute_Ocomp__fun__commute) ).
thf(343,axiom,
! [F: a > c > c] :
( ! [Y2: a,X2: a] :
( ( comp_c_c_c @ ( F @ Y2 ) @ ( F @ X2 ) )
= ( comp_c_c_c @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( finite746615251te_a_c @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comp__fun__commute_Ointro) ).
thf(345,axiom,
( finite746615251te_a_c
= ( ^ [F2: a > c > c] :
! [Y3: a,X3: a] :
( ( comp_c_c_c @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
= ( comp_c_c_c @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_comp__fun__commute__def) ).
thf(347,axiom,
! [F: a > c > c,G: a > a] :
( ( finite746615251te_a_c @ F )
=> ( finite746615251te_a_c @ ( comp_a_c_c_a @ F @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comp__fun__commute_Ocomp__comp__fun__commute) ).
thf(350,axiom,
! [F: a > c > c,X: a,Z: c,A: fset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ X @ ( ffold_a_c @ F @ Z @ A ) )
= ( ffold_a_c @ F @ ( F @ X @ Z ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_comp__fun__commute_Offold__fun__left__comm) ).
thf(352,axiom,
! [F: a > c > c,Z: c,A: set_a,X: c,Y: c] :
( ( finite746615251te_a_c @ F )
=> ( ( finite1511629768ph_a_c @ F @ Z @ A @ X )
=> ( ( finite1511629768ph_a_c @ F @ Z @ A @ Y )
=> ( Y = X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_comp__fun__commute_Ofold__graph__determ) ).
thf(354,axiom,
! [F: a > c > c] :
( ( finite40241358em_a_c @ F )
=> ( finite746615251te_a_c @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_comp__fun__idem_Oaxioms_I1_J) ).
thf(356,axiom,
! [F: a > c > c,X: a,S: c,M: multiset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ X @ ( fold_mset_a_c @ F @ S @ M ) )
= ( fold_mset_a_c @ F @ ( F @ X @ S ) @ M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_comp__fun__commute_Ofold__mset__fun__left__comm) ).
thf(358,axiom,
! [F: a > c > c,G: a > c > c,H: c > c,W: c,A: multiset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( finite746615251te_a_c @ G )
=> ( ! [X2: a,Y2: c] :
( ( H @ ( G @ X2 @ Y2 ) )
= ( F @ X2 @ ( H @ Y2 ) ) )
=> ( ( H @ ( fold_mset_a_c @ G @ W @ A ) )
= ( fold_mset_a_c @ F @ ( H @ W ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_comp__fun__commute_Ofold__mset__fusion) ).
thf(362,axiom,
! [F: a > c > c,Y: a,X: a,Z: c] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ Y @ ( F @ X @ Z ) )
= ( F @ X @ ( F @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_comp__fun__commute_Ofun__left__comm) ).
thf(363,axiom,
finite746615251te_a_c @ f1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(364,conjecture,
finite746615251te_a_c @ f1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(365,negated_conjecture,
( ( finite746615251te_a_c @ f1 )
= $false ),
inference(negate_conjecture,[status(cth)],[364]) ).
thf(366,plain,
( ( finite746615251te_a_c @ f1 )
= $false ),
inference(unfold_def,[status(thm)],[365]) ).
thf(367,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(368,plain,
( ( ! [F: a > c > c,Y: a,X: a] :
( ( finite746615251te_a_c @ F )
=> ( ( comp_c_c_c @ ( F @ Y ) @ ( F @ X ) )
= ( comp_c_c_c @ ( F @ X ) @ ( F @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(369,plain,
( ( ! [F: a > c > c] :
( ! [Y2: a,X2: a] :
( ( comp_c_c_c @ ( F @ Y2 ) @ ( F @ X2 ) )
= ( comp_c_c_c @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( finite746615251te_a_c @ F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(370,plain,
( ( finite746615251te_a_c
= ( ^ [F2: a > c > c] :
! [Y3: a,X3: a] :
( ( comp_c_c_c @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
= ( comp_c_c_c @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(371,plain,
( ( ! [F: a > c > c,G: a > a] :
( ( finite746615251te_a_c @ F )
=> ( finite746615251te_a_c @ ( comp_a_c_c_a @ F @ G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(372,plain,
( ( ! [F: a > c > c,X: a,Z: c,A: fset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ X @ ( ffold_a_c @ F @ Z @ A ) )
= ( ffold_a_c @ F @ ( F @ X @ Z ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(373,plain,
( ( ! [F: a > c > c,Z: c,A: set_a,X: c,Y: c] :
( ( finite746615251te_a_c @ F )
=> ( ( finite1511629768ph_a_c @ F @ Z @ A @ X )
=> ( ( finite1511629768ph_a_c @ F @ Z @ A @ Y )
=> ( Y = X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(374,plain,
( ( ! [F: a > c > c] :
( ( finite40241358em_a_c @ F )
=> ( finite746615251te_a_c @ F ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(375,plain,
( ( ! [F: a > c > c,X: a,S: c,M: multiset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ X @ ( fold_mset_a_c @ F @ S @ M ) )
= ( fold_mset_a_c @ F @ ( F @ X @ S ) @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(376,plain,
( ( ! [F: a > c > c,G: a > c > c,H: c > c,W: c,A: multiset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( finite746615251te_a_c @ G )
=> ( ! [X2: a,Y2: c] :
( ( H @ ( G @ X2 @ Y2 ) )
= ( F @ X2 @ ( H @ Y2 ) ) )
=> ( ( H @ ( fold_mset_a_c @ G @ W @ A ) )
= ( fold_mset_a_c @ F @ ( H @ W ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(377,plain,
( ( ! [F: a > c > c,Y: a,X: a,Z: c] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ Y @ ( F @ X @ Z ) )
= ( F @ X @ ( F @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(378,plain,
( ( finite746615251te_a_c @ f1 )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(379,plain,
( ( ~ ( finite746615251te_a_c @ f1 ) )
= $true ),
inference(polarity_switch,[status(thm)],[366]) ).
thf(380,plain,
( ( finite746615251te_a_c @ f1 )
= $true ),
inference(copy,[status(thm)],[378]) ).
thf(381,plain,
( ( ! [F: a > c > c,Y: a,X: a,Z: c] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ Y @ ( F @ X @ Z ) )
= ( F @ X @ ( F @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(382,plain,
( ( ! [F: a > c > c,G: a > c > c,H: c > c,W: c,A: multiset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( finite746615251te_a_c @ G )
=> ( ! [X2: a,Y2: c] :
( ( H @ ( G @ X2 @ Y2 ) )
= ( F @ X2 @ ( H @ Y2 ) ) )
=> ( ( H @ ( fold_mset_a_c @ G @ W @ A ) )
= ( fold_mset_a_c @ F @ ( H @ W ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(383,plain,
( ( ! [F: a > c > c,X: a,S: c,M: multiset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ X @ ( fold_mset_a_c @ F @ S @ M ) )
= ( fold_mset_a_c @ F @ ( F @ X @ S ) @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(384,plain,
( ( ! [F: a > c > c] :
( ( finite40241358em_a_c @ F )
=> ( finite746615251te_a_c @ F ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(385,plain,
( ( ! [F: a > c > c,Z: c,A: set_a,X: c,Y: c] :
( ( finite746615251te_a_c @ F )
=> ( ( finite1511629768ph_a_c @ F @ Z @ A @ X )
=> ( ( finite1511629768ph_a_c @ F @ Z @ A @ Y )
=> ( Y = X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(386,plain,
( ( ! [F: a > c > c,X: a,Z: c,A: fset_a] :
( ( finite746615251te_a_c @ F )
=> ( ( F @ X @ ( ffold_a_c @ F @ Z @ A ) )
= ( ffold_a_c @ F @ ( F @ X @ Z ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(387,plain,
( ( ! [F: a > c > c,G: a > a] :
( ( finite746615251te_a_c @ F )
=> ( finite746615251te_a_c @ ( comp_a_c_c_a @ F @ G ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(388,plain,
( ( finite746615251te_a_c
= ( ^ [F2: a > c > c] :
! [Y3: a,X3: a] :
( ( comp_c_c_c @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
= ( comp_c_c_c @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(389,plain,
( ( ! [F: a > c > c] :
( ! [Y2: a,X2: a] :
( ( comp_c_c_c @ ( F @ Y2 ) @ ( F @ X2 ) )
= ( comp_c_c_c @ ( F @ X2 ) @ ( F @ Y2 ) ) )
=> ( finite746615251te_a_c @ F ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(390,plain,
( ( ! [F: a > c > c,Y: a,X: a] :
( ( finite746615251te_a_c @ F )
=> ( ( comp_c_c_c @ ( F @ Y ) @ ( F @ X ) )
= ( comp_c_c_c @ ( F @ X ) @ ( F @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(391,plain,
( ( ! [P: $o] :
( ( P = $true )
| ( P = $false ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(392,plain,
( ( ~ ( finite746615251te_a_c @ f1 ) )
= $true ),
inference(copy,[status(thm)],[379]) ).
thf(393,plain,
( ( ! [SX0: a > c > c,SX1: a,SX2: c,SX3: multiset_a] :
( ~ ( finite746615251te_a_c @ SX0 )
| ( ( SX0 @ SX1 @ ( fold_mset_a_c @ SX0 @ SX2 @ SX3 ) )
= ( fold_mset_a_c @ SX0 @ ( SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(394,plain,
( ( ! [SX0: a > c > c,SX1: a > c > c,SX2: c > c,SX3: c,SX4: multiset_a] :
( ~ ( finite746615251te_a_c @ SX0 )
| ~ ( finite746615251te_a_c @ SX1 )
| ~ ! [SX5: a,SX6: c] :
( ( SX2 @ ( SX1 @ SX5 @ SX6 ) )
= ( SX0 @ SX5 @ ( SX2 @ SX6 ) ) )
| ( ( SX2 @ ( fold_mset_a_c @ SX1 @ SX3 @ SX4 ) )
= ( fold_mset_a_c @ SX0 @ ( SX2 @ SX3 ) @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(395,plain,
( ( ! [SX0: a > c > c] :
( ~ ( finite40241358em_a_c @ SX0 )
| ( finite746615251te_a_c @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(396,plain,
( ( ! [SX0: a > c > c,SX1: a,SX2: a] :
( ~ ( finite746615251te_a_c @ SX0 )
| ( ( comp_c_c_c @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) )
= ( comp_c_c_c @ ( SX0 @ SX2 ) @ ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(397,plain,
( ( ! [SX0: a > c > c,SX1: a > a] :
( ~ ( finite746615251te_a_c @ SX0 )
| ( finite746615251te_a_c @ ( comp_a_c_c_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(398,plain,
( ( ! [SX0: a > c > c] :
( ~ ! [SX1: a,SX2: a] :
( ( comp_c_c_c @ ( SX0 @ SX1 ) @ ( SX0 @ SX2 ) )
= ( comp_c_c_c @ ( SX0 @ SX2 ) @ ( SX0 @ SX1 ) ) )
| ( finite746615251te_a_c @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(399,plain,
( ( ! [SX0: a > c > c,SX1: a,SX2: a,SX3: c] :
( ~ ( finite746615251te_a_c @ SX0 )
| ( ( SX0 @ SX1 @ ( SX0 @ SX2 @ SX3 ) )
= ( SX0 @ SX2 @ ( SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(400,plain,
( ( ! [SX0: a > c > c,SX1: c,SX2: set_a,SX3: c,SX4: c] :
( ~ ( finite746615251te_a_c @ SX0 )
| ~ ( finite1511629768ph_a_c @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( finite1511629768ph_a_c @ SX0 @ SX1 @ SX2 @ SX4 )
| ( SX4 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(401,plain,
( ( ! [SX0: a > c > c,SX1: a,SX2: c,SX3: fset_a] :
( ~ ( finite746615251te_a_c @ SX0 )
| ( ( SX0 @ SX1 @ ( ffold_a_c @ SX0 @ SX2 @ SX3 ) )
= ( ffold_a_c @ SX0 @ ( SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(402,plain,
( ( ! [SV1: a > c > c] :
( ( finite746615251te_a_c @ SV1 )
= ( ! [SY37: a,SY38: a] :
( ( comp_c_c_c @ ( SV1 @ SY37 ) @ ( SV1 @ SY38 ) )
= ( comp_c_c_c @ ( SV1 @ SY38 ) @ ( SV1 @ SY37 ) ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[388]) ).
thf(403,plain,
( ( finite746615251te_a_c
= ( ^ [F2: a > c > c] :
! [Y3: a,X3: a] :
( ( comp_c_c_c @ ( F2 @ Y3 ) @ ( F2 @ X3 ) )
= ( comp_c_c_c @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[388]) ).
thf(404,plain,
! [SV2: $o] :
( ( ( SV2 = $true )
| ( SV2 = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[391]) ).
thf(405,plain,
( ( ( $true = $true )
| ( $true = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[391]) ).
thf(406,plain,
( ( ( $false = $true )
| ( $false = $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[391]) ).
thf(407,plain,
( ( finite746615251te_a_c @ f1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(408,plain,
! [SV3: a > c > c] :
( ( ! [SY39: a,SY40: c,SY41: multiset_a] :
( ~ ( finite746615251te_a_c @ SV3 )
| ( ( SV3 @ SY39 @ ( fold_mset_a_c @ SV3 @ SY40 @ SY41 ) )
= ( fold_mset_a_c @ SV3 @ ( SV3 @ SY39 @ SY40 ) @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(409,plain,
! [SV4: a > c > c] :
( ( ! [SY42: a > c > c,SY43: c > c,SY44: c,SY45: multiset_a] :
( ~ ( finite746615251te_a_c @ SV4 )
| ~ ( finite746615251te_a_c @ SY42 )
| ~ ! [SY46: a,SY47: c] :
( ( SY43 @ ( SY42 @ SY46 @ SY47 ) )
= ( SV4 @ SY46 @ ( SY43 @ SY47 ) ) )
| ( ( SY43 @ ( fold_mset_a_c @ SY42 @ SY44 @ SY45 ) )
= ( fold_mset_a_c @ SV4 @ ( SY43 @ SY44 ) @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(410,plain,
! [SV5: a > c > c] :
( ( ~ ( finite40241358em_a_c @ SV5 )
| ( finite746615251te_a_c @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(411,plain,
! [SV6: a > c > c] :
( ( ! [SY48: a,SY49: a] :
( ~ ( finite746615251te_a_c @ SV6 )
| ( ( comp_c_c_c @ ( SV6 @ SY48 ) @ ( SV6 @ SY49 ) )
= ( comp_c_c_c @ ( SV6 @ SY49 ) @ ( SV6 @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(412,plain,
! [SV7: a > c > c] :
( ( ! [SY50: a > a] :
( ~ ( finite746615251te_a_c @ SV7 )
| ( finite746615251te_a_c @ ( comp_a_c_c_a @ SV7 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(413,plain,
! [SV8: a > c > c] :
( ( ~ ! [SY51: a,SY52: a] :
( ( comp_c_c_c @ ( SV8 @ SY51 ) @ ( SV8 @ SY52 ) )
= ( comp_c_c_c @ ( SV8 @ SY52 ) @ ( SV8 @ SY51 ) ) )
| ( finite746615251te_a_c @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(414,plain,
! [SV9: a > c > c] :
( ( ! [SY53: a,SY54: a,SY55: c] :
( ~ ( finite746615251te_a_c @ SV9 )
| ( ( SV9 @ SY53 @ ( SV9 @ SY54 @ SY55 ) )
= ( SV9 @ SY54 @ ( SV9 @ SY53 @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(415,plain,
! [SV10: a > c > c] :
( ( ! [SY56: c,SY57: set_a,SY58: c,SY59: c] :
( ~ ( finite746615251te_a_c @ SV10 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SY56 @ SY57 @ SY58 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SY56 @ SY57 @ SY59 )
| ( SY59 = SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(416,plain,
! [SV11: a > c > c] :
( ( ! [SY60: a,SY61: c,SY62: fset_a] :
( ~ ( finite746615251te_a_c @ SV11 )
| ( ( SV11 @ SY60 @ ( ffold_a_c @ SV11 @ SY61 @ SY62 ) )
= ( ffold_a_c @ SV11 @ ( SV11 @ SY60 @ SY61 ) @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(417,plain,
! [SV12: a > c > c] :
( ( ( finite746615251te_a_c @ SV12 )
= ( ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(418,plain,
! [SV2: $o] :
( ( ( SV2 = $true )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(419,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(420,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(421,plain,
! [SV13: a,SV3: a > c > c] :
( ( ! [SY65: c,SY66: multiset_a] :
( ~ ( finite746615251te_a_c @ SV3 )
| ( ( SV3 @ SV13 @ ( fold_mset_a_c @ SV3 @ SY65 @ SY66 ) )
= ( fold_mset_a_c @ SV3 @ ( SV3 @ SV13 @ SY65 ) @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(422,plain,
! [SV14: a > c > c,SV4: a > c > c] :
( ( ! [SY67: c > c,SY68: c,SY69: multiset_a] :
( ~ ( finite746615251te_a_c @ SV4 )
| ~ ( finite746615251te_a_c @ SV14 )
| ~ ! [SY70: a,SY71: c] :
( ( SY67 @ ( SV14 @ SY70 @ SY71 ) )
= ( SV4 @ SY70 @ ( SY67 @ SY71 ) ) )
| ( ( SY67 @ ( fold_mset_a_c @ SV14 @ SY68 @ SY69 ) )
= ( fold_mset_a_c @ SV4 @ ( SY67 @ SY68 ) @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(423,plain,
! [SV5: a > c > c] :
( ( ( ~ ( finite40241358em_a_c @ SV5 ) )
= $true )
| ( ( finite746615251te_a_c @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(424,plain,
! [SV15: a,SV6: a > c > c] :
( ( ! [SY72: a] :
( ~ ( finite746615251te_a_c @ SV6 )
| ( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SY72 ) )
= ( comp_c_c_c @ ( SV6 @ SY72 ) @ ( SV6 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(425,plain,
! [SV16: a > a,SV7: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV7 )
| ( finite746615251te_a_c @ ( comp_a_c_c_a @ SV7 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(426,plain,
! [SV8: a > c > c] :
( ( ( ~ ! [SY51: a,SY52: a] :
( ( comp_c_c_c @ ( SV8 @ SY51 ) @ ( SV8 @ SY52 ) )
= ( comp_c_c_c @ ( SV8 @ SY52 ) @ ( SV8 @ SY51 ) ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(427,plain,
! [SV17: a,SV9: a > c > c] :
( ( ! [SY73: a,SY74: c] :
( ~ ( finite746615251te_a_c @ SV9 )
| ( ( SV9 @ SV17 @ ( SV9 @ SY73 @ SY74 ) )
= ( SV9 @ SY73 @ ( SV9 @ SV17 @ SY74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(428,plain,
! [SV18: c,SV10: a > c > c] :
( ( ! [SY75: set_a,SY76: c,SY77: c] :
( ~ ( finite746615251te_a_c @ SV10 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SY75 @ SY76 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SY75 @ SY77 )
| ( SY77 = SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(429,plain,
! [SV19: a,SV11: a > c > c] :
( ( ! [SY78: c,SY79: fset_a] :
( ~ ( finite746615251te_a_c @ SV11 )
| ( ( SV11 @ SV19 @ ( ffold_a_c @ SV11 @ SY78 @ SY79 ) )
= ( ffold_a_c @ SV11 @ ( SV11 @ SV19 @ SY78 ) @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(430,plain,
! [SV12: a > c > c] :
( ( ~ ( ( finite746615251te_a_c @ SV12 )
| ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
| ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[417]) ).
thf(431,plain,
! [SV12: a > c > c] :
( ( ( finite746615251te_a_c @ SV12 )
= ( ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $true )
| ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[418]) ).
thf(433,plain,
! [SV2: $o] :
( ( ( SV2 = $true )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[418]) ).
thf(434,plain,
( ( ( ~ ( $true
| $true )
| ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[419]) ).
thf(435,plain,
( ( ( $true = $true )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[419]) ).
thf(436,plain,
( ( ( ~ ( $false
| $true )
| ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[420]) ).
thf(437,plain,
( ( ( $false = $true )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[420]) ).
thf(438,plain,
! [SV20: c,SV13: a,SV3: a > c > c] :
( ( ! [SY80: multiset_a] :
( ~ ( finite746615251te_a_c @ SV3 )
| ( ( SV3 @ SV13 @ ( fold_mset_a_c @ SV3 @ SV20 @ SY80 ) )
= ( fold_mset_a_c @ SV3 @ ( SV3 @ SV13 @ SV20 ) @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(439,plain,
! [SV21: c > c,SV14: a > c > c,SV4: a > c > c] :
( ( ! [SY81: c,SY82: multiset_a] :
( ~ ( finite746615251te_a_c @ SV4 )
| ~ ( finite746615251te_a_c @ SV14 )
| ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SY81 @ SY82 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SY81 ) @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(440,plain,
! [SV5: a > c > c] :
( ( ( finite40241358em_a_c @ SV5 )
= $false )
| ( ( finite746615251te_a_c @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(441,plain,
! [SV22: a,SV15: a,SV6: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV6 )
| ( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SV22 ) )
= ( comp_c_c_c @ ( SV6 @ SV22 ) @ ( SV6 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(442,plain,
! [SV16: a > a,SV7: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV7 ) )
= $true )
| ( ( finite746615251te_a_c @ ( comp_a_c_c_a @ SV7 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(443,plain,
! [SV8: a > c > c] :
( ( ( ! [SY51: a,SY52: a] :
( ( comp_c_c_c @ ( SV8 @ SY51 ) @ ( SV8 @ SY52 ) )
= ( comp_c_c_c @ ( SV8 @ SY52 ) @ ( SV8 @ SY51 ) ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(444,plain,
! [SV23: a,SV17: a,SV9: a > c > c] :
( ( ! [SY85: c] :
( ~ ( finite746615251te_a_c @ SV9 )
| ( ( SV9 @ SV17 @ ( SV9 @ SV23 @ SY85 ) )
= ( SV9 @ SV23 @ ( SV9 @ SV17 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(445,plain,
! [SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ! [SY86: c,SY87: c] :
( ~ ( finite746615251te_a_c @ SV10 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SY86 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SY87 )
| ( SY87 = SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(446,plain,
! [SV25: c,SV19: a,SV11: a > c > c] :
( ( ! [SY88: fset_a] :
( ~ ( finite746615251te_a_c @ SV11 )
| ( ( SV11 @ SV19 @ ( ffold_a_c @ SV11 @ SV25 @ SY88 ) )
= ( ffold_a_c @ SV11 @ ( SV11 @ SV19 @ SV25 ) @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(447,plain,
! [SV12: a > c > c] :
( ( ( ~ ( ( finite746615251te_a_c @ SV12 )
| ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(448,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $true ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(449,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[433]) ).
thf(450,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[433]) ).
thf(451,plain,
( ( ( ~ ( $true
| $true ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(452,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[435]) ).
thf(453,plain,
( ( ( $true = $false )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[435]) ).
thf(454,plain,
( ( ( ~ ( $false
| $true ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(455,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(456,plain,
( ( ( $false = $false )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_equal_pos,[status(thm)],[437]) ).
thf(457,plain,
! [SV26: multiset_a,SV20: c,SV13: a,SV3: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV3 )
| ( ( SV3 @ SV13 @ ( fold_mset_a_c @ SV3 @ SV20 @ SV26 ) )
= ( fold_mset_a_c @ SV3 @ ( SV3 @ SV13 @ SV20 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(458,plain,
! [SV27: c,SV21: c > c,SV14: a > c > c,SV4: a > c > c] :
( ( ! [SY89: multiset_a] :
( ~ ( finite746615251te_a_c @ SV4 )
| ~ ( finite746615251te_a_c @ SV14 )
| ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SY89 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(459,plain,
! [SV22: a,SV15: a,SV6: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV6 ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SV22 ) )
= ( comp_c_c_c @ ( SV6 @ SV22 ) @ ( SV6 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(460,plain,
! [SV16: a > a,SV7: a > c > c] :
( ( ( finite746615251te_a_c @ SV7 )
= $false )
| ( ( finite746615251te_a_c @ ( comp_a_c_c_a @ SV7 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(461,plain,
! [SV8: a > c > c] :
( ( ( ! [SY92: a] :
( ( comp_c_c_c @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ ( SV8 @ SY92 ) )
= ( comp_c_c_c @ ( SV8 @ SY92 ) @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[443]) ).
thf(462,plain,
! [SV28: c,SV23: a,SV17: a,SV9: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV9 )
| ( ( SV9 @ SV17 @ ( SV9 @ SV23 @ SV28 ) )
= ( SV9 @ SV23 @ ( SV9 @ SV17 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(463,plain,
! [SV29: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ! [SY93: c] :
( ~ ( finite746615251te_a_c @ SV10 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SY93 )
| ( SY93 = SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(464,plain,
! [SV30: fset_a,SV25: c,SV19: a,SV11: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV11 )
| ( ( SV11 @ SV19 @ ( ffold_a_c @ SV11 @ SV25 @ SV30 ) )
= ( ffold_a_c @ SV11 @ ( SV11 @ SV19 @ SV25 ) @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(465,plain,
! [SV12: a > c > c] :
( ( ( ( finite746615251te_a_c @ SV12 )
| ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(466,plain,
! [SV2: $o] :
( ( ( SV2
| $true )
= $false )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(467,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(468,plain,
( ( ( $true
| $true )
= $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(469,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(470,plain,
( ( ( $false
| $true )
= $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(471,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(472,plain,
! [SV26: multiset_a,SV20: c,SV13: a,SV3: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV3 ) )
= $true )
| ( ( ( SV3 @ SV13 @ ( fold_mset_a_c @ SV3 @ SV20 @ SV26 ) )
= ( fold_mset_a_c @ SV3 @ ( SV3 @ SV13 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(473,plain,
! [SV31: multiset_a,SV27: c,SV21: c > c,SV14: a > c > c,SV4: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV4 )
| ~ ( finite746615251te_a_c @ SV14 )
| ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(474,plain,
! [SV22: a,SV15: a,SV6: a > c > c] :
( ( ( finite746615251te_a_c @ SV6 )
= $false )
| ( ( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SV22 ) )
= ( comp_c_c_c @ ( SV6 @ SV22 ) @ ( SV6 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(475,plain,
! [SV8: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) )
= ( comp_c_c_c @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[461]) ).
thf(476,plain,
! [SV28: c,SV23: a,SV17: a,SV9: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV9 ) )
= $true )
| ( ( ( SV9 @ SV17 @ ( SV9 @ SV23 @ SV28 ) )
= ( SV9 @ SV23 @ ( SV9 @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(477,plain,
! [SV32: c,SV29: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ~ ( finite746615251te_a_c @ SV10 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 )
| ( SV32 = SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(478,plain,
! [SV30: fset_a,SV25: c,SV19: a,SV11: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV11 ) )
= $true )
| ( ( ( SV11 @ SV19 @ ( ffold_a_c @ SV11 @ SV25 @ SV30 ) )
= ( ffold_a_c @ SV11 @ ( SV11 @ SV19 @ SV25 ) @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(479,plain,
! [SV12: a > c > c] :
( ( ( finite746615251te_a_c @ SV12 )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(480,plain,
! [SV12: a > c > c] :
( ( ( ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(481,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(482,plain,
! [SV2: $o] :
( ( $true = $false )
| ( ( ~ ( ~ SV2
| ~ $true ) )
= $true )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(483,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(484,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(485,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $true ) )
= $true )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(486,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(487,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(488,plain,
( ( $true = $false )
| ( ( ~ ( ~ $false
| ~ $true ) )
= $true )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(489,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(490,plain,
! [SV26: multiset_a,SV20: c,SV13: a,SV3: a > c > c] :
( ( ( finite746615251te_a_c @ SV3 )
= $false )
| ( ( ( SV3 @ SV13 @ ( fold_mset_a_c @ SV3 @ SV20 @ SV26 ) )
= ( fold_mset_a_c @ SV3 @ ( SV3 @ SV13 @ SV20 ) @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(491,plain,
! [SV31: multiset_a,SV27: c,SV21: c > c,SV14: a > c > c,SV4: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV4 ) )
= $true )
| ( ( ~ ( finite746615251te_a_c @ SV14 )
| ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(492,plain,
! [SV22: a,SV15: a,SV6: a > c > c] :
( ( ( ! [SV33: c] :
( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SV22 ) @ SV33 )
= ( comp_c_c_c @ ( SV6 @ SV22 ) @ ( SV6 @ SV15 ) @ SV33 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV6 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[474]) ).
thf(493,plain,
! [SV22: a,SV15: a,SV6: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SV22 ) )
= ( comp_c_c_c @ ( SV6 @ SV22 ) @ ( SV6 @ SV15 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV6 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[474]) ).
thf(494,plain,
! [SV8: a > c > c] :
( ( ( ! [SV34: c] :
( ( comp_c_c_c @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) @ SV34 )
= ( comp_c_c_c @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ SV34 ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[475]) ).
thf(495,plain,
! [SV8: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) )
= ( comp_c_c_c @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[475]) ).
thf(496,plain,
! [SV28: c,SV23: a,SV17: a,SV9: a > c > c] :
( ( ( finite746615251te_a_c @ SV9 )
= $false )
| ( ( ( SV9 @ SV17 @ ( SV9 @ SV23 @ SV28 ) )
= ( SV9 @ SV23 @ ( SV9 @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(497,plain,
! [SV32: c,SV29: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV10 ) )
= $true )
| ( ( ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 )
| ( SV32 = SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(498,plain,
! [SV30: fset_a,SV25: c,SV19: a,SV11: a > c > c] :
( ( ( finite746615251te_a_c @ SV11 )
= $false )
| ( ( ( SV11 @ SV19 @ ( ffold_a_c @ SV11 @ SV25 @ SV30 ) )
= ( ffold_a_c @ SV11 @ ( SV11 @ SV19 @ SV25 ) @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(499,plain,
! [SV12: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(500,plain,
! [SV12: a > c > c] :
( ( ( ! [SY96: a] :
( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ SY96 ) )
= ( comp_c_c_c @ ( SV12 @ SY96 ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[480]) ).
thf(501,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $true )
= $false )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(502,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $true )
= $false )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(503,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(504,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(505,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(506,plain,
( ( ( ~ $true
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(507,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(508,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(509,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(510,plain,
( ( ( ~ $false
| ~ $true )
= $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(511,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(512,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(513,plain,
! [SV31: multiset_a,SV27: c,SV21: c > c,SV14: a > c > c,SV4: a > c > c] :
( ( ( finite746615251te_a_c @ SV4 )
= $false )
| ( ( ~ ( finite746615251te_a_c @ SV14 )
| ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(514,plain,
! [SV35: c,SV22: a,SV15: a,SV6: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV6 @ SV15 ) @ ( SV6 @ SV22 ) @ SV35 )
= ( comp_c_c_c @ ( SV6 @ SV22 ) @ ( SV6 @ SV15 ) @ SV35 ) )
= $true )
| ( ( finite746615251te_a_c @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(515,plain,
! [SV8: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) @ ( sK4_SV34 @ SV8 ) )
= ( comp_c_c_c @ ( SV8 @ ( sK2_SY92 @ SV8 ) ) @ ( SV8 @ ( sK1_SY51 @ SV8 ) ) @ ( sK4_SV34 @ SV8 ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[494]) ).
thf(516,plain,
! [SV32: c,SV29: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ( finite746615251te_a_c @ SV10 )
= $false )
| ( ( ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
| ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 )
| ( SV32 = SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(517,plain,
! [SV12: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV12 ) )
= $false )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(518,plain,
! [SV12: a > c > c] :
( ( ( ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(519,plain,
! [SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[500]) ).
thf(520,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(521,plain,
! [SV2: $o] :
( ( ( ~ $true ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(522,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(523,plain,
! [SV2: $o] :
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[502]) ).
thf(524,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(525,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(526,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(527,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(528,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(529,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[506]) ).
thf(530,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(531,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(532,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(533,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[509]) ).
thf(534,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(535,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(536,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(537,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(538,plain,
! [SV31: multiset_a,SV27: c,SV4: a > c > c,SV21: c > c,SV14: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV14 ) )
= $true )
| ( ( ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(539,plain,
! [SV32: c,SV29: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ( ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 ) )
= $true )
| ( ( ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 )
| ( SV32 = SV29 ) )
= $true )
| ( ( finite746615251te_a_c @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(540,plain,
! [SV12: a > c > c] :
( ( ( finite746615251te_a_c @ SV12 )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(541,plain,
! [SV12: a > c > c] :
( ( ( ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(542,plain,
! [SV12: a > c > c] :
( ( ( ! [SV36: c] :
( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ SV36 )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ SV36 ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[519]) ).
thf(543,plain,
! [SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[519]) ).
thf(544,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(545,plain,
! [SV2: $o] :
( ( $true = $true )
| ( SV2 = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(546,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(547,plain,
! [SV2: $o] :
( ( $true = $true )
| ( $true = $false )
| ( ( SV2 = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(548,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(549,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(550,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(551,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(552,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(553,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(554,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(555,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(556,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(557,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(558,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(559,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(560,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(561,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(562,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(563,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $false = $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(564,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(565,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(566,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(567,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(568,plain,
! [SV31: multiset_a,SV27: c,SV4: a > c > c,SV21: c > c,SV14: a > c > c] :
( ( ( finite746615251te_a_c @ SV14 )
= $false )
| ( ( ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) )
| ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(569,plain,
! [SV32: c,SV29: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
= $false )
| ( ( ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 )
| ( SV32 = SV29 ) )
= $true )
| ( ( finite746615251te_a_c @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(570,plain,
! [SV37: a,SV12: a > c > c] :
( ( ( ! [SY97: a] :
( ( comp_c_c_c @ ( SV12 @ SV37 ) @ ( SV12 @ SY97 ) )
= ( comp_c_c_c @ ( SV12 @ SY97 ) @ ( SV12 @ SV37 ) ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(571,plain,
! [SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false )
| ( ( ~ ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[542]) ).
thf(572,plain,
! [SV12: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(573,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[544]) ).
thf(574,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[544]) ).
thf(575,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(576,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[545]) ).
thf(577,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[546]) ).
thf(578,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[546]) ).
thf(579,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false )
| ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[547]) ).
thf(580,plain,
! [SV2: $o] :
( ( ( SV2 = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[547]) ).
thf(581,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(582,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(583,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(584,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( ( SV2 = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(585,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[552]) ).
thf(586,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[552]) ).
thf(587,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[553]) ).
thf(588,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[553]) ).
thf(589,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[554]) ).
thf(590,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[554]) ).
thf(591,plain,
( ( ( ~ ( $true
| $false )
| ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[555]) ).
thf(592,plain,
( ( ( $true = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[555]) ).
thf(593,plain,
( ( $true = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(594,plain,
( ( $false = $true )
| ( $true = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(595,plain,
( ( $true = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(596,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $true = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(597,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[560]) ).
thf(598,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[560]) ).
thf(599,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[561]) ).
thf(600,plain,
( ( ( $false = $false )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[561]) ).
thf(601,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[562]) ).
thf(602,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[562]) ).
thf(603,plain,
( ( ( ~ ( $false
| $false )
| ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[563]) ).
thf(604,plain,
( ( ( $false = $false )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_equal_pos,[status(thm)],[563]) ).
thf(605,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(606,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(607,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(608,plain,
( ( $false = $true )
| ( $false = $false )
| ( ( $false = $true )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(609,plain,
! [SV31: multiset_a,SV27: c,SV4: a > c > c,SV14: a > c > c,SV21: c > c] :
( ( ( ~ ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) ) )
= $true )
| ( ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) )
= $true )
| ( ( finite746615251te_a_c @ SV14 )
= $false )
| ( ( finite746615251te_a_c @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(610,plain,
! [SV29: c,SV32: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ( ~ ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 ) )
= $true )
| ( ( SV32 = SV29 )
= $true )
| ( ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
= $false )
| ( ( finite746615251te_a_c @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(611,plain,
! [SV38: a,SV37: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV37 ) @ ( SV12 @ SV38 ) )
= ( comp_c_c_c @ ( SV12 @ SV38 ) @ ( SV12 @ SV37 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(612,plain,
! [SV12: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV12 )
| ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(613,plain,
! [SV12: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV12 ) )
= $false )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(614,plain,
! [SV12: a > c > c] :
( ( ( ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(615,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(616,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(617,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(618,plain,
! [SV2: $o] :
( ( ( ~ ( SV2
| $false ) )
= $true )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(619,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(620,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(621,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(622,plain,
( ( ( ~ ( $true
| $false ) )
= $true )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(623,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(624,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(625,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(626,plain,
( ( ( ~ ( $false
| $false ) )
= $true )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(627,plain,
! [SV31: multiset_a,SV27: c,SV4: a > c > c,SV14: a > c > c,SV21: c > c] :
( ( ( ! [SY83: a,SY84: c] :
( ( SV21 @ ( SV14 @ SY83 @ SY84 ) )
= ( SV4 @ SY83 @ ( SV21 @ SY84 ) ) ) )
= $false )
| ( ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) )
= $true )
| ( ( finite746615251te_a_c @ SV14 )
= $false )
| ( ( finite746615251te_a_c @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(628,plain,
! [SV29: c,SV32: c,SV24: set_a,SV18: c,SV10: a > c > c] :
( ( ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV32 )
= $false )
| ( ( SV32 = SV29 )
= $true )
| ( ( finite1511629768ph_a_c @ SV10 @ SV18 @ SV24 @ SV29 )
= $false )
| ( ( finite746615251te_a_c @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(629,plain,
! [SV38: a,SV37: a,SV12: a > c > c] :
( ( ( ! [SV39: c] :
( ( comp_c_c_c @ ( SV12 @ SV37 ) @ ( SV12 @ SV38 ) @ SV39 )
= ( comp_c_c_c @ ( SV12 @ SV38 ) @ ( SV12 @ SV37 ) @ SV39 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[611]) ).
thf(630,plain,
! [SV38: a,SV37: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV37 ) @ ( SV12 @ SV38 ) )
= ( comp_c_c_c @ ( SV12 @ SV38 ) @ ( SV12 @ SV37 ) ) )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[611]) ).
thf(631,plain,
! [SV12: a > c > c] :
( ( ( ~ ( finite746615251te_a_c @ SV12 ) )
= $false )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(632,plain,
! [SV12: a > c > c] :
( ( ( ~ ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $false )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(633,plain,
! [SV12: a > c > c] :
( ( ( finite746615251te_a_c @ SV12 )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(634,plain,
! [SV12: a > c > c] :
( ( ( ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(635,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(636,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(637,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(638,plain,
! [SV2: $o] :
( ( ( SV2
| $false )
= $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(639,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(640,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(641,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(642,plain,
( ( ( $true
| $false )
= $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(643,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(644,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(645,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(646,plain,
( ( ( $false
| $false )
= $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(647,plain,
! [SV4: a > c > c,SV27: c,SV31: multiset_a,SV14: a > c > c,SV21: c > c] :
( ( ( ! [SY98: c] :
( ( SV21 @ ( SV14 @ ( sK7_SY83 @ SV31 @ SV27 @ SV4 @ SV14 @ SV21 ) @ SY98 ) )
= ( SV4 @ ( sK7_SY83 @ SV31 @ SV27 @ SV4 @ SV14 @ SV21 ) @ ( SV21 @ SY98 ) ) ) )
= $false )
| ( ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) )
= $true )
| ( ( finite746615251te_a_c @ SV14 )
= $false )
| ( ( finite746615251te_a_c @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[627]) ).
thf(648,plain,
! [SV40: c,SV38: a,SV37: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV37 ) @ ( SV12 @ SV38 ) @ SV40 )
= ( comp_c_c_c @ ( SV12 @ SV38 ) @ ( SV12 @ SV37 ) @ SV40 ) )
= $true )
| ( ( finite746615251te_a_c @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(649,plain,
! [SV12: a > c > c] :
( ( ( finite746615251te_a_c @ SV12 )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[631]) ).
thf(650,plain,
! [SV12: a > c > c] :
( ( ( ! [SY63: a,SY64: a] :
( ( comp_c_c_c @ ( SV12 @ SY63 ) @ ( SV12 @ SY64 ) )
= ( comp_c_c_c @ ( SV12 @ SY64 ) @ ( SV12 @ SY63 ) ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(651,plain,
! [SV41: a,SV12: a > c > c] :
( ( ( ! [SY99: a] :
( ( comp_c_c_c @ ( SV12 @ SV41 ) @ ( SV12 @ SY99 ) )
= ( comp_c_c_c @ ( SV12 @ SY99 ) @ ( SV12 @ SV41 ) ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(652,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(653,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(654,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(655,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(656,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(657,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(658,plain,
! [SV2: $o] :
( ( SV2 = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(659,plain,
! [SV2: $o] :
( ( $false = $false )
| ( ( ~ ( ~ SV2
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(660,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(661,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(662,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(663,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[640]) ).
thf(664,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(665,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(666,plain,
( ( $true = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(667,plain,
( ( $false = $false )
| ( ( ~ ( ~ $true
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(668,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(669,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(670,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(671,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(672,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(673,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(674,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(675,plain,
( ( $false = $false )
| ( ( ~ ( ~ $false
| ~ $false ) )
= $true )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(676,plain,
! [SV4: a > c > c,SV27: c,SV31: multiset_a,SV14: a > c > c,SV21: c > c] :
( ( ( ( SV21 @ ( SV14 @ ( sK7_SY83 @ SV31 @ SV27 @ SV4 @ SV14 @ SV21 ) @ ( sK8_SY98 @ SV4 @ SV27 @ SV31 @ SV14 @ SV21 ) ) )
= ( SV4 @ ( sK7_SY83 @ SV31 @ SV27 @ SV4 @ SV14 @ SV21 ) @ ( SV21 @ ( sK8_SY98 @ SV4 @ SV27 @ SV31 @ SV14 @ SV21 ) ) ) )
= $false )
| ( ( ( SV21 @ ( fold_mset_a_c @ SV14 @ SV27 @ SV31 ) )
= ( fold_mset_a_c @ SV4 @ ( SV21 @ SV27 ) @ SV31 ) )
= $true )
| ( ( finite746615251te_a_c @ SV14 )
= $false )
| ( ( finite746615251te_a_c @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[647]) ).
thf(677,plain,
! [SV42: a,SV12: a > c > c] :
( ( ( ! [SY100: a] :
( ( comp_c_c_c @ ( SV12 @ SV42 ) @ ( SV12 @ SY100 ) )
= ( comp_c_c_c @ ( SV12 @ SY100 ) @ ( SV12 @ SV42 ) ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(678,plain,
! [SV43: a,SV41: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV41 ) @ ( SV12 @ SV43 ) )
= ( comp_c_c_c @ ( SV12 @ SV43 ) @ ( SV12 @ SV41 ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(679,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(680,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(681,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(682,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(683,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(684,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(685,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(686,plain,
! [SV2: $o] :
( ( ( ~ SV2
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(687,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(688,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(689,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(690,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(691,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(692,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(693,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(694,plain,
( ( ( ~ $true
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(695,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(696,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(697,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(698,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(699,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(700,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(701,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(702,plain,
( ( ( ~ $false
| ~ $false )
= $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(703,plain,
! [SV44: a,SV42: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV42 ) @ ( SV12 @ SV44 ) )
= ( comp_c_c_c @ ( SV12 @ SV44 ) @ ( SV12 @ SV42 ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(704,plain,
! [SV43: a,SV41: a,SV12: a > c > c] :
( ( ( ! [SV45: c] :
( ( comp_c_c_c @ ( SV12 @ SV41 ) @ ( SV12 @ SV43 ) @ SV45 )
= ( comp_c_c_c @ ( SV12 @ SV43 ) @ ( SV12 @ SV41 ) @ SV45 ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[678]) ).
thf(705,plain,
! [SV43: a,SV41: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV41 ) @ ( SV12 @ SV43 ) )
= ( comp_c_c_c @ ( SV12 @ SV43 ) @ ( SV12 @ SV41 ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[678]) ).
thf(706,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(707,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(708,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(709,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(710,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(711,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(712,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(713,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[682]) ).
thf(714,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(715,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[683]) ).
thf(716,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(717,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(718,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(719,plain,
! [SV2: $o] :
( ( ( ~ $false ) = $false )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(720,plain,
! [SV2: $o] :
( ( ( ~ SV2 ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(721,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(722,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(723,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(724,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(725,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(726,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(727,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[689]) ).
thf(728,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(729,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(730,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(731,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(732,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(733,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[692]) ).
thf(734,plain,
( ( ( ~ $true ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(735,plain,
( ( ( ~ $false ) = $false )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(736,plain,
( ( ( ~ $true ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(737,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(738,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(739,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(740,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(741,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(742,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(743,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[697]) ).
thf(744,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(745,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[698]) ).
thf(746,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(747,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(748,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(749,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(750,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(751,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(752,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(753,plain,
( ( ( ~ $false ) = $false )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(754,plain,
! [SV44: a,SV42: a,SV12: a > c > c] :
( ( ( ! [SV46: c] :
( ( comp_c_c_c @ ( SV12 @ SV42 ) @ ( SV12 @ SV44 ) @ SV46 )
= ( comp_c_c_c @ ( SV12 @ SV44 ) @ ( SV12 @ SV42 ) @ SV46 ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[703]) ).
thf(755,plain,
! [SV44: a,SV42: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV42 ) @ ( SV12 @ SV44 ) )
= ( comp_c_c_c @ ( SV12 @ SV44 ) @ ( SV12 @ SV42 ) ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_equal_pos,[status(thm)],[703]) ).
thf(756,plain,
! [SV47: c,SV43: a,SV41: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV41 ) @ ( SV12 @ SV43 ) @ SV47 )
= ( comp_c_c_c @ ( SV12 @ SV43 ) @ ( SV12 @ SV41 ) @ SV47 ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(757,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(758,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(759,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(760,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(761,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(762,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(763,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(764,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( SV2 = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(765,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(766,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(767,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(768,plain,
! [SV2: $o] :
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( SV2 = $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(769,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(770,plain,
! [SV2: $o] :
( ( $false = $true )
| ( SV2 = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(771,plain,
! [SV2: $o] :
( ( SV2 = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(772,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(773,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(774,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(775,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(776,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(777,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(778,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(779,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(780,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(781,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(782,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(783,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(784,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(785,plain,
( ( $true = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(786,plain,
( ( $false = $true )
| ( $true = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(787,plain,
( ( $true = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(788,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(789,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(790,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(791,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(792,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(793,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(794,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(795,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(796,plain,
( ( $false = $true )
| ( $false = $false )
| ( $false = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(797,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(798,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(799,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(800,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $false = $true ) ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(801,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(802,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(803,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(804,plain,
( ( $false = $true )
| ( $false = $false )
| ( $true = $false )
| ( $true = $true ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(805,plain,
! [SV48: c,SV44: a,SV42: a,SV12: a > c > c] :
( ( ( ( comp_c_c_c @ ( SV12 @ SV42 ) @ ( SV12 @ SV44 ) @ SV48 )
= ( comp_c_c_c @ ( SV12 @ SV44 ) @ ( SV12 @ SV42 ) @ SV48 ) )
= $true )
| ( ( ( comp_c_c_c @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) )
= ( comp_c_c_c @ ( SV12 @ ( sK5_SY96 @ SV12 ) ) @ ( SV12 @ ( sK3_SY63 @ SV12 ) ) @ ( sK6_SV36 @ SV12 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(806,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[380,805,804,803,802,801,800,799,798,797,796,795,794,793,792,791,790,789,788,787,786,785,784,783,782,781,780,779,778,777,776,775,774,773,772,771,770,769,768,767,766,765,764,763,762,761,760,759,758,757,756,755,705,676,649,648,633,630,628,608,607,606,605,604,602,600,598,596,595,594,593,592,590,588,586,584,583,582,581,580,578,576,574,540,515,514,498,496,495,493,490,460,456,453,450,440,431,407,403]) ).
thf(807,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[806]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP128^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Oct 6 11:17:54 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.60/1.23 ..
% 5.60/1.23
% 5.60/1.23 No.of.Axioms: 12
% 5.60/1.23
% 5.60/1.23 Length.of.Defs: 0
% 5.60/1.23
% 5.60/1.23 Contains.Choice.Funs: false
% 5.60/1.23 ...........
% 5.60/1.23
% 5.60/1.23 ********************************
% 5.60/1.23 * All subproblems solved! *
% 5.60/1.23 ********************************
% 5.60/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:806,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.60/1.23
% 5.60/1.23 %**** Beginning of derivation protocol ****
% 5.60/1.23 % SZS output start CNFRefutation
% See solution above
% 5.60/1.24
% 5.60/1.24 %**** End of derivation protocol ****
% 5.60/1.24 %**** no. of clauses in derivation: 456 ****
% 5.60/1.24 %**** clause counter: 806 ****
% 5.60/1.24
% 5.60/1.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:806,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------