%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO174^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:34 AM UTC 2026
% Result : Theorem 1.57s 1.49s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 189
% Syntax : Number of formulae : 885 ( 1 unt; 0 typ; 112 def)
% Number of atoms : 7366 (1789 equ; 0 cnn)
% Maximal formula atoms : 46 ( 8 avg)
% Number of connectives : 5633 (1423 ~;2022 |; 133 &;1789 @)
% ( 192 <=>; 72 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 195 ( 192 usr; 178 con; 0-2 aty)
% Number of variables : 977 ( 0 ^; 713 !; 264 ?; 977 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_2,type,
cS: $i > $o ).
thf(func_def_3,type,
cR: $i > $o ).
thf(func_def_13,type,
sK6: $i > $i ).
thf(func_def_22,type,
sK15: $i > $i ).
thf(func_def_25,type,
sK18: $i > $i ).
thf(func_def_34,type,
sK27: $i > $i ).
thf(func_def_37,type,
sK30: $i > $i ).
thf(func_def_46,type,
sK39: $i > $i ).
thf(func_def_49,type,
sK42: $i > $i ).
thf(func_def_58,type,
sK51: $i > $i ).
thf(func_def_61,type,
sK54: $i > $i ).
thf(func_def_70,type,
sK63: $i > $i ).
thf(func_def_71,type,
sK64: $i > $i ).
thf(func_def_79,type,
sK72: $i > $i ).
thf(f1752,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f266,f274,f289,f293,f304,f308,f323,f331,f342,f347,f359,f363,f376,f381,f389,f393,f401,f402,f411,f416,f428,f432,f440,f444,f452,f456,f463,f467,f471,f475,f480,f481,f482,f483,f484,f493,f501,f510,f511,f512,f513,f514,f522,f526,f535,f536,f549,f554,f559,f564,f565,f566,f571,f572,f581,f586,f595,f596,f605,f610,f622,f626,f631,f632,f645,f650,f655,f656,f664,f668,f669,f670,f671,f672,f677,f678,f687,f688,f693,f694,f699,f700,f701,f702,f703,f704,f713,f718,f723,f724,f729,f730,f735,f736,f745,f746,f751,f752,f759,f761,f771,f774,f778,f781,f784,f788,f791,f795,f799,f803,f806,f809,f815,f819,f827,f829,f836,f846,f851,f855,f858,f863,f874,f883,f888,f898,f901,f912,f918,f931,f938,f944,f963,f973,f987,f993,f1013,f1051,f1064,f1078,f1099,f1101,f1117,f1123,f1129,f1132,f1134,f1144,f1147,f1149,f1172,f1175,f1185,f1197,f1202,f1209,f1212,f1221,f1252,f1262,f1266,f1269,f1285,f1314,f1317,f1319,f1330,f1363,f1366,f1416,f1438,f1440,f1442,f1446,f1448,f1450,f1461,f1469,f1479,f1484,f1518,f1526,f1533,f1550,f1553,f1573,f1592,f1609,f1612,f1618,f1622,f1638,f1644,f1658,f1662,f1687,f1745,f1751]) ).
thf(f1751,plain,
( ~ spl76_47
| ~ spl76_55 ),
inference(avatar_contradiction_clause,[status(thm)],[f1750]) ).
thf(f1750,plain,
( $false
| ~ spl76_47
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1747]) ).
thf(f1747,plain,
( ( $false = $true )
| ~ spl76_47
| ~ spl76_55 ),
inference(superposition,[status(thm)],[f462,f1697]) ).
thf(f1697,plain,
( ! [X22: $i] :
( $false
= ( cP @ ( sK39 @ X22 ) ) )
| ~ spl76_47
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1695]) ).
thf(f1695,plain,
( ! [X22: $i] :
( ( $false
= ( cP @ ( sK39 @ X22 ) ) )
| ( $false = $true ) )
| ~ spl76_47
| ~ spl76_55 ),
inference(backward_demodulation,[status(thm)],[f431,f462]) ).
thf(f431,plain,
( ! [X22: $i] :
( ( $false
= ( cP @ ( sK39 @ X22 ) ) )
| ( $false
= ( cP @ X22 ) ) )
| ~ spl76_47 ),
inference(avatar_component_clause,[status(thm)],[f430]) ).
thf(f430,definition,
( spl76_47
<=> ! [X22: $i] :
( ( $false
= ( cP @ X22 ) )
| ( $false
= ( cP @ ( sK39 @ X22 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_47])],[avatar_definition]) ).
thf(f462,plain,
( ! [X44: $i] :
( $true
= ( cP @ X44 ) )
| ~ spl76_55 ),
inference(avatar_component_clause,[status(thm)],[f461]) ).
thf(f461,definition,
( spl76_55
<=> ! [X44: $i] :
( $true
= ( cP @ X44 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_55])],[avatar_definition]) ).
thf(f1745,plain,
( ~ spl76_55
| ~ spl76_98 ),
inference(avatar_contradiction_clause,[status(thm)],[f1744]) ).
thf(f1744,plain,
( $false
| ~ spl76_55
| ~ spl76_98 ),
inference(trivial_inequality_removal,[status(thm)],[f1740]) ).
thf(f1740,plain,
( ( $false = $true )
| ~ spl76_55
| ~ spl76_98 ),
inference(superposition,[status(thm)],[f1696,f462]) ).
thf(f1696,plain,
( ! [X28: $i] :
( $false
= ( cP @ ( sK42 @ X28 ) ) )
| ~ spl76_55
| ~ spl76_98 ),
inference(trivial_inequality_removal,[status(thm)],[f1694]) ).
thf(f1694,plain,
( ! [X28: $i] :
( ( $false
= ( cP @ ( sK42 @ X28 ) ) )
| ( $false = $true ) )
| ~ spl76_55
| ~ spl76_98 ),
inference(backward_demodulation,[status(thm)],[f667,f462]) ).
thf(f667,plain,
( ! [X28: $i] :
( ( $false
= ( cP @ ( sK42 @ X28 ) ) )
| ( $false
= ( cP @ X28 ) ) )
| ~ spl76_98 ),
inference(avatar_component_clause,[status(thm)],[f666]) ).
thf(f666,definition,
( spl76_98
<=> ! [X28: $i] :
( ( $false
= ( cP @ ( sK42 @ X28 ) ) )
| ( $false
= ( cP @ X28 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_98])],[avatar_definition]) ).
thf(f1687,plain,
( ~ spl76_4
| spl76_96 ),
inference(avatar_contradiction_clause,[status(thm)],[f1686]) ).
thf(f1686,plain,
( $false
| ~ spl76_4
| spl76_96 ),
inference(trivial_inequality_removal,[status(thm)],[f1685]) ).
thf(f1685,plain,
( ( $true != $true )
| ~ spl76_4
| spl76_96 ),
inference(superposition,[status(thm)],[f660,f257]) ).
thf(f257,plain,
( ! [X35: $i] :
( ( cR @ X35 )
= $true )
| ~ spl76_4 ),
inference(avatar_component_clause,[status(thm)],[f256]) ).
thf(f256,definition,
( spl76_4
<=> ! [X35: $i] :
( ( cR @ X35 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_4])],[avatar_definition]) ).
thf(f660,plain,
( ( ( cR @ sK40 )
!= $true )
| spl76_96 ),
inference(avatar_component_clause,[status(thm)],[f658]) ).
thf(f658,definition,
( spl76_96
<=> ( ( cR @ sK40 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_96])],[avatar_definition]) ).
thf(f1662,plain,
( ~ spl76_22
| ~ spl76_92 ),
inference(avatar_contradiction_clause,[status(thm)],[f1661]) ).
thf(f1661,plain,
( $false
| ~ spl76_22
| ~ spl76_92 ),
inference(trivial_inequality_removal,[status(thm)],[f1660]) ).
thf(f1660,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_92 ),
inference(forward_demodulation,[status(thm)],[f640,f326]) ).
thf(f326,plain,
( ! [X19: $i] :
( $false
= ( cQ @ X19 ) )
| ~ spl76_22 ),
inference(avatar_component_clause,[status(thm)],[f325]) ).
thf(f325,definition,
( spl76_22
<=> ! [X19: $i] :
( $false
= ( cQ @ X19 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_22])],[avatar_definition]) ).
thf(f640,plain,
( ( ( cQ @ sK43 )
= $true )
| ~ spl76_92 ),
inference(avatar_component_clause,[status(thm)],[f638]) ).
thf(f638,definition,
( spl76_92
<=> ( ( cQ @ sK43 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_92])],[avatar_definition]) ).
thf(f1658,plain,
( ~ spl76_4
| spl76_91 ),
inference(avatar_contradiction_clause,[status(thm)],[f1657]) ).
thf(f1657,plain,
( $false
| ~ spl76_4
| spl76_91 ),
inference(subsumption_resolution,[status(thm)],[f636,f257]) ).
thf(f636,plain,
( ( $true
!= ( cR @ sK44 ) )
| spl76_91 ),
inference(avatar_component_clause,[status(thm)],[f634]) ).
thf(f634,definition,
( spl76_91
<=> ( $true
= ( cR @ sK44 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_91])],[avatar_definition]) ).
thf(f1644,plain,
( ~ spl76_93
| ~ spl76_94 ),
inference(avatar_contradiction_clause,[status(thm)],[f1643]) ).
thf(f1643,plain,
( $false
| ~ spl76_93
| ~ spl76_94 ),
inference(trivial_inequality_removal,[status(thm)],[f1642]) ).
thf(f1642,plain,
( ( $false = $true )
| ~ spl76_93
| ~ spl76_94 ),
inference(forward_demodulation,[status(thm)],[f649,f644]) ).
thf(f644,plain,
( ( $false
= ( cP @ sK45 ) )
| ~ spl76_93 ),
inference(avatar_component_clause,[status(thm)],[f642]) ).
thf(f642,definition,
( spl76_93
<=> ( $false
= ( cP @ sK45 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_93])],[avatar_definition]) ).
thf(f649,plain,
( ( $true
= ( cP @ sK45 ) )
| ~ spl76_94 ),
inference(avatar_component_clause,[status(thm)],[f647]) ).
thf(f647,definition,
( spl76_94
<=> ( $true
= ( cP @ sK45 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_94])],[avatar_definition]) ).
thf(f1638,plain,
( ~ spl76_22
| ~ spl76_103 ),
inference(avatar_contradiction_clause,[status(thm)],[f1637]) ).
thf(f1637,plain,
( $false
| ~ spl76_22
| ~ spl76_103 ),
inference(trivial_inequality_removal,[status(thm)],[f1636]) ).
thf(f1636,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_103 ),
inference(forward_demodulation,[status(thm)],[f698,f326]) ).
thf(f698,plain,
( ( ( cQ @ sK41 )
= $true )
| ~ spl76_103 ),
inference(avatar_component_clause,[status(thm)],[f696]) ).
thf(f696,definition,
( spl76_103
<=> ( ( cQ @ sK41 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_103])],[avatar_definition]) ).
thf(f1622,plain,
( ~ spl76_24
| ~ spl76_97 ),
inference(avatar_contradiction_clause,[status(thm)],[f1621]) ).
thf(f1621,plain,
( $false
| ~ spl76_24
| ~ spl76_97 ),
inference(subsumption_resolution,[status(thm)],[f1620,f334]) ).
thf(f334,plain,
( ! [X9: $i] :
( ( cP @ X9 )
!= $true )
| ~ spl76_24 ),
inference(avatar_component_clause,[status(thm)],[f333]) ).
thf(f333,definition,
( spl76_24
<=> ! [X9: $i] :
( ( cP @ X9 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_24])],[avatar_definition]) ).
thf(f1620,plain,
( ! [X28: $i] :
( $true
= ( cP @ X28 ) )
| ~ spl76_24
| ~ spl76_97 ),
inference(subsumption_resolution,[status(thm)],[f663,f334]) ).
thf(f663,plain,
( ! [X28: $i] :
( ( $true
= ( cP @ ( sK42 @ X28 ) ) )
| ( $true
= ( cP @ X28 ) ) )
| ~ spl76_97 ),
inference(avatar_component_clause,[status(thm)],[f662]) ).
thf(f662,definition,
( spl76_97
<=> ! [X28: $i] :
( ( $true
= ( cP @ ( sK42 @ X28 ) ) )
| ( $true
= ( cP @ X28 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_97])],[avatar_definition]) ).
thf(f1618,plain,
( ~ spl76_11
| ~ spl76_103 ),
inference(avatar_contradiction_clause,[status(thm)],[f1617]) ).
thf(f1617,plain,
( $false
| ~ spl76_11
| ~ spl76_103 ),
inference(subsumption_resolution,[status(thm)],[f698,f284]) ).
thf(f284,plain,
( ! [X45: $i] :
( $true
!= ( cQ @ X45 ) )
| ~ spl76_11 ),
inference(avatar_component_clause,[status(thm)],[f283]) ).
thf(f283,definition,
( spl76_11
<=> ! [X45: $i] :
( $true
!= ( cQ @ X45 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_11])],[avatar_definition]) ).
thf(f1612,plain,
( ~ spl76_7
| ~ spl76_33 ),
inference(avatar_contradiction_clause,[status(thm)],[f1611]) ).
thf(f1611,plain,
( $false
| ~ spl76_7
| ~ spl76_33 ),
inference(trivial_inequality_removal,[status(thm)],[f1610]) ).
thf(f1610,plain,
( ( $false = $true )
| ~ spl76_7
| ~ spl76_33 ),
inference(forward_demodulation,[status(thm)],[f371,f269]) ).
thf(f269,plain,
( ! [X35: $i] :
( $false
= ( cR @ X35 ) )
| ~ spl76_7 ),
inference(avatar_component_clause,[status(thm)],[f268]) ).
thf(f268,definition,
( spl76_7
<=> ! [X35: $i] :
( $false
= ( cR @ X35 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_7])],[avatar_definition]) ).
thf(f371,plain,
( ( ( cR @ sK68 )
= $true )
| ~ spl76_33 ),
inference(avatar_component_clause,[status(thm)],[f369]) ).
thf(f369,definition,
( spl76_33
<=> ( ( cR @ sK68 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_33])],[avatar_definition]) ).
thf(f1609,plain,
( ~ spl76_11
| ~ spl76_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f1608]) ).
thf(f1608,plain,
( $false
| ~ spl76_11
| ~ spl76_36 ),
inference(subsumption_resolution,[status(thm)],[f1607,f284]) ).
thf(f1607,plain,
( ! [X0: $i] :
( ( cQ @ X0 )
= $true )
| ~ spl76_11
| ~ spl76_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1606]) ).
thf(f1606,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl76_11
| ~ spl76_36 ),
inference(superposition,[status(thm)],[f284,f384]) ).
thf(f384,plain,
( ! [X0: $i] :
( ( $true
= ( cQ @ ( sK64 @ X0 ) ) )
| ( ( cQ @ X0 )
= $true ) )
| ~ spl76_36 ),
inference(avatar_component_clause,[status(thm)],[f383]) ).
thf(f383,definition,
( spl76_36
<=> ! [X0: $i] :
( ( ( cQ @ X0 )
= $true )
| ( $true
= ( cQ @ ( sK64 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_36])],[avatar_definition]) ).
thf(f1592,plain,
( ~ spl76_11
| ~ spl76_105 ),
inference(avatar_contradiction_clause,[status(thm)],[f1591]) ).
thf(f1591,plain,
( $false
| ~ spl76_11
| ~ spl76_105 ),
inference(trivial_inequality_removal,[status(thm)],[f1590]) ).
thf(f1590,plain,
( ( $true != $true )
| ~ spl76_11
| ~ spl76_105 ),
inference(superposition,[status(thm)],[f284,f712]) ).
thf(f712,plain,
( ( $true
= ( cQ @ sK36 ) )
| ~ spl76_105 ),
inference(avatar_component_clause,[status(thm)],[f710]) ).
thf(f710,definition,
( spl76_105
<=> ( $true
= ( cQ @ sK36 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_105])],[avatar_definition]) ).
thf(f1573,plain,
( ~ spl76_7
| ~ spl76_37 ),
inference(avatar_contradiction_clause,[status(thm)],[f1572]) ).
thf(f1572,plain,
( $false
| ~ spl76_7
| ~ spl76_37 ),
inference(trivial_inequality_removal,[status(thm)],[f1571]) ).
thf(f1571,plain,
( ( $false = $true )
| ~ spl76_7
| ~ spl76_37 ),
inference(forward_demodulation,[status(thm)],[f388,f269]) ).
thf(f388,plain,
( ( $true
= ( cR @ sK66 ) )
| ~ spl76_37 ),
inference(avatar_component_clause,[status(thm)],[f386]) ).
thf(f386,definition,
( spl76_37
<=> ( $true
= ( cR @ sK66 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_37])],[avatar_definition]) ).
thf(f1553,plain,
( ~ spl76_22
| ~ spl76_105 ),
inference(avatar_contradiction_clause,[status(thm)],[f1552]) ).
thf(f1552,plain,
( $false
| ~ spl76_22
| ~ spl76_105 ),
inference(trivial_inequality_removal,[status(thm)],[f1551]) ).
thf(f1551,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_105 ),
inference(forward_demodulation,[status(thm)],[f712,f326]) ).
thf(f1550,plain,
( ~ spl76_24
| ~ spl76_44 ),
inference(avatar_contradiction_clause,[status(thm)],[f1549]) ).
thf(f1549,plain,
( $false
| ~ spl76_24
| ~ spl76_44 ),
inference(subsumption_resolution,[status(thm)],[f1548,f334]) ).
thf(f1548,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl76_24
| ~ spl76_44 ),
inference(trivial_inequality_removal,[status(thm)],[f1547]) ).
thf(f1547,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl76_24
| ~ spl76_44 ),
inference(superposition,[status(thm)],[f334,f419]) ).
thf(f419,plain,
( ! [X22: $i] :
( ( ( cP @ ( sK39 @ X22 ) )
= $true )
| ( $true
= ( cP @ X22 ) ) )
| ~ spl76_44 ),
inference(avatar_component_clause,[status(thm)],[f418]) ).
thf(f418,definition,
( spl76_44
<=> ! [X22: $i] :
( ( $true
= ( cP @ X22 ) )
| ( ( cP @ ( sK39 @ X22 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl76_44])],[avatar_definition]) ).
thf(f1533,plain,
( ~ spl76_44
| ~ spl76_62 ),
inference(avatar_contradiction_clause,[status(thm)],[f1532]) ).
thf(f1532,plain,
( $false
| ~ spl76_44
| ~ spl76_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1531]) ).
thf(f1531,plain,
( ( $false = $true )
| ~ spl76_44
| ~ spl76_62 ),
inference(forward_demodulation,[status(thm)],[f1530,f496]) ).
thf(f496,plain,
( ! [X37: $i] :
( ( cP @ X37 )
= $false )
| ~ spl76_62 ),
inference(avatar_component_clause,[status(thm)],[f495]) ).
thf(f495,definition,
( spl76_62
<=> ! [X37: $i] :
( ( cP @ X37 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl76_62])],[avatar_definition]) ).
thf(f1530,plain,
( ! [X22: $i] :
( ( cP @ ( sK39 @ X22 ) )
= $true )
| ~ spl76_44
| ~ spl76_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1529]) ).
thf(f1529,plain,
( ! [X22: $i] :
( ( $false = $true )
| ( ( cP @ ( sK39 @ X22 ) )
= $true ) )
| ~ spl76_44
| ~ spl76_62 ),
inference(forward_demodulation,[status(thm)],[f419,f496]) ).
thf(f1526,plain,
( ~ spl76_22
| ~ spl76_36 ),
inference(avatar_contradiction_clause,[status(thm)],[f1525]) ).
thf(f1525,plain,
( $false
| ~ spl76_22
| ~ spl76_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1524]) ).
thf(f1524,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_36 ),
inference(forward_demodulation,[status(thm)],[f1519,f326]) ).
thf(f1519,plain,
( ! [X0: $i] :
( $true
= ( cQ @ ( sK64 @ X0 ) ) )
| ~ spl76_22
| ~ spl76_36 ),
inference(trivial_inequality_removal,[status(thm)],[f1506]) ).
thf(f1506,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $true
= ( cQ @ ( sK64 @ X0 ) ) ) )
| ~ spl76_22
| ~ spl76_36 ),
inference(backward_demodulation,[status(thm)],[f384,f326]) ).
thf(f1518,plain,
( ~ spl76_22
| ~ spl76_45 ),
inference(avatar_contradiction_clause,[status(thm)],[f1517]) ).
thf(f1517,plain,
( $false
| ~ spl76_22
| ~ spl76_45 ),
inference(trivial_inequality_removal,[status(thm)],[f1509]) ).
thf(f1509,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_45 ),
inference(backward_demodulation,[status(thm)],[f423,f326]) ).
thf(f423,plain,
( ( ( cQ @ sK37 )
= $true )
| ~ spl76_45 ),
inference(avatar_component_clause,[status(thm)],[f421]) ).
thf(f421,definition,
( spl76_45
<=> ( ( cQ @ sK37 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_45])],[avatar_definition]) ).
thf(f1484,plain,
( ~ spl76_32
| ~ spl76_35 ),
inference(avatar_contradiction_clause,[status(thm)],[f1483]) ).
thf(f1483,plain,
( $false
| ~ spl76_32
| ~ spl76_35 ),
inference(trivial_inequality_removal,[status(thm)],[f1482]) ).
thf(f1482,plain,
( ( $false = $true )
| ~ spl76_32
| ~ spl76_35 ),
inference(forward_demodulation,[status(thm)],[f367,f380]) ).
thf(f380,plain,
( ( ( cQ @ sK67 )
= $false )
| ~ spl76_35 ),
inference(avatar_component_clause,[status(thm)],[f378]) ).
thf(f378,definition,
( spl76_35
<=> ( ( cQ @ sK67 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl76_35])],[avatar_definition]) ).
thf(f367,plain,
( ( ( cQ @ sK67 )
= $true )
| ~ spl76_32 ),
inference(avatar_component_clause,[status(thm)],[f365]) ).
thf(f365,definition,
( spl76_32
<=> ( ( cQ @ sK67 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_32])],[avatar_definition]) ).
thf(f1479,plain,
( ~ spl76_104
| ~ spl76_106 ),
inference(avatar_contradiction_clause,[status(thm)],[f1478]) ).
thf(f1478,plain,
( $false
| ~ spl76_104
| ~ spl76_106 ),
inference(trivial_inequality_removal,[status(thm)],[f1477]) ).
thf(f1477,plain,
( ( $false = $true )
| ~ spl76_104
| ~ spl76_106 ),
inference(backward_demodulation,[status(thm)],[f708,f717]) ).
thf(f717,plain,
( ( ( cP @ sK34 )
= $false )
| ~ spl76_106 ),
inference(avatar_component_clause,[status(thm)],[f715]) ).
thf(f715,definition,
( spl76_106
<=> ( ( cP @ sK34 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl76_106])],[avatar_definition]) ).
thf(f708,plain,
( ( ( cP @ sK34 )
= $true )
| ~ spl76_104 ),
inference(avatar_component_clause,[status(thm)],[f706]) ).
thf(f706,definition,
( spl76_104
<=> ( ( cP @ sK34 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_104])],[avatar_definition]) ).
thf(f1469,plain,
( ~ spl76_25
| ~ spl76_81 ),
inference(avatar_contradiction_clause,[status(thm)],[f1468]) ).
thf(f1468,plain,
( $false
| ~ spl76_25
| ~ spl76_81 ),
inference(trivial_inequality_removal,[status(thm)],[f1465]) ).
thf(f1465,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_81 ),
inference(backward_demodulation,[status(thm)],[f590,f337]) ).
thf(f337,plain,
( ! [X11: $i] :
( ( cS @ X11 )
= $false )
| ~ spl76_25 ),
inference(avatar_component_clause,[status(thm)],[f336]) ).
thf(f336,definition,
( spl76_25
<=> ! [X11: $i] :
( ( cS @ X11 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl76_25])],[avatar_definition]) ).
thf(f590,plain,
( ( ( cS @ sK7 )
= $true )
| ~ spl76_81 ),
inference(avatar_component_clause,[status(thm)],[f588]) ).
thf(f588,definition,
( spl76_81
<=> ( ( cS @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_81])],[avatar_definition]) ).
thf(f1461,plain,
( ~ spl76_20
| ~ spl76_38 ),
inference(avatar_contradiction_clause,[status(thm)],[f1460]) ).
thf(f1460,plain,
( $false
| ~ spl76_20
| ~ spl76_38 ),
inference(trivial_inequality_removal,[status(thm)],[f1456]) ).
thf(f1456,plain,
( ( $false = $true )
| ~ spl76_20
| ~ spl76_38 ),
inference(superposition,[status(thm)],[f1452,f318]) ).
thf(f318,plain,
( ! [X19: $i] :
( $true
= ( cQ @ X19 ) )
| ~ spl76_20 ),
inference(avatar_component_clause,[status(thm)],[f317]) ).
thf(f317,definition,
( spl76_20
<=> ! [X19: $i] :
( $true
= ( cQ @ X19 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_20])],[avatar_definition]) ).
thf(f1452,plain,
( ! [X0: $i] :
( $false
= ( cQ @ ( sK64 @ X0 ) ) )
| ~ spl76_20
| ~ spl76_38 ),
inference(trivial_inequality_removal,[status(thm)],[f1451]) ).
thf(f1451,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( cQ @ ( sK64 @ X0 ) ) ) )
| ~ spl76_20
| ~ spl76_38 ),
inference(forward_demodulation,[status(thm)],[f392,f318]) ).
thf(f392,plain,
( ! [X0: $i] :
( ( $false
= ( cQ @ ( sK64 @ X0 ) ) )
| ( ( cQ @ X0 )
= $false ) )
| ~ spl76_38 ),
inference(avatar_component_clause,[status(thm)],[f391]) ).
thf(f391,definition,
( spl76_38
<=> ! [X0: $i] :
( ( $false
= ( cQ @ ( sK64 @ X0 ) ) )
| ( ( cQ @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl76_38])],[avatar_definition]) ).
thf(f1450,plain,
( ~ spl76_55
| spl76_109 ),
inference(avatar_contradiction_clause,[status(thm)],[f1449]) ).
thf(f1449,plain,
( $false
| ~ spl76_55
| spl76_109 ),
inference(subsumption_resolution,[status(thm)],[f733,f462]) ).
thf(f733,plain,
( ( ( cP @ sK60 )
!= $true )
| spl76_109 ),
inference(avatar_component_clause,[status(thm)],[f732]) ).
thf(f732,definition,
( spl76_109
<=> ( ( cP @ sK60 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_109])],[avatar_definition]) ).
thf(f1448,plain,
( ~ spl76_19
| spl76_34 ),
inference(avatar_contradiction_clause,[status(thm)],[f1447]) ).
thf(f1447,plain,
( $false
| ~ spl76_19
| spl76_34 ),
inference(subsumption_resolution,[status(thm)],[f375,f315]) ).
thf(f315,plain,
( ! [X23: $i] :
( ( cS @ X23 )
= $true )
| ~ spl76_19 ),
inference(avatar_component_clause,[status(thm)],[f314]) ).
thf(f314,definition,
( spl76_19
<=> ! [X23: $i] :
( ( cS @ X23 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_19])],[avatar_definition]) ).
thf(f375,plain,
( ( $true
!= ( cS @ sK69 ) )
| spl76_34 ),
inference(avatar_component_clause,[status(thm)],[f373]) ).
thf(f373,definition,
( spl76_34
<=> ( $true
= ( cS @ sK69 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_34])],[avatar_definition]) ).
thf(f1446,plain,
( ~ spl76_19
| spl76_39 ),
inference(avatar_contradiction_clause,[status(thm)],[f1445]) ).
thf(f1445,plain,
( $false
| ~ spl76_19
| spl76_39 ),
inference(subsumption_resolution,[status(thm)],[f397,f315]) ).
thf(f397,plain,
( ( $true
!= ( cS @ sK65 ) )
| spl76_39 ),
inference(avatar_component_clause,[status(thm)],[f395]) ).
thf(f395,definition,
( spl76_39
<=> ( $true
= ( cS @ sK65 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_39])],[avatar_definition]) ).
thf(f1442,plain,
( ~ spl76_4
| spl76_46 ),
inference(avatar_contradiction_clause,[status(thm)],[f1441]) ).
thf(f1441,plain,
( $false
| ~ spl76_4
| spl76_46 ),
inference(subsumption_resolution,[status(thm)],[f427,f257]) ).
thf(f427,plain,
( ( $true
!= ( cR @ sK38 ) )
| spl76_46 ),
inference(avatar_component_clause,[status(thm)],[f425]) ).
thf(f425,definition,
( spl76_46
<=> ( $true
= ( cR @ sK38 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_46])],[avatar_definition]) ).
thf(f1440,plain,
( ~ spl76_4
| spl76_108 ),
inference(avatar_contradiction_clause,[status(thm)],[f1439]) ).
thf(f1439,plain,
( $false
| ~ spl76_4
| spl76_108 ),
inference(subsumption_resolution,[status(thm)],[f728,f257]) ).
thf(f728,plain,
( ( ( cR @ sK35 )
!= $true )
| spl76_108 ),
inference(avatar_component_clause,[status(thm)],[f726]) ).
thf(f726,definition,
( spl76_108
<=> ( ( cR @ sK35 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_108])],[avatar_definition]) ).
thf(f1438,plain,
( ~ spl76_19
| ~ spl76_58 ),
inference(avatar_contradiction_clause,[status(thm)],[f1437]) ).
thf(f1437,plain,
( $false
| ~ spl76_19
| ~ spl76_58 ),
inference(trivial_inequality_removal,[status(thm)],[f1433]) ).
thf(f1433,plain,
( ( $false = $true )
| ~ spl76_19
| ~ spl76_58 ),
inference(superposition,[status(thm)],[f1386,f315]) ).
thf(f1386,plain,
( ! [X22: $i] :
( ( cS @ ( sK63 @ X22 ) )
= $false )
| ~ spl76_19
| ~ spl76_58 ),
inference(trivial_inequality_removal,[status(thm)],[f1385]) ).
thf(f1385,plain,
( ! [X22: $i] :
( ( ( cS @ ( sK63 @ X22 ) )
= $false )
| ( $false = $true ) )
| ~ spl76_19
| ~ spl76_58 ),
inference(backward_demodulation,[status(thm)],[f474,f315]) ).
thf(f474,plain,
( ! [X22: $i] :
( ( $false
= ( cS @ X22 ) )
| ( ( cS @ ( sK63 @ X22 ) )
= $false ) )
| ~ spl76_58 ),
inference(avatar_component_clause,[status(thm)],[f473]) ).
thf(f473,definition,
( spl76_58
<=> ! [X22: $i] :
( ( ( cS @ ( sK63 @ X22 ) )
= $false )
| ( $false
= ( cS @ X22 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_58])],[avatar_definition]) ).
thf(f1416,plain,
( ~ spl76_19
| spl76_112 ),
inference(avatar_contradiction_clause,[status(thm)],[f1415]) ).
thf(f1415,plain,
( $false
| ~ spl76_19
| spl76_112 ),
inference(trivial_inequality_removal,[status(thm)],[f1400]) ).
thf(f1400,plain,
( ( $true != $true )
| ~ spl76_19
| spl76_112 ),
inference(superposition,[status(thm)],[f749,f315]) ).
thf(f749,plain,
( ( ( cS @ sK12 )
!= $true )
| spl76_112 ),
inference(avatar_component_clause,[status(thm)],[f748]) ).
thf(f748,definition,
( spl76_112
<=> ( ( cS @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_112])],[avatar_definition]) ).
thf(f1366,plain,
( ~ spl76_75
| ~ spl76_76 ),
inference(avatar_contradiction_clause,[status(thm)],[f1365]) ).
thf(f1365,plain,
( $false
| ~ spl76_75
| ~ spl76_76 ),
inference(trivial_inequality_removal,[status(thm)],[f1364]) ).
thf(f1364,plain,
( ( $false = $true )
| ~ spl76_75
| ~ spl76_76 ),
inference(backward_demodulation,[status(thm)],[f563,f558]) ).
thf(f558,plain,
( ( $false
= ( cR @ sK9 ) )
| ~ spl76_75 ),
inference(avatar_component_clause,[status(thm)],[f556]) ).
thf(f556,definition,
( spl76_75
<=> ( $false
= ( cR @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_75])],[avatar_definition]) ).
thf(f563,plain,
( ( $true
= ( cR @ sK9 ) )
| ~ spl76_76 ),
inference(avatar_component_clause,[status(thm)],[f561]) ).
thf(f561,definition,
( spl76_76
<=> ( $true
= ( cR @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_76])],[avatar_definition]) ).
thf(f1363,plain,
( ~ spl76_15
| ~ spl76_40 ),
inference(avatar_contradiction_clause,[status(thm)],[f1362]) ).
thf(f1362,plain,
( $false
| ~ spl76_15
| ~ spl76_40 ),
inference(subsumption_resolution,[status(thm)],[f1361,f400]) ).
thf(f400,plain,
( ! [X2: $i] :
( $true
!= ( cR @ X2 ) )
| ~ spl76_40 ),
inference(avatar_component_clause,[status(thm)],[f399]) ).
thf(f399,definition,
( spl76_40
<=> ! [X2: $i] :
( $true
!= ( cR @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_40])],[avatar_definition]) ).
thf(f1361,plain,
( ! [X0: $i] :
( ( cR @ X0 )
= $true )
| ~ spl76_15
| ~ spl76_40 ),
inference(trivial_inequality_removal,[status(thm)],[f1360]) ).
thf(f1360,plain,
( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl76_15
| ~ spl76_40 ),
inference(superposition,[status(thm)],[f400,f300]) ).
thf(f300,plain,
( ! [X4: $i] :
( ( ( cR @ ( sK6 @ X4 ) )
= $true )
| ( $true
= ( cR @ X4 ) ) )
| ~ spl76_15 ),
inference(avatar_component_clause,[status(thm)],[f299]) ).
thf(f299,definition,
( spl76_15
<=> ! [X4: $i] :
( ( ( cR @ ( sK6 @ X4 ) )
= $true )
| ( $true
= ( cR @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_15])],[avatar_definition]) ).
thf(f1330,plain,
( spl76_14
| ~ spl76_55 ),
inference(avatar_contradiction_clause,[status(thm)],[f1329]) ).
thf(f1329,plain,
( $false
| spl76_14
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1323]) ).
thf(f1323,plain,
( ( $true != $true )
| spl76_14
| ~ spl76_55 ),
inference(superposition,[status(thm)],[f297,f462]) ).
thf(f297,plain,
( ( $true
!= ( cP @ sK4 ) )
| spl76_14 ),
inference(avatar_component_clause,[status(thm)],[f295]) ).
thf(f295,definition,
( spl76_14
<=> ( $true
= ( cP @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_14])],[avatar_definition]) ).
thf(f1319,plain,
( ~ spl76_55
| spl76_82 ),
inference(avatar_contradiction_clause,[status(thm)],[f1318]) ).
thf(f1318,plain,
( $false
| ~ spl76_55
| spl76_82 ),
inference(subsumption_resolution,[status(thm)],[f594,f462]) ).
thf(f594,plain,
( ( ( cP @ sK8 )
!= $true )
| spl76_82 ),
inference(avatar_component_clause,[status(thm)],[f592]) ).
thf(f592,definition,
( spl76_82
<=> ( ( cP @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_82])],[avatar_definition]) ).
thf(f1317,plain,
( ~ spl76_25
| ~ spl76_90 ),
inference(avatar_contradiction_clause,[status(thm)],[f1316]) ).
thf(f1316,plain,
( $false
| ~ spl76_25
| ~ spl76_90 ),
inference(trivial_inequality_removal,[status(thm)],[f1315]) ).
thf(f1315,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_90 ),
inference(forward_demodulation,[status(thm)],[f630,f337]) ).
thf(f630,plain,
( ( ( cS @ sK5 )
= $true )
| ~ spl76_90 ),
inference(avatar_component_clause,[status(thm)],[f628]) ).
thf(f628,definition,
( spl76_90
<=> ( ( cS @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_90])],[avatar_definition]) ).
thf(f1314,plain,
( ~ spl76_4
| ~ spl76_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f1313]) ).
thf(f1313,plain,
( $false
| ~ spl76_4
| ~ spl76_17 ),
inference(trivial_inequality_removal,[status(thm)],[f1310]) ).
thf(f1310,plain,
( ( $false = $true )
| ~ spl76_4
| ~ spl76_17 ),
inference(superposition,[status(thm)],[f257,f1296]) ).
thf(f1296,plain,
( ! [X4: $i] :
( $false
= ( cR @ ( sK6 @ X4 ) ) )
| ~ spl76_4
| ~ spl76_17 ),
inference(trivial_inequality_removal,[status(thm)],[f1295]) ).
thf(f1295,plain,
( ! [X4: $i] :
( ( $false = $true )
| ( $false
= ( cR @ ( sK6 @ X4 ) ) ) )
| ~ spl76_4
| ~ spl76_17 ),
inference(forward_demodulation,[status(thm)],[f307,f257]) ).
thf(f307,plain,
( ! [X4: $i] :
( ( $false
= ( cR @ X4 ) )
| ( $false
= ( cR @ ( sK6 @ X4 ) ) ) )
| ~ spl76_17 ),
inference(avatar_component_clause,[status(thm)],[f306]) ).
thf(f306,definition,
( spl76_17
<=> ! [X4: $i] :
( ( $false
= ( cR @ X4 ) )
| ( $false
= ( cR @ ( sK6 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_17])],[avatar_definition]) ).
thf(f1285,plain,
( ~ spl76_4
| ~ spl76_56 ),
inference(avatar_contradiction_clause,[status(thm)],[f1284]) ).
thf(f1284,plain,
( $false
| ~ spl76_4
| ~ spl76_56 ),
inference(trivial_inequality_removal,[status(thm)],[f1281]) ).
thf(f1281,plain,
( ( $false = $true )
| ~ spl76_4
| ~ spl76_56 ),
inference(superposition,[status(thm)],[f257,f1271]) ).
thf(f1271,plain,
( ! [X46: $i] :
( $false
= ( cR @ ( sK27 @ X46 ) ) )
| ~ spl76_4
| ~ spl76_56 ),
inference(trivial_inequality_removal,[status(thm)],[f1270]) ).
thf(f1270,plain,
( ! [X46: $i] :
( ( $false
= ( cR @ ( sK27 @ X46 ) ) )
| ( $false = $true ) )
| ~ spl76_4
| ~ spl76_56 ),
inference(backward_demodulation,[status(thm)],[f466,f257]) ).
thf(f466,plain,
( ! [X46: $i] :
( ( $false
= ( cR @ ( sK27 @ X46 ) ) )
| ( ( cR @ X46 )
= $false ) )
| ~ spl76_56 ),
inference(avatar_component_clause,[status(thm)],[f465]) ).
thf(f465,definition,
( spl76_56
<=> ! [X46: $i] :
( ( $false
= ( cR @ ( sK27 @ X46 ) ) )
| ( ( cR @ X46 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl76_56])],[avatar_definition]) ).
thf(f1269,plain,
( ~ spl76_62
| ~ spl76_109 ),
inference(avatar_contradiction_clause,[status(thm)],[f1268]) ).
thf(f1268,plain,
( $false
| ~ spl76_62
| ~ spl76_109 ),
inference(trivial_inequality_removal,[status(thm)],[f1267]) ).
thf(f1267,plain,
( ( $false = $true )
| ~ spl76_62
| ~ spl76_109 ),
inference(forward_demodulation,[status(thm)],[f734,f496]) ).
thf(f734,plain,
( ( ( cP @ sK60 )
= $true )
| ~ spl76_109 ),
inference(avatar_component_clause,[status(thm)],[f732]) ).
thf(f1266,plain,
( ~ spl76_79
| ~ spl76_80 ),
inference(avatar_contradiction_clause,[status(thm)],[f1265]) ).
thf(f1265,plain,
( $false
| ~ spl76_79
| ~ spl76_80 ),
inference(trivial_inequality_removal,[status(thm)],[f1264]) ).
thf(f1264,plain,
( ( $false = $true )
| ~ spl76_79
| ~ spl76_80 ),
inference(forward_demodulation,[status(thm)],[f585,f580]) ).
thf(f580,plain,
( ( $false
= ( cR @ sK22 ) )
| ~ spl76_79 ),
inference(avatar_component_clause,[status(thm)],[f578]) ).
thf(f578,definition,
( spl76_79
<=> ( $false
= ( cR @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_79])],[avatar_definition]) ).
thf(f585,plain,
( ( $true
= ( cR @ sK22 ) )
| ~ spl76_80 ),
inference(avatar_component_clause,[status(thm)],[f583]) ).
thf(f583,definition,
( spl76_80
<=> ( $true
= ( cR @ sK22 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_80])],[avatar_definition]) ).
thf(f1262,plain,
( ~ spl76_16
| ~ spl76_57 ),
inference(avatar_contradiction_clause,[status(thm)],[f1261]) ).
thf(f1261,plain,
( $false
| ~ spl76_16
| ~ spl76_57 ),
inference(subsumption_resolution,[status(thm)],[f1260,f303]) ).
thf(f303,plain,
( ! [X1: $i] :
( ( cS @ X1 )
!= $true )
| ~ spl76_16 ),
inference(avatar_component_clause,[status(thm)],[f302]) ).
thf(f302,definition,
( spl76_16
<=> ! [X1: $i] :
( ( cS @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_16])],[avatar_definition]) ).
thf(f1260,plain,
( ! [X0: $i] :
( ( cS @ X0 )
= $true )
| ~ spl76_16
| ~ spl76_57 ),
inference(trivial_inequality_removal,[status(thm)],[f1259]) ).
thf(f1259,plain,
( ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl76_16
| ~ spl76_57 ),
inference(superposition,[status(thm)],[f303,f470]) ).
thf(f470,plain,
( ! [X22: $i] :
( ( ( cS @ ( sK63 @ X22 ) )
= $true )
| ( $true
= ( cS @ X22 ) ) )
| ~ spl76_57 ),
inference(avatar_component_clause,[status(thm)],[f469]) ).
thf(f469,definition,
( spl76_57
<=> ! [X22: $i] :
( ( ( cS @ ( sK63 @ X22 ) )
= $true )
| ( $true
= ( cS @ X22 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_57])],[avatar_definition]) ).
thf(f1252,plain,
( ~ spl76_16
| ~ spl76_107 ),
inference(avatar_contradiction_clause,[status(thm)],[f1251]) ).
thf(f1251,plain,
( $false
| ~ spl76_16
| ~ spl76_107 ),
inference(trivial_inequality_removal,[status(thm)],[f1250]) ).
thf(f1250,plain,
( ( $true != $true )
| ~ spl76_16
| ~ spl76_107 ),
inference(superposition,[status(thm)],[f303,f722]) ).
thf(f722,plain,
( ( ( cS @ sK24 )
= $true )
| ~ spl76_107 ),
inference(avatar_component_clause,[status(thm)],[f720]) ).
thf(f720,definition,
( spl76_107
<=> ( ( cS @ sK24 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_107])],[avatar_definition]) ).
thf(f1221,plain,
( ~ spl76_62
| ~ spl76_70 ),
inference(avatar_contradiction_clause,[status(thm)],[f1220]) ).
thf(f1220,plain,
( $false
| ~ spl76_62
| ~ spl76_70 ),
inference(trivial_inequality_removal,[status(thm)],[f1219]) ).
thf(f1219,plain,
( ( $false = $true )
| ~ spl76_62
| ~ spl76_70 ),
inference(backward_demodulation,[status(thm)],[f534,f496]) ).
thf(f534,plain,
( ( $true
= ( cP @ sK61 ) )
| ~ spl76_70 ),
inference(avatar_component_clause,[status(thm)],[f532]) ).
thf(f532,definition,
( spl76_70
<=> ( $true
= ( cP @ sK61 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_70])],[avatar_definition]) ).
thf(f1212,plain,
( ~ spl76_25
| ~ spl76_107 ),
inference(avatar_contradiction_clause,[status(thm)],[f1211]) ).
thf(f1211,plain,
( $false
| ~ spl76_25
| ~ spl76_107 ),
inference(trivial_inequality_removal,[status(thm)],[f1210]) ).
thf(f1210,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_107 ),
inference(forward_demodulation,[status(thm)],[f722,f337]) ).
thf(f1209,plain,
( ~ spl76_40
| ~ spl76_54 ),
inference(avatar_contradiction_clause,[status(thm)],[f1208]) ).
thf(f1208,plain,
( $false
| ~ spl76_40
| ~ spl76_54 ),
inference(subsumption_resolution,[status(thm)],[f1207,f400]) ).
thf(f1207,plain,
( ! [X0: $i] :
( ( cR @ X0 )
= $true )
| ~ spl76_40
| ~ spl76_54 ),
inference(trivial_inequality_removal,[status(thm)],[f1206]) ).
thf(f1206,plain,
( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl76_40
| ~ spl76_54 ),
inference(superposition,[status(thm)],[f400,f459]) ).
thf(f459,plain,
( ! [X46: $i] :
( ( ( cR @ ( sK27 @ X46 ) )
= $true )
| ( ( cR @ X46 )
= $true ) )
| ~ spl76_54 ),
inference(avatar_component_clause,[status(thm)],[f458]) ).
thf(f458,definition,
( spl76_54
<=> ! [X46: $i] :
( ( ( cR @ X46 )
= $true )
| ( ( cR @ ( sK27 @ X46 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl76_54])],[avatar_definition]) ).
thf(f1202,plain,
( ~ spl76_25
| ~ spl76_57 ),
inference(avatar_contradiction_clause,[status(thm)],[f1201]) ).
thf(f1201,plain,
( $false
| ~ spl76_25
| ~ spl76_57 ),
inference(trivial_inequality_removal,[status(thm)],[f1200]) ).
thf(f1200,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_57 ),
inference(forward_demodulation,[status(thm)],[f1199,f337]) ).
thf(f1199,plain,
( ! [X22: $i] :
( $true
= ( cS @ X22 ) )
| ~ spl76_25
| ~ spl76_57 ),
inference(trivial_inequality_removal,[status(thm)],[f1198]) ).
thf(f1198,plain,
( ! [X22: $i] :
( ( $true
= ( cS @ X22 ) )
| ( $false = $true ) )
| ~ spl76_25
| ~ spl76_57 ),
inference(forward_demodulation,[status(thm)],[f470,f337]) ).
thf(f1197,plain,
( ~ spl76_20
| spl76_69 ),
inference(avatar_contradiction_clause,[status(thm)],[f1196]) ).
thf(f1196,plain,
( $false
| ~ spl76_20
| spl76_69 ),
inference(trivial_inequality_removal,[status(thm)],[f1195]) ).
thf(f1195,plain,
( ( $true != $true )
| ~ spl76_20
| spl76_69 ),
inference(superposition,[status(thm)],[f530,f318]) ).
thf(f530,plain,
( ( $true
!= ( cQ @ sK62 ) )
| spl76_69 ),
inference(avatar_component_clause,[status(thm)],[f528]) ).
thf(f528,definition,
( spl76_69
<=> ( $true
= ( cQ @ sK62 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_69])],[avatar_definition]) ).
thf(f1185,plain,
( ~ spl76_25
| ~ spl76_101 ),
inference(avatar_contradiction_clause,[status(thm)],[f1184]) ).
thf(f1184,plain,
( $false
| ~ spl76_25
| ~ spl76_101 ),
inference(trivial_inequality_removal,[status(thm)],[f1181]) ).
thf(f1181,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_101 ),
inference(backward_demodulation,[status(thm)],[f686,f337]) ).
thf(f686,plain,
( ( ( cS @ sK25 )
= $true )
| ~ spl76_101 ),
inference(avatar_component_clause,[status(thm)],[f684]) ).
thf(f684,definition,
( spl76_101
<=> ( ( cS @ sK25 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_101])],[avatar_definition]) ).
thf(f1175,plain,
( ~ spl76_41
| ~ spl76_43 ),
inference(avatar_contradiction_clause,[status(thm)],[f1174]) ).
thf(f1174,plain,
( $false
| ~ spl76_41
| ~ spl76_43 ),
inference(trivial_inequality_removal,[status(thm)],[f1173]) ).
thf(f1173,plain,
( ( $false = $true )
| ~ spl76_41
| ~ spl76_43 ),
inference(forward_demodulation,[status(thm)],[f406,f415]) ).
thf(f415,plain,
( ( ( cS @ sK58 )
= $false )
| ~ spl76_43 ),
inference(avatar_component_clause,[status(thm)],[f413]) ).
thf(f413,definition,
( spl76_43
<=> ( ( cS @ sK58 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl76_43])],[avatar_definition]) ).
thf(f406,plain,
( ( ( cS @ sK58 )
= $true )
| ~ spl76_41 ),
inference(avatar_component_clause,[status(thm)],[f404]) ).
thf(f404,definition,
( spl76_41
<=> ( ( cS @ sK58 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_41])],[avatar_definition]) ).
thf(f1172,plain,
( ~ spl76_20
| spl76_42 ),
inference(avatar_contradiction_clause,[status(thm)],[f1171]) ).
thf(f1171,plain,
( $false
| ~ spl76_20
| spl76_42 ),
inference(trivial_inequality_removal,[status(thm)],[f1170]) ).
thf(f1170,plain,
( ( $true != $true )
| ~ spl76_20
| spl76_42 ),
inference(superposition,[status(thm)],[f410,f318]) ).
thf(f410,plain,
( ( ( cQ @ sK59 )
!= $true )
| spl76_42 ),
inference(avatar_component_clause,[status(thm)],[f408]) ).
thf(f408,definition,
( spl76_42
<=> ( ( cQ @ sK59 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_42])],[avatar_definition]) ).
thf(f1149,plain,
( ~ spl76_55
| spl76_78 ),
inference(avatar_contradiction_clause,[status(thm)],[f1148]) ).
thf(f1148,plain,
( $false
| ~ spl76_55
| spl76_78 ),
inference(subsumption_resolution,[status(thm)],[f576,f462]) ).
thf(f576,plain,
( ( $true
!= ( cP @ sK23 ) )
| spl76_78 ),
inference(avatar_component_clause,[status(thm)],[f574]) ).
thf(f574,definition,
( spl76_78
<=> ( $true
= ( cP @ sK23 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_78])],[avatar_definition]) ).
thf(f1147,plain,
( ~ spl76_55
| spl76_100 ),
inference(avatar_contradiction_clause,[status(thm)],[f1146]) ).
thf(f1146,plain,
( $false
| ~ spl76_55
| spl76_100 ),
inference(subsumption_resolution,[status(thm)],[f682,f462]) ).
thf(f682,plain,
( ( ( cP @ sK26 )
!= $true )
| spl76_100 ),
inference(avatar_component_clause,[status(thm)],[f680]) ).
thf(f680,definition,
( spl76_100
<=> ( ( cP @ sK26 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_100])],[avatar_definition]) ).
thf(f1144,plain,
( ~ spl76_2
| ~ spl76_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f1143]) ).
thf(f1143,plain,
( $false
| ~ spl76_2
| ~ spl76_25 ),
inference(trivial_inequality_removal,[status(thm)],[f1142]) ).
thf(f1142,plain,
( ( $false = $true )
| ~ spl76_2
| ~ spl76_25 ),
inference(forward_demodulation,[status(thm)],[f250,f337]) ).
thf(f250,plain,
( ( ( cS @ sK19 )
= $true )
| ~ spl76_2 ),
inference(avatar_component_clause,[status(thm)],[f248]) ).
thf(f248,definition,
( spl76_2
<=> ( ( cS @ sK19 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_2])],[avatar_definition]) ).
thf(f1134,plain,
( ~ spl76_24
| ~ spl76_55 ),
inference(avatar_contradiction_clause,[status(thm)],[f1133]) ).
thf(f1133,plain,
( $false
| ~ spl76_24
| ~ spl76_55 ),
inference(subsumption_resolution,[status(thm)],[f334,f462]) ).
thf(f1132,plain,
( ~ spl76_25
| ~ spl76_88 ),
inference(avatar_contradiction_clause,[status(thm)],[f1131]) ).
thf(f1131,plain,
( $false
| ~ spl76_25
| ~ spl76_88 ),
inference(trivial_inequality_removal,[status(thm)],[f1130]) ).
thf(f1130,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_88 ),
inference(forward_demodulation,[status(thm)],[f621,f337]) ).
thf(f621,plain,
( ( $true
= ( cS @ sK13 ) )
| ~ spl76_88 ),
inference(avatar_component_clause,[status(thm)],[f619]) ).
thf(f619,definition,
( spl76_88
<=> ( $true
= ( cS @ sK13 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_88])],[avatar_definition]) ).
thf(f1129,plain,
( ~ spl76_55
| ~ spl76_68 ),
inference(avatar_contradiction_clause,[status(thm)],[f1128]) ).
thf(f1128,plain,
( $false
| ~ spl76_55
| ~ spl76_68 ),
inference(trivial_inequality_removal,[status(thm)],[f1124]) ).
thf(f1124,plain,
( ( $false = $true )
| ~ spl76_55
| ~ spl76_68 ),
inference(superposition,[status(thm)],[f1071,f462]) ).
thf(f1071,plain,
( ! [X4: $i] :
( $false
= ( cP @ ( sK30 @ X4 ) ) )
| ~ spl76_55
| ~ spl76_68 ),
inference(trivial_inequality_removal,[status(thm)],[f1070]) ).
thf(f1070,plain,
( ! [X4: $i] :
( ( $false
= ( cP @ ( sK30 @ X4 ) ) )
| ( $false = $true ) )
| ~ spl76_55
| ~ spl76_68 ),
inference(forward_demodulation,[status(thm)],[f525,f462]) ).
thf(f525,plain,
( ! [X4: $i] :
( ( ( cP @ X4 )
= $false )
| ( $false
= ( cP @ ( sK30 @ X4 ) ) ) )
| ~ spl76_68 ),
inference(avatar_component_clause,[status(thm)],[f524]) ).
thf(f524,definition,
( spl76_68
<=> ! [X4: $i] :
( ( $false
= ( cP @ ( sK30 @ X4 ) ) )
| ( ( cP @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl76_68])],[avatar_definition]) ).
thf(f1123,plain,
( ~ spl76_13
| ~ spl76_55 ),
inference(avatar_contradiction_clause,[status(thm)],[f1122]) ).
thf(f1122,plain,
( $false
| ~ spl76_13
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1118]) ).
thf(f1118,plain,
( ( $false = $true )
| ~ spl76_13
| ~ spl76_55 ),
inference(superposition,[status(thm)],[f1069,f462]) ).
thf(f1069,plain,
( ! [X46: $i] :
( ( cP @ ( sK51 @ X46 ) )
= $false )
| ~ spl76_13
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1068]) ).
thf(f1068,plain,
( ! [X46: $i] :
( ( $false = $true )
| ( ( cP @ ( sK51 @ X46 ) )
= $false ) )
| ~ spl76_13
| ~ spl76_55 ),
inference(backward_demodulation,[status(thm)],[f292,f462]) ).
thf(f292,plain,
( ! [X46: $i] :
( ( ( cP @ ( sK51 @ X46 ) )
= $false )
| ( $false
= ( cP @ X46 ) ) )
| ~ spl76_13 ),
inference(avatar_component_clause,[status(thm)],[f291]) ).
thf(f291,definition,
( spl76_13
<=> ! [X46: $i] :
( ( $false
= ( cP @ X46 ) )
| ( ( cP @ ( sK51 @ X46 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl76_13])],[avatar_definition]) ).
thf(f1117,plain,
( ~ spl76_55
| spl76_84 ),
inference(avatar_contradiction_clause,[status(thm)],[f1116]) ).
thf(f1116,plain,
( $false
| ~ spl76_55
| spl76_84 ),
inference(trivial_inequality_removal,[status(thm)],[f1115]) ).
thf(f1115,plain,
( ( $true != $true )
| ~ spl76_55
| spl76_84 ),
inference(superposition,[status(thm)],[f604,f462]) ).
thf(f604,plain,
( ( $true
!= ( cP @ sK11 ) )
| spl76_84 ),
inference(avatar_component_clause,[status(thm)],[f602]) ).
thf(f602,definition,
( spl76_84
<=> ( $true
= ( cP @ sK11 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_84])],[avatar_definition]) ).
thf(f1101,plain,
( spl76_48
| ~ spl76_55 ),
inference(avatar_contradiction_clause,[status(thm)],[f1100]) ).
thf(f1100,plain,
( $false
| spl76_48
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1093]) ).
thf(f1093,plain,
( ( $true != $true )
| spl76_48
| ~ spl76_55 ),
inference(superposition,[status(thm)],[f436,f462]) ).
thf(f436,plain,
( ( ( cP @ sK16 )
!= $true )
| spl76_48 ),
inference(avatar_component_clause,[status(thm)],[f434]) ).
thf(f434,definition,
( spl76_48
<=> ( ( cP @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_48])],[avatar_definition]) ).
thf(f1099,plain,
( spl76_3
| ~ spl76_55 ),
inference(avatar_contradiction_clause,[status(thm)],[f1098]) ).
thf(f1098,plain,
( $false
| spl76_3
| ~ spl76_55 ),
inference(trivial_inequality_removal,[status(thm)],[f1094]) ).
thf(f1094,plain,
( ( $true != $true )
| spl76_3
| ~ spl76_55 ),
inference(superposition,[status(thm)],[f254,f462]) ).
thf(f254,plain,
( ( ( cP @ sK20 )
!= $true )
| spl76_3 ),
inference(avatar_component_clause,[status(thm)],[f252]) ).
thf(f252,definition,
( spl76_3
<=> ( ( cP @ sK20 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_3])],[avatar_definition]) ).
thf(f1078,plain,
( ~ spl76_55
| spl76_87 ),
inference(avatar_contradiction_clause,[status(thm)],[f1077]) ).
thf(f1077,plain,
( $false
| ~ spl76_55
| spl76_87 ),
inference(subsumption_resolution,[status(thm)],[f617,f462]) ).
thf(f617,plain,
( ( ( cP @ sK14 )
!= $true )
| spl76_87 ),
inference(avatar_component_clause,[status(thm)],[f615]) ).
thf(f615,definition,
( spl76_87
<=> ( ( cP @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_87])],[avatar_definition]) ).
thf(f1064,plain,
( ~ spl76_62
| ~ spl76_65 ),
inference(avatar_contradiction_clause,[status(thm)],[f1063]) ).
thf(f1063,plain,
( $false
| ~ spl76_62
| ~ spl76_65 ),
inference(trivial_inequality_removal,[status(thm)],[f1062]) ).
thf(f1062,plain,
( ( $false = $true )
| ~ spl76_62
| ~ spl76_65 ),
inference(forward_demodulation,[status(thm)],[f509,f496]) ).
thf(f509,plain,
( ( ( cP @ sK55 )
= $true )
| ~ spl76_65 ),
inference(avatar_component_clause,[status(thm)],[f507]) ).
thf(f507,definition,
( spl76_65
<=> ( ( cP @ sK55 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_65])],[avatar_definition]) ).
thf(f1051,plain,
( ~ spl76_20
| ~ spl76_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f1050]) ).
thf(f1050,plain,
( $false
| ~ spl76_20
| ~ spl76_31 ),
inference(trivial_inequality_removal,[status(thm)],[f1046]) ).
thf(f1046,plain,
( ( $false = $true )
| ~ spl76_20
| ~ spl76_31 ),
inference(superposition,[status(thm)],[f1020,f318]) ).
thf(f1020,plain,
( ! [X16: $i] :
( $false
= ( cQ @ ( sK72 @ X16 ) ) )
| ~ spl76_20
| ~ spl76_31 ),
inference(trivial_inequality_removal,[status(thm)],[f1019]) ).
thf(f1019,plain,
( ! [X16: $i] :
( ( $false
= ( cQ @ ( sK72 @ X16 ) ) )
| ( $false = $true ) )
| ~ spl76_20
| ~ spl76_31 ),
inference(forward_demodulation,[status(thm)],[f362,f318]) ).
thf(f362,plain,
( ! [X16: $i] :
( ( $false
= ( cQ @ ( sK72 @ X16 ) ) )
| ( $false
= ( cQ @ X16 ) ) )
| ~ spl76_31 ),
inference(avatar_component_clause,[status(thm)],[f361]) ).
thf(f361,definition,
( spl76_31
<=> ! [X16: $i] :
( ( $false
= ( cQ @ ( sK72 @ X16 ) ) )
| ( $false
= ( cQ @ X16 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_31])],[avatar_definition]) ).
thf(f1013,plain,
( ~ spl76_4
| ~ spl76_89 ),
inference(avatar_contradiction_clause,[status(thm)],[f1012]) ).
thf(f1012,plain,
( $false
| ~ spl76_4
| ~ spl76_89 ),
inference(trivial_inequality_removal,[status(thm)],[f1008]) ).
thf(f1008,plain,
( ( $false = $true )
| ~ spl76_4
| ~ spl76_89 ),
inference(superposition,[status(thm)],[f990,f257]) ).
thf(f990,plain,
( ! [X22: $i] :
( $false
= ( cR @ ( sK15 @ X22 ) ) )
| ~ spl76_4
| ~ spl76_89 ),
inference(trivial_inequality_removal,[status(thm)],[f989]) ).
thf(f989,plain,
( ! [X22: $i] :
( ( $false
= ( cR @ ( sK15 @ X22 ) ) )
| ( $false = $true ) )
| ~ spl76_4
| ~ spl76_89 ),
inference(forward_demodulation,[status(thm)],[f625,f257]) ).
thf(f625,plain,
( ! [X22: $i] :
( ( $false
= ( cR @ ( sK15 @ X22 ) ) )
| ( ( cR @ X22 )
= $false ) )
| ~ spl76_89 ),
inference(avatar_component_clause,[status(thm)],[f624]) ).
thf(f624,definition,
( spl76_89
<=> ! [X22: $i] :
( ( $false
= ( cR @ ( sK15 @ X22 ) ) )
| ( ( cR @ X22 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl76_89])],[avatar_definition]) ).
thf(f993,plain,
( ~ spl76_22
| ~ spl76_110 ),
inference(avatar_contradiction_clause,[status(thm)],[f992]) ).
thf(f992,plain,
( $false
| ~ spl76_22
| ~ spl76_110 ),
inference(trivial_inequality_removal,[status(thm)],[f991]) ).
thf(f991,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_110 ),
inference(forward_demodulation,[status(thm)],[f740,f326]) ).
thf(f740,plain,
( ( $true
= ( cQ @ sK49 ) )
| ~ spl76_110 ),
inference(avatar_component_clause,[status(thm)],[f738]) ).
thf(f738,definition,
( spl76_110
<=> ( $true
= ( cQ @ sK49 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_110])],[avatar_definition]) ).
thf(f987,plain,
( ~ spl76_7
| ~ spl76_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f986]) ).
thf(f986,plain,
( $false
| ~ spl76_7
| ~ spl76_29 ),
inference(trivial_inequality_removal,[status(thm)],[f985]) ).
thf(f985,plain,
( ( $false = $true )
| ~ spl76_7
| ~ spl76_29 ),
inference(forward_demodulation,[status(thm)],[f355,f269]) ).
thf(f355,plain,
( ( $true
= ( cR @ sK70 ) )
| ~ spl76_29 ),
inference(avatar_component_clause,[status(thm)],[f353]) ).
thf(f353,definition,
( spl76_29
<=> ( $true
= ( cR @ sK70 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_29])],[avatar_definition]) ).
thf(f973,plain,
( ~ spl76_10
| ~ spl76_24 ),
inference(avatar_contradiction_clause,[status(thm)],[f972]) ).
thf(f972,plain,
( $false
| ~ spl76_10
| ~ spl76_24 ),
inference(subsumption_resolution,[status(thm)],[f971,f334]) ).
thf(f971,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl76_10
| ~ spl76_24 ),
inference(trivial_inequality_removal,[status(thm)],[f970]) ).
thf(f970,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP @ X0 )
= $true ) )
| ~ spl76_10
| ~ spl76_24 ),
inference(superposition,[status(thm)],[f334,f281]) ).
thf(f281,plain,
( ! [X46: $i] :
( ( ( cP @ ( sK51 @ X46 ) )
= $true )
| ( ( cP @ X46 )
= $true ) )
| ~ spl76_10 ),
inference(avatar_component_clause,[status(thm)],[f280]) ).
thf(f280,definition,
( spl76_10
<=> ! [X46: $i] :
( ( ( cP @ ( sK51 @ X46 ) )
= $true )
| ( ( cP @ X46 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl76_10])],[avatar_definition]) ).
thf(f963,plain,
( ~ spl76_40
| ~ spl76_86 ),
inference(avatar_contradiction_clause,[status(thm)],[f962]) ).
thf(f962,plain,
( $false
| ~ spl76_40
| ~ spl76_86 ),
inference(subsumption_resolution,[status(thm)],[f961,f400]) ).
thf(f961,plain,
( ! [X22: $i] :
( ( cR @ X22 )
= $true )
| ~ spl76_40
| ~ spl76_86 ),
inference(subsumption_resolution,[status(thm)],[f613,f400]) ).
thf(f613,plain,
( ! [X22: $i] :
( ( $true
= ( cR @ ( sK15 @ X22 ) ) )
| ( ( cR @ X22 )
= $true ) )
| ~ spl76_86 ),
inference(avatar_component_clause,[status(thm)],[f612]) ).
thf(f612,definition,
( spl76_86
<=> ! [X22: $i] :
( ( ( cR @ X22 )
= $true )
| ( $true
= ( cR @ ( sK15 @ X22 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_86])],[avatar_definition]) ).
thf(f944,plain,
( ~ spl76_7
| ~ spl76_86 ),
inference(avatar_contradiction_clause,[status(thm)],[f943]) ).
thf(f943,plain,
( $false
| ~ spl76_7
| ~ spl76_86 ),
inference(trivial_inequality_removal,[status(thm)],[f942]) ).
thf(f942,plain,
( ( $false = $true )
| ~ spl76_7
| ~ spl76_86 ),
inference(forward_demodulation,[status(thm)],[f941,f269]) ).
thf(f941,plain,
( ! [X22: $i] :
( ( cR @ X22 )
= $true )
| ~ spl76_7
| ~ spl76_86 ),
inference(trivial_inequality_removal,[status(thm)],[f940]) ).
thf(f940,plain,
( ! [X22: $i] :
( ( $false = $true )
| ( ( cR @ X22 )
= $true ) )
| ~ spl76_7
| ~ spl76_86 ),
inference(forward_demodulation,[status(thm)],[f613,f269]) ).
thf(f938,plain,
( ~ spl76_60
| ~ spl76_63 ),
inference(avatar_contradiction_clause,[status(thm)],[f937]) ).
thf(f937,plain,
( $false
| ~ spl76_60
| ~ spl76_63 ),
inference(trivial_inequality_removal,[status(thm)],[f936]) ).
thf(f936,plain,
( ( $false = $true )
| ~ spl76_60
| ~ spl76_63 ),
inference(forward_demodulation,[status(thm)],[f500,f488]) ).
thf(f488,plain,
( ( $false
= ( cP @ sK46 ) )
| ~ spl76_60 ),
inference(avatar_component_clause,[status(thm)],[f486]) ).
thf(f486,definition,
( spl76_60
<=> ( $false
= ( cP @ sK46 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_60])],[avatar_definition]) ).
thf(f500,plain,
( ( ( cP @ sK46 )
= $true )
| ~ spl76_63 ),
inference(avatar_component_clause,[status(thm)],[f498]) ).
thf(f498,definition,
( spl76_63
<=> ( ( cP @ sK46 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_63])],[avatar_definition]) ).
thf(f931,plain,
( ~ spl76_22
| ~ spl76_61 ),
inference(avatar_contradiction_clause,[status(thm)],[f930]) ).
thf(f930,plain,
( $false
| ~ spl76_22
| ~ spl76_61 ),
inference(trivial_inequality_removal,[status(thm)],[f926]) ).
thf(f926,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_61 ),
inference(backward_demodulation,[status(thm)],[f492,f326]) ).
thf(f492,plain,
( ( ( cQ @ sK48 )
= $true )
| ~ spl76_61 ),
inference(avatar_component_clause,[status(thm)],[f490]) ).
thf(f490,definition,
( spl76_61
<=> ( ( cQ @ sK48 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_61])],[avatar_definition]) ).
thf(f918,plain,
( ~ spl76_25
| ~ spl76_112 ),
inference(avatar_contradiction_clause,[status(thm)],[f917]) ).
thf(f917,plain,
( $false
| ~ spl76_25
| ~ spl76_112 ),
inference(trivial_inequality_removal,[status(thm)],[f916]) ).
thf(f916,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_112 ),
inference(forward_demodulation,[status(thm)],[f750,f337]) ).
thf(f750,plain,
( ( ( cS @ sK12 )
= $true )
| ~ spl76_112 ),
inference(avatar_component_clause,[status(thm)],[f748]) ).
thf(f912,plain,
( ~ spl76_83
| ~ spl76_85 ),
inference(avatar_contradiction_clause,[status(thm)],[f911]) ).
thf(f911,plain,
( $false
| ~ spl76_83
| ~ spl76_85 ),
inference(trivial_inequality_removal,[status(thm)],[f910]) ).
thf(f910,plain,
( ( $false = $true )
| ~ spl76_83
| ~ spl76_85 ),
inference(forward_demodulation,[status(thm)],[f600,f609]) ).
thf(f609,plain,
( ( $false
= ( cR @ sK10 ) )
| ~ spl76_85 ),
inference(avatar_component_clause,[status(thm)],[f607]) ).
thf(f607,definition,
( spl76_85
<=> ( $false
= ( cR @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_85])],[avatar_definition]) ).
thf(f600,plain,
( ( ( cR @ sK10 )
= $true )
| ~ spl76_83 ),
inference(avatar_component_clause,[status(thm)],[f598]) ).
thf(f598,definition,
( spl76_83
<=> ( ( cR @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_83])],[avatar_definition]) ).
thf(f901,plain,
( ~ spl76_7
| ~ spl76_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f900]) ).
thf(f900,plain,
( $false
| ~ spl76_7
| ~ spl76_18 ),
inference(trivial_inequality_removal,[status(thm)],[f899]) ).
thf(f899,plain,
( ( $false = $true )
| ~ spl76_7
| ~ spl76_18 ),
inference(forward_demodulation,[status(thm)],[f312,f269]) ).
thf(f312,plain,
( ( ( cR @ sK75 )
= $true )
| ~ spl76_18 ),
inference(avatar_component_clause,[status(thm)],[f310]) ).
thf(f310,definition,
( spl76_18
<=> ( ( cR @ sK75 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_18])],[avatar_definition]) ).
thf(f898,plain,
( ~ spl76_22
| ~ spl76_95 ),
inference(avatar_contradiction_clause,[status(thm)],[f897]) ).
thf(f897,plain,
( $false
| ~ spl76_22
| ~ spl76_95 ),
inference(trivial_inequality_removal,[status(thm)],[f896]) ).
thf(f896,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_95 ),
inference(forward_demodulation,[status(thm)],[f654,f326]) ).
thf(f654,plain,
( ( ( cQ @ sK29 )
= $true )
| ~ spl76_95 ),
inference(avatar_component_clause,[status(thm)],[f652]) ).
thf(f652,definition,
( spl76_95
<=> ( ( cQ @ sK29 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_95])],[avatar_definition]) ).
thf(f888,plain,
( ~ spl76_11
| ~ spl76_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f887]) ).
thf(f887,plain,
( $false
| ~ spl76_11
| ~ spl76_30 ),
inference(subsumption_resolution,[status(thm)],[f886,f284]) ).
thf(f886,plain,
( ! [X16: $i] :
( $true
= ( cQ @ ( sK72 @ X16 ) ) )
| ~ spl76_11
| ~ spl76_30 ),
inference(subsumption_resolution,[status(thm)],[f358,f284]) ).
thf(f358,plain,
( ! [X16: $i] :
( ( $true
= ( cQ @ ( sK72 @ X16 ) ) )
| ( ( cQ @ X16 )
= $true ) )
| ~ spl76_30 ),
inference(avatar_component_clause,[status(thm)],[f357]) ).
thf(f357,definition,
( spl76_30
<=> ! [X16: $i] :
( ( $true
= ( cQ @ ( sK72 @ X16 ) ) )
| ( ( cQ @ X16 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl76_30])],[avatar_definition]) ).
thf(f883,plain,
( ~ spl76_22
| ~ spl76_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f882]) ).
thf(f882,plain,
( $false
| ~ spl76_22
| ~ spl76_30 ),
inference(trivial_inequality_removal,[status(thm)],[f881]) ).
thf(f881,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_30 ),
inference(forward_demodulation,[status(thm)],[f880,f326]) ).
thf(f880,plain,
( ! [X16: $i] :
( ( cQ @ X16 )
= $true )
| ~ spl76_22
| ~ spl76_30 ),
inference(trivial_inequality_removal,[status(thm)],[f879]) ).
thf(f879,plain,
( ! [X16: $i] :
( ( ( cQ @ X16 )
= $true )
| ( $false = $true ) )
| ~ spl76_22
| ~ spl76_30 ),
inference(forward_demodulation,[status(thm)],[f358,f326]) ).
thf(f874,plain,
( ~ spl76_25
| ~ spl76_99 ),
inference(avatar_contradiction_clause,[status(thm)],[f873]) ).
thf(f873,plain,
( $false
| ~ spl76_25
| ~ spl76_99 ),
inference(trivial_inequality_removal,[status(thm)],[f871]) ).
thf(f871,plain,
( ( $false = $true )
| ~ spl76_25
| ~ spl76_99 ),
inference(backward_demodulation,[status(thm)],[f676,f337]) ).
thf(f676,plain,
( ( ( cS @ sK17 )
= $true )
| ~ spl76_99 ),
inference(avatar_component_clause,[status(thm)],[f674]) ).
thf(f674,definition,
( spl76_99
<=> ( ( cS @ sK17 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_99])],[avatar_definition]) ).
thf(f863,plain,
( ~ spl76_16
| ~ spl76_51 ),
inference(avatar_contradiction_clause,[status(thm)],[f862]) ).
thf(f862,plain,
( $false
| ~ spl76_16
| ~ spl76_51 ),
inference(subsumption_resolution,[status(thm)],[f861,f303]) ).
thf(f861,plain,
( ! [X4: $i] :
( ( cS @ X4 )
= $true )
| ~ spl76_16
| ~ spl76_51 ),
inference(subsumption_resolution,[status(thm)],[f447,f303]) ).
thf(f447,plain,
( ! [X4: $i] :
( ( ( cS @ ( sK54 @ X4 ) )
= $true )
| ( ( cS @ X4 )
= $true ) )
| ~ spl76_51 ),
inference(avatar_component_clause,[status(thm)],[f446]) ).
thf(f446,definition,
( spl76_51
<=> ! [X4: $i] :
( ( ( cS @ ( sK54 @ X4 ) )
= $true )
| ( ( cS @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl76_51])],[avatar_definition]) ).
thf(f858,plain,
( ~ spl76_26
| ~ spl76_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f857]) ).
thf(f857,plain,
( $false
| ~ spl76_26
| ~ spl76_27 ),
inference(trivial_inequality_removal,[status(thm)],[f856]) ).
thf(f856,plain,
( ( $false = $true )
| ~ spl76_26
| ~ spl76_27 ),
inference(backward_demodulation,[status(thm)],[f341,f346]) ).
thf(f346,plain,
( ( ( cS @ sK57 )
= $false )
| ~ spl76_27 ),
inference(avatar_component_clause,[status(thm)],[f344]) ).
thf(f344,definition,
( spl76_27
<=> ( ( cS @ sK57 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl76_27])],[avatar_definition]) ).
thf(f341,plain,
( ( ( cS @ sK57 )
= $true )
| ~ spl76_26 ),
inference(avatar_component_clause,[status(thm)],[f339]) ).
thf(f339,definition,
( spl76_26
<=> ( ( cS @ sK57 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_26])],[avatar_definition]) ).
thf(f855,plain,
( ~ spl76_18
| ~ spl76_40 ),
inference(avatar_contradiction_clause,[status(thm)],[f854]) ).
thf(f854,plain,
( $false
| ~ spl76_18
| ~ spl76_40 ),
inference(subsumption_resolution,[status(thm)],[f312,f400]) ).
thf(f851,plain,
( ~ spl76_6
| ~ spl76_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f850]) ).
thf(f850,plain,
( $false
| ~ spl76_6
| ~ spl76_8 ),
inference(trivial_inequality_removal,[status(thm)],[f849]) ).
thf(f849,plain,
( ( $false = $true )
| ~ spl76_6
| ~ spl76_8 ),
inference(backward_demodulation,[status(thm)],[f273,f265]) ).
thf(f265,plain,
( ( $false
= ( cR @ sK21 ) )
| ~ spl76_6 ),
inference(avatar_component_clause,[status(thm)],[f263]) ).
thf(f263,definition,
( spl76_6
<=> ( $false
= ( cR @ sK21 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_6])],[avatar_definition]) ).
thf(f273,plain,
( ( $true
= ( cR @ sK21 ) )
| ~ spl76_8 ),
inference(avatar_component_clause,[status(thm)],[f271]) ).
thf(f271,definition,
( spl76_8
<=> ( $true
= ( cR @ sK21 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_8])],[avatar_definition]) ).
thf(f846,plain,
( ~ spl76_40
| ~ spl76_49 ),
inference(avatar_contradiction_clause,[status(thm)],[f845]) ).
thf(f845,plain,
( $false
| ~ spl76_40
| ~ spl76_49 ),
inference(subsumption_resolution,[status(thm)],[f844,f400]) ).
thf(f844,plain,
( ! [X28: $i] :
( ( cR @ ( sK18 @ X28 ) )
= $true )
| ~ spl76_40
| ~ spl76_49 ),
inference(subsumption_resolution,[status(thm)],[f439,f400]) ).
thf(f439,plain,
( ! [X28: $i] :
( ( $true
= ( cR @ X28 ) )
| ( ( cR @ ( sK18 @ X28 ) )
= $true ) )
| ~ spl76_49 ),
inference(avatar_component_clause,[status(thm)],[f438]) ).
thf(f438,definition,
( spl76_49
<=> ! [X28: $i] :
( ( ( cR @ ( sK18 @ X28 ) )
= $true )
| ( $true
= ( cR @ X28 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_49])],[avatar_definition]) ).
thf(f836,plain,
( ~ spl76_62
| ~ spl76_102 ),
inference(avatar_contradiction_clause,[status(thm)],[f835]) ).
thf(f835,plain,
( $false
| ~ spl76_62
| ~ spl76_102 ),
inference(trivial_inequality_removal,[status(thm)],[f833]) ).
thf(f833,plain,
( ( $false = $true )
| ~ spl76_62
| ~ spl76_102 ),
inference(backward_demodulation,[status(thm)],[f692,f496]) ).
thf(f692,plain,
( ( ( cP @ sK53 )
= $true )
| ~ spl76_102 ),
inference(avatar_component_clause,[status(thm)],[f690]) ).
thf(f690,definition,
( spl76_102
<=> ( ( cP @ sK53 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_102])],[avatar_definition]) ).
thf(f829,plain,
( ~ spl76_4
| ~ spl76_40 ),
inference(avatar_contradiction_clause,[status(thm)],[f828]) ).
thf(f828,plain,
( $false
| ~ spl76_4
| ~ spl76_40 ),
inference(subsumption_resolution,[status(thm)],[f400,f257]) ).
thf(f827,plain,
( ~ spl76_19
| ~ spl76_53 ),
inference(avatar_contradiction_clause,[status(thm)],[f826]) ).
thf(f826,plain,
( $false
| ~ spl76_19
| ~ spl76_53 ),
inference(trivial_inequality_removal,[status(thm)],[f823]) ).
thf(f823,plain,
( ( $false = $true )
| ~ spl76_19
| ~ spl76_53 ),
inference(superposition,[status(thm)],[f315,f821]) ).
thf(f821,plain,
( ! [X4: $i] :
( $false
= ( cS @ ( sK54 @ X4 ) ) )
| ~ spl76_19
| ~ spl76_53 ),
inference(trivial_inequality_removal,[status(thm)],[f820]) ).
thf(f820,plain,
( ! [X4: $i] :
( ( $false
= ( cS @ ( sK54 @ X4 ) ) )
| ( $false = $true ) )
| ~ spl76_19
| ~ spl76_53 ),
inference(forward_demodulation,[status(thm)],[f455,f315]) ).
thf(f455,plain,
( ! [X4: $i] :
( ( $false
= ( cS @ ( sK54 @ X4 ) ) )
| ( ( cS @ X4 )
= $false ) )
| ~ spl76_53 ),
inference(avatar_component_clause,[status(thm)],[f454]) ).
thf(f454,definition,
( spl76_53
<=> ! [X4: $i] :
( ( ( cS @ X4 )
= $false )
| ( $false
= ( cS @ ( sK54 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_53])],[avatar_definition]) ).
thf(f819,plain,
( ~ spl76_24
| ~ spl76_67 ),
inference(avatar_contradiction_clause,[status(thm)],[f818]) ).
thf(f818,plain,
( $false
| ~ spl76_24
| ~ spl76_67 ),
inference(subsumption_resolution,[status(thm)],[f817,f334]) ).
thf(f817,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl76_24
| ~ spl76_67 ),
inference(trivial_inequality_removal,[status(thm)],[f816]) ).
thf(f816,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl76_24
| ~ spl76_67 ),
inference(superposition,[status(thm)],[f334,f521]) ).
thf(f521,plain,
( ! [X4: $i] :
( ( $true
= ( cP @ ( sK30 @ X4 ) ) )
| ( ( cP @ X4 )
= $true ) )
| ~ spl76_67 ),
inference(avatar_component_clause,[status(thm)],[f520]) ).
thf(f520,definition,
( spl76_67
<=> ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
| ( $true
= ( cP @ ( sK30 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_67])],[avatar_definition]) ).
thf(f815,plain,
( ~ spl76_4
| ~ spl76_50 ),
inference(avatar_contradiction_clause,[status(thm)],[f814]) ).
thf(f814,plain,
( $false
| ~ spl76_4
| ~ spl76_50 ),
inference(trivial_inequality_removal,[status(thm)],[f810]) ).
thf(f810,plain,
( ( $false = $true )
| ~ spl76_4
| ~ spl76_50 ),
inference(superposition,[status(thm)],[f768,f257]) ).
thf(f768,plain,
( ! [X28: $i] :
( $false
= ( cR @ ( sK18 @ X28 ) ) )
| ~ spl76_4
| ~ spl76_50 ),
inference(trivial_inequality_removal,[status(thm)],[f767]) ).
thf(f767,plain,
( ! [X28: $i] :
( ( $false
= ( cR @ ( sK18 @ X28 ) ) )
| ( $false = $true ) )
| ~ spl76_4
| ~ spl76_50 ),
inference(backward_demodulation,[status(thm)],[f443,f257]) ).
thf(f443,plain,
( ! [X28: $i] :
( ( $false
= ( cR @ ( sK18 @ X28 ) ) )
| ( $false
= ( cR @ X28 ) ) )
| ~ spl76_50 ),
inference(avatar_component_clause,[status(thm)],[f442]) ).
thf(f442,definition,
( spl76_50
<=> ! [X28: $i] :
( ( $false
= ( cR @ X28 ) )
| ( $false
= ( cR @ ( sK18 @ X28 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl76_50])],[avatar_definition]) ).
thf(f809,plain,
( ~ spl76_4
| spl76_111 ),
inference(avatar_contradiction_clause,[status(thm)],[f808]) ).
thf(f808,plain,
( $false
| ~ spl76_4
| spl76_111 ),
inference(trivial_inequality_removal,[status(thm)],[f807]) ).
thf(f807,plain,
( ( $true != $true )
| ~ spl76_4
| spl76_111 ),
inference(superposition,[status(thm)],[f744,f257]) ).
thf(f744,plain,
( ( $true
!= ( cR @ sK50 ) )
| spl76_111 ),
inference(avatar_component_clause,[status(thm)],[f742]) ).
thf(f742,definition,
( spl76_111
<=> ( $true
= ( cR @ sK50 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_111])],[avatar_definition]) ).
thf(f806,plain,
( ~ spl76_24
| ~ spl76_102 ),
inference(avatar_contradiction_clause,[status(thm)],[f805]) ).
thf(f805,plain,
( $false
| ~ spl76_24
| ~ spl76_102 ),
inference(trivial_inequality_removal,[status(thm)],[f804]) ).
thf(f804,plain,
( ( $true != $true )
| ~ spl76_24
| ~ spl76_102 ),
inference(superposition,[status(thm)],[f334,f692]) ).
thf(f803,plain,
( ~ spl76_4
| spl76_77 ),
inference(avatar_contradiction_clause,[status(thm)],[f802]) ).
thf(f802,plain,
( $false
| ~ spl76_4
| spl76_77 ),
inference(trivial_inequality_removal,[status(thm)],[f801]) ).
thf(f801,plain,
( ( $true != $true )
| ~ spl76_4
| spl76_77 ),
inference(superposition,[status(thm)],[f570,f257]) ).
thf(f570,plain,
( ( $true
!= ( cR @ sK47 ) )
| spl76_77 ),
inference(avatar_component_clause,[status(thm)],[f568]) ).
thf(f568,definition,
( spl76_77
<=> ( $true
= ( cR @ sK47 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_77])],[avatar_definition]) ).
thf(f799,plain,
( ~ spl76_20
| spl76_64 ),
inference(avatar_contradiction_clause,[status(thm)],[f798]) ).
thf(f798,plain,
( $false
| ~ spl76_20
| spl76_64 ),
inference(trivial_inequality_removal,[status(thm)],[f797]) ).
thf(f797,plain,
( ( $true != $true )
| ~ spl76_20
| spl76_64 ),
inference(superposition,[status(thm)],[f505,f318]) ).
thf(f505,plain,
( ( $true
!= ( cQ @ sK56 ) )
| spl76_64 ),
inference(avatar_component_clause,[status(thm)],[f503]) ).
thf(f503,definition,
( spl76_64
<=> ( $true
= ( cQ @ sK56 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_64])],[avatar_definition]) ).
thf(f795,plain,
( ~ spl76_20
| spl76_52 ),
inference(avatar_contradiction_clause,[status(thm)],[f794]) ).
thf(f794,plain,
( $false
| ~ spl76_20
| spl76_52 ),
inference(subsumption_resolution,[status(thm)],[f451,f318]) ).
thf(f451,plain,
( ( ( cQ @ sK52 )
!= $true )
| spl76_52 ),
inference(avatar_component_clause,[status(thm)],[f449]) ).
thf(f449,definition,
( spl76_52
<=> ( ( cQ @ sK52 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_52])],[avatar_definition]) ).
thf(f791,plain,
( ~ spl76_11
| ~ spl76_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f790]) ).
thf(f790,plain,
( $false
| ~ spl76_11
| ~ spl76_20 ),
inference(subsumption_resolution,[status(thm)],[f318,f284]) ).
thf(f788,plain,
( ~ spl76_21
| ~ spl76_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f787]) ).
thf(f787,plain,
( $false
| ~ spl76_21
| ~ spl76_23 ),
inference(trivial_inequality_removal,[status(thm)],[f786]) ).
thf(f786,plain,
( ( $false = $true )
| ~ spl76_21
| ~ spl76_23 ),
inference(forward_demodulation,[status(thm)],[f330,f322]) ).
thf(f322,plain,
( ( $false
= ( cQ @ sK73 ) )
| ~ spl76_21 ),
inference(avatar_component_clause,[status(thm)],[f320]) ).
thf(f320,definition,
( spl76_21
<=> ( $false
= ( cQ @ sK73 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_21])],[avatar_definition]) ).
thf(f330,plain,
( ( $true
= ( cQ @ sK73 ) )
| ~ spl76_23 ),
inference(avatar_component_clause,[status(thm)],[f328]) ).
thf(f328,definition,
( spl76_23
<=> ( $true
= ( cQ @ sK73 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_23])],[avatar_definition]) ).
thf(f784,plain,
( ~ spl76_72
| ~ spl76_74 ),
inference(avatar_contradiction_clause,[status(thm)],[f783]) ).
thf(f783,plain,
( $false
| ~ spl76_72
| ~ spl76_74 ),
inference(trivial_inequality_removal,[status(thm)],[f782]) ).
thf(f782,plain,
( ( $false = $true )
| ~ spl76_72
| ~ spl76_74 ),
inference(forward_demodulation,[status(thm)],[f544,f553]) ).
thf(f553,plain,
( ( $false
= ( cP @ sK33 ) )
| ~ spl76_74 ),
inference(avatar_component_clause,[status(thm)],[f551]) ).
thf(f551,definition,
( spl76_74
<=> ( $false
= ( cP @ sK33 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_74])],[avatar_definition]) ).
thf(f544,plain,
( ( ( cP @ sK33 )
= $true )
| ~ spl76_72 ),
inference(avatar_component_clause,[status(thm)],[f542]) ).
thf(f542,definition,
( spl76_72
<=> ( ( cP @ sK33 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_72])],[avatar_definition]) ).
thf(f781,plain,
( ~ spl76_22
| ~ spl76_71 ),
inference(avatar_contradiction_clause,[status(thm)],[f780]) ).
thf(f780,plain,
( $false
| ~ spl76_22
| ~ spl76_71 ),
inference(trivial_inequality_removal,[status(thm)],[f779]) ).
thf(f779,plain,
( ( $false = $true )
| ~ spl76_22
| ~ spl76_71 ),
inference(forward_demodulation,[status(thm)],[f540,f326]) ).
thf(f540,plain,
( ( ( cQ @ sK31 )
= $true )
| ~ spl76_71 ),
inference(avatar_component_clause,[status(thm)],[f538]) ).
thf(f538,definition,
( spl76_71
<=> ( ( cQ @ sK31 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_71])],[avatar_definition]) ).
thf(f778,plain,
( ~ spl76_4
| spl76_73 ),
inference(avatar_contradiction_clause,[status(thm)],[f777]) ).
thf(f777,plain,
( $false
| ~ spl76_4
| spl76_73 ),
inference(trivial_inequality_removal,[status(thm)],[f776]) ).
thf(f776,plain,
( ( $true != $true )
| ~ spl76_4
| spl76_73 ),
inference(superposition,[status(thm)],[f548,f257]) ).
thf(f548,plain,
( ( $true
!= ( cR @ sK32 ) )
| spl76_73 ),
inference(avatar_component_clause,[status(thm)],[f546]) ).
thf(f546,definition,
( spl76_73
<=> ( $true
= ( cR @ sK32 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_73])],[avatar_definition]) ).
thf(f774,plain,
( ~ spl76_4
| spl76_66 ),
inference(avatar_contradiction_clause,[status(thm)],[f773]) ).
thf(f773,plain,
( $false
| ~ spl76_4
| spl76_66 ),
inference(trivial_inequality_removal,[status(thm)],[f772]) ).
thf(f772,plain,
( ( $true != $true )
| ~ spl76_4
| spl76_66 ),
inference(superposition,[status(thm)],[f518,f257]) ).
thf(f518,plain,
( ( $true
!= ( cR @ sK28 ) )
| spl76_66 ),
inference(avatar_component_clause,[status(thm)],[f516]) ).
thf(f516,definition,
( spl76_66
<=> ( $true
= ( cR @ sK28 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_66])],[avatar_definition]) ).
thf(f771,plain,
( ~ spl76_19
| spl76_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f770]) ).
thf(f770,plain,
( $false
| ~ spl76_19
| spl76_28 ),
inference(trivial_inequality_removal,[status(thm)],[f769]) ).
thf(f769,plain,
( ( $true != $true )
| ~ spl76_19
| spl76_28 ),
inference(superposition,[status(thm)],[f351,f315]) ).
thf(f351,plain,
( ( $true
!= ( cS @ sK71 ) )
| spl76_28 ),
inference(avatar_component_clause,[status(thm)],[f349]) ).
thf(f349,definition,
( spl76_28
<=> ( $true
= ( cS @ sK71 ) ) ),
introduced(definition,[new_symbols(naming,[spl76_28])],[avatar_definition]) ).
thf(f761,plain,
( ~ spl76_19
| spl76_59 ),
inference(avatar_contradiction_clause,[status(thm)],[f760]) ).
thf(f760,plain,
( $false
| ~ spl76_19
| spl76_59 ),
inference(subsumption_resolution,[status(thm)],[f479,f315]) ).
thf(f479,plain,
( ( ( cS @ sK74 )
!= $true )
| spl76_59 ),
inference(avatar_component_clause,[status(thm)],[f477]) ).
thf(f477,definition,
( spl76_59
<=> ( ( cS @ sK74 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl76_59])],[avatar_definition]) ).
thf(f759,plain,
( ~ spl76_16
| ~ spl76_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f758]) ).
thf(f758,plain,
( $false
| ~ spl76_16
| ~ spl76_19 ),
inference(subsumption_resolution,[status(thm)],[f303,f315]) ).
thf(f752,plain,
( spl76_4
| spl76_112
| spl76_5
| spl76_85
| spl76_55
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f148,f244,f461,f607,f259,f748,f256]) ).
thf(f259,definition,
( spl76_5
<=> ( sP3 = $true ) ),
introduced(definition,[new_symbols(naming,[spl76_5])],[avatar_definition]) ).
thf(f244,definition,
( spl76_1
<=> ( sP1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl76_1])],[avatar_definition]) ).
thf(f148,plain,
! [X16: $i,X13: $i] :
( ( $false
= ( cR @ sK10 ) )
| ( sP1 = $true )
| ( $true
= ( cP @ X16 ) )
| ( sP3 = $true )
| ( $true
= ( cR @ X13 ) )
| ( ( cS @ sK12 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f107,plain,
! [X16: $i,X13: $i] :
( ( ( cS @ sK12 )
= $true )
| ( $true
= ( cP @ X16 ) )
| ( ( cR @ sK10 )
= ( cR @ X13 ) )
| ( sP3 = $true )
| ( sP1 = $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sP3 = $true )
| ( ( ( ( ( ( ( $true
!= ( cP @ sK4 ) )
| ! [X1: $i] :
( ( cS @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
| ( ( cS @ sK5 )
= $true ) ) )
| ! [X4: $i] :
( ( cR @ ( sK6 @ X4 ) )
!= ( cR @ X4 ) ) )
& ( ( ( ( ( cS @ sK7 )
= $true )
| ( ( cP @ sK8 )
!= $true ) )
& ( ! [X8: $i] :
( ( cP @ X8 )
= $true )
| ! [X9: $i] :
( $true
!= ( cS @ X9 ) ) ) )
| ! [X11: $i] :
( ( cR @ X11 )
= ( cR @ sK9 ) ) ) )
| ( sP1 != $true ) )
& ( ( ( ! [X13: $i] :
( ( cR @ sK10 )
= ( cR @ X13 ) )
| ( ( ( $true
!= ( cP @ sK11 ) )
| ! [X15: $i] :
( $true
!= ( cS @ X15 ) ) )
& ( ! [X16: $i] :
( $true
= ( cP @ X16 ) )
| ( ( cS @ sK12 )
= $true ) ) ) )
& ( ( ( ( $true
= ( cS @ sK13 ) )
| ( ( cP @ sK14 )
!= $true ) )
& ( ! [X20: $i] :
( ( cP @ X20 )
= $true )
| ! [X21: $i] :
( ( cS @ X21 )
!= $true ) ) )
| ! [X22: $i] :
( ( cR @ X22 )
!= ( cR @ ( sK15 @ X22 ) ) ) ) )
| ( sP1 = $true ) ) ) )
& ( ( ( ( sP1 = $true )
| ( ( ( ( ( ( cP @ sK16 )
!= $true )
| ! [X25: $i] :
( ( cS @ X25 )
!= $true ) )
& ( ! [X26: $i] :
( ( cP @ X26 )
= $true )
| ( ( cS @ sK17 )
= $true ) ) )
| ! [X28: $i] :
( ( cR @ ( sK18 @ X28 ) )
!= ( cR @ X28 ) ) )
& ( ( ( ( ( cS @ sK19 )
= $true )
| ( ( cP @ sK20 )
!= $true ) )
& ( ! [X32: $i] :
( $true
= ( cP @ X32 ) )
| ! [X33: $i] :
( ( cS @ X33 )
!= $true ) ) )
| ! [X35: $i] :
( ( cR @ X35 )
= ( cR @ sK21 ) ) ) ) )
& ( ( ( ! [X37: $i] :
( ( cR @ X37 )
= ( cR @ sK22 ) )
| ( ( ( $true
!= ( cP @ sK23 ) )
| ! [X39: $i] :
( $true
!= ( cS @ X39 ) ) )
& ( ! [X40: $i] :
( ( cP @ X40 )
= $true )
| ( ( cS @ sK24 )
= $true ) ) ) )
& ( ( ( ( ( cS @ sK25 )
= $true )
| ( ( cP @ sK26 )
!= $true ) )
& ( ! [X44: $i] :
( $true
= ( cP @ X44 ) )
| ! [X45: $i] :
( ( cS @ X45 )
!= $true ) ) )
| ! [X46: $i] :
( ( cR @ X46 )
!= ( cR @ ( sK27 @ X46 ) ) ) ) )
| ( sP1 != $true ) ) )
| ( sP3 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27])],[f13,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14]) ).
thf(f14,plain,
( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
=> ( $true
!= ( cP @ sK4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X3: $i] :
( ( cS @ X3 )
= $true )
=> ( ( cS @ sK5 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X4: $i] :
( ? [X5: $i] :
( ( cR @ X5 )
!= ( cR @ X4 ) )
=> ( ( cR @ ( sK6 @ X4 ) )
!= ( cR @ X4 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X6: $i] :
( $true
= ( cS @ X6 ) )
=> ( ( cS @ sK7 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X7: $i] :
( $true
!= ( cP @ X7 ) )
=> ( ( cP @ sK8 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X10: $i] :
! [X11: $i] :
( ( cR @ X11 )
= ( cR @ X10 ) )
=> ! [X11: $i] :
( ( cR @ X11 )
= ( cR @ sK9 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X12: $i] :
! [X13: $i] :
( ( cR @ X12 )
= ( cR @ X13 ) )
=> ! [X13: $i] :
( ( cR @ sK10 )
= ( cR @ X13 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X14: $i] :
( $true
!= ( cP @ X14 ) )
=> ( $true
!= ( cP @ sK11 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X17: $i] :
( $true
= ( cS @ X17 ) )
=> ( ( cS @ sK12 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X18: $i] :
( $true
= ( cS @ X18 ) )
=> ( $true
= ( cS @ sK13 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X19: $i] :
( ( cP @ X19 )
!= $true )
=> ( ( cP @ sK14 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X22: $i] :
( ? [X23: $i] :
( ( cR @ X22 )
!= ( cR @ X23 ) )
=> ( ( cR @ X22 )
!= ( cR @ ( sK15 @ X22 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
( ? [X24: $i] :
( ( cP @ X24 )
!= $true )
=> ( ( cP @ sK16 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X27: $i] :
( $true
= ( cS @ X27 ) )
=> ( ( cS @ sK17 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
! [X28: $i] :
( ? [X29: $i] :
( ( cR @ X29 )
!= ( cR @ X28 ) )
=> ( ( cR @ ( sK18 @ X28 ) )
!= ( cR @ X28 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X30: $i] :
( ( cS @ X30 )
= $true )
=> ( ( cS @ sK19 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X31: $i] :
( $true
!= ( cP @ X31 ) )
=> ( ( cP @ sK20 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X34: $i] :
! [X35: $i] :
( ( cR @ X35 )
= ( cR @ X34 ) )
=> ! [X35: $i] :
( ( cR @ X35 )
= ( cR @ sK21 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f32,plain,
( ? [X36: $i] :
! [X37: $i] :
( ( cR @ X37 )
= ( cR @ X36 ) )
=> ! [X37: $i] :
( ( cR @ X37 )
= ( cR @ sK22 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f33,plain,
( ? [X38: $i] :
( ( cP @ X38 )
!= $true )
=> ( $true
!= ( cP @ sK23 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ? [X41: $i] :
( ( cS @ X41 )
= $true )
=> ( ( cS @ sK24 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f35,plain,
( ? [X42: $i] :
( ( cS @ X42 )
= $true )
=> ( ( cS @ sK25 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f36,plain,
( ? [X43: $i] :
( $true
!= ( cP @ X43 ) )
=> ( ( cP @ sK26 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f37,plain,
! [X46: $i] :
( ? [X47: $i] :
( ( cR @ X46 )
!= ( cR @ X47 ) )
=> ( ( cR @ X46 )
!= ( cR @ ( sK27 @ X46 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( ( sP3 = $true )
| ( ( ( ( ( ( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cS @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cS @ X3 )
= $true ) ) )
| ! [X4: $i] :
? [X5: $i] :
( ( cR @ X5 )
!= ( cR @ X4 ) ) )
& ( ( ( ? [X6: $i] :
( $true
= ( cS @ X6 ) )
| ? [X7: $i] :
( $true
!= ( cP @ X7 ) ) )
& ( ! [X8: $i] :
( ( cP @ X8 )
= $true )
| ! [X9: $i] :
( $true
!= ( cS @ X9 ) ) ) )
| ? [X10: $i] :
! [X11: $i] :
( ( cR @ X11 )
= ( cR @ X10 ) ) ) )
| ( sP1 != $true ) )
& ( ( ( ? [X12: $i] :
! [X13: $i] :
( ( cR @ X12 )
= ( cR @ X13 ) )
| ( ( ? [X14: $i] :
( $true
!= ( cP @ X14 ) )
| ! [X15: $i] :
( $true
!= ( cS @ X15 ) ) )
& ( ! [X16: $i] :
( $true
= ( cP @ X16 ) )
| ? [X17: $i] :
( $true
= ( cS @ X17 ) ) ) ) )
& ( ( ( ? [X18: $i] :
( $true
= ( cS @ X18 ) )
| ? [X19: $i] :
( ( cP @ X19 )
!= $true ) )
& ( ! [X20: $i] :
( ( cP @ X20 )
= $true )
| ! [X21: $i] :
( ( cS @ X21 )
!= $true ) ) )
| ! [X22: $i] :
? [X23: $i] :
( ( cR @ X22 )
!= ( cR @ X23 ) ) ) )
| ( sP1 = $true ) ) ) )
& ( ( ( ( sP1 = $true )
| ( ( ( ( ? [X24: $i] :
( ( cP @ X24 )
!= $true )
| ! [X25: $i] :
( ( cS @ X25 )
!= $true ) )
& ( ! [X26: $i] :
( ( cP @ X26 )
= $true )
| ? [X27: $i] :
( $true
= ( cS @ X27 ) ) ) )
| ! [X28: $i] :
? [X29: $i] :
( ( cR @ X29 )
!= ( cR @ X28 ) ) )
& ( ( ( ? [X30: $i] :
( ( cS @ X30 )
= $true )
| ? [X31: $i] :
( $true
!= ( cP @ X31 ) ) )
& ( ! [X32: $i] :
( $true
= ( cP @ X32 ) )
| ! [X33: $i] :
( ( cS @ X33 )
!= $true ) ) )
| ? [X34: $i] :
! [X35: $i] :
( ( cR @ X35 )
= ( cR @ X34 ) ) ) ) )
& ( ( ( ? [X36: $i] :
! [X37: $i] :
( ( cR @ X37 )
= ( cR @ X36 ) )
| ( ( ? [X38: $i] :
( ( cP @ X38 )
!= $true )
| ! [X39: $i] :
( $true
!= ( cS @ X39 ) ) )
& ( ! [X40: $i] :
( ( cP @ X40 )
= $true )
| ? [X41: $i] :
( ( cS @ X41 )
= $true ) ) ) )
& ( ( ( ? [X42: $i] :
( ( cS @ X42 )
= $true )
| ? [X43: $i] :
( $true
!= ( cP @ X43 ) ) )
& ( ! [X44: $i] :
( $true
= ( cP @ X44 ) )
| ! [X45: $i] :
( ( cS @ X45 )
!= $true ) ) )
| ! [X46: $i] :
? [X47: $i] :
( ( cR @ X46 )
!= ( cR @ X47 ) ) ) )
| ( sP1 != $true ) ) )
| ( sP3 != $true ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( sP3 = $true )
| ( ( ( ( ( ( ? [X3: $i] :
( $true
!= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ? [X2: $i] :
( ( cS @ X2 )
= $true ) ) )
| ! [X0: $i] :
? [X1: $i] :
( ( cR @ X1 )
!= ( cR @ X0 ) ) )
& ( ( ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
| ? [X3: $i] :
( $true
!= ( cP @ X3 ) ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) ) )
| ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) ) ) )
| ( sP1 != $true ) )
& ( ( ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) )
| ( ( ? [X3: $i] :
( $true
!= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ? [X2: $i] :
( ( cS @ X2 )
= $true ) ) ) )
& ( ( ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
| ? [X3: $i] :
( $true
!= ( cP @ X3 ) ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) ) )
| ! [X0: $i] :
? [X1: $i] :
( ( cR @ X1 )
!= ( cR @ X0 ) ) ) )
| ( sP1 = $true ) ) ) )
& ( ( ( ( sP1 = $true )
| ( ( ( ( ? [X3: $i] :
( $true
!= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ? [X2: $i] :
( ( cS @ X2 )
= $true ) ) )
| ! [X0: $i] :
? [X1: $i] :
( ( cR @ X1 )
!= ( cR @ X0 ) ) )
& ( ( ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
| ? [X3: $i] :
( $true
!= ( cP @ X3 ) ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) ) )
| ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) ) ) ) )
& ( ( ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) )
| ( ( ? [X3: $i] :
( $true
!= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ? [X2: $i] :
( ( cS @ X2 )
= $true ) ) ) )
& ( ( ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
| ? [X3: $i] :
( $true
!= ( cP @ X3 ) ) )
& ( ! [X3: $i] :
( $true
= ( cP @ X3 ) )
| ! [X2: $i] :
( ( cS @ X2 )
!= $true ) ) )
| ! [X0: $i] :
? [X1: $i] :
( ( cR @ X1 )
!= ( cR @ X0 ) ) ) )
| ( sP1 != $true ) ) )
| ( sP3 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( sP3 = $true )
<=> ( ( sP1 = $true )
<=> ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) )
<=> ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
<=> ! [X3: $i] :
( $true
= ( cP @ X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f751,plain,
( spl76_5
| spl76_112
| spl76_7
| spl76_55
| spl76_1
| spl76_83 ),
inference(avatar_split_clause,[status(thm)],[f147,f598,f244,f461,f268,f748,f259]) ).
thf(f147,plain,
! [X16: $i,X13: $i] :
( ( $true
= ( cP @ X16 ) )
| ( ( cR @ sK10 )
= $true )
| ( $false
= ( cR @ X13 ) )
| ( sP1 = $true )
| ( sP3 = $true )
| ( ( cS @ sK12 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f107]) ).
thf(f746,plain,
( ~ spl76_9
| spl76_13
| ~ spl76_12
| spl76_110
| ~ spl76_111 ),
inference(avatar_split_clause,[status(thm)],[f150,f742,f738,f286,f291,f276]) ).
thf(f276,definition,
( spl76_9
<=> ( $true = sP0 ) ),
introduced(definition,[new_symbols(naming,[spl76_9])],[avatar_definition]) ).
thf(f286,definition,
( spl76_12
<=> ( sP2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl76_12])],[avatar_definition]) ).
thf(f150,plain,
! [X46: $i] :
( ( $true
= ( cQ @ sK49 ) )
| ( $true
!= ( cR @ sK50 ) )
| ( sP2 != $true )
| ( $true != sP0 )
| ( $false
= ( cP @ X46 ) )
| ( ( cP @ ( sK51 @ X46 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X46: $i] :
( ( $true
= ( cQ @ sK49 ) )
| ( ( cP @ ( sK51 @ X46 ) )
!= ( cP @ X46 ) )
| ( $true != sP0 )
| ( $true
!= ( cR @ sK50 ) )
| ( sP2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f65,plain,
( ( ( sP2 = $true )
| ( ( ( ( ( ( ( $true
!= ( cR @ sK28 ) )
| ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cR @ X2 ) )
| ( ( cQ @ sK29 )
= $true ) ) )
| ! [X4: $i] :
( ( cP @ X4 )
!= ( cP @ ( sK30 @ X4 ) ) ) )
& ( ( ( ( ( cQ @ sK31 )
= $true )
| ( $true
!= ( cR @ sK32 ) ) )
& ( ! [X8: $i] :
( ( cR @ X8 )
= $true )
| ! [X9: $i] :
( $true
!= ( cQ @ X9 ) ) ) )
| ! [X11: $i] :
( ( cP @ sK33 )
= ( cP @ X11 ) ) ) )
| ( $true != sP0 ) )
& ( ( ( ! [X13: $i] :
( ( cP @ sK34 )
= ( cP @ X13 ) )
| ( ( ( ( cR @ sK35 )
!= $true )
| ! [X15: $i] :
( ( cQ @ X15 )
!= $true ) )
& ( ! [X16: $i] :
( $true
= ( cR @ X16 ) )
| ( $true
= ( cQ @ sK36 ) ) ) ) )
& ( ( ( ( ( cQ @ sK37 )
= $true )
| ( $true
!= ( cR @ sK38 ) ) )
& ( ! [X20: $i] :
( $true
= ( cR @ X20 ) )
| ! [X21: $i] :
( $true
!= ( cQ @ X21 ) ) ) )
| ! [X22: $i] :
( ( cP @ ( sK39 @ X22 ) )
!= ( cP @ X22 ) ) ) )
| ( $true = sP0 ) ) ) )
& ( ( ( ( $true = sP0 )
| ( ( ( ( ( ( cR @ sK40 )
!= $true )
| ! [X25: $i] :
( $true
!= ( cQ @ X25 ) ) )
& ( ! [X26: $i] :
( ( cR @ X26 )
= $true )
| ( ( cQ @ sK41 )
= $true ) ) )
| ! [X28: $i] :
( ( cP @ X28 )
!= ( cP @ ( sK42 @ X28 ) ) ) )
& ( ( ( ( ( cQ @ sK43 )
= $true )
| ( $true
!= ( cR @ sK44 ) ) )
& ( ! [X32: $i] :
( $true
= ( cR @ X32 ) )
| ! [X33: $i] :
( $true
!= ( cQ @ X33 ) ) ) )
| ! [X35: $i] :
( ( cP @ X35 )
= ( cP @ sK45 ) ) ) ) )
& ( ( ( ! [X37: $i] :
( ( cP @ X37 )
= ( cP @ sK46 ) )
| ( ( ( $true
!= ( cR @ sK47 ) )
| ! [X39: $i] :
( ( cQ @ X39 )
!= $true ) )
& ( ! [X40: $i] :
( $true
= ( cR @ X40 ) )
| ( ( cQ @ sK48 )
= $true ) ) ) )
& ( ( ( ( $true
= ( cQ @ sK49 ) )
| ( $true
!= ( cR @ sK50 ) ) )
& ( ! [X44: $i] :
( ( cR @ X44 )
= $true )
| ! [X45: $i] :
( $true
!= ( cQ @ X45 ) ) ) )
| ! [X46: $i] :
( ( cP @ ( sK51 @ X46 ) )
!= ( cP @ X46 ) ) ) )
| ( $true != sP0 ) ) )
| ( sP2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36,sK37,sK38,sK39,sK40,sK41,sK42,sK43,sK44,sK45,sK46,sK47,sK48,sK49,sK50,sK51])],[f40,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41]) ).
thf(f41,plain,
( ? [X0: $i] :
( ( cR @ X0 )
!= $true )
=> ( $true
!= ( cR @ sK28 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ? [X3: $i] :
( ( cQ @ X3 )
= $true )
=> ( ( cQ @ sK29 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
! [X4: $i] :
( ? [X5: $i] :
( ( cP @ X4 )
!= ( cP @ X5 ) )
=> ( ( cP @ X4 )
!= ( cP @ ( sK30 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X6: $i] :
( $true
= ( cQ @ X6 ) )
=> ( ( cQ @ sK31 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f45,plain,
( ? [X7: $i] :
( ( cR @ X7 )
!= $true )
=> ( $true
!= ( cR @ sK32 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
( ? [X10: $i] :
! [X11: $i] :
( ( cP @ X10 )
= ( cP @ X11 ) )
=> ! [X11: $i] :
( ( cP @ sK33 )
= ( cP @ X11 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ? [X12: $i] :
! [X13: $i] :
( ( cP @ X12 )
= ( cP @ X13 ) )
=> ! [X13: $i] :
( ( cP @ sK34 )
= ( cP @ X13 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f48,plain,
( ? [X14: $i] :
( ( cR @ X14 )
!= $true )
=> ( ( cR @ sK35 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f49,plain,
( ? [X17: $i] :
( $true
= ( cQ @ X17 ) )
=> ( $true
= ( cQ @ sK36 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f50,plain,
( ? [X18: $i] :
( ( cQ @ X18 )
= $true )
=> ( ( cQ @ sK37 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f51,plain,
( ? [X19: $i] :
( ( cR @ X19 )
!= $true )
=> ( $true
!= ( cR @ sK38 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f52,plain,
! [X22: $i] :
( ? [X23: $i] :
( ( cP @ X23 )
!= ( cP @ X22 ) )
=> ( ( cP @ ( sK39 @ X22 ) )
!= ( cP @ X22 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f53,plain,
( ? [X24: $i] :
( ( cR @ X24 )
!= $true )
=> ( ( cR @ sK40 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ? [X27: $i] :
( ( cQ @ X27 )
= $true )
=> ( ( cQ @ sK41 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f55,plain,
! [X28: $i] :
( ? [X29: $i] :
( ( cP @ X29 )
!= ( cP @ X28 ) )
=> ( ( cP @ X28 )
!= ( cP @ ( sK42 @ X28 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f56,plain,
( ? [X30: $i] :
( ( cQ @ X30 )
= $true )
=> ( ( cQ @ sK43 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f57,plain,
( ? [X31: $i] :
( ( cR @ X31 )
!= $true )
=> ( $true
!= ( cR @ sK44 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
( ? [X34: $i] :
! [X35: $i] :
( ( cP @ X35 )
= ( cP @ X34 ) )
=> ! [X35: $i] :
( ( cP @ X35 )
= ( cP @ sK45 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f59,plain,
( ? [X36: $i] :
! [X37: $i] :
( ( cP @ X37 )
= ( cP @ X36 ) )
=> ! [X37: $i] :
( ( cP @ X37 )
= ( cP @ sK46 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f60,plain,
( ? [X38: $i] :
( ( cR @ X38 )
!= $true )
=> ( $true
!= ( cR @ sK47 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f61,plain,
( ? [X41: $i] :
( ( cQ @ X41 )
= $true )
=> ( ( cQ @ sK48 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f62,plain,
( ? [X42: $i] :
( ( cQ @ X42 )
= $true )
=> ( $true
= ( cQ @ sK49 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f63,plain,
( ? [X43: $i] :
( $true
!= ( cR @ X43 ) )
=> ( $true
!= ( cR @ sK50 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f64,plain,
! [X46: $i] :
( ? [X47: $i] :
( ( cP @ X47 )
!= ( cP @ X46 ) )
=> ( ( cP @ ( sK51 @ X46 ) )
!= ( cP @ X46 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f40,plain,
( ( ( sP2 = $true )
| ( ( ( ( ( ( ? [X0: $i] :
( ( cR @ X0 )
!= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cR @ X2 ) )
| ? [X3: $i] :
( ( cQ @ X3 )
= $true ) ) )
| ! [X4: $i] :
? [X5: $i] :
( ( cP @ X4 )
!= ( cP @ X5 ) ) )
& ( ( ( ? [X6: $i] :
( $true
= ( cQ @ X6 ) )
| ? [X7: $i] :
( ( cR @ X7 )
!= $true ) )
& ( ! [X8: $i] :
( ( cR @ X8 )
= $true )
| ! [X9: $i] :
( $true
!= ( cQ @ X9 ) ) ) )
| ? [X10: $i] :
! [X11: $i] :
( ( cP @ X10 )
= ( cP @ X11 ) ) ) )
| ( $true != sP0 ) )
& ( ( ( ? [X12: $i] :
! [X13: $i] :
( ( cP @ X12 )
= ( cP @ X13 ) )
| ( ( ? [X14: $i] :
( ( cR @ X14 )
!= $true )
| ! [X15: $i] :
( ( cQ @ X15 )
!= $true ) )
& ( ! [X16: $i] :
( $true
= ( cR @ X16 ) )
| ? [X17: $i] :
( $true
= ( cQ @ X17 ) ) ) ) )
& ( ( ( ? [X18: $i] :
( ( cQ @ X18 )
= $true )
| ? [X19: $i] :
( ( cR @ X19 )
!= $true ) )
& ( ! [X20: $i] :
( $true
= ( cR @ X20 ) )
| ! [X21: $i] :
( $true
!= ( cQ @ X21 ) ) ) )
| ! [X22: $i] :
? [X23: $i] :
( ( cP @ X23 )
!= ( cP @ X22 ) ) ) )
| ( $true = sP0 ) ) ) )
& ( ( ( ( $true = sP0 )
| ( ( ( ( ? [X24: $i] :
( ( cR @ X24 )
!= $true )
| ! [X25: $i] :
( $true
!= ( cQ @ X25 ) ) )
& ( ! [X26: $i] :
( ( cR @ X26 )
= $true )
| ? [X27: $i] :
( ( cQ @ X27 )
= $true ) ) )
| ! [X28: $i] :
? [X29: $i] :
( ( cP @ X29 )
!= ( cP @ X28 ) ) )
& ( ( ( ? [X30: $i] :
( ( cQ @ X30 )
= $true )
| ? [X31: $i] :
( ( cR @ X31 )
!= $true ) )
& ( ! [X32: $i] :
( $true
= ( cR @ X32 ) )
| ! [X33: $i] :
( $true
!= ( cQ @ X33 ) ) ) )
| ? [X34: $i] :
! [X35: $i] :
( ( cP @ X35 )
= ( cP @ X34 ) ) ) ) )
& ( ( ( ? [X36: $i] :
! [X37: $i] :
( ( cP @ X37 )
= ( cP @ X36 ) )
| ( ( ? [X38: $i] :
( ( cR @ X38 )
!= $true )
| ! [X39: $i] :
( ( cQ @ X39 )
!= $true ) )
& ( ! [X40: $i] :
( $true
= ( cR @ X40 ) )
| ? [X41: $i] :
( ( cQ @ X41 )
= $true ) ) ) )
& ( ( ( ? [X42: $i] :
( ( cQ @ X42 )
= $true )
| ? [X43: $i] :
( $true
!= ( cR @ X43 ) ) )
& ( ! [X44: $i] :
( ( cR @ X44 )
= $true )
| ! [X45: $i] :
( $true
!= ( cQ @ X45 ) ) ) )
| ! [X46: $i] :
? [X47: $i] :
( ( cP @ X47 )
!= ( cP @ X46 ) ) ) )
| ( $true != sP0 ) ) )
| ( sP2 != $true ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( sP2 = $true )
| ( ( ( ( ( ( ? [X12: $i] :
( ( cR @ X12 )
!= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ? [X13: $i] :
( $true
= ( cQ @ X13 ) ) ) )
| ! [X14: $i] :
? [X15: $i] :
( ( cP @ X15 )
!= ( cP @ X14 ) ) )
& ( ( ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
| ? [X12: $i] :
( ( cR @ X12 )
!= $true ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) ) )
| ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) ) ) )
| ( $true != sP0 ) )
& ( ( ( ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) )
| ( ( ? [X12: $i] :
( ( cR @ X12 )
!= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ? [X13: $i] :
( $true
= ( cQ @ X13 ) ) ) ) )
& ( ( ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
| ? [X12: $i] :
( ( cR @ X12 )
!= $true ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) ) )
| ! [X14: $i] :
? [X15: $i] :
( ( cP @ X15 )
!= ( cP @ X14 ) ) ) )
| ( $true = sP0 ) ) ) )
& ( ( ( ( $true = sP0 )
| ( ( ( ( ? [X12: $i] :
( ( cR @ X12 )
!= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ? [X13: $i] :
( $true
= ( cQ @ X13 ) ) ) )
| ! [X14: $i] :
? [X15: $i] :
( ( cP @ X15 )
!= ( cP @ X14 ) ) )
& ( ( ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
| ? [X12: $i] :
( ( cR @ X12 )
!= $true ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) ) )
| ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) ) ) ) )
& ( ( ( ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) )
| ( ( ? [X12: $i] :
( ( cR @ X12 )
!= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ? [X13: $i] :
( $true
= ( cQ @ X13 ) ) ) ) )
& ( ( ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
| ? [X12: $i] :
( ( cR @ X12 )
!= $true ) )
& ( ! [X12: $i] :
( ( cR @ X12 )
= $true )
| ! [X13: $i] :
( $true
!= ( cQ @ X13 ) ) ) )
| ! [X14: $i] :
? [X15: $i] :
( ( cP @ X15 )
!= ( cP @ X14 ) ) ) )
| ( $true != sP0 ) ) )
| ( sP2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( sP2 = $true )
<=> ( ( $true = sP0 )
<=> ( ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) )
<=> ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
<=> ! [X12: $i] :
( ( cR @ X12 )
= $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f745,plain,
( spl76_110
| ~ spl76_111
| ~ spl76_12
| spl76_10
| ~ spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f149,f276,f280,f286,f742,f738]) ).
thf(f149,plain,
! [X46: $i] :
( ( $true
= ( cQ @ sK49 ) )
| ( $true != sP0 )
| ( ( cP @ X46 )
= $true )
| ( ( cP @ ( sK51 @ X46 ) )
= $true )
| ( sP2 != $true )
| ( $true
!= ( cR @ sK50 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f736,plain,
( spl76_43
| ~ spl76_1
| spl76_109
| spl76_19
| spl76_20 ),
inference(avatar_split_clause,[status(thm)],[f152,f317,f314,f732,f244,f413]) ).
thf(f152,plain,
! [X16: $i,X13: $i] :
( ( ( cP @ sK60 )
= $true )
| ( sP1 != $true )
| ( $true
= ( cS @ X13 ) )
| ( ( cQ @ X16 )
= $true )
| ( ( cS @ sK58 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f131,plain,
! [X16: $i,X13: $i] :
( ( ( cQ @ X16 )
= $true )
| ( ( cP @ sK60 )
= $true )
| ( ( cS @ sK58 )
= ( cS @ X13 ) )
| ( sP1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( sP1 = $true )
| ( ( ( ( ( ( cQ @ sK52 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cQ @ X2 ) )
| ( ( cP @ sK53 )
= $true ) ) )
| ! [X4: $i] :
( ( cS @ X4 )
!= ( cS @ ( sK54 @ X4 ) ) ) )
& ( ( ( ( ( cP @ sK55 )
= $true )
| ( $true
!= ( cQ @ sK56 ) ) )
& ( ! [X8: $i] :
( $true
= ( cQ @ X8 ) )
| ! [X9: $i] :
( ( cP @ X9 )
!= $true ) ) )
| ! [X11: $i] :
( ( cS @ sK57 )
= ( cS @ X11 ) ) ) ) )
& ( ( ( ! [X13: $i] :
( ( cS @ sK58 )
= ( cS @ X13 ) )
| ( ( ( ( cQ @ sK59 )
!= $true )
| ! [X15: $i] :
( $true
!= ( cP @ X15 ) ) )
& ( ! [X16: $i] :
( ( cQ @ X16 )
= $true )
| ( ( cP @ sK60 )
= $true ) ) ) )
& ( ( ( ( $true
= ( cP @ sK61 ) )
| ( $true
!= ( cQ @ sK62 ) ) )
& ( ! [X20: $i] :
( ( cQ @ X20 )
= $true )
| ! [X21: $i] :
( ( cP @ X21 )
!= $true ) ) )
| ! [X22: $i] :
( ( cS @ ( sK63 @ X22 ) )
!= ( cS @ X22 ) ) ) )
| ( sP1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61,sK62,sK63])],[f67,f79,f78,f77,f76,f75,f74,f73,f72,f71,f70,f69,f68]) ).
thf(f68,plain,
( ? [X0: $i] :
( ( cQ @ X0 )
!= $true )
=> ( ( cQ @ sK52 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f69,plain,
( ? [X3: $i] :
( $true
= ( cP @ X3 ) )
=> ( ( cP @ sK53 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f70,plain,
! [X4: $i] :
( ? [X5: $i] :
( ( cS @ X4 )
!= ( cS @ X5 ) )
=> ( ( cS @ X4 )
!= ( cS @ ( sK54 @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f71,plain,
( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
=> ( ( cP @ sK55 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f72,plain,
( ? [X7: $i] :
( ( cQ @ X7 )
!= $true )
=> ( $true
!= ( cQ @ sK56 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f73,plain,
( ? [X10: $i] :
! [X11: $i] :
( ( cS @ X11 )
= ( cS @ X10 ) )
=> ! [X11: $i] :
( ( cS @ sK57 )
= ( cS @ X11 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f74,plain,
( ? [X12: $i] :
! [X13: $i] :
( ( cS @ X12 )
= ( cS @ X13 ) )
=> ! [X13: $i] :
( ( cS @ sK58 )
= ( cS @ X13 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f75,plain,
( ? [X14: $i] :
( $true
!= ( cQ @ X14 ) )
=> ( ( cQ @ sK59 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f76,plain,
( ? [X17: $i] :
( ( cP @ X17 )
= $true )
=> ( ( cP @ sK60 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f77,plain,
( ? [X18: $i] :
( $true
= ( cP @ X18 ) )
=> ( $true
= ( cP @ sK61 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f78,plain,
( ? [X19: $i] :
( $true
!= ( cQ @ X19 ) )
=> ( $true
!= ( cQ @ sK62 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f79,plain,
! [X22: $i] :
( ? [X23: $i] :
( ( cS @ X23 )
!= ( cS @ X22 ) )
=> ( ( cS @ ( sK63 @ X22 ) )
!= ( cS @ X22 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f67,plain,
( ( ( sP1 = $true )
| ( ( ( ( ? [X0: $i] :
( ( cQ @ X0 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cQ @ X2 ) )
| ? [X3: $i] :
( $true
= ( cP @ X3 ) ) ) )
| ! [X4: $i] :
? [X5: $i] :
( ( cS @ X4 )
!= ( cS @ X5 ) ) )
& ( ( ( ? [X6: $i] :
( $true
= ( cP @ X6 ) )
| ? [X7: $i] :
( ( cQ @ X7 )
!= $true ) )
& ( ! [X8: $i] :
( $true
= ( cQ @ X8 ) )
| ! [X9: $i] :
( ( cP @ X9 )
!= $true ) ) )
| ? [X10: $i] :
! [X11: $i] :
( ( cS @ X11 )
= ( cS @ X10 ) ) ) ) )
& ( ( ( ? [X12: $i] :
! [X13: $i] :
( ( cS @ X12 )
= ( cS @ X13 ) )
| ( ( ? [X14: $i] :
( $true
!= ( cQ @ X14 ) )
| ! [X15: $i] :
( $true
!= ( cP @ X15 ) ) )
& ( ! [X16: $i] :
( ( cQ @ X16 )
= $true )
| ? [X17: $i] :
( ( cP @ X17 )
= $true ) ) ) )
& ( ( ( ? [X18: $i] :
( $true
= ( cP @ X18 ) )
| ? [X19: $i] :
( $true
!= ( cQ @ X19 ) ) )
& ( ! [X20: $i] :
( ( cQ @ X20 )
= $true )
| ! [X21: $i] :
( ( cP @ X21 )
!= $true ) ) )
| ! [X22: $i] :
? [X23: $i] :
( ( cS @ X23 )
!= ( cS @ X22 ) ) ) )
| ( sP1 != $true ) ) ),
inference(rectify,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ( sP1 = $true )
| ( ( ( ( ? [X5: $i] :
( ( cQ @ X5 )
!= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) )
& ( ! [X5: $i] :
( ( cQ @ X5 )
= $true )
| ? [X4: $i] :
( ( cP @ X4 )
= $true ) ) )
| ! [X6: $i] :
? [X7: $i] :
( ( cS @ X7 )
!= ( cS @ X6 ) ) )
& ( ( ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
| ? [X5: $i] :
( ( cQ @ X5 )
!= $true ) )
& ( ! [X5: $i] :
( ( cQ @ X5 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) ) )
| ? [X6: $i] :
! [X7: $i] :
( ( cS @ X7 )
= ( cS @ X6 ) ) ) ) )
& ( ( ( ? [X6: $i] :
! [X7: $i] :
( ( cS @ X7 )
= ( cS @ X6 ) )
| ( ( ? [X5: $i] :
( ( cQ @ X5 )
!= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) )
& ( ! [X5: $i] :
( ( cQ @ X5 )
= $true )
| ? [X4: $i] :
( ( cP @ X4 )
= $true ) ) ) )
& ( ( ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
| ? [X5: $i] :
( ( cQ @ X5 )
!= $true ) )
& ( ! [X5: $i] :
( ( cQ @ X5 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) ) )
| ! [X6: $i] :
? [X7: $i] :
( ( cS @ X7 )
!= ( cS @ X6 ) ) ) )
| ( sP1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( sP1 = $true )
<=> ( ? [X6: $i] :
! [X7: $i] :
( ( cS @ X7 )
= ( cS @ X6 ) )
<=> ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
<=> ! [X5: $i] :
( ( cQ @ X5 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f735,plain,
( spl76_41
| spl76_109
| spl76_25
| spl76_20
| ~ spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f151,f244,f317,f336,f732,f404]) ).
thf(f151,plain,
! [X16: $i,X13: $i] :
( ( $false
= ( cS @ X13 ) )
| ( sP1 != $true )
| ( ( cQ @ X16 )
= $true )
| ( ( cS @ sK58 )
= $true )
| ( ( cP @ sK60 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f131]) ).
thf(f730,plain,
( spl76_55
| spl76_11
| spl76_106
| spl76_12
| ~ spl76_108
| spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f154,f276,f726,f286,f715,f283,f461]) ).
thf(f154,plain,
! [X15: $i,X13: $i] :
( ( $true
= ( cP @ X13 ) )
| ( $true = sP0 )
| ( ( cR @ sK35 )
!= $true )
| ( sP2 = $true )
| ( ( cQ @ X15 )
!= $true )
| ( ( cP @ sK34 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f124,plain,
! [X15: $i,X13: $i] :
( ( ( cR @ sK35 )
!= $true )
| ( sP2 = $true )
| ( ( cQ @ X15 )
!= $true )
| ( $true = sP0 )
| ( ( cP @ sK34 )
= ( cP @ X13 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f729,plain,
( spl76_11
| ~ spl76_108
| spl76_104
| spl76_12
| spl76_9
| spl76_62 ),
inference(avatar_split_clause,[status(thm)],[f153,f495,f276,f286,f706,f726,f283]) ).
thf(f153,plain,
! [X15: $i,X13: $i] :
( ( $true = sP0 )
| ( ( cR @ sK35 )
!= $true )
| ( sP2 = $true )
| ( ( cP @ sK34 )
= $true )
| ( $false
= ( cP @ X13 ) )
| ( ( cQ @ X15 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f124]) ).
thf(f724,plain,
( spl76_7
| ~ spl76_1
| spl76_80
| spl76_107
| spl76_55
| ~ spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f156,f259,f461,f720,f583,f244,f268]) ).
thf(f156,plain,
! [X40: $i,X37: $i] :
( ( ( cP @ X40 )
= $true )
| ( ( cR @ X37 )
= $false )
| ( $true
= ( cR @ sK22 ) )
| ( ( cS @ sK24 )
= $true )
| ( sP1 != $true )
| ( sP3 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X40: $i,X37: $i] :
( ( sP1 != $true )
| ( ( cR @ X37 )
= ( cR @ sK22 ) )
| ( ( cP @ X40 )
= $true )
| ( ( cS @ sK24 )
= $true )
| ( sP3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f723,plain,
( spl76_4
| spl76_107
| spl76_55
| ~ spl76_5
| spl76_79
| ~ spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f155,f244,f578,f259,f461,f720,f256]) ).
thf(f155,plain,
! [X40: $i,X37: $i] :
( ( $false
= ( cR @ sK22 ) )
| ( sP3 != $true )
| ( sP1 != $true )
| ( ( cS @ sK24 )
= $true )
| ( ( cP @ X40 )
= $true )
| ( ( cR @ X37 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f99]) ).
thf(f718,plain,
( spl76_105
| spl76_4
| spl76_55
| spl76_106
| spl76_9
| spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f158,f286,f276,f715,f461,f256,f710]) ).
thf(f158,plain,
! [X16: $i,X13: $i] :
( ( $true
= ( cP @ X13 ) )
| ( ( cP @ sK34 )
= $false )
| ( $true = sP0 )
| ( $true
= ( cQ @ sK36 ) )
| ( $true
= ( cR @ X16 ) )
| ( sP2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f123,plain,
! [X16: $i,X13: $i] :
( ( $true
= ( cQ @ sK36 ) )
| ( $true
= ( cR @ X16 ) )
| ( $true = sP0 )
| ( ( cP @ sK34 )
= ( cP @ X13 ) )
| ( sP2 = $true ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f713,plain,
( spl76_62
| spl76_104
| spl76_9
| spl76_12
| spl76_4
| spl76_105 ),
inference(avatar_split_clause,[status(thm)],[f157,f710,f256,f286,f276,f706,f495]) ).
thf(f157,plain,
! [X16: $i,X13: $i] :
( ( $true
= ( cQ @ sK36 ) )
| ( $true
= ( cR @ X16 ) )
| ( ( cP @ sK34 )
= $true )
| ( $false
= ( cP @ X13 ) )
| ( sP2 = $true )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f123]) ).
thf(f704,plain,
( ~ spl76_9
| spl76_19
| spl76_40
| spl76_31 ),
inference(avatar_split_clause,[status(thm)],[f160,f361,f399,f314,f276]) ).
thf(f160,plain,
! [X16: $i,X12: $i,X13: $i] :
( ( $true
!= ( cR @ X13 ) )
| ( ( cS @ X12 )
= $true )
| ( $false
= ( cQ @ X16 ) )
| ( $true != sP0 )
| ( $false
= ( cQ @ ( sK72 @ X16 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
! [X16: $i,X12: $i,X13: $i] :
( ( $true != sP0 )
| ( $true
!= ( cR @ X13 ) )
| ( ( cQ @ X16 )
!= ( cQ @ ( sK72 @ X16 ) ) )
| ( ( cS @ X12 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f95,plain,
( ( ( $true = sP0 )
| ( ( ! [X0: $i] :
( ( cQ @ X0 )
!= ( cQ @ ( sK64 @ X0 ) ) )
| ( ( ! [X2: $i] :
( $true
!= ( cR @ X2 ) )
| ( $true
!= ( cS @ sK65 ) ) )
& ( ( $true
= ( cR @ sK66 ) )
| ! [X5: $i] :
( ( cS @ X5 )
= $true ) ) ) )
& ( ! [X7: $i] :
( ( cQ @ sK67 )
= ( cQ @ X7 ) )
| ( ( ! [X8: $i] :
( ( cS @ X8 )
= $true )
| ! [X9: $i] :
( ( cR @ X9 )
!= $true ) )
& ( ( ( cR @ sK68 )
= $true )
| ( $true
!= ( cS @ sK69 ) ) ) ) ) ) )
& ( ( ( ( ( ! [X12: $i] :
( ( cS @ X12 )
= $true )
| ! [X13: $i] :
( $true
!= ( cR @ X13 ) ) )
& ( ( $true
= ( cR @ sK70 ) )
| ( $true
!= ( cS @ sK71 ) ) ) )
| ! [X16: $i] :
( ( cQ @ X16 )
!= ( cQ @ ( sK72 @ X16 ) ) ) )
& ( ! [X19: $i] :
( ( cQ @ X19 )
= ( cQ @ sK73 ) )
| ( ( ! [X20: $i] :
( $true
!= ( cR @ X20 ) )
| ( ( cS @ sK74 )
!= $true ) )
& ( ( ( cR @ sK75 )
= $true )
| ! [X23: $i] :
( ( cS @ X23 )
= $true ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65,sK66,sK67,sK68,sK69,sK70,sK71,sK72,sK73,sK74,sK75])],[f82,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83]) ).
thf(f83,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( cQ @ X0 )
!= ( cQ @ X1 ) )
=> ( ( cQ @ X0 )
!= ( cQ @ ( sK64 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f84,plain,
( ? [X3: $i] :
( ( cS @ X3 )
!= $true )
=> ( $true
!= ( cS @ sK65 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f85,plain,
( ? [X4: $i] :
( $true
= ( cR @ X4 ) )
=> ( $true
= ( cR @ sK66 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f86,plain,
( ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X7 )
= ( cQ @ X6 ) )
=> ! [X7: $i] :
( ( cQ @ sK67 )
= ( cQ @ X7 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f87,plain,
( ? [X10: $i] :
( $true
= ( cR @ X10 ) )
=> ( ( cR @ sK68 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f88,plain,
( ? [X11: $i] :
( ( cS @ X11 )
!= $true )
=> ( $true
!= ( cS @ sK69 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f89,plain,
( ? [X14: $i] :
( ( cR @ X14 )
= $true )
=> ( $true
= ( cR @ sK70 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f90,plain,
( ? [X15: $i] :
( $true
!= ( cS @ X15 ) )
=> ( $true
!= ( cS @ sK71 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f91,plain,
! [X16: $i] :
( ? [X17: $i] :
( ( cQ @ X16 )
!= ( cQ @ X17 ) )
=> ( ( cQ @ X16 )
!= ( cQ @ ( sK72 @ X16 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f92,plain,
( ? [X18: $i] :
! [X19: $i] :
( ( cQ @ X18 )
= ( cQ @ X19 ) )
=> ! [X19: $i] :
( ( cQ @ X19 )
= ( cQ @ sK73 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f93,plain,
( ? [X21: $i] :
( ( cS @ X21 )
!= $true )
=> ( ( cS @ sK74 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f94,plain,
( ? [X22: $i] :
( ( cR @ X22 )
= $true )
=> ( ( cR @ sK75 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f82,plain,
( ( ( $true = sP0 )
| ( ( ! [X0: $i] :
? [X1: $i] :
( ( cQ @ X0 )
!= ( cQ @ X1 ) )
| ( ( ! [X2: $i] :
( $true
!= ( cR @ X2 ) )
| ? [X3: $i] :
( ( cS @ X3 )
!= $true ) )
& ( ? [X4: $i] :
( $true
= ( cR @ X4 ) )
| ! [X5: $i] :
( ( cS @ X5 )
= $true ) ) ) )
& ( ? [X6: $i] :
! [X7: $i] :
( ( cQ @ X7 )
= ( cQ @ X6 ) )
| ( ( ! [X8: $i] :
( ( cS @ X8 )
= $true )
| ! [X9: $i] :
( ( cR @ X9 )
!= $true ) )
& ( ? [X10: $i] :
( $true
= ( cR @ X10 ) )
| ? [X11: $i] :
( ( cS @ X11 )
!= $true ) ) ) ) ) )
& ( ( ( ( ( ! [X12: $i] :
( ( cS @ X12 )
= $true )
| ! [X13: $i] :
( $true
!= ( cR @ X13 ) ) )
& ( ? [X14: $i] :
( ( cR @ X14 )
= $true )
| ? [X15: $i] :
( $true
!= ( cS @ X15 ) ) ) )
| ! [X16: $i] :
? [X17: $i] :
( ( cQ @ X16 )
!= ( cQ @ X17 ) ) )
& ( ? [X18: $i] :
! [X19: $i] :
( ( cQ @ X18 )
= ( cQ @ X19 ) )
| ( ( ! [X20: $i] :
( $true
!= ( cR @ X20 ) )
| ? [X21: $i] :
( ( cS @ X21 )
!= $true ) )
& ( ? [X22: $i] :
( ( cR @ X22 )
= $true )
| ! [X23: $i] :
( ( cS @ X23 )
= $true ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(rectify,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( $true = sP0 )
| ( ( ! [X8: $i] :
? [X9: $i] :
( ( cQ @ X9 )
!= ( cQ @ X8 ) )
| ( ( ! [X10: $i] :
( $true
!= ( cR @ X10 ) )
| ? [X11: $i] :
( ( cS @ X11 )
!= $true ) )
& ( ? [X10: $i] :
( $true
= ( cR @ X10 ) )
| ! [X11: $i] :
( ( cS @ X11 )
= $true ) ) ) )
& ( ? [X8: $i] :
! [X9: $i] :
( ( cQ @ X9 )
= ( cQ @ X8 ) )
| ( ( ! [X11: $i] :
( ( cS @ X11 )
= $true )
| ! [X10: $i] :
( $true
!= ( cR @ X10 ) ) )
& ( ? [X10: $i] :
( $true
= ( cR @ X10 ) )
| ? [X11: $i] :
( ( cS @ X11 )
!= $true ) ) ) ) ) )
& ( ( ( ( ( ! [X11: $i] :
( ( cS @ X11 )
= $true )
| ! [X10: $i] :
( $true
!= ( cR @ X10 ) ) )
& ( ? [X10: $i] :
( $true
= ( cR @ X10 ) )
| ? [X11: $i] :
( ( cS @ X11 )
!= $true ) ) )
| ! [X8: $i] :
? [X9: $i] :
( ( cQ @ X9 )
!= ( cQ @ X8 ) ) )
& ( ? [X8: $i] :
! [X9: $i] :
( ( cQ @ X9 )
= ( cQ @ X8 ) )
| ( ( ! [X10: $i] :
( $true
!= ( cR @ X10 ) )
| ? [X11: $i] :
( ( cS @ X11 )
!= $true ) )
& ( ? [X10: $i] :
( $true
= ( cR @ X10 ) )
| ! [X11: $i] :
( ( cS @ X11 )
= $true ) ) ) ) )
| ( $true != sP0 ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( $true = sP0 )
<=> ( ( ! [X11: $i] :
( ( cS @ X11 )
= $true )
<=> ? [X10: $i] :
( $true
= ( cR @ X10 ) ) )
<=> ? [X8: $i] :
! [X9: $i] :
( ( cQ @ X9 )
= ( cQ @ X8 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f703,plain,
( spl76_30
| spl76_19
| spl76_40
| ~ spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f159,f276,f399,f314,f357]) ).
thf(f159,plain,
! [X16: $i,X12: $i,X13: $i] :
( ( ( cQ @ X16 )
= $true )
| ( ( cS @ X12 )
= $true )
| ( $true
= ( cQ @ ( sK72 @ X16 ) ) )
| ( $true
!= ( cR @ X13 ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f702,plain,
( spl76_11
| spl76_62
| ~ spl76_12
| spl76_4
| spl76_9
| spl76_94 ),
inference(avatar_split_clause,[status(thm)],[f162,f647,f276,f256,f286,f495,f283]) ).
thf(f162,plain,
! [X35: $i,X32: $i,X33: $i] :
( ( $true
= ( cR @ X32 ) )
| ( sP2 != $true )
| ( $true
!= ( cQ @ X33 ) )
| ( ( cP @ X35 )
= $false )
| ( $true
= ( cP @ sK45 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f117,plain,
! [X35: $i,X32: $i,X33: $i] :
( ( sP2 != $true )
| ( $true
!= ( cQ @ X33 ) )
| ( $true = sP0 )
| ( $true
= ( cR @ X32 ) )
| ( ( cP @ X35 )
= ( cP @ sK45 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f701,plain,
( spl76_4
| spl76_9
| spl76_55
| spl76_93
| ~ spl76_12
| spl76_11 ),
inference(avatar_split_clause,[status(thm)],[f161,f283,f286,f642,f461,f276,f256]) ).
thf(f161,plain,
! [X35: $i,X32: $i,X33: $i] :
( ( ( cP @ X35 )
= $true )
| ( $true
= ( cR @ X32 ) )
| ( sP2 != $true )
| ( $true
!= ( cQ @ X33 ) )
| ( $false
= ( cP @ sK45 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f117]) ).
thf(f700,plain,
( spl76_98
| spl76_103
| spl76_4
| ~ spl76_12
| spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f164,f276,f286,f256,f696,f666]) ).
thf(f164,plain,
! [X28: $i,X26: $i] :
( ( sP2 != $true )
| ( ( cR @ X26 )
= $true )
| ( $false
= ( cP @ X28 ) )
| ( $true = sP0 )
| ( ( cQ @ sK41 )
= $true )
| ( $false
= ( cP @ ( sK42 @ X28 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f119,plain,
! [X28: $i,X26: $i] :
( ( ( cP @ X28 )
!= ( cP @ ( sK42 @ X28 ) ) )
| ( $true = sP0 )
| ( ( cQ @ sK41 )
= $true )
| ( sP2 != $true )
| ( ( cR @ X26 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f699,plain,
( spl76_4
| spl76_103
| spl76_97
| ~ spl76_12
| spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f163,f276,f286,f662,f696,f256]) ).
thf(f163,plain,
! [X28: $i,X26: $i] :
( ( $true = sP0 )
| ( $true
= ( cP @ ( sK42 @ X28 ) ) )
| ( ( cQ @ sK41 )
= $true )
| ( ( cR @ X26 )
= $true )
| ( sP2 != $true )
| ( $true
= ( cP @ X28 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f119]) ).
thf(f694,plain,
( spl76_1
| spl76_20
| spl76_102
| spl76_53 ),
inference(avatar_split_clause,[status(thm)],[f166,f454,f690,f317,f244]) ).
thf(f166,plain,
! [X2: $i,X4: $i] :
( ( ( cP @ sK53 )
= $true )
| ( sP1 = $true )
| ( $false
= ( cS @ ( sK54 @ X4 ) ) )
| ( ( cS @ X4 )
= $false )
| ( $true
= ( cQ @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
! [X2: $i,X4: $i] :
( ( sP1 = $true )
| ( ( cS @ X4 )
!= ( cS @ ( sK54 @ X4 ) ) )
| ( $true
= ( cQ @ X2 ) )
| ( ( cP @ sK53 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f693,plain,
( spl76_51
| spl76_20
| spl76_1
| spl76_102 ),
inference(avatar_split_clause,[status(thm)],[f165,f690,f244,f317,f446]) ).
thf(f165,plain,
! [X2: $i,X4: $i] :
( ( ( cS @ X4 )
= $true )
| ( sP1 = $true )
| ( $true
= ( cQ @ X2 ) )
| ( ( cP @ sK53 )
= $true )
| ( ( cS @ ( sK54 @ X4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f688,plain,
( ~ spl76_1
| spl76_56
| ~ spl76_5
| spl76_101
| ~ spl76_100 ),
inference(avatar_split_clause,[status(thm)],[f168,f680,f684,f259,f465,f244]) ).
thf(f168,plain,
! [X46: $i] :
( ( ( cP @ sK26 )
!= $true )
| ( sP1 != $true )
| ( sP3 != $true )
| ( ( cR @ X46 )
= $false )
| ( $false
= ( cR @ ( sK27 @ X46 ) ) )
| ( ( cS @ sK25 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X46: $i] :
( ( ( cS @ sK25 )
= $true )
| ( sP3 != $true )
| ( sP1 != $true )
| ( ( cR @ X46 )
!= ( cR @ ( sK27 @ X46 ) ) )
| ( ( cP @ sK26 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f687,plain,
( ~ spl76_1
| ~ spl76_100
| ~ spl76_5
| spl76_54
| spl76_101 ),
inference(avatar_split_clause,[status(thm)],[f167,f684,f458,f259,f680,f244]) ).
thf(f167,plain,
! [X46: $i] :
( ( sP1 != $true )
| ( sP3 != $true )
| ( ( cR @ X46 )
= $true )
| ( ( cS @ sK25 )
= $true )
| ( ( cP @ sK26 )
!= $true )
| ( ( cR @ ( sK27 @ X46 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f98]) ).
thf(f678,plain,
( spl76_99
| ~ spl76_5
| spl76_55
| spl76_50
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f170,f244,f442,f461,f259,f674]) ).
thf(f170,plain,
! [X28: $i,X26: $i] :
( ( ( cP @ X26 )
= $true )
| ( $false
= ( cR @ X28 ) )
| ( sP1 = $true )
| ( sP3 != $true )
| ( ( cS @ sK17 )
= $true )
| ( $false
= ( cR @ ( sK18 @ X28 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X28: $i,X26: $i] :
( ( sP3 != $true )
| ( ( cR @ ( sK18 @ X28 ) )
!= ( cR @ X28 ) )
| ( sP1 = $true )
| ( ( cP @ X26 )
= $true )
| ( ( cS @ sK17 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f677,plain,
( spl76_55
| spl76_1
| ~ spl76_5
| spl76_99
| spl76_49 ),
inference(avatar_split_clause,[status(thm)],[f169,f438,f674,f259,f244,f461]) ).
thf(f169,plain,
! [X28: $i,X26: $i] :
( ( ( cP @ X26 )
= $true )
| ( sP1 = $true )
| ( $true
= ( cR @ X28 ) )
| ( ( cS @ sK17 )
= $true )
| ( sP3 != $true )
| ( ( cR @ ( sK18 @ X28 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f672,plain,
( spl76_12
| spl76_4
| spl76_55
| ~ spl76_9
| spl76_11
| spl76_74 ),
inference(avatar_split_clause,[status(thm)],[f172,f551,f283,f276,f461,f256,f286]) ).
thf(f172,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( sP2 = $true )
| ( $true != sP0 )
| ( $true
= ( cP @ X11 ) )
| ( $false
= ( cP @ sK33 ) )
| ( $true
!= ( cQ @ X9 ) )
| ( ( cR @ X8 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f125,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( ( cP @ sK33 )
= ( cP @ X11 ) )
| ( $true != sP0 )
| ( $true
!= ( cQ @ X9 ) )
| ( sP2 = $true )
| ( ( cR @ X8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f671,plain,
( spl76_72
| spl76_4
| spl76_62
| ~ spl76_9
| spl76_11
| spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f171,f286,f283,f276,f495,f256,f542]) ).
thf(f171,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( $false
= ( cP @ X11 ) )
| ( $true != sP0 )
| ( ( cR @ X8 )
= $true )
| ( ( cP @ sK33 )
= $true )
| ( sP2 = $true )
| ( $true
!= ( cQ @ X9 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f125]) ).
thf(f670,plain,
( spl76_16
| spl76_1
| spl76_5
| spl76_55
| spl76_89 ),
inference(avatar_split_clause,[status(thm)],[f174,f624,f461,f259,f244,f302]) ).
thf(f174,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( ( cR @ X22 )
= $false )
| ( sP1 = $true )
| ( sP3 = $true )
| ( ( cS @ X21 )
!= $true )
| ( ( cP @ X20 )
= $true )
| ( $false
= ( cR @ ( sK15 @ X22 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f105,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( ( cS @ X21 )
!= $true )
| ( ( cR @ X22 )
!= ( cR @ ( sK15 @ X22 ) ) )
| ( ( cP @ X20 )
= $true )
| ( sP1 = $true )
| ( sP3 = $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f669,plain,
( spl76_5
| spl76_86
| spl76_1
| spl76_55
| spl76_16 ),
inference(avatar_split_clause,[status(thm)],[f173,f302,f461,f244,f612,f259]) ).
thf(f173,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( ( cR @ X22 )
= $true )
| ( sP1 = $true )
| ( sP3 = $true )
| ( ( cS @ X21 )
!= $true )
| ( ( cP @ X20 )
= $true )
| ( $true
= ( cR @ ( sK15 @ X22 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f105]) ).
thf(f668,plain,
( spl76_11
| spl76_9
| spl76_98
| ~ spl76_12
| ~ spl76_96 ),
inference(avatar_split_clause,[status(thm)],[f176,f658,f286,f666,f276,f283]) ).
thf(f176,plain,
! [X28: $i,X25: $i] :
( ( $true
!= ( cQ @ X25 ) )
| ( $false
= ( cP @ ( sK42 @ X28 ) ) )
| ( sP2 != $true )
| ( $true = sP0 )
| ( $false
= ( cP @ X28 ) )
| ( ( cR @ sK40 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f120,plain,
! [X28: $i,X25: $i] :
( ( sP2 != $true )
| ( ( cP @ X28 )
!= ( cP @ ( sK42 @ X28 ) ) )
| ( $true
!= ( cQ @ X25 ) )
| ( $true = sP0 )
| ( ( cR @ sK40 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f664,plain,
( ~ spl76_96
| spl76_11
| ~ spl76_12
| spl76_97
| spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f175,f276,f662,f286,f283,f658]) ).
thf(f175,plain,
! [X28: $i,X25: $i] :
( ( $true = sP0 )
| ( $true
= ( cP @ ( sK42 @ X28 ) ) )
| ( $true
!= ( cQ @ X25 ) )
| ( $true
= ( cP @ X28 ) )
| ( ( cR @ sK40 )
!= $true )
| ( sP2 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f120]) ).
thf(f656,plain,
( spl76_12
| spl76_95
| ~ spl76_9
| spl76_4
| spl76_68 ),
inference(avatar_split_clause,[status(thm)],[f178,f524,f256,f276,f652,f286]) ).
thf(f178,plain,
! [X2: $i,X4: $i] :
( ( $true != sP0 )
| ( ( cP @ X4 )
= $false )
| ( sP2 = $true )
| ( $true
= ( cR @ X2 ) )
| ( ( cQ @ sK29 )
= $true )
| ( $false
= ( cP @ ( sK30 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f127,plain,
! [X2: $i,X4: $i] :
( ( ( cP @ X4 )
!= ( cP @ ( sK30 @ X4 ) ) )
| ( $true != sP0 )
| ( $true
= ( cR @ X2 ) )
| ( ( cQ @ sK29 )
= $true )
| ( sP2 = $true ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f655,plain,
( spl76_95
| spl76_4
| spl76_67
| spl76_12
| ~ spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f177,f276,f286,f520,f256,f652]) ).
thf(f177,plain,
! [X2: $i,X4: $i] :
( ( $true != sP0 )
| ( $true
= ( cR @ X2 ) )
| ( ( cQ @ sK29 )
= $true )
| ( $true
= ( cP @ ( sK30 @ X4 ) ) )
| ( sP2 = $true )
| ( ( cP @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f127]) ).
thf(f650,plain,
( spl76_62
| spl76_9
| ~ spl76_91
| spl76_92
| spl76_94
| ~ spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f180,f286,f647,f638,f634,f276,f495]) ).
thf(f180,plain,
! [X35: $i] :
( ( ( cQ @ sK43 )
= $true )
| ( $true
!= ( cR @ sK44 ) )
| ( ( cP @ X35 )
= $false )
| ( $true
= ( cP @ sK45 ) )
| ( sP2 != $true )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f118,plain,
! [X35: $i] :
( ( $true
!= ( cR @ sK44 ) )
| ( ( cQ @ sK43 )
= $true )
| ( sP2 != $true )
| ( ( cP @ X35 )
= ( cP @ sK45 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f645,plain,
( ~ spl76_91
| spl76_55
| spl76_92
| ~ spl76_12
| spl76_9
| spl76_93 ),
inference(avatar_split_clause,[status(thm)],[f179,f642,f276,f286,f638,f461,f634]) ).
thf(f179,plain,
! [X35: $i] :
( ( sP2 != $true )
| ( ( cQ @ sK43 )
= $true )
| ( ( cP @ X35 )
= $true )
| ( $false
= ( cP @ sK45 ) )
| ( $true
!= ( cR @ sK44 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f118]) ).
thf(f632,plain,
( spl76_17
| spl76_90
| spl76_5
| ~ spl76_1
| spl76_55 ),
inference(avatar_split_clause,[status(thm)],[f182,f461,f244,f259,f628,f306]) ).
thf(f182,plain,
! [X2: $i,X4: $i] :
( ( sP1 != $true )
| ( $true
= ( cP @ X2 ) )
| ( $false
= ( cR @ X4 ) )
| ( sP3 = $true )
| ( ( cS @ sK5 )
= $true )
| ( $false
= ( cR @ ( sK6 @ X4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
! [X2: $i,X4: $i] :
( ( $true
= ( cP @ X2 ) )
| ( sP3 = $true )
| ( ( cR @ ( sK6 @ X4 ) )
!= ( cR @ X4 ) )
| ( sP1 != $true )
| ( ( cS @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f631,plain,
( ~ spl76_1
| spl76_55
| spl76_5
| spl76_90
| spl76_15 ),
inference(avatar_split_clause,[status(thm)],[f181,f299,f628,f259,f461,f244]) ).
thf(f181,plain,
! [X2: $i,X4: $i] :
( ( sP3 = $true )
| ( ( cS @ sK5 )
= $true )
| ( $true
= ( cP @ X2 ) )
| ( $true
= ( cR @ X4 ) )
| ( sP1 != $true )
| ( ( cR @ ( sK6 @ X4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f111]) ).
thf(f626,plain,
( ~ spl76_87
| spl76_88
| spl76_5
| spl76_89
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f184,f244,f624,f259,f619,f615]) ).
thf(f184,plain,
! [X22: $i] :
( ( $false
= ( cR @ ( sK15 @ X22 ) ) )
| ( sP3 = $true )
| ( ( cR @ X22 )
= $false )
| ( $true
= ( cS @ sK13 ) )
| ( ( cP @ sK14 )
!= $true )
| ( sP1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f106,plain,
! [X22: $i] :
( ( sP1 = $true )
| ( sP3 = $true )
| ( ( cP @ sK14 )
!= $true )
| ( $true
= ( cS @ sK13 ) )
| ( ( cR @ X22 )
!= ( cR @ ( sK15 @ X22 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f622,plain,
( spl76_1
| spl76_86
| spl76_5
| ~ spl76_87
| spl76_88 ),
inference(avatar_split_clause,[status(thm)],[f183,f619,f615,f259,f612,f244]) ).
thf(f183,plain,
! [X22: $i] :
( ( sP1 = $true )
| ( sP3 = $true )
| ( ( cR @ X22 )
= $true )
| ( $true
= ( cS @ sK13 ) )
| ( $true
= ( cR @ ( sK15 @ X22 ) ) )
| ( ( cP @ sK14 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f106]) ).
thf(f610,plain,
( spl76_85
| ~ spl76_84
| spl76_1
| spl76_4
| spl76_16
| spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f186,f259,f302,f256,f244,f602,f607]) ).
thf(f186,plain,
! [X15: $i,X13: $i] :
( ( sP1 = $true )
| ( $false
= ( cR @ sK10 ) )
| ( $true
!= ( cP @ sK11 ) )
| ( sP3 = $true )
| ( $true
= ( cR @ X13 ) )
| ( $true
!= ( cS @ X15 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f108,plain,
! [X15: $i,X13: $i] :
( ( $true
!= ( cP @ sK11 ) )
| ( $true
!= ( cS @ X15 ) )
| ( ( cR @ sK10 )
= ( cR @ X13 ) )
| ( sP1 = $true )
| ( sP3 = $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f605,plain,
( spl76_16
| spl76_83
| spl76_7
| ~ spl76_84
| spl76_1
| spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f185,f259,f244,f602,f268,f598,f302]) ).
thf(f185,plain,
! [X15: $i,X13: $i] :
( ( sP3 = $true )
| ( $false
= ( cR @ X13 ) )
| ( sP1 = $true )
| ( $true
!= ( cP @ sK11 ) )
| ( $true
!= ( cS @ X15 ) )
| ( ( cR @ sK10 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f108]) ).
thf(f596,plain,
( spl76_76
| ~ spl76_82
| spl76_7
| ~ spl76_1
| spl76_81
| spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f188,f259,f588,f244,f268,f592,f561]) ).
thf(f188,plain,
! [X11: $i] :
( ( sP1 != $true )
| ( $true
= ( cR @ sK9 ) )
| ( ( cS @ sK7 )
= $true )
| ( sP3 = $true )
| ( ( cP @ sK8 )
!= $true )
| ( ( cR @ X11 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f110,plain,
! [X11: $i] :
( ( ( cR @ X11 )
= ( cR @ sK9 ) )
| ( ( cP @ sK8 )
!= $true )
| ( ( cS @ sK7 )
= $true )
| ( sP3 = $true )
| ( sP1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f595,plain,
( spl76_81
| ~ spl76_1
| spl76_75
| spl76_5
| spl76_4
| ~ spl76_82 ),
inference(avatar_split_clause,[status(thm)],[f187,f592,f256,f259,f556,f244,f588]) ).
thf(f187,plain,
! [X11: $i] :
( ( ( cR @ X11 )
= $true )
| ( $false
= ( cR @ sK9 ) )
| ( sP3 = $true )
| ( ( cS @ sK7 )
= $true )
| ( sP1 != $true )
| ( ( cP @ sK8 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f110]) ).
thf(f586,plain,
( ~ spl76_78
| spl76_80
| spl76_7
| ~ spl76_5
| spl76_16
| ~ spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f190,f244,f302,f259,f268,f583,f574]) ).
thf(f190,plain,
! [X39: $i,X37: $i] :
( ( sP1 != $true )
| ( ( cR @ X37 )
= $false )
| ( sP3 != $true )
| ( $true
= ( cR @ sK22 ) )
| ( $true
!= ( cS @ X39 ) )
| ( $true
!= ( cP @ sK23 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X39: $i,X37: $i] :
( ( sP3 != $true )
| ( ( cR @ X37 )
= ( cR @ sK22 ) )
| ( sP1 != $true )
| ( $true
!= ( cP @ sK23 ) )
| ( $true
!= ( cS @ X39 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f581,plain,
( ~ spl76_5
| ~ spl76_78
| spl76_16
| ~ spl76_1
| spl76_79
| spl76_4 ),
inference(avatar_split_clause,[status(thm)],[f189,f256,f578,f244,f302,f574,f259]) ).
thf(f189,plain,
! [X39: $i,X37: $i] :
( ( $true
!= ( cS @ X39 ) )
| ( $true
!= ( cP @ sK23 ) )
| ( $false
= ( cR @ sK22 ) )
| ( ( cR @ X37 )
= $true )
| ( sP1 != $true )
| ( sP3 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f572,plain,
( spl76_11
| ~ spl76_77
| spl76_63
| spl76_62
| ~ spl76_12
| ~ spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f192,f276,f286,f495,f498,f568,f283]) ).
thf(f192,plain,
! [X39: $i,X37: $i] :
( ( sP2 != $true )
| ( ( cP @ X37 )
= $false )
| ( ( cP @ sK46 )
= $true )
| ( $true != sP0 )
| ( $true
!= ( cR @ sK47 ) )
| ( ( cQ @ X39 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f116,plain,
! [X39: $i,X37: $i] :
( ( $true != sP0 )
| ( ( cQ @ X39 )
!= $true )
| ( $true
!= ( cR @ sK47 ) )
| ( sP2 != $true )
| ( ( cP @ X37 )
= ( cP @ sK46 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f571,plain,
( ~ spl76_9
| spl76_60
| spl76_11
| ~ spl76_77
| ~ spl76_12
| spl76_55 ),
inference(avatar_split_clause,[status(thm)],[f191,f461,f286,f568,f283,f486,f276]) ).
thf(f191,plain,
! [X39: $i,X37: $i] :
( ( ( cP @ X37 )
= $true )
| ( ( cQ @ X39 )
!= $true )
| ( $true != sP0 )
| ( $false
= ( cP @ sK46 ) )
| ( $true
!= ( cR @ sK47 ) )
| ( sP2 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f116]) ).
thf(f566,plain,
( spl76_47
| spl76_4
| spl76_11
| spl76_9
| spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f194,f286,f276,f283,f256,f430]) ).
thf(f194,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( $true
!= ( cQ @ X21 ) )
| ( $false
= ( cP @ ( sK39 @ X22 ) ) )
| ( $true
= ( cR @ X20 ) )
| ( sP2 = $true )
| ( $false
= ( cP @ X22 ) )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f121,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( $true
!= ( cQ @ X21 ) )
| ( $true
= ( cR @ X20 ) )
| ( $true = sP0 )
| ( sP2 = $true )
| ( ( cP @ ( sK39 @ X22 ) )
!= ( cP @ X22 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f565,plain,
( spl76_44
| spl76_12
| spl76_9
| spl76_11
| spl76_4 ),
inference(avatar_split_clause,[status(thm)],[f193,f256,f283,f276,f286,f418]) ).
thf(f193,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( sP2 = $true )
| ( ( cP @ ( sK39 @ X22 ) )
= $true )
| ( $true
!= ( cQ @ X21 ) )
| ( $true
= ( cR @ X20 ) )
| ( $true = sP0 )
| ( $true
= ( cP @ X22 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f121]) ).
thf(f564,plain,
( spl76_5
| ~ spl76_1
| spl76_76
| spl76_7
| spl76_55
| spl76_16 ),
inference(avatar_split_clause,[status(thm)],[f196,f302,f461,f268,f561,f244,f259]) ).
thf(f196,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( ( cR @ X11 )
= $false )
| ( $true
!= ( cS @ X9 ) )
| ( sP3 = $true )
| ( sP1 != $true )
| ( ( cP @ X8 )
= $true )
| ( $true
= ( cR @ sK9 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f109,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( ( cP @ X8 )
= $true )
| ( $true
!= ( cS @ X9 ) )
| ( sP3 = $true )
| ( sP1 != $true )
| ( ( cR @ X11 )
= ( cR @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f559,plain,
( spl76_75
| spl76_16
| spl76_5
| ~ spl76_1
| spl76_4
| spl76_55 ),
inference(avatar_split_clause,[status(thm)],[f195,f461,f256,f244,f259,f302,f556]) ).
thf(f195,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( $false
= ( cR @ sK9 ) )
| ( sP3 = $true )
| ( $true
!= ( cS @ X9 ) )
| ( ( cR @ X11 )
= $true )
| ( sP1 != $true )
| ( ( cP @ X8 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f109]) ).
thf(f554,plain,
( ~ spl76_73
| spl76_74
| spl76_12
| ~ spl76_9
| spl76_71
| spl76_55 ),
inference(avatar_split_clause,[status(thm)],[f198,f461,f538,f276,f286,f551,f546]) ).
thf(f198,plain,
! [X11: $i] :
( ( $false
= ( cP @ sK33 ) )
| ( $true
!= ( cR @ sK32 ) )
| ( $true != sP0 )
| ( sP2 = $true )
| ( ( cQ @ sK31 )
= $true )
| ( $true
= ( cP @ X11 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f126,plain,
! [X11: $i] :
( ( $true != sP0 )
| ( ( cQ @ sK31 )
= $true )
| ( ( cP @ sK33 )
= ( cP @ X11 ) )
| ( sP2 = $true )
| ( $true
!= ( cR @ sK32 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f549,plain,
( spl76_62
| ~ spl76_9
| spl76_71
| spl76_12
| spl76_72
| ~ spl76_73 ),
inference(avatar_split_clause,[status(thm)],[f197,f546,f542,f286,f538,f276,f495]) ).
thf(f197,plain,
! [X11: $i] :
( ( $true
!= ( cR @ sK32 ) )
| ( $true != sP0 )
| ( $false
= ( cP @ X11 ) )
| ( ( cQ @ sK31 )
= $true )
| ( sP2 = $true )
| ( ( cP @ sK33 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f126]) ).
thf(f536,plain,
( spl76_70
| ~ spl76_69
| spl76_58
| ~ spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f200,f244,f473,f528,f532]) ).
thf(f200,plain,
! [X22: $i] :
( ( sP1 != $true )
| ( $false
= ( cS @ X22 ) )
| ( ( cS @ ( sK63 @ X22 ) )
= $false )
| ( $true
= ( cP @ sK61 ) )
| ( $true
!= ( cQ @ sK62 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f130,plain,
! [X22: $i] :
( ( ( cS @ ( sK63 @ X22 ) )
!= ( cS @ X22 ) )
| ( $true
!= ( cQ @ sK62 ) )
| ( sP1 != $true )
| ( $true
= ( cP @ sK61 ) ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f535,plain,
( ~ spl76_69
| ~ spl76_1
| spl76_70
| spl76_57 ),
inference(avatar_split_clause,[status(thm)],[f199,f469,f532,f244,f528]) ).
thf(f199,plain,
! [X22: $i] :
( ( sP1 != $true )
| ( $true
!= ( cQ @ sK62 ) )
| ( ( cS @ ( sK63 @ X22 ) )
= $true )
| ( $true
= ( cS @ X22 ) )
| ( $true
= ( cP @ sK61 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f130]) ).
thf(f526,plain,
( spl76_11
| spl76_12
| ~ spl76_9
| spl76_68
| ~ spl76_66 ),
inference(avatar_split_clause,[status(thm)],[f202,f516,f524,f276,f286,f283]) ).
thf(f202,plain,
! [X1: $i,X4: $i] :
( ( $true
!= ( cR @ sK28 ) )
| ( $false
= ( cP @ ( sK30 @ X4 ) ) )
| ( sP2 = $true )
| ( $true != sP0 )
| ( ( cP @ X4 )
= $false )
| ( ( cQ @ X1 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
! [X1: $i,X4: $i] :
( ( ( cQ @ X1 )
!= $true )
| ( $true
!= ( cR @ sK28 ) )
| ( ( cP @ X4 )
!= ( cP @ ( sK30 @ X4 ) ) )
| ( sP2 = $true )
| ( $true != sP0 ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f522,plain,
( ~ spl76_9
| spl76_12
| ~ spl76_66
| spl76_11
| spl76_67 ),
inference(avatar_split_clause,[status(thm)],[f201,f520,f283,f516,f286,f276]) ).
thf(f201,plain,
! [X1: $i,X4: $i] :
( ( sP2 = $true )
| ( ( cP @ X4 )
= $true )
| ( ( cQ @ X1 )
!= $true )
| ( $true
= ( cP @ ( sK30 @ X4 ) ) )
| ( $true != sP0 )
| ( $true
!= ( cR @ sK28 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f514,plain,
( spl76_12
| spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f145,f259,f286]) ).
thf(f145,plain,
( ( sP3 = $true )
| ( sP2 = $true ) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
thf(f96,plain,
( ( ( sP3 != $true )
| ( sP2 != $true ) )
& ( ( sP3 = $true )
| ( sP2 = $true ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sP2 = $true )
<~> ( sP3 = $true ) ),
inference(definition_folding,[status(thm)],[f6,f10,f9,f8,f7]) ).
thf(f6,plain,
( ( ( ( ! [X11: $i] :
( ( cS @ X11 )
= $true )
<=> ? [X10: $i] :
( $true
= ( cR @ X10 ) ) )
<=> ? [X8: $i] :
! [X9: $i] :
( ( cQ @ X9 )
= ( cQ @ X8 ) ) )
<=> ( ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) )
<=> ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
<=> ! [X12: $i] :
( ( cR @ X12 )
= $true ) ) ) )
<~> ( ( ? [X6: $i] :
! [X7: $i] :
( ( cS @ X7 )
= ( cS @ X6 ) )
<=> ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
<=> ! [X5: $i] :
( ( cQ @ X5 )
= $true ) ) )
<=> ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) )
<=> ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
<=> ! [X3: $i] :
( $true
= ( cP @ X3 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ? [X6: $i] :
! [X7: $i] :
( ( cS @ X7 )
= ( cS @ X6 ) )
<=> ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
<=> ! [X5: $i] :
( ( cQ @ X5 )
= $true ) ) )
<=> ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X1 )
= ( cR @ X0 ) )
<=> ( ? [X2: $i] :
( ( cS @ X2 )
= $true )
<=> ! [X3: $i] :
( $true
= ( cP @ X3 ) ) ) ) )
<=> ( ( ( ! [X11: $i] :
( ( cS @ X11 )
= $true )
<=> ? [X10: $i] :
( $true
= ( cR @ X10 ) ) )
<=> ? [X8: $i] :
! [X9: $i] :
( ( cQ @ X9 )
= ( cQ @ X8 ) ) )
<=> ( ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
= ( cP @ X14 ) )
<=> ( ? [X13: $i] :
( $true
= ( cQ @ X13 ) )
<=> ! [X12: $i] :
( ( cR @ X12 )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X0 )
<=> ( cR @ X1 ) )
<=> ( ? [X2: $i] : ( cS @ X2 )
<=> ! [X3: $i] : ( cP @ X3 ) ) )
<=> ( ( ? [X4: $i] : ( cP @ X4 )
<=> ! [X5: $i] : ( cQ @ X5 ) )
<=> ? [X6: $i] :
! [X7: $i] :
( ( cS @ X7 )
<=> ( cS @ X6 ) ) ) )
<=> ( ( ? [X8: $i] :
! [X9: $i] :
( ( cQ @ X9 )
<=> ( cQ @ X8 ) )
<=> ( ? [X10: $i] : ( cR @ X10 )
<=> ! [X11: $i] : ( cS @ X11 ) ) )
<=> ( ( ! [X12: $i] : ( cR @ X12 )
<=> ? [X13: $i] : ( cQ @ X13 ) )
<=> ? [X14: $i] :
! [X15: $i] :
( ( cP @ X15 )
<=> ( cP @ X14 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X0 )
<=> ( cR @ X1 ) )
<=> ( ? [X0: $i] : ( cS @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) ) )
<=> ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cQ @ X1 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cS @ X1 )
<=> ( cS @ X0 ) ) ) )
<=> ( ( ? [X0: $i] :
! [X1: $i] :
( ( cQ @ X1 )
<=> ( cQ @ X0 ) )
<=> ( ? [X0: $i] : ( cR @ X0 )
<=> ! [X1: $i] : ( cS @ X1 ) ) )
<=> ( ( ! [X1: $i] : ( cR @ X1 )
<=> ? [X0: $i] : ( cQ @ X0 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cP @ X1 )
<=> ( cP @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ? [X0: $i] :
! [X1: $i] :
( ( cR @ X0 )
<=> ( cR @ X1 ) )
<=> ( ? [X0: $i] : ( cS @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) ) )
<=> ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cQ @ X1 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cS @ X1 )
<=> ( cS @ X0 ) ) ) )
<=> ( ( ? [X0: $i] :
! [X1: $i] :
( ( cQ @ X1 )
<=> ( cQ @ X0 ) )
<=> ( ? [X0: $i] : ( cR @ X0 )
<=> ! [X1: $i] : ( cS @ X1 ) ) )
<=> ( ( ! [X1: $i] : ( cR @ X1 )
<=> ? [X0: $i] : ( cQ @ X0 ) )
<=> ? [X0: $i] :
! [X1: $i] :
( ( cP @ X1 )
<=> ( cP @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.DDLV6Zgj3R/DTF2THF_10908.p',cTHM138) ).
thf(f513,plain,
( spl76_8
| spl76_55
| spl76_7
| spl76_16
| ~ spl76_5
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f204,f244,f259,f302,f268,f461,f271]) ).
thf(f204,plain,
! [X35: $i,X32: $i,X33: $i] :
( ( $false
= ( cR @ X35 ) )
| ( $true
= ( cR @ sK21 ) )
| ( $true
= ( cP @ X32 ) )
| ( sP1 = $true )
| ( ( cS @ X33 )
!= $true )
| ( sP3 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X35: $i,X32: $i,X33: $i] :
( ( ( cS @ X33 )
!= $true )
| ( $true
= ( cP @ X32 ) )
| ( sP1 = $true )
| ( ( cR @ X35 )
= ( cR @ sK21 ) )
| ( sP3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f512,plain,
( spl76_6
| spl76_55
| spl76_4
| ~ spl76_5
| spl76_16
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f203,f244,f302,f259,f256,f461,f263]) ).
thf(f203,plain,
! [X35: $i,X32: $i,X33: $i] :
( ( $false
= ( cR @ sK21 ) )
| ( ( cR @ X35 )
= $true )
| ( sP3 != $true )
| ( ( cS @ X33 )
!= $true )
| ( $true
= ( cP @ X32 ) )
| ( sP1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f101]) ).
thf(f511,plain,
( spl76_27
| spl76_65
| spl76_19
| ~ spl76_64
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f206,f244,f503,f314,f507,f344]) ).
thf(f206,plain,
! [X11: $i] :
( ( ( cS @ sK57 )
= $false )
| ( ( cS @ X11 )
= $true )
| ( sP1 = $true )
| ( $true
!= ( cQ @ sK56 ) )
| ( ( cP @ sK55 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f134,plain,
! [X11: $i] :
( ( $true
!= ( cQ @ sK56 ) )
| ( sP1 = $true )
| ( ( cP @ sK55 )
= $true )
| ( ( cS @ sK57 )
= ( cS @ X11 ) ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f510,plain,
( ~ spl76_64
| spl76_65
| spl76_1
| spl76_25
| spl76_26 ),
inference(avatar_split_clause,[status(thm)],[f205,f339,f336,f244,f507,f503]) ).
thf(f205,plain,
! [X11: $i] :
( ( sP1 = $true )
| ( ( cP @ sK55 )
= $true )
| ( $true
!= ( cQ @ sK56 ) )
| ( ( cS @ sK57 )
= $true )
| ( ( cS @ X11 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f134]) ).
thf(f501,plain,
( ~ spl76_9
| ~ spl76_12
| spl76_62
| spl76_61
| spl76_4
| spl76_63 ),
inference(avatar_split_clause,[status(thm)],[f208,f498,f256,f490,f495,f286,f276]) ).
thf(f208,plain,
! [X40: $i,X37: $i] :
( ( sP2 != $true )
| ( ( cP @ sK46 )
= $true )
| ( ( cP @ X37 )
= $false )
| ( ( cQ @ sK48 )
= $true )
| ( $true != sP0 )
| ( $true
= ( cR @ X40 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f115,plain,
! [X40: $i,X37: $i] :
( ( $true != sP0 )
| ( sP2 != $true )
| ( ( cP @ X37 )
= ( cP @ sK46 ) )
| ( ( cQ @ sK48 )
= $true )
| ( $true
= ( cR @ X40 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f493,plain,
( ~ spl76_12
| spl76_4
| spl76_60
| spl76_61
| ~ spl76_9
| spl76_55 ),
inference(avatar_split_clause,[status(thm)],[f207,f461,f276,f490,f486,f256,f286]) ).
thf(f207,plain,
! [X40: $i,X37: $i] :
( ( $true != sP0 )
| ( ( cP @ X37 )
= $true )
| ( $false
= ( cP @ sK46 ) )
| ( $true
= ( cR @ X40 ) )
| ( ( cQ @ sK48 )
= $true )
| ( sP2 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f115]) ).
thf(f484,plain,
( spl76_20
| spl76_19
| spl76_35
| spl76_9
| spl76_40 ),
inference(avatar_split_clause,[status(thm)],[f210,f399,f276,f378,f314,f317]) ).
thf(f210,plain,
! [X8: $i,X9: $i,X7: $i] :
( ( ( cS @ X8 )
= $true )
| ( ( cQ @ X7 )
= $true )
| ( ( cQ @ sK67 )
= $false )
| ( $true = sP0 )
| ( ( cR @ X9 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f142,plain,
! [X8: $i,X9: $i,X7: $i] :
( ( ( cQ @ sK67 )
= ( cQ @ X7 ) )
| ( ( cR @ X9 )
!= $true )
| ( $true = sP0 )
| ( ( cS @ X8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f483,plain,
( spl76_9
| spl76_40
| spl76_22
| spl76_32
| spl76_19 ),
inference(avatar_split_clause,[status(thm)],[f209,f314,f365,f325,f399,f276]) ).
thf(f209,plain,
! [X8: $i,X9: $i,X7: $i] :
( ( $true = sP0 )
| ( ( cS @ X8 )
= $true )
| ( ( cR @ X9 )
!= $true )
| ( ( cQ @ X7 )
= $false )
| ( ( cQ @ sK67 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f142]) ).
thf(f482,plain,
( ~ spl76_5
| ~ spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f146,f286,f259]) ).
thf(f146,plain,
( ( sP2 != $true )
| ( sP3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
thf(f481,plain,
( spl76_23
| ~ spl76_9
| ~ spl76_59
| spl76_40
| spl76_22 ),
inference(avatar_split_clause,[status(thm)],[f212,f325,f399,f477,f276,f328]) ).
thf(f212,plain,
! [X19: $i,X20: $i] :
( ( ( cS @ sK74 )
!= $true )
| ( $true
= ( cQ @ sK73 ) )
| ( $false
= ( cQ @ X19 ) )
| ( $true
!= ( cR @ X20 ) )
| ( $true != sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f138]) ).
thf(f138,plain,
! [X19: $i,X20: $i] :
( ( ( cQ @ X19 )
= ( cQ @ sK73 ) )
| ( $true != sP0 )
| ( $true
!= ( cR @ X20 ) )
| ( ( cS @ sK74 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f480,plain,
( ~ spl76_59
| spl76_21
| ~ spl76_9
| spl76_40
| spl76_20 ),
inference(avatar_split_clause,[status(thm)],[f211,f317,f399,f276,f320,f477]) ).
thf(f211,plain,
! [X19: $i,X20: $i] :
( ( $true
!= ( cR @ X20 ) )
| ( ( cS @ sK74 )
!= $true )
| ( $true != sP0 )
| ( $true
= ( cQ @ X19 ) )
| ( $false
= ( cQ @ sK73 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f138]) ).
thf(f475,plain,
( spl76_24
| ~ spl76_1
| spl76_58
| spl76_20 ),
inference(avatar_split_clause,[status(thm)],[f214,f317,f473,f244,f333]) ).
thf(f214,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( ( cS @ ( sK63 @ X22 ) )
= $false )
| ( sP1 != $true )
| ( $false
= ( cS @ X22 ) )
| ( ( cP @ X21 )
!= $true )
| ( ( cQ @ X20 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f129,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( ( cP @ X21 )
!= $true )
| ( ( cS @ ( sK63 @ X22 ) )
!= ( cS @ X22 ) )
| ( ( cQ @ X20 )
= $true )
| ( sP1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f471,plain,
( spl76_57
| spl76_20
| ~ spl76_1
| spl76_24 ),
inference(avatar_split_clause,[status(thm)],[f213,f333,f244,f317,f469]) ).
thf(f213,plain,
! [X21: $i,X22: $i,X20: $i] :
( ( ( cP @ X21 )
!= $true )
| ( ( cQ @ X20 )
= $true )
| ( ( cS @ ( sK63 @ X22 ) )
= $true )
| ( $true
= ( cS @ X22 ) )
| ( sP1 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f129]) ).
thf(f467,plain,
( spl76_55
| ~ spl76_1
| spl76_16
| ~ spl76_5
| spl76_56 ),
inference(avatar_split_clause,[status(thm)],[f216,f465,f259,f302,f244,f461]) ).
thf(f216,plain,
! [X46: $i,X44: $i,X45: $i] :
( ( $false
= ( cR @ ( sK27 @ X46 ) ) )
| ( sP1 != $true )
| ( ( cR @ X46 )
= $false )
| ( $true
= ( cP @ X44 ) )
| ( ( cS @ X45 )
!= $true )
| ( sP3 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X46: $i,X44: $i,X45: $i] :
( ( ( cR @ X46 )
!= ( cR @ ( sK27 @ X46 ) ) )
| ( ( cS @ X45 )
!= $true )
| ( $true
= ( cP @ X44 ) )
| ( sP3 != $true )
| ( sP1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f463,plain,
( spl76_54
| spl76_16
| ~ spl76_1
| ~ spl76_5
| spl76_55 ),
inference(avatar_split_clause,[status(thm)],[f215,f461,f259,f244,f302,f458]) ).
thf(f215,plain,
! [X46: $i,X44: $i,X45: $i] :
( ( ( cS @ X45 )
!= $true )
| ( ( cR @ X46 )
= $true )
| ( sP3 != $true )
| ( $true
= ( cP @ X44 ) )
| ( sP1 != $true )
| ( ( cR @ ( sK27 @ X46 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f456,plain,
( spl76_53
| ~ spl76_52
| spl76_1
| spl76_24 ),
inference(avatar_split_clause,[status(thm)],[f218,f333,f244,f449,f454]) ).
thf(f218,plain,
! [X1: $i,X4: $i] :
( ( sP1 = $true )
| ( ( cP @ X1 )
!= $true )
| ( ( cS @ X4 )
= $false )
| ( $false
= ( cS @ ( sK54 @ X4 ) ) )
| ( ( cQ @ sK52 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
! [X1: $i,X4: $i] :
( ( ( cS @ X4 )
!= ( cS @ ( sK54 @ X4 ) ) )
| ( ( cQ @ sK52 )
!= $true )
| ( sP1 = $true )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f452,plain,
( spl76_24
| spl76_51
| spl76_1
| ~ spl76_52 ),
inference(avatar_split_clause,[status(thm)],[f217,f449,f244,f446,f333]) ).
thf(f217,plain,
! [X1: $i,X4: $i] :
( ( ( cQ @ sK52 )
!= $true )
| ( sP1 = $true )
| ( ( cS @ ( sK54 @ X4 ) )
= $true )
| ( ( cS @ X4 )
= $true )
| ( ( cP @ X1 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f136]) ).
thf(f444,plain,
( spl76_50
| spl76_16
| ~ spl76_48
| ~ spl76_5
| spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f220,f244,f259,f434,f302,f442]) ).
thf(f220,plain,
! [X28: $i,X25: $i] :
( ( $false
= ( cR @ X28 ) )
| ( sP3 != $true )
| ( ( cP @ sK16 )
!= $true )
| ( $false
= ( cR @ ( sK18 @ X28 ) ) )
| ( ( cS @ X25 )
!= $true )
| ( sP1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X28: $i,X25: $i] :
( ( sP1 = $true )
| ( sP3 != $true )
| ( ( cS @ X25 )
!= $true )
| ( ( cP @ sK16 )
!= $true )
| ( ( cR @ ( sK18 @ X28 ) )
!= ( cR @ X28 ) ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f440,plain,
( ~ spl76_48
| spl76_16
| spl76_1
| spl76_49
| ~ spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f219,f259,f438,f244,f302,f434]) ).
thf(f219,plain,
! [X28: $i,X25: $i] :
( ( ( cR @ ( sK18 @ X28 ) )
= $true )
| ( $true
= ( cR @ X28 ) )
| ( ( cS @ X25 )
!= $true )
| ( ( cP @ sK16 )
!= $true )
| ( sP3 != $true )
| ( sP1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f432,plain,
( spl76_9
| spl76_47
| spl76_12
| ~ spl76_46
| spl76_45 ),
inference(avatar_split_clause,[status(thm)],[f222,f421,f425,f286,f430,f276]) ).
thf(f222,plain,
! [X22: $i] :
( ( ( cQ @ sK37 )
= $true )
| ( $false
= ( cP @ X22 ) )
| ( $true = sP0 )
| ( sP2 = $true )
| ( $false
= ( cP @ ( sK39 @ X22 ) ) )
| ( $true
!= ( cR @ sK38 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f122,plain,
! [X22: $i] :
( ( sP2 = $true )
| ( $true
!= ( cR @ sK38 ) )
| ( ( cQ @ sK37 )
= $true )
| ( ( cP @ ( sK39 @ X22 ) )
!= ( cP @ X22 ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f428,plain,
( spl76_44
| spl76_9
| spl76_45
| ~ spl76_46
| spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f221,f286,f425,f421,f276,f418]) ).
thf(f221,plain,
! [X22: $i] :
( ( $true
!= ( cR @ sK38 ) )
| ( $true
= ( cP @ X22 ) )
| ( $true = sP0 )
| ( ( cP @ ( sK39 @ X22 ) )
= $true )
| ( ( cQ @ sK37 )
= $true )
| ( sP2 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f122]) ).
thf(f416,plain,
( spl76_19
| spl76_24
| spl76_43
| ~ spl76_1
| ~ spl76_42 ),
inference(avatar_split_clause,[status(thm)],[f224,f408,f244,f413,f333,f314]) ).
thf(f224,plain,
! [X15: $i,X13: $i] :
( ( $true
!= ( cP @ X15 ) )
| ( ( cS @ sK58 )
= $false )
| ( sP1 != $true )
| ( ( cQ @ sK59 )
!= $true )
| ( $true
= ( cS @ X13 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f132,plain,
! [X15: $i,X13: $i] :
( ( sP1 != $true )
| ( ( cS @ sK58 )
= ( cS @ X13 ) )
| ( $true
!= ( cP @ X15 ) )
| ( ( cQ @ sK59 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f411,plain,
( spl76_41
| ~ spl76_42
| spl76_25
| ~ spl76_1
| spl76_24 ),
inference(avatar_split_clause,[status(thm)],[f223,f333,f244,f336,f408,f404]) ).
thf(f223,plain,
! [X15: $i,X13: $i] :
( ( ( cS @ sK58 )
= $true )
| ( $false
= ( cS @ X13 ) )
| ( sP1 != $true )
| ( $true
!= ( cP @ X15 ) )
| ( ( cQ @ sK59 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f132]) ).
thf(f402,plain,
( spl76_9
| ~ spl76_39
| spl76_38
| spl76_40 ),
inference(avatar_split_clause,[status(thm)],[f226,f399,f391,f395,f276]) ).
thf(f226,plain,
! [X2: $i,X0: $i] :
( ( $true
!= ( cS @ sK65 ) )
| ( $false
= ( cQ @ ( sK64 @ X0 ) ) )
| ( $true = sP0 )
| ( $true
!= ( cR @ X2 ) )
| ( ( cQ @ X0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f144,plain,
! [X2: $i,X0: $i] :
( ( ( cQ @ X0 )
!= ( cQ @ ( sK64 @ X0 ) ) )
| ( $true = sP0 )
| ( $true
!= ( cR @ X2 ) )
| ( $true
!= ( cS @ sK65 ) ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f401,plain,
( spl76_9
| ~ spl76_39
| spl76_36
| spl76_40 ),
inference(avatar_split_clause,[status(thm)],[f225,f399,f383,f395,f276]) ).
thf(f225,plain,
! [X2: $i,X0: $i] :
( ( $true
!= ( cS @ sK65 ) )
| ( $true = sP0 )
| ( $true
= ( cQ @ ( sK64 @ X0 ) ) )
| ( ( cQ @ X0 )
= $true )
| ( $true
!= ( cR @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f144]) ).
thf(f393,plain,
( spl76_9
| spl76_38
| spl76_19
| spl76_37 ),
inference(avatar_split_clause,[status(thm)],[f228,f386,f314,f391,f276]) ).
thf(f228,plain,
! [X0: $i,X5: $i] :
( ( $false
= ( cQ @ ( sK64 @ X0 ) ) )
| ( $true = sP0 )
| ( $true
= ( cR @ sK66 ) )
| ( ( cQ @ X0 )
= $false )
| ( ( cS @ X5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f143,plain,
! [X0: $i,X5: $i] :
( ( $true
= ( cR @ sK66 ) )
| ( ( cS @ X5 )
= $true )
| ( ( cQ @ X0 )
!= ( cQ @ ( sK64 @ X0 ) ) )
| ( $true = sP0 ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f389,plain,
( spl76_36
| spl76_9
| spl76_19
| spl76_37 ),
inference(avatar_split_clause,[status(thm)],[f227,f386,f314,f276,f383]) ).
thf(f227,plain,
! [X0: $i,X5: $i] :
( ( $true
= ( cR @ sK66 ) )
| ( ( cQ @ X0 )
= $true )
| ( $true
= ( cQ @ ( sK64 @ X0 ) ) )
| ( ( cS @ X5 )
= $true )
| ( $true = sP0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f143]) ).
thf(f381,plain,
( spl76_33
| spl76_20
| ~ spl76_34
| spl76_35
| spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f230,f276,f378,f373,f317,f369]) ).
thf(f230,plain,
! [X7: $i] :
( ( $true = sP0 )
| ( $true
!= ( cS @ sK69 ) )
| ( ( cQ @ sK67 )
= $false )
| ( ( cR @ sK68 )
= $true )
| ( ( cQ @ X7 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f141,plain,
! [X7: $i] :
( ( $true = sP0 )
| ( ( cQ @ sK67 )
= ( cQ @ X7 ) )
| ( $true
!= ( cS @ sK69 ) )
| ( ( cR @ sK68 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f376,plain,
( spl76_32
| spl76_33
| spl76_22
| ~ spl76_34
| spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f229,f276,f373,f325,f369,f365]) ).
thf(f229,plain,
! [X7: $i] :
( ( ( cR @ sK68 )
= $true )
| ( $true = sP0 )
| ( ( cQ @ sK67 )
= $true )
| ( ( cQ @ X7 )
= $false )
| ( $true
!= ( cS @ sK69 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f141]) ).
thf(f363,plain,
( ~ spl76_28
| spl76_31
| ~ spl76_9
| spl76_29 ),
inference(avatar_split_clause,[status(thm)],[f232,f353,f276,f361,f349]) ).
thf(f232,plain,
! [X16: $i] :
( ( $false
= ( cQ @ ( sK72 @ X16 ) ) )
| ( $true != sP0 )
| ( $true
!= ( cS @ sK71 ) )
| ( $true
= ( cR @ sK70 ) )
| ( $false
= ( cQ @ X16 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
! [X16: $i] :
( ( $true != sP0 )
| ( $true
= ( cR @ sK70 ) )
| ( ( cQ @ X16 )
!= ( cQ @ ( sK72 @ X16 ) ) )
| ( $true
!= ( cS @ sK71 ) ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f359,plain,
( ~ spl76_28
| spl76_29
| spl76_30
| ~ spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f231,f276,f357,f353,f349]) ).
thf(f231,plain,
! [X16: $i] :
( ( $true != sP0 )
| ( $true
= ( cQ @ ( sK72 @ X16 ) ) )
| ( $true
!= ( cS @ sK71 ) )
| ( ( cQ @ X16 )
= $true )
| ( $true
= ( cR @ sK70 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f347,plain,
( spl76_24
| spl76_20
| spl76_27
| spl76_1
| spl76_19 ),
inference(avatar_split_clause,[status(thm)],[f234,f314,f244,f344,f317,f333]) ).
thf(f234,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( ( cS @ X11 )
= $true )
| ( ( cS @ sK57 )
= $false )
| ( ( cP @ X9 )
!= $true )
| ( $true
= ( cQ @ X8 ) )
| ( sP1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f133]) ).
thf(f133,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( ( cP @ X9 )
!= $true )
| ( $true
= ( cQ @ X8 ) )
| ( ( cS @ sK57 )
= ( cS @ X11 ) )
| ( sP1 = $true ) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
thf(f342,plain,
( spl76_20
| spl76_24
| spl76_25
| spl76_1
| spl76_26 ),
inference(avatar_split_clause,[status(thm)],[f233,f339,f244,f336,f333,f317]) ).
thf(f233,plain,
! [X11: $i,X8: $i,X9: $i] :
( ( ( cS @ sK57 )
= $true )
| ( sP1 = $true )
| ( ( cS @ X11 )
= $false )
| ( $true
= ( cQ @ X8 ) )
| ( ( cP @ X9 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f133]) ).
thf(f331,plain,
( spl76_22
| spl76_19
| spl76_23
| spl76_18
| ~ spl76_9 ),
inference(avatar_split_clause,[status(thm)],[f236,f276,f310,f328,f314,f325]) ).
thf(f236,plain,
! [X19: $i,X23: $i] :
( ( ( cR @ sK75 )
= $true )
| ( $true != sP0 )
| ( $false
= ( cQ @ X19 ) )
| ( $true
= ( cQ @ sK73 ) )
| ( ( cS @ X23 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
! [X19: $i,X23: $i] :
( ( $true != sP0 )
| ( ( cR @ sK75 )
= $true )
| ( ( cQ @ X19 )
= ( cQ @ sK73 ) )
| ( ( cS @ X23 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
thf(f323,plain,
( spl76_18
| spl76_19
| spl76_20
| ~ spl76_9
| spl76_21 ),
inference(avatar_split_clause,[status(thm)],[f235,f320,f276,f317,f314,f310]) ).
thf(f235,plain,
! [X19: $i,X23: $i] :
( ( $true != sP0 )
| ( $true
= ( cQ @ X19 ) )
| ( $false
= ( cQ @ sK73 ) )
| ( ( cS @ X23 )
= $true )
| ( ( cR @ sK75 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f308,plain,
( spl76_5
| ~ spl76_14
| spl76_17
| spl76_16
| ~ spl76_1 ),
inference(avatar_split_clause,[status(thm)],[f238,f244,f302,f306,f295,f259]) ).
thf(f238,plain,
! [X1: $i,X4: $i] :
( ( $false
= ( cR @ X4 ) )
| ( $false
= ( cR @ ( sK6 @ X4 ) ) )
| ( sP3 = $true )
| ( ( cS @ X1 )
!= $true )
| ( $true
!= ( cP @ sK4 ) )
| ( sP1 != $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i,X4: $i] :
( ( ( cR @ ( sK6 @ X4 ) )
!= ( cR @ X4 ) )
| ( ( cS @ X1 )
!= $true )
| ( sP1 != $true )
| ( $true
!= ( cP @ sK4 ) )
| ( sP3 = $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f304,plain,
( ~ spl76_14
| ~ spl76_1
| spl76_15
| spl76_16
| spl76_5 ),
inference(avatar_split_clause,[status(thm)],[f237,f259,f302,f299,f244,f295]) ).
thf(f237,plain,
! [X1: $i,X4: $i] :
( ( ( cR @ ( sK6 @ X4 ) )
= $true )
| ( $true
!= ( cP @ sK4 ) )
| ( ( cS @ X1 )
!= $true )
| ( sP3 = $true )
| ( sP1 != $true )
| ( $true
= ( cR @ X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f293,plain,
( ~ spl76_9
| spl76_13
| spl76_4
| spl76_11
| ~ spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f240,f286,f283,f256,f291,f276]) ).
thf(f240,plain,
! [X46: $i,X44: $i,X45: $i] :
( ( ( cR @ X44 )
= $true )
| ( $true
!= ( cQ @ X45 ) )
| ( sP2 != $true )
| ( $true != sP0 )
| ( $false
= ( cP @ X46 ) )
| ( ( cP @ ( sK51 @ X46 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X46: $i,X44: $i,X45: $i] :
( ( ( cR @ X44 )
= $true )
| ( sP2 != $true )
| ( $true
!= ( cQ @ X45 ) )
| ( $true != sP0 )
| ( ( cP @ ( sK51 @ X46 ) )
!= ( cP @ X46 ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f289,plain,
( ~ spl76_9
| spl76_10
| spl76_4
| spl76_11
| ~ spl76_12 ),
inference(avatar_split_clause,[status(thm)],[f239,f286,f283,f256,f280,f276]) ).
thf(f239,plain,
! [X46: $i,X44: $i,X45: $i] :
( ( ( cP @ ( sK51 @ X46 ) )
= $true )
| ( ( cP @ X46 )
= $true )
| ( $true
!= ( cQ @ X45 ) )
| ( $true != sP0 )
| ( sP2 != $true )
| ( ( cR @ X44 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f274,plain,
( ~ spl76_3
| ~ spl76_5
| spl76_7
| spl76_1
| spl76_2
| spl76_8 ),
inference(avatar_split_clause,[status(thm)],[f242,f271,f248,f244,f268,f259,f252]) ).
thf(f242,plain,
! [X35: $i] :
( ( ( cS @ sK19 )
= $true )
| ( ( cP @ sK20 )
!= $true )
| ( $false
= ( cR @ X35 ) )
| ( $true
= ( cR @ sK21 ) )
| ( sP3 != $true )
| ( sP1 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
thf(f102,plain,
! [X35: $i] :
( ( ( cR @ X35 )
= ( cR @ sK21 ) )
| ( sP3 != $true )
| ( sP1 = $true )
| ( ( cS @ sK19 )
= $true )
| ( ( cP @ sK20 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f266,plain,
( spl76_1
| spl76_2
| ~ spl76_3
| spl76_4
| ~ spl76_5
| spl76_6 ),
inference(avatar_split_clause,[status(thm)],[f241,f263,f259,f256,f252,f248,f244]) ).
thf(f241,plain,
! [X35: $i] :
( ( sP3 != $true )
| ( ( cP @ sK20 )
!= $true )
| ( ( cR @ X35 )
= $true )
| ( sP1 = $true )
| ( $false
= ( cR @ sK21 ) )
| ( ( cS @ sK19 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO174^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n002.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:25:33 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO174^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem from BASIC-FO-THMS
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_1055 [Bro09]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.33 v8.2.0, 0.27 v8.1.0, 0.33 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.0.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.75 v5.2.0, 0.50 v4.1.0, 1.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 5 ( 0 unt; 4 typ; 0 def)
% 0.16/0.39 % Number of atoms : 16 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 16 ( 16 avg)
% 0.16/0.39 % Number of connectives : 31 ( 0 ~; 0 |; 0 &; 16 @)
% 0.16/0.39 % ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 8 ( 8 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 4 ( 4 usr; 0 con; 1-1 aty)
% 0.16/0.39 % Number of variables : 16 ( 0 ^; 8 !; 8 ?; 16 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(cQ,type,
% 0.16/0.39 cQ: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cP,type,
% 0.16/0.39 cP: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cS,type,
% 0.16/0.39 cS: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cR,type,
% 0.16/0.39 cR: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM138,conjecture,
% 0.16/0.39 ( ( ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( cP @ Xx )
% 0.16/0.39 <=> ( cP @ Xy ) )
% 0.16/0.39 <=> ( ? [Xx: $i] : ( cQ @ Xx )
% 0.16/0.39 <=> ! [Xy: $i] : ( cR @ Xy ) ) )
% 0.16/0.39 <=> ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( cQ @ Xx )
% 0.16/0.39 <=> ( cQ @ Xy ) )
% 0.16/0.39 <=> ( ? [Xx: $i] : ( cR @ Xx )
% 0.16/0.39 <=> ! [Xy: $i] : ( cS @ Xy ) ) ) )
% 0.16/0.39 <=> ( ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( cR @ Xx )
% 0.16/0.39 <=> ( cR @ Xy ) )
% 0.16/0.39 <=> ( ? [Xx: $i] : ( cS @ Xx )
% 0.16/0.39 <=> ! [Xy: $i] : ( cP @ Xy ) ) )
% 0.16/0.39 <=> ( ? [Xx: $i] :
% 0.16/0.39 ! [Xy: $i] :
% 0.16/0.39 ( ( cS @ Xx )
% 0.16/0.39 <=> ( cS @ Xy ) )
% 0.16/0.39 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 0.16/0.39 <=> ! [Xy: $i] : ( cQ @ Xy ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 14:25:34 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DDLV6Zgj3R/DTF2DTF10908.p
% See solution above
% 1.36/1.29 ------------------------
% 1.57/1.30 ---- Cleaned THF ---
% 1.57/1.30 thf(cQ,type,
% 1.57/1.30 cQ: $i > $o ).
% 1.57/1.30
% 1.57/1.30 thf(cP,type,
% 1.57/1.30 cP: $i > $o ).
% 1.57/1.30
% 1.57/1.30 thf(cS,type,
% 1.57/1.30 cS: $i > $o ).
% 1.57/1.30
% 1.57/1.30 thf(cR,type,
% 1.57/1.30 cR: $i > $o ).
% 1.57/1.30
% 1.57/1.30 thf(cTHM138,conjecture,
% 1.57/1.30 ( ( ( ? [Xx: $i] :
% 1.57/1.30 ! [Xy: $i] :
% 1.57/1.30 ( ( cP @ Xx )
% 1.57/1.30 <=> ( cP @ Xy ) )
% 1.57/1.30 <=> ( ? [Xx: $i] : ( cQ @ Xx )
% 1.57/1.30 <=> ! [Xy: $i] : ( cR @ Xy ) ) )
% 1.57/1.30 <=> ( ? [Xx: $i] :
% 1.57/1.30 ! [Xy: $i] :
% 1.57/1.30 ( ( cQ @ Xx )
% 1.57/1.30 <=> ( cQ @ Xy ) )
% 1.57/1.30 <=> ( ? [Xx: $i] : ( cR @ Xx )
% 1.57/1.30 <=> ! [Xy: $i] : ( cS @ Xy ) ) ) )
% 1.57/1.30 <=> ( ( ? [Xx: $i] :
% 1.57/1.30 ! [Xy: $i] :
% 1.57/1.30 ( ( cR @ Xx )
% 1.57/1.30 <=> ( cR @ Xy ) )
% 1.57/1.30 <=> ( ? [Xx: $i] : ( cS @ Xx )
% 1.57/1.30 <=> ! [Xy: $i] : ( cP @ Xy ) ) )
% 1.57/1.30 <=> ( ? [Xx: $i] :
% 1.57/1.30 ! [Xy: $i] :
% 1.57/1.30 ( ( cS @ Xx )
% 1.57/1.30 <=> ( cS @ Xy ) )
% 1.57/1.30 <=> ( ? [Xx: $i] : ( cP @ Xx )
% 1.57/1.30 <=> ! [Xy: $i] : ( cQ @ Xy ) ) ) ) ) ).
% 1.57/1.30 ------------------------
% 1.57/1.32 % (11009)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/27Mi)
% 1.57/1.32 % (11008)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/4Mi)
% 1.57/1.32 % (11007)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/183Mi)
% 1.57/1.32 % (11010)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/2Mi)
% 1.57/1.32 % (11011)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/2Mi)
% 1.57/1.32 % (11012)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/275Mi)
% 1.57/1.32 % (11013)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/18Mi)
% 1.57/1.32 % (11010)Instruction limit reached!
% 1.57/1.32 % (11010)------------------------------
% 1.57/1.32 % (11010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (11010)Termination reason: Unknown
% 1.57/1.32 % (11010)Termination phase: Preprocessing 3
% 1.57/1.32 % (11011)Instruction limit reached!
% 1.57/1.32 % (11011)------------------------------
% 1.57/1.32 % (11011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (11011)Termination reason: Unknown
% 1.57/1.32 % (11011)Termination phase: Saturation
% 1.57/1.32
% 1.57/1.32 % (11011)Memory used [KB]: 1023
% 1.57/1.32 % (11011)Time elapsed: 0.003 s
% 1.57/1.32 % (11011)Instructions burned: 2 (million)
% 1.57/1.32 % (11011)------------------------------
% 1.57/1.32 % (11011)------------------------------
% 1.57/1.32
% 1.57/1.32 % (11010)Memory used [KB]: 1023
% 1.57/1.32 % (11010)Time elapsed: 0.003 s
% 1.57/1.32 % (11010)Instructions burned: 2 (million)
% 1.57/1.32 % (11010)------------------------------
% 1.57/1.32 % (11010)------------------------------
% 1.57/1.32 % (11008)Instruction limit reached!
% 1.57/1.32 % (11008)------------------------------
% 1.57/1.32 % (11008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.32 % (11008)Termination reason: Unknown
% 1.57/1.32 % (11008)Termination phase: Preprocessing 3
% 1.57/1.32
% 1.57/1.32 % (11008)Memory used [KB]: 1023
% 1.57/1.32 % (11008)Time elapsed: 0.004 s
% 1.57/1.32 % (11008)Instructions burned: 4 (million)
% 1.57/1.32 % (11008)------------------------------
% 1.57/1.32 % (11008)------------------------------
% 1.57/1.33 % (11012)Refutation not found, incomplete strategy
% 1.57/1.33 % (11012)------------------------------
% 1.57/1.33 % (11012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.33 % (11012)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.33
% 1.57/1.33
% 1.57/1.33 % (11012)Memory used [KB]: 5628
% 1.57/1.33 % (11012)Time elapsed: 0.007 s
% 1.57/1.33 % (11012)Instructions burned: 10 (million)
% 1.57/1.33 % (11012)------------------------------
% 1.57/1.33 % (11012)------------------------------
% 1.57/1.33 % (11013)Instruction limit reached!
% 1.57/1.33 % (11013)------------------------------
% 1.57/1.33 % (11013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.33 % (11013)Termination reason: Unknown
% 1.57/1.33 % (11013)Termination phase: Saturation
% 1.57/1.33
% 1.57/1.33 % (11013)Memory used [KB]: 5756
% 1.57/1.33 % (11013)Time elapsed: 0.011 s
% 1.57/1.33 % (11013)Instructions burned: 18 (million)
% 1.57/1.33 % (11013)------------------------------
% 1.57/1.33 % (11013)------------------------------
% 1.57/1.33 % (11009)Instruction limit reached!
% 1.57/1.33 % (11009)------------------------------
% 1.57/1.33 % (11009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.33 % (11009)Termination reason: Unknown
% 1.57/1.33 % (11009)Termination phase: Saturation
% 1.57/1.33
% 1.57/1.33 % (11009)Memory used [KB]: 5756
% 1.57/1.33 % (11009)Time elapsed: 0.015 s
% 1.57/1.33 % (11009)Instructions burned: 28 (million)
% 1.57/1.33 % (11009)------------------------------
% 1.57/1.33 % (11009)------------------------------
% 1.57/1.34 % (11014)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/3Mi)
% 1.57/1.34 % (11015)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/37Mi)
% 1.57/1.34 % (11016)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/15Mi)
% 1.57/1.34 % (11014)Instruction limit reached!
% 1.57/1.34 % (11014)------------------------------
% 1.57/1.34 % (11014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (11014)Termination reason: Unknown
% 1.57/1.34 % (11014)Termination phase: Preprocessing 3
% 1.57/1.34
% 1.57/1.34 % (11014)Memory used [KB]: 1023
% 1.57/1.34 % (11014)Time elapsed: 0.003 s
% 1.57/1.34 % (11014)Instructions burned: 3 (million)
% 1.57/1.34 % (11014)------------------------------
% 1.57/1.34 % (11014)------------------------------
% 1.57/1.34 % (11017)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/3Mi)
% 1.57/1.34 % (11017)Instruction limit reached!
% 1.57/1.34 % (11017)------------------------------
% 1.57/1.34 % (11017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (11017)Termination reason: Unknown
% 1.57/1.34 % (11017)Termination phase: Preprocessing 3
% 1.57/1.34
% 1.57/1.34 % (11017)Memory used [KB]: 1023
% 1.57/1.34 % (11017)Time elapsed: 0.003 s
% 1.57/1.34 % (11017)Instructions burned: 3 (million)
% 1.57/1.34 % (11017)------------------------------
% 1.57/1.34 % (11017)------------------------------
% 1.57/1.35 % (11018)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/1041Mi)
% 1.57/1.35 % (11016)Instruction limit reached!
% 1.57/1.35 % (11016)------------------------------
% 1.57/1.35 % (11016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (11016)Termination reason: Unknown
% 1.57/1.35 % (11016)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (11016)Memory used [KB]: 5756
% 1.57/1.35 % (11016)Time elapsed: 0.010 s
% 1.57/1.35 % (11016)Instructions burned: 15 (million)
% 1.57/1.35 % (11016)------------------------------
% 1.57/1.35 % (11016)------------------------------
% 1.57/1.35 % (11019)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/7Mi)
% 1.57/1.35 % (11019)Instruction limit reached!
% 1.57/1.35 % (11019)------------------------------
% 1.57/1.35 % (11019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.35 % (11019)Termination reason: Unknown
% 1.57/1.35 % (11019)Termination phase: Saturation
% 1.57/1.35
% 1.57/1.35 % (11019)Memory used [KB]: 1151
% 1.57/1.35 % (11019)Time elapsed: 0.005 s
% 1.57/1.35 % (11019)Instructions burned: 7 (million)
% 1.57/1.35 % (11019)------------------------------
% 1.57/1.35 % (11019)------------------------------
% 1.57/1.36 % (11020)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/16Mi)
% 1.57/1.36 % (11015)Instruction limit reached!
% 1.57/1.36 % (11015)------------------------------
% 1.57/1.36 % (11015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (11015)Termination reason: Unknown
% 1.57/1.36 % (11015)Termination phase: Saturation
% 1.57/1.36
% 1.57/1.36 % (11015)Memory used [KB]: 5628
% 1.57/1.36 % (11015)Time elapsed: 0.020 s
% 1.57/1.36 % (11015)Instructions burned: 37 (million)
% 1.57/1.36 % (11015)------------------------------
% 1.57/1.36 % (11015)------------------------------
% 1.57/1.36 % (11021)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/3Mi)
% 1.57/1.36 % (11021)Instruction limit reached!
% 1.57/1.36 % (11021)------------------------------
% 1.57/1.36 % (11021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (11021)Termination reason: Unknown
% 1.57/1.36 % (11021)Termination phase: Preprocessing 3
% 1.57/1.36
% 1.57/1.36 % (11021)Memory used [KB]: 1023
% 1.57/1.36 % (11021)Time elapsed: 0.003 s
% 1.57/1.36 % (11021)Instructions burned: 4 (million)
% 1.57/1.36 % (11021)------------------------------
% 1.57/1.36 % (11021)------------------------------
% 1.57/1.36 % (11022)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/3Mi)
% 1.57/1.36 % (11020)Instruction limit reached!
% 1.57/1.36 % (11020)------------------------------
% 1.57/1.36 % (11020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.36 % (11020)Termination reason: Unknown
% 1.57/1.36 % (11020)Termination phase: Saturation
% 1.57/1.36
% 1.57/1.36 % (11020)Memory used [KB]: 5756
% 1.57/1.36 % (11020)Time elapsed: 0.010 s
% 1.57/1.36 % (11020)Instructions burned: 17 (million)
% 1.57/1.37 % (11020)------------------------------
% 1.57/1.37 % (11020)------------------------------
% 1.57/1.37 % (11022)Instruction limit reached!
% 1.57/1.37 % (11022)------------------------------
% 1.57/1.37 % (11022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.37 % (11022)Termination reason: Unknown
% 1.57/1.37 % (11022)Termination phase: Preprocessing 3
% 1.57/1.37
% 1.57/1.37 % (11022)Memory used [KB]: 1023
% 1.57/1.37 % (11022)Time elapsed: 0.003 s
% 1.57/1.37 % (11022)Instructions burned: 3 (million)
% 1.57/1.37 % (11022)------------------------------
% 1.57/1.37 % (11022)------------------------------
% 1.57/1.37 % (11023)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/7Mi)
% 1.57/1.37 % (11024)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/3Mi)
% 1.57/1.37 % (11023)Instruction limit reached!
% 1.57/1.37 % (11023)------------------------------
% 1.57/1.37 % (11023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.37 % (11023)Termination reason: Unknown
% 1.57/1.37 % (11023)Termination phase: Saturation
% 1.57/1.37
% 1.57/1.37 % (11023)Memory used [KB]: 5628
% 1.57/1.37 % (11023)Time elapsed: 0.005 s
% 1.57/1.37 % (11023)Instructions burned: 7 (million)
% 1.57/1.37 % (11023)------------------------------
% 1.57/1.37 % (11023)------------------------------
% 1.57/1.38 % (11024)Instruction limit reached!
% 1.57/1.38 % (11024)------------------------------
% 1.57/1.38 % (11024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.38 % (11024)Termination reason: Unknown
% 1.57/1.38 % (11024)Termination phase: Saturation
% 1.57/1.38
% 1.57/1.38 % (11024)Memory used [KB]: 5500
% 1.57/1.38 % (11024)Time elapsed: 0.003 s
% 1.57/1.38 % (11024)Instructions burned: 3 (million)
% 1.57/1.38 % (11024)------------------------------
% 1.57/1.38 % (11024)------------------------------
% 1.57/1.38 % (11025)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/4Mi)
% 1.57/1.38 % (11025)Instruction limit reached!
% 1.57/1.38 % (11025)------------------------------
% 1.57/1.38 % (11025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.38 % (11025)Termination reason: Unknown
% 1.57/1.38 % (11025)Termination phase: Preprocessing 3
% 1.57/1.38
% 1.57/1.38 % (11025)Memory used [KB]: 1023
% 1.57/1.38 % (11025)Time elapsed: 0.003 s
% 1.57/1.38 % (11025)Instructions burned: 4 (million)
% 1.57/1.38 % (11025)------------------------------
% 1.57/1.38 % (11025)------------------------------
% 1.57/1.38 % (11026)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/18Mi)
% 1.57/1.38 % (11027)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/710Mi)
% 1.57/1.39 % (11028)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/6Mi)
% 1.57/1.39 % (11026)Instruction limit reached!
% 1.57/1.39 % (11026)------------------------------
% 1.57/1.39 % (11026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.39 % (11026)Termination reason: Unknown
% 1.57/1.39 % (11026)Termination phase: Saturation
% 1.57/1.39
% 1.57/1.39 % (11026)Memory used [KB]: 5884
% 1.57/1.39 % (11026)Time elapsed: 0.011 s
% 1.57/1.39 % (11026)Instructions burned: 19 (million)
% 1.57/1.39 % (11026)------------------------------
% 1.57/1.39 % (11026)------------------------------
% 1.57/1.39 % (11029)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/902Mi)
% 1.57/1.39 % (11028)Instruction limit reached!
% 1.57/1.39 % (11028)------------------------------
% 1.57/1.39 % (11028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.39 % (11028)Termination reason: Unknown
% 1.57/1.39 % (11028)Termination phase: Saturation
% 1.57/1.39
% 1.57/1.39 % (11028)Memory used [KB]: 5628
% 1.57/1.39 % (11028)Time elapsed: 0.005 s
% 1.57/1.39 % (11028)Instructions burned: 7 (million)
% 1.57/1.39 % (11028)------------------------------
% 1.57/1.39 % (11028)------------------------------
% 1.57/1.40 % (11029)Refutation not found, incomplete strategy
% 1.57/1.40 % (11029)------------------------------
% 1.57/1.40 % (11029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.40 % (11029)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.40
% 1.57/1.40
% 1.57/1.40 % (11029)Memory used [KB]: 5628
% 1.57/1.40 % (11029)Time elapsed: 0.006 s
% 1.57/1.40 % (11029)Instructions burned: 7 (million)
% 1.57/1.40 % (11029)------------------------------
% 1.57/1.40 % (11029)------------------------------
% 1.57/1.40 % (11030)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/21Mi)
% 1.57/1.41 % (11031)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/5Mi)
% 1.57/1.41 % (11030)Instruction limit reached!
% 1.57/1.41 % (11030)------------------------------
% 1.57/1.41 % (11030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.41 % (11030)Termination reason: Unknown
% 1.57/1.41 % (11030)Termination phase: Saturation
% 1.57/1.41
% 1.57/1.41 % (11030)Memory used [KB]: 6140
% 1.57/1.41 % (11030)Time elapsed: 0.013 s
% 1.57/1.41 % (11030)Instructions burned: 22 (million)
% 1.57/1.41 % (11030)------------------------------
% 1.57/1.41 % (11030)------------------------------
% 1.57/1.41 % (11032)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/6Mi)
% 1.57/1.41 % (11031)Instruction limit reached!
% 1.57/1.41 % (11031)------------------------------
% 1.57/1.41 % (11031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.41 % (11031)Termination reason: Unknown
% 1.57/1.41 % (11031)Termination phase: Saturation
% 1.57/1.41
% 1.57/1.41 % (11031)Memory used [KB]: 5500
% 1.57/1.41 % (11031)Time elapsed: 0.005 s
% 1.57/1.41 % (11031)Instructions burned: 7 (million)
% 1.57/1.41 % (11031)------------------------------
% 1.57/1.41 % (11031)------------------------------
% 1.57/1.41 % (11033)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/377Mi)
% 1.57/1.41 % (11032)Instruction limit reached!
% 1.57/1.41 % (11032)------------------------------
% 1.57/1.41 % (11032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.41 % (11032)Termination reason: Unknown
% 1.57/1.41 % (11032)Termination phase: Saturation
% 1.57/1.41
% 1.57/1.41 % (11032)Memory used [KB]: 5500
% 1.57/1.41 % (11032)Time elapsed: 0.005 s
% 1.57/1.41 % (11032)Instructions burned: 7 (million)
% 1.57/1.41 % (11032)------------------------------
% 1.57/1.41 % (11032)------------------------------
% 1.57/1.42 % (11007)Instruction limit reached!
% 1.57/1.42 % (11007)------------------------------
% 1.57/1.42 % (11007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.42 % (11007)Termination reason: Unknown
% 1.57/1.42 % (11007)Termination phase: Saturation
% 1.57/1.42
% 1.57/1.42 % (11007)Memory used [KB]: 6652
% 1.57/1.42 % (11007)Time elapsed: 0.103 s
% 1.57/1.42 % (11007)Instructions burned: 184 (million)
% 1.57/1.42 % (11007)------------------------------
% 1.57/1.42 % (11007)------------------------------
% 1.57/1.42 % (11034)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/779Mi)
% 1.57/1.43 % (11035)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/19Mi)
% 1.57/1.43 % (11036)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_10908 for (2999ds/879Mi)
% 1.57/1.44 % (11035)Instruction limit reached!
% 1.57/1.44 % (11035)------------------------------
% 1.57/1.44 % (11035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.44 % (11035)Termination reason: Unknown
% 1.57/1.44 % (11035)Termination phase: Saturation
% 1.57/1.44
% 1.57/1.44 % (11035)Memory used [KB]: 5500
% 1.57/1.44 % (11035)Time elapsed: 0.011 s
% 1.57/1.44 % (11035)Instructions burned: 19 (million)
% 1.57/1.44 % (11035)------------------------------
% 1.57/1.44 % (11035)------------------------------
% 1.57/1.44 % (11037)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_10908 for (2998ds/17Mi)
% 1.57/1.45 % (11037)Instruction limit reached!
% 1.57/1.45 % (11037)------------------------------
% 1.57/1.45 % (11037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.45 % (11037)Termination reason: Unknown
% 1.57/1.45 % (11037)Termination phase: Saturation
% 1.57/1.45
% 1.57/1.45 % (11037)Memory used [KB]: 5884
% 1.57/1.45 % (11037)Time elapsed: 0.010 s
% 1.57/1.45 % (11037)Instructions burned: 17 (million)
% 1.57/1.45 % (11037)------------------------------
% 1.57/1.45 % (11037)------------------------------
% 1.57/1.45 % (11038)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_10908 for (2998ds/3Mi)
% 1.57/1.45 % (11038)Instruction limit reached!
% 1.57/1.45 % (11038)------------------------------
% 1.57/1.45 % (11038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.45 % (11038)Termination reason: Unknown
% 1.57/1.45 % (11038)Termination phase: Preprocessing 3
% 1.57/1.45
% 1.57/1.45 % (11038)Memory used [KB]: 1023
% 1.57/1.45 % (11038)Time elapsed: 0.003 s
% 1.57/1.45 % (11038)Instructions burned: 3 (million)
% 1.57/1.45 % (11038)------------------------------
% 1.57/1.45 % (11038)------------------------------
% 1.57/1.46 % (11039)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_10908 for (2998ds/30Mi)
% 1.57/1.47 % (11040)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_10908 for (2998ds/127Mi)
% 1.57/1.47 % (11027)First to succeed.
% 1.57/1.47 % (11039)Refutation not found, incomplete strategy
% 1.57/1.47 % (11039)------------------------------
% 1.57/1.47 % (11039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.47 % (11039)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.47
% 1.57/1.47
% 1.57/1.47 % (11039)Memory used [KB]: 5884
% 1.57/1.47 % (11039)Time elapsed: 0.013 s
% 1.57/1.47 % (11039)Instructions burned: 19 (million)
% 1.57/1.47 % (11039)------------------------------
% 1.57/1.47 % (11039)------------------------------
% 1.57/1.49 % (11027)Refutation found. Thanks to Tanya!
% 1.57/1.49 % SZS status Theorem for DTF2THF_10908
% 1.57/1.49 % SZS output start Proof for DTF2THF_10908
% 1.57/1.49 thf(func_def_0, type, cQ: $i > $o).
% 1.57/1.49 thf(func_def_1, type, cP: $i > $o).
% 1.57/1.49 thf(func_def_2, type, cS: $i > $o).
% 1.57/1.49 thf(func_def_3, type, cR: $i > $o).
% 1.57/1.49 thf(func_def_13, type, sK6: $i > $i).
% 1.57/1.49 thf(func_def_22, type, sK15: $i > $i).
% 1.57/1.49 thf(func_def_25, type, sK18: $i > $i).
% 1.57/1.49 thf(func_def_34, type, sK27: $i > $i).
% 1.57/1.49 thf(func_def_37, type, sK30: $i > $i).
% 1.57/1.49 thf(func_def_46, type, sK39: $i > $i).
% 1.57/1.49 thf(func_def_49, type, sK42: $i > $i).
% 1.57/1.49 thf(func_def_58, type, sK51: $i > $i).
% 1.57/1.49 thf(func_def_61, type, sK54: $i > $i).
% 1.57/1.49 thf(func_def_70, type, sK63: $i > $i).
% 1.57/1.49 thf(func_def_71, type, sK64: $i > $i).
% 1.57/1.49 thf(func_def_79, type, sK72: $i > $i).
% 1.57/1.49 thf(f1752,plain,(
% 1.57/1.49 $false),
% 1.57/1.49 inference(avatar_sat_refutation,[status(thm)],[f266,f274,f289,f293,f304,f308,f323,f331,f342,f347,f359,f363,f376,f381,f389,f393,f401,f402,f411,f416,f428,f432,f440,f444,f452,f456,f463,f467,f471,f475,f480,f481,f482,f483,f484,f493,f501,f510,f511,f512,f513,f514,f522,f526,f535,f536,f549,f554,f559,f564,f565,f566,f571,f572,f581,f586,f595,f596,f605,f610,f622,f626,f631,f632,f645,f650,f655,f656,f664,f668,f669,f670,f671,f672,f677,f678,f687,f688,f693,f694,f699,f700,f701,f702,f703,f704,f713,f718,f723,f724,f729,f730,f735,f736,f745,f746,f751,f752,f759,f761,f771,f774,f778,f781,f784,f788,f791,f795,f799,f803,f806,f809,f815,f819,f827,f829,f836,f846,f851,f855,f858,f863,f874,f883,f888,f898,f901,f912,f918,f931,f938,f944,f963,f973,f987,f993,f1013,f1051,f1064,f1078,f1099,f1101,f1117,f1123,f1129,f1132,f1134,f1144,f1147,f1149,f1172,f1175,f1185,f1197,f1202,f1209,f1212,f1221,f1252,f1262,f1266,f1269,f1285,f1314,f1317,f1319,f1330,f1363,f1366,f1416,f1438,f1440,f1442,f1446,f1448,f1450,f1461,f1469,f1479,f1484,f1518,f1526,f1533,f1550,f1553,f1573,f1592,f1609,f1612,f1618,f1622,f1638,f1644,f1658,f1662,f1687,f1745,f1751])).
% 1.57/1.49 thf(f1751,plain,(
% 1.57/1.49 ~spl76_47 | ~spl76_55),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1750])).
% 1.57/1.49 thf(f1750,plain,(
% 1.57/1.49 $false | (~spl76_47 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1747])).
% 1.57/1.49 thf(f1747,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_47 | ~spl76_55)),
% 1.57/1.49 inference(superposition,[status(thm)],[f462,f1697])).
% 1.57/1.49 thf(f1697,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cP @ (sK39 @ X22)))) ) | (~spl76_47 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1695])).
% 1.57/1.49 thf(f1695,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cP @ (sK39 @ X22))) | ($false = $true)) ) | (~spl76_47 | ~spl76_55)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f431,f462])).
% 1.57/1.49 thf(f431,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cP @ (sK39 @ X22))) | ($false = (cP @ X22))) ) | ~spl76_47),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f430])).
% 1.57/1.49 thf(f430,definition,(
% 1.57/1.49 spl76_47 <=> ! [X22 : $i] : (($false = (cP @ X22)) | ($false = (cP @ (sK39 @ X22))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_47])],[avatar_definition])).
% 1.57/1.49 thf(f462,plain,(
% 1.57/1.49 ( ! [X44 : $i] : (($true = (cP @ X44))) ) | ~spl76_55),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f461])).
% 1.57/1.49 thf(f461,definition,(
% 1.57/1.49 spl76_55 <=> ! [X44 : $i] : ($true = (cP @ X44))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_55])],[avatar_definition])).
% 1.57/1.49 thf(f1745,plain,(
% 1.57/1.49 ~spl76_55 | ~spl76_98),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1744])).
% 1.57/1.49 thf(f1744,plain,(
% 1.57/1.49 $false | (~spl76_55 | ~spl76_98)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1740])).
% 1.57/1.49 thf(f1740,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_55 | ~spl76_98)),
% 1.57/1.49 inference(superposition,[status(thm)],[f1696,f462])).
% 1.57/1.49 thf(f1696,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($false = (cP @ (sK42 @ X28)))) ) | (~spl76_55 | ~spl76_98)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1694])).
% 1.57/1.49 thf(f1694,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($false = (cP @ (sK42 @ X28))) | ($false = $true)) ) | (~spl76_55 | ~spl76_98)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f667,f462])).
% 1.57/1.49 thf(f667,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($false = (cP @ (sK42 @ X28))) | ($false = (cP @ X28))) ) | ~spl76_98),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f666])).
% 1.57/1.49 thf(f666,definition,(
% 1.57/1.49 spl76_98 <=> ! [X28 : $i] : (($false = (cP @ (sK42 @ X28))) | ($false = (cP @ X28)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_98])],[avatar_definition])).
% 1.57/1.49 thf(f1687,plain,(
% 1.57/1.49 ~spl76_4 | spl76_96),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1686])).
% 1.57/1.49 thf(f1686,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_96)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1685])).
% 1.57/1.49 thf(f1685,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_4 | spl76_96)),
% 1.57/1.49 inference(superposition,[status(thm)],[f660,f257])).
% 1.57/1.49 thf(f257,plain,(
% 1.57/1.49 ( ! [X35 : $i] : (((cR @ X35) = $true)) ) | ~spl76_4),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f256])).
% 1.57/1.49 thf(f256,definition,(
% 1.57/1.49 spl76_4 <=> ! [X35 : $i] : ((cR @ X35) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_4])],[avatar_definition])).
% 1.57/1.49 thf(f660,plain,(
% 1.57/1.49 ((cR @ sK40) != $true) | spl76_96),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f658])).
% 1.57/1.49 thf(f658,definition,(
% 1.57/1.49 spl76_96 <=> ((cR @ sK40) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_96])],[avatar_definition])).
% 1.57/1.49 thf(f1662,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_92),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1661])).
% 1.57/1.49 thf(f1661,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_92)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1660])).
% 1.57/1.49 thf(f1660,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_92)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f640,f326])).
% 1.57/1.49 thf(f326,plain,(
% 1.57/1.49 ( ! [X19 : $i] : (($false = (cQ @ X19))) ) | ~spl76_22),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f325])).
% 1.57/1.49 thf(f325,definition,(
% 1.57/1.49 spl76_22 <=> ! [X19 : $i] : ($false = (cQ @ X19))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_22])],[avatar_definition])).
% 1.57/1.49 thf(f640,plain,(
% 1.57/1.49 ((cQ @ sK43) = $true) | ~spl76_92),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f638])).
% 1.57/1.49 thf(f638,definition,(
% 1.57/1.49 spl76_92 <=> ((cQ @ sK43) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_92])],[avatar_definition])).
% 1.57/1.49 thf(f1658,plain,(
% 1.57/1.49 ~spl76_4 | spl76_91),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1657])).
% 1.57/1.49 thf(f1657,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_91)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f636,f257])).
% 1.57/1.49 thf(f636,plain,(
% 1.57/1.49 ($true != (cR @ sK44)) | spl76_91),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f634])).
% 1.57/1.49 thf(f634,definition,(
% 1.57/1.49 spl76_91 <=> ($true = (cR @ sK44))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_91])],[avatar_definition])).
% 1.57/1.49 thf(f1644,plain,(
% 1.57/1.49 ~spl76_93 | ~spl76_94),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1643])).
% 1.57/1.49 thf(f1643,plain,(
% 1.57/1.49 $false | (~spl76_93 | ~spl76_94)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1642])).
% 1.57/1.49 thf(f1642,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_93 | ~spl76_94)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f649,f644])).
% 1.57/1.49 thf(f644,plain,(
% 1.57/1.49 ($false = (cP @ sK45)) | ~spl76_93),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f642])).
% 1.57/1.49 thf(f642,definition,(
% 1.57/1.49 spl76_93 <=> ($false = (cP @ sK45))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_93])],[avatar_definition])).
% 1.57/1.49 thf(f649,plain,(
% 1.57/1.49 ($true = (cP @ sK45)) | ~spl76_94),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f647])).
% 1.57/1.49 thf(f647,definition,(
% 1.57/1.49 spl76_94 <=> ($true = (cP @ sK45))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_94])],[avatar_definition])).
% 1.57/1.49 thf(f1638,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_103),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1637])).
% 1.57/1.49 thf(f1637,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_103)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1636])).
% 1.57/1.49 thf(f1636,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_103)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f698,f326])).
% 1.57/1.49 thf(f698,plain,(
% 1.57/1.49 ((cQ @ sK41) = $true) | ~spl76_103),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f696])).
% 1.57/1.49 thf(f696,definition,(
% 1.57/1.49 spl76_103 <=> ((cQ @ sK41) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_103])],[avatar_definition])).
% 1.57/1.49 thf(f1622,plain,(
% 1.57/1.49 ~spl76_24 | ~spl76_97),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1621])).
% 1.57/1.49 thf(f1621,plain,(
% 1.57/1.49 $false | (~spl76_24 | ~spl76_97)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f1620,f334])).
% 1.57/1.49 thf(f334,plain,(
% 1.57/1.49 ( ! [X9 : $i] : (((cP @ X9) != $true)) ) | ~spl76_24),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f333])).
% 1.57/1.49 thf(f333,definition,(
% 1.57/1.49 spl76_24 <=> ! [X9 : $i] : ((cP @ X9) != $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_24])],[avatar_definition])).
% 1.57/1.49 thf(f1620,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($true = (cP @ X28))) ) | (~spl76_24 | ~spl76_97)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f663,f334])).
% 1.57/1.49 thf(f663,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($true = (cP @ (sK42 @ X28))) | ($true = (cP @ X28))) ) | ~spl76_97),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f662])).
% 1.57/1.49 thf(f662,definition,(
% 1.57/1.49 spl76_97 <=> ! [X28 : $i] : (($true = (cP @ (sK42 @ X28))) | ($true = (cP @ X28)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_97])],[avatar_definition])).
% 1.57/1.49 thf(f1618,plain,(
% 1.57/1.49 ~spl76_11 | ~spl76_103),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1617])).
% 1.57/1.49 thf(f1617,plain,(
% 1.57/1.49 $false | (~spl76_11 | ~spl76_103)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f698,f284])).
% 1.57/1.49 thf(f284,plain,(
% 1.57/1.49 ( ! [X45 : $i] : (($true != (cQ @ X45))) ) | ~spl76_11),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f283])).
% 1.57/1.49 thf(f283,definition,(
% 1.57/1.49 spl76_11 <=> ! [X45 : $i] : ($true != (cQ @ X45))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_11])],[avatar_definition])).
% 1.57/1.49 thf(f1612,plain,(
% 1.57/1.49 ~spl76_7 | ~spl76_33),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1611])).
% 1.57/1.49 thf(f1611,plain,(
% 1.57/1.49 $false | (~spl76_7 | ~spl76_33)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1610])).
% 1.57/1.49 thf(f1610,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_7 | ~spl76_33)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f371,f269])).
% 1.57/1.49 thf(f269,plain,(
% 1.57/1.49 ( ! [X35 : $i] : (($false = (cR @ X35))) ) | ~spl76_7),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f268])).
% 1.57/1.49 thf(f268,definition,(
% 1.57/1.49 spl76_7 <=> ! [X35 : $i] : ($false = (cR @ X35))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_7])],[avatar_definition])).
% 1.57/1.49 thf(f371,plain,(
% 1.57/1.49 ((cR @ sK68) = $true) | ~spl76_33),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f369])).
% 1.57/1.49 thf(f369,definition,(
% 1.57/1.49 spl76_33 <=> ((cR @ sK68) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_33])],[avatar_definition])).
% 1.57/1.49 thf(f1609,plain,(
% 1.57/1.49 ~spl76_11 | ~spl76_36),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1608])).
% 1.57/1.49 thf(f1608,plain,(
% 1.57/1.49 $false | (~spl76_11 | ~spl76_36)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f1607,f284])).
% 1.57/1.49 thf(f1607,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cQ @ X0) = $true)) ) | (~spl76_11 | ~spl76_36)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1606])).
% 1.57/1.49 thf(f1606,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cQ @ X0) = $true) | ($true != $true)) ) | (~spl76_11 | ~spl76_36)),
% 1.57/1.49 inference(superposition,[status(thm)],[f284,f384])).
% 1.57/1.49 thf(f384,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($true = (cQ @ (sK64 @ X0))) | ((cQ @ X0) = $true)) ) | ~spl76_36),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f383])).
% 1.57/1.49 thf(f383,definition,(
% 1.57/1.49 spl76_36 <=> ! [X0 : $i] : (((cQ @ X0) = $true) | ($true = (cQ @ (sK64 @ X0))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_36])],[avatar_definition])).
% 1.57/1.49 thf(f1592,plain,(
% 1.57/1.49 ~spl76_11 | ~spl76_105),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1591])).
% 1.57/1.49 thf(f1591,plain,(
% 1.57/1.49 $false | (~spl76_11 | ~spl76_105)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1590])).
% 1.57/1.49 thf(f1590,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_11 | ~spl76_105)),
% 1.57/1.49 inference(superposition,[status(thm)],[f284,f712])).
% 1.57/1.49 thf(f712,plain,(
% 1.57/1.49 ($true = (cQ @ sK36)) | ~spl76_105),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f710])).
% 1.57/1.49 thf(f710,definition,(
% 1.57/1.49 spl76_105 <=> ($true = (cQ @ sK36))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_105])],[avatar_definition])).
% 1.57/1.49 thf(f1573,plain,(
% 1.57/1.49 ~spl76_7 | ~spl76_37),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1572])).
% 1.57/1.49 thf(f1572,plain,(
% 1.57/1.49 $false | (~spl76_7 | ~spl76_37)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1571])).
% 1.57/1.49 thf(f1571,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_7 | ~spl76_37)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f388,f269])).
% 1.57/1.49 thf(f388,plain,(
% 1.57/1.49 ($true = (cR @ sK66)) | ~spl76_37),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f386])).
% 1.57/1.49 thf(f386,definition,(
% 1.57/1.49 spl76_37 <=> ($true = (cR @ sK66))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_37])],[avatar_definition])).
% 1.57/1.49 thf(f1553,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_105),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1552])).
% 1.57/1.49 thf(f1552,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_105)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1551])).
% 1.57/1.49 thf(f1551,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_105)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f712,f326])).
% 1.57/1.49 thf(f1550,plain,(
% 1.57/1.49 ~spl76_24 | ~spl76_44),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1549])).
% 1.57/1.49 thf(f1549,plain,(
% 1.57/1.49 $false | (~spl76_24 | ~spl76_44)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f1548,f334])).
% 1.57/1.49 thf(f1548,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl76_24 | ~spl76_44)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1547])).
% 1.57/1.49 thf(f1547,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($true != $true) | ((cP @ X0) = $true)) ) | (~spl76_24 | ~spl76_44)),
% 1.57/1.49 inference(superposition,[status(thm)],[f334,f419])).
% 1.57/1.49 thf(f419,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cP @ (sK39 @ X22)) = $true) | ($true = (cP @ X22))) ) | ~spl76_44),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f418])).
% 1.57/1.49 thf(f418,definition,(
% 1.57/1.49 spl76_44 <=> ! [X22 : $i] : (($true = (cP @ X22)) | ((cP @ (sK39 @ X22)) = $true))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_44])],[avatar_definition])).
% 1.57/1.49 thf(f1533,plain,(
% 1.57/1.49 ~spl76_44 | ~spl76_62),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1532])).
% 1.57/1.49 thf(f1532,plain,(
% 1.57/1.49 $false | (~spl76_44 | ~spl76_62)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1531])).
% 1.57/1.49 thf(f1531,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_44 | ~spl76_62)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f1530,f496])).
% 1.57/1.49 thf(f496,plain,(
% 1.57/1.49 ( ! [X37 : $i] : (((cP @ X37) = $false)) ) | ~spl76_62),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f495])).
% 1.57/1.49 thf(f495,definition,(
% 1.57/1.49 spl76_62 <=> ! [X37 : $i] : ((cP @ X37) = $false)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_62])],[avatar_definition])).
% 1.57/1.49 thf(f1530,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cP @ (sK39 @ X22)) = $true)) ) | (~spl76_44 | ~spl76_62)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1529])).
% 1.57/1.49 thf(f1529,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = $true) | ((cP @ (sK39 @ X22)) = $true)) ) | (~spl76_44 | ~spl76_62)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f419,f496])).
% 1.57/1.49 thf(f1526,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_36),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1525])).
% 1.57/1.49 thf(f1525,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_36)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1524])).
% 1.57/1.49 thf(f1524,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_36)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f1519,f326])).
% 1.57/1.49 thf(f1519,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($true = (cQ @ (sK64 @ X0)))) ) | (~spl76_22 | ~spl76_36)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1506])).
% 1.57/1.49 thf(f1506,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($false = $true) | ($true = (cQ @ (sK64 @ X0)))) ) | (~spl76_22 | ~spl76_36)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f384,f326])).
% 1.57/1.49 thf(f1518,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_45),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1517])).
% 1.57/1.49 thf(f1517,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_45)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1509])).
% 1.57/1.49 thf(f1509,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_45)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f423,f326])).
% 1.57/1.49 thf(f423,plain,(
% 1.57/1.49 ((cQ @ sK37) = $true) | ~spl76_45),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f421])).
% 1.57/1.49 thf(f421,definition,(
% 1.57/1.49 spl76_45 <=> ((cQ @ sK37) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_45])],[avatar_definition])).
% 1.57/1.49 thf(f1484,plain,(
% 1.57/1.49 ~spl76_32 | ~spl76_35),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1483])).
% 1.57/1.49 thf(f1483,plain,(
% 1.57/1.49 $false | (~spl76_32 | ~spl76_35)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1482])).
% 1.57/1.49 thf(f1482,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_32 | ~spl76_35)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f367,f380])).
% 1.57/1.49 thf(f380,plain,(
% 1.57/1.49 ((cQ @ sK67) = $false) | ~spl76_35),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f378])).
% 1.57/1.49 thf(f378,definition,(
% 1.57/1.49 spl76_35 <=> ((cQ @ sK67) = $false)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_35])],[avatar_definition])).
% 1.57/1.49 thf(f367,plain,(
% 1.57/1.49 ((cQ @ sK67) = $true) | ~spl76_32),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f365])).
% 1.57/1.49 thf(f365,definition,(
% 1.57/1.49 spl76_32 <=> ((cQ @ sK67) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_32])],[avatar_definition])).
% 1.57/1.49 thf(f1479,plain,(
% 1.57/1.49 ~spl76_104 | ~spl76_106),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1478])).
% 1.57/1.49 thf(f1478,plain,(
% 1.57/1.49 $false | (~spl76_104 | ~spl76_106)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1477])).
% 1.57/1.49 thf(f1477,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_104 | ~spl76_106)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f708,f717])).
% 1.57/1.49 thf(f717,plain,(
% 1.57/1.49 ((cP @ sK34) = $false) | ~spl76_106),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f715])).
% 1.57/1.49 thf(f715,definition,(
% 1.57/1.49 spl76_106 <=> ((cP @ sK34) = $false)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_106])],[avatar_definition])).
% 1.57/1.49 thf(f708,plain,(
% 1.57/1.49 ((cP @ sK34) = $true) | ~spl76_104),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f706])).
% 1.57/1.49 thf(f706,definition,(
% 1.57/1.49 spl76_104 <=> ((cP @ sK34) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_104])],[avatar_definition])).
% 1.57/1.49 thf(f1469,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_81),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1468])).
% 1.57/1.49 thf(f1468,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_81)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1465])).
% 1.57/1.49 thf(f1465,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_81)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f590,f337])).
% 1.57/1.49 thf(f337,plain,(
% 1.57/1.49 ( ! [X11 : $i] : (((cS @ X11) = $false)) ) | ~spl76_25),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f336])).
% 1.57/1.49 thf(f336,definition,(
% 1.57/1.49 spl76_25 <=> ! [X11 : $i] : ((cS @ X11) = $false)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_25])],[avatar_definition])).
% 1.57/1.49 thf(f590,plain,(
% 1.57/1.49 ((cS @ sK7) = $true) | ~spl76_81),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f588])).
% 1.57/1.49 thf(f588,definition,(
% 1.57/1.49 spl76_81 <=> ((cS @ sK7) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_81])],[avatar_definition])).
% 1.57/1.49 thf(f1461,plain,(
% 1.57/1.49 ~spl76_20 | ~spl76_38),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1460])).
% 1.57/1.49 thf(f1460,plain,(
% 1.57/1.49 $false | (~spl76_20 | ~spl76_38)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1456])).
% 1.57/1.49 thf(f1456,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_20 | ~spl76_38)),
% 1.57/1.49 inference(superposition,[status(thm)],[f1452,f318])).
% 1.57/1.49 thf(f318,plain,(
% 1.57/1.49 ( ! [X19 : $i] : (($true = (cQ @ X19))) ) | ~spl76_20),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f317])).
% 1.57/1.49 thf(f317,definition,(
% 1.57/1.49 spl76_20 <=> ! [X19 : $i] : ($true = (cQ @ X19))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_20])],[avatar_definition])).
% 1.57/1.49 thf(f1452,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($false = (cQ @ (sK64 @ X0)))) ) | (~spl76_20 | ~spl76_38)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1451])).
% 1.57/1.49 thf(f1451,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($false = $true) | ($false = (cQ @ (sK64 @ X0)))) ) | (~spl76_20 | ~spl76_38)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f392,f318])).
% 1.57/1.49 thf(f392,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($false = (cQ @ (sK64 @ X0))) | ((cQ @ X0) = $false)) ) | ~spl76_38),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f391])).
% 1.57/1.49 thf(f391,definition,(
% 1.57/1.49 spl76_38 <=> ! [X0 : $i] : (($false = (cQ @ (sK64 @ X0))) | ((cQ @ X0) = $false))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_38])],[avatar_definition])).
% 1.57/1.49 thf(f1450,plain,(
% 1.57/1.49 ~spl76_55 | spl76_109),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1449])).
% 1.57/1.49 thf(f1449,plain,(
% 1.57/1.49 $false | (~spl76_55 | spl76_109)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f733,f462])).
% 1.57/1.49 thf(f733,plain,(
% 1.57/1.49 ((cP @ sK60) != $true) | spl76_109),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f732])).
% 1.57/1.49 thf(f732,definition,(
% 1.57/1.49 spl76_109 <=> ((cP @ sK60) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_109])],[avatar_definition])).
% 1.57/1.49 thf(f1448,plain,(
% 1.57/1.49 ~spl76_19 | spl76_34),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1447])).
% 1.57/1.49 thf(f1447,plain,(
% 1.57/1.49 $false | (~spl76_19 | spl76_34)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f375,f315])).
% 1.57/1.49 thf(f315,plain,(
% 1.57/1.49 ( ! [X23 : $i] : (((cS @ X23) = $true)) ) | ~spl76_19),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f314])).
% 1.57/1.49 thf(f314,definition,(
% 1.57/1.49 spl76_19 <=> ! [X23 : $i] : ((cS @ X23) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_19])],[avatar_definition])).
% 1.57/1.49 thf(f375,plain,(
% 1.57/1.49 ($true != (cS @ sK69)) | spl76_34),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f373])).
% 1.57/1.49 thf(f373,definition,(
% 1.57/1.49 spl76_34 <=> ($true = (cS @ sK69))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_34])],[avatar_definition])).
% 1.57/1.49 thf(f1446,plain,(
% 1.57/1.49 ~spl76_19 | spl76_39),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1445])).
% 1.57/1.49 thf(f1445,plain,(
% 1.57/1.49 $false | (~spl76_19 | spl76_39)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f397,f315])).
% 1.57/1.49 thf(f397,plain,(
% 1.57/1.49 ($true != (cS @ sK65)) | spl76_39),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f395])).
% 1.57/1.49 thf(f395,definition,(
% 1.57/1.49 spl76_39 <=> ($true = (cS @ sK65))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_39])],[avatar_definition])).
% 1.57/1.49 thf(f1442,plain,(
% 1.57/1.49 ~spl76_4 | spl76_46),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1441])).
% 1.57/1.49 thf(f1441,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_46)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f427,f257])).
% 1.57/1.49 thf(f427,plain,(
% 1.57/1.49 ($true != (cR @ sK38)) | spl76_46),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f425])).
% 1.57/1.49 thf(f425,definition,(
% 1.57/1.49 spl76_46 <=> ($true = (cR @ sK38))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_46])],[avatar_definition])).
% 1.57/1.49 thf(f1440,plain,(
% 1.57/1.49 ~spl76_4 | spl76_108),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1439])).
% 1.57/1.49 thf(f1439,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_108)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f728,f257])).
% 1.57/1.49 thf(f728,plain,(
% 1.57/1.49 ((cR @ sK35) != $true) | spl76_108),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f726])).
% 1.57/1.49 thf(f726,definition,(
% 1.57/1.49 spl76_108 <=> ((cR @ sK35) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_108])],[avatar_definition])).
% 1.57/1.49 thf(f1438,plain,(
% 1.57/1.49 ~spl76_19 | ~spl76_58),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1437])).
% 1.57/1.49 thf(f1437,plain,(
% 1.57/1.49 $false | (~spl76_19 | ~spl76_58)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1433])).
% 1.57/1.49 thf(f1433,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_19 | ~spl76_58)),
% 1.57/1.49 inference(superposition,[status(thm)],[f1386,f315])).
% 1.57/1.49 thf(f1386,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cS @ (sK63 @ X22)) = $false)) ) | (~spl76_19 | ~spl76_58)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1385])).
% 1.57/1.49 thf(f1385,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cS @ (sK63 @ X22)) = $false) | ($false = $true)) ) | (~spl76_19 | ~spl76_58)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f474,f315])).
% 1.57/1.49 thf(f474,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cS @ X22)) | ((cS @ (sK63 @ X22)) = $false)) ) | ~spl76_58),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f473])).
% 1.57/1.49 thf(f473,definition,(
% 1.57/1.49 spl76_58 <=> ! [X22 : $i] : (((cS @ (sK63 @ X22)) = $false) | ($false = (cS @ X22)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_58])],[avatar_definition])).
% 1.57/1.49 thf(f1416,plain,(
% 1.57/1.49 ~spl76_19 | spl76_112),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1415])).
% 1.57/1.49 thf(f1415,plain,(
% 1.57/1.49 $false | (~spl76_19 | spl76_112)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1400])).
% 1.57/1.49 thf(f1400,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_19 | spl76_112)),
% 1.57/1.49 inference(superposition,[status(thm)],[f749,f315])).
% 1.57/1.49 thf(f749,plain,(
% 1.57/1.49 ((cS @ sK12) != $true) | spl76_112),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f748])).
% 1.57/1.49 thf(f748,definition,(
% 1.57/1.49 spl76_112 <=> ((cS @ sK12) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_112])],[avatar_definition])).
% 1.57/1.49 thf(f1366,plain,(
% 1.57/1.49 ~spl76_75 | ~spl76_76),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1365])).
% 1.57/1.49 thf(f1365,plain,(
% 1.57/1.49 $false | (~spl76_75 | ~spl76_76)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1364])).
% 1.57/1.49 thf(f1364,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_75 | ~spl76_76)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f563,f558])).
% 1.57/1.49 thf(f558,plain,(
% 1.57/1.49 ($false = (cR @ sK9)) | ~spl76_75),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f556])).
% 1.57/1.49 thf(f556,definition,(
% 1.57/1.49 spl76_75 <=> ($false = (cR @ sK9))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_75])],[avatar_definition])).
% 1.57/1.49 thf(f563,plain,(
% 1.57/1.49 ($true = (cR @ sK9)) | ~spl76_76),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f561])).
% 1.57/1.49 thf(f561,definition,(
% 1.57/1.49 spl76_76 <=> ($true = (cR @ sK9))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_76])],[avatar_definition])).
% 1.57/1.49 thf(f1363,plain,(
% 1.57/1.49 ~spl76_15 | ~spl76_40),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1362])).
% 1.57/1.49 thf(f1362,plain,(
% 1.57/1.49 $false | (~spl76_15 | ~spl76_40)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f1361,f400])).
% 1.57/1.49 thf(f400,plain,(
% 1.57/1.49 ( ! [X2 : $i] : (($true != (cR @ X2))) ) | ~spl76_40),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f399])).
% 1.57/1.49 thf(f399,definition,(
% 1.57/1.49 spl76_40 <=> ! [X2 : $i] : ($true != (cR @ X2))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_40])],[avatar_definition])).
% 1.57/1.49 thf(f1361,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cR @ X0) = $true)) ) | (~spl76_15 | ~spl76_40)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1360])).
% 1.57/1.49 thf(f1360,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cR @ X0) = $true) | ($true != $true)) ) | (~spl76_15 | ~spl76_40)),
% 1.57/1.49 inference(superposition,[status(thm)],[f400,f300])).
% 1.57/1.49 thf(f300,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (((cR @ (sK6 @ X4)) = $true) | ($true = (cR @ X4))) ) | ~spl76_15),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f299])).
% 1.57/1.49 thf(f299,definition,(
% 1.57/1.49 spl76_15 <=> ! [X4 : $i] : (((cR @ (sK6 @ X4)) = $true) | ($true = (cR @ X4)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_15])],[avatar_definition])).
% 1.57/1.49 thf(f1330,plain,(
% 1.57/1.49 spl76_14 | ~spl76_55),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1329])).
% 1.57/1.49 thf(f1329,plain,(
% 1.57/1.49 $false | (spl76_14 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1323])).
% 1.57/1.49 thf(f1323,plain,(
% 1.57/1.49 ($true != $true) | (spl76_14 | ~spl76_55)),
% 1.57/1.49 inference(superposition,[status(thm)],[f297,f462])).
% 1.57/1.49 thf(f297,plain,(
% 1.57/1.49 ($true != (cP @ sK4)) | spl76_14),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f295])).
% 1.57/1.49 thf(f295,definition,(
% 1.57/1.49 spl76_14 <=> ($true = (cP @ sK4))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_14])],[avatar_definition])).
% 1.57/1.49 thf(f1319,plain,(
% 1.57/1.49 ~spl76_55 | spl76_82),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1318])).
% 1.57/1.49 thf(f1318,plain,(
% 1.57/1.49 $false | (~spl76_55 | spl76_82)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f594,f462])).
% 1.57/1.49 thf(f594,plain,(
% 1.57/1.49 ((cP @ sK8) != $true) | spl76_82),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f592])).
% 1.57/1.49 thf(f592,definition,(
% 1.57/1.49 spl76_82 <=> ((cP @ sK8) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_82])],[avatar_definition])).
% 1.57/1.49 thf(f1317,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_90),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1316])).
% 1.57/1.49 thf(f1316,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_90)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1315])).
% 1.57/1.49 thf(f1315,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_90)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f630,f337])).
% 1.57/1.49 thf(f630,plain,(
% 1.57/1.49 ((cS @ sK5) = $true) | ~spl76_90),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f628])).
% 1.57/1.49 thf(f628,definition,(
% 1.57/1.49 spl76_90 <=> ((cS @ sK5) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_90])],[avatar_definition])).
% 1.57/1.49 thf(f1314,plain,(
% 1.57/1.49 ~spl76_4 | ~spl76_17),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1313])).
% 1.57/1.49 thf(f1313,plain,(
% 1.57/1.49 $false | (~spl76_4 | ~spl76_17)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1310])).
% 1.57/1.49 thf(f1310,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_4 | ~spl76_17)),
% 1.57/1.49 inference(superposition,[status(thm)],[f257,f1296])).
% 1.57/1.49 thf(f1296,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cR @ (sK6 @ X4)))) ) | (~spl76_4 | ~spl76_17)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1295])).
% 1.57/1.49 thf(f1295,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = $true) | ($false = (cR @ (sK6 @ X4)))) ) | (~spl76_4 | ~spl76_17)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f307,f257])).
% 1.57/1.49 thf(f307,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cR @ X4)) | ($false = (cR @ (sK6 @ X4)))) ) | ~spl76_17),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f306])).
% 1.57/1.49 thf(f306,definition,(
% 1.57/1.49 spl76_17 <=> ! [X4 : $i] : (($false = (cR @ X4)) | ($false = (cR @ (sK6 @ X4))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_17])],[avatar_definition])).
% 1.57/1.49 thf(f1285,plain,(
% 1.57/1.49 ~spl76_4 | ~spl76_56),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1284])).
% 1.57/1.49 thf(f1284,plain,(
% 1.57/1.49 $false | (~spl76_4 | ~spl76_56)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1281])).
% 1.57/1.49 thf(f1281,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_4 | ~spl76_56)),
% 1.57/1.49 inference(superposition,[status(thm)],[f257,f1271])).
% 1.57/1.49 thf(f1271,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($false = (cR @ (sK27 @ X46)))) ) | (~spl76_4 | ~spl76_56)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1270])).
% 1.57/1.49 thf(f1270,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($false = (cR @ (sK27 @ X46))) | ($false = $true)) ) | (~spl76_4 | ~spl76_56)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f466,f257])).
% 1.57/1.49 thf(f466,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($false = (cR @ (sK27 @ X46))) | ((cR @ X46) = $false)) ) | ~spl76_56),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f465])).
% 1.57/1.49 thf(f465,definition,(
% 1.57/1.49 spl76_56 <=> ! [X46 : $i] : (($false = (cR @ (sK27 @ X46))) | ((cR @ X46) = $false))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_56])],[avatar_definition])).
% 1.57/1.49 thf(f1269,plain,(
% 1.57/1.49 ~spl76_62 | ~spl76_109),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1268])).
% 1.57/1.49 thf(f1268,plain,(
% 1.57/1.49 $false | (~spl76_62 | ~spl76_109)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1267])).
% 1.57/1.49 thf(f1267,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_62 | ~spl76_109)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f734,f496])).
% 1.57/1.49 thf(f734,plain,(
% 1.57/1.49 ((cP @ sK60) = $true) | ~spl76_109),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f732])).
% 1.57/1.49 thf(f1266,plain,(
% 1.57/1.49 ~spl76_79 | ~spl76_80),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1265])).
% 1.57/1.49 thf(f1265,plain,(
% 1.57/1.49 $false | (~spl76_79 | ~spl76_80)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1264])).
% 1.57/1.49 thf(f1264,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_79 | ~spl76_80)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f585,f580])).
% 1.57/1.49 thf(f580,plain,(
% 1.57/1.49 ($false = (cR @ sK22)) | ~spl76_79),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f578])).
% 1.57/1.49 thf(f578,definition,(
% 1.57/1.49 spl76_79 <=> ($false = (cR @ sK22))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_79])],[avatar_definition])).
% 1.57/1.49 thf(f585,plain,(
% 1.57/1.49 ($true = (cR @ sK22)) | ~spl76_80),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f583])).
% 1.57/1.49 thf(f583,definition,(
% 1.57/1.49 spl76_80 <=> ($true = (cR @ sK22))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_80])],[avatar_definition])).
% 1.57/1.49 thf(f1262,plain,(
% 1.57/1.49 ~spl76_16 | ~spl76_57),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1261])).
% 1.57/1.49 thf(f1261,plain,(
% 1.57/1.49 $false | (~spl76_16 | ~spl76_57)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f1260,f303])).
% 1.57/1.49 thf(f303,plain,(
% 1.57/1.49 ( ! [X1 : $i] : (((cS @ X1) != $true)) ) | ~spl76_16),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f302])).
% 1.57/1.49 thf(f302,definition,(
% 1.57/1.49 spl76_16 <=> ! [X1 : $i] : ((cS @ X1) != $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_16])],[avatar_definition])).
% 1.57/1.49 thf(f1260,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cS @ X0) = $true)) ) | (~spl76_16 | ~spl76_57)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1259])).
% 1.57/1.49 thf(f1259,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cS @ X0) = $true) | ($true != $true)) ) | (~spl76_16 | ~spl76_57)),
% 1.57/1.49 inference(superposition,[status(thm)],[f303,f470])).
% 1.57/1.49 thf(f470,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cS @ (sK63 @ X22)) = $true) | ($true = (cS @ X22))) ) | ~spl76_57),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f469])).
% 1.57/1.49 thf(f469,definition,(
% 1.57/1.49 spl76_57 <=> ! [X22 : $i] : (((cS @ (sK63 @ X22)) = $true) | ($true = (cS @ X22)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_57])],[avatar_definition])).
% 1.57/1.49 thf(f1252,plain,(
% 1.57/1.49 ~spl76_16 | ~spl76_107),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1251])).
% 1.57/1.49 thf(f1251,plain,(
% 1.57/1.49 $false | (~spl76_16 | ~spl76_107)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1250])).
% 1.57/1.49 thf(f1250,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_16 | ~spl76_107)),
% 1.57/1.49 inference(superposition,[status(thm)],[f303,f722])).
% 1.57/1.49 thf(f722,plain,(
% 1.57/1.49 ((cS @ sK24) = $true) | ~spl76_107),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f720])).
% 1.57/1.49 thf(f720,definition,(
% 1.57/1.49 spl76_107 <=> ((cS @ sK24) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_107])],[avatar_definition])).
% 1.57/1.49 thf(f1221,plain,(
% 1.57/1.49 ~spl76_62 | ~spl76_70),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1220])).
% 1.57/1.49 thf(f1220,plain,(
% 1.57/1.49 $false | (~spl76_62 | ~spl76_70)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1219])).
% 1.57/1.49 thf(f1219,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_62 | ~spl76_70)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f534,f496])).
% 1.57/1.49 thf(f534,plain,(
% 1.57/1.49 ($true = (cP @ sK61)) | ~spl76_70),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f532])).
% 1.57/1.49 thf(f532,definition,(
% 1.57/1.49 spl76_70 <=> ($true = (cP @ sK61))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_70])],[avatar_definition])).
% 1.57/1.49 thf(f1212,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_107),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1211])).
% 1.57/1.49 thf(f1211,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_107)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1210])).
% 1.57/1.49 thf(f1210,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_107)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f722,f337])).
% 1.57/1.49 thf(f1209,plain,(
% 1.57/1.49 ~spl76_40 | ~spl76_54),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1208])).
% 1.57/1.49 thf(f1208,plain,(
% 1.57/1.49 $false | (~spl76_40 | ~spl76_54)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f1207,f400])).
% 1.57/1.49 thf(f1207,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cR @ X0) = $true)) ) | (~spl76_40 | ~spl76_54)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1206])).
% 1.57/1.49 thf(f1206,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cR @ X0) = $true) | ($true != $true)) ) | (~spl76_40 | ~spl76_54)),
% 1.57/1.49 inference(superposition,[status(thm)],[f400,f459])).
% 1.57/1.49 thf(f459,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (((cR @ (sK27 @ X46)) = $true) | ((cR @ X46) = $true)) ) | ~spl76_54),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f458])).
% 1.57/1.49 thf(f458,definition,(
% 1.57/1.49 spl76_54 <=> ! [X46 : $i] : (((cR @ X46) = $true) | ((cR @ (sK27 @ X46)) = $true))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_54])],[avatar_definition])).
% 1.57/1.49 thf(f1202,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_57),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1201])).
% 1.57/1.49 thf(f1201,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_57)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1200])).
% 1.57/1.49 thf(f1200,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_57)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f1199,f337])).
% 1.57/1.49 thf(f1199,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($true = (cS @ X22))) ) | (~spl76_25 | ~spl76_57)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1198])).
% 1.57/1.49 thf(f1198,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($true = (cS @ X22)) | ($false = $true)) ) | (~spl76_25 | ~spl76_57)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f470,f337])).
% 1.57/1.49 thf(f1197,plain,(
% 1.57/1.49 ~spl76_20 | spl76_69),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1196])).
% 1.57/1.49 thf(f1196,plain,(
% 1.57/1.49 $false | (~spl76_20 | spl76_69)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1195])).
% 1.57/1.49 thf(f1195,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_20 | spl76_69)),
% 1.57/1.49 inference(superposition,[status(thm)],[f530,f318])).
% 1.57/1.49 thf(f530,plain,(
% 1.57/1.49 ($true != (cQ @ sK62)) | spl76_69),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f528])).
% 1.57/1.49 thf(f528,definition,(
% 1.57/1.49 spl76_69 <=> ($true = (cQ @ sK62))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_69])],[avatar_definition])).
% 1.57/1.49 thf(f1185,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_101),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1184])).
% 1.57/1.49 thf(f1184,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_101)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1181])).
% 1.57/1.49 thf(f1181,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_101)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f686,f337])).
% 1.57/1.49 thf(f686,plain,(
% 1.57/1.49 ((cS @ sK25) = $true) | ~spl76_101),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f684])).
% 1.57/1.49 thf(f684,definition,(
% 1.57/1.49 spl76_101 <=> ((cS @ sK25) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_101])],[avatar_definition])).
% 1.57/1.49 thf(f1175,plain,(
% 1.57/1.49 ~spl76_41 | ~spl76_43),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1174])).
% 1.57/1.49 thf(f1174,plain,(
% 1.57/1.49 $false | (~spl76_41 | ~spl76_43)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1173])).
% 1.57/1.49 thf(f1173,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_41 | ~spl76_43)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f406,f415])).
% 1.57/1.49 thf(f415,plain,(
% 1.57/1.49 ((cS @ sK58) = $false) | ~spl76_43),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f413])).
% 1.57/1.49 thf(f413,definition,(
% 1.57/1.49 spl76_43 <=> ((cS @ sK58) = $false)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_43])],[avatar_definition])).
% 1.57/1.49 thf(f406,plain,(
% 1.57/1.49 ((cS @ sK58) = $true) | ~spl76_41),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f404])).
% 1.57/1.49 thf(f404,definition,(
% 1.57/1.49 spl76_41 <=> ((cS @ sK58) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_41])],[avatar_definition])).
% 1.57/1.49 thf(f1172,plain,(
% 1.57/1.49 ~spl76_20 | spl76_42),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1171])).
% 1.57/1.49 thf(f1171,plain,(
% 1.57/1.49 $false | (~spl76_20 | spl76_42)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1170])).
% 1.57/1.49 thf(f1170,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_20 | spl76_42)),
% 1.57/1.49 inference(superposition,[status(thm)],[f410,f318])).
% 1.57/1.49 thf(f410,plain,(
% 1.57/1.49 ((cQ @ sK59) != $true) | spl76_42),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f408])).
% 1.57/1.49 thf(f408,definition,(
% 1.57/1.49 spl76_42 <=> ((cQ @ sK59) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_42])],[avatar_definition])).
% 1.57/1.49 thf(f1149,plain,(
% 1.57/1.49 ~spl76_55 | spl76_78),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1148])).
% 1.57/1.49 thf(f1148,plain,(
% 1.57/1.49 $false | (~spl76_55 | spl76_78)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f576,f462])).
% 1.57/1.49 thf(f576,plain,(
% 1.57/1.49 ($true != (cP @ sK23)) | spl76_78),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f574])).
% 1.57/1.49 thf(f574,definition,(
% 1.57/1.49 spl76_78 <=> ($true = (cP @ sK23))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_78])],[avatar_definition])).
% 1.57/1.49 thf(f1147,plain,(
% 1.57/1.49 ~spl76_55 | spl76_100),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1146])).
% 1.57/1.49 thf(f1146,plain,(
% 1.57/1.49 $false | (~spl76_55 | spl76_100)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f682,f462])).
% 1.57/1.49 thf(f682,plain,(
% 1.57/1.49 ((cP @ sK26) != $true) | spl76_100),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f680])).
% 1.57/1.49 thf(f680,definition,(
% 1.57/1.49 spl76_100 <=> ((cP @ sK26) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_100])],[avatar_definition])).
% 1.57/1.49 thf(f1144,plain,(
% 1.57/1.49 ~spl76_2 | ~spl76_25),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1143])).
% 1.57/1.49 thf(f1143,plain,(
% 1.57/1.49 $false | (~spl76_2 | ~spl76_25)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1142])).
% 1.57/1.49 thf(f1142,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_2 | ~spl76_25)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f250,f337])).
% 1.57/1.49 thf(f250,plain,(
% 1.57/1.49 ((cS @ sK19) = $true) | ~spl76_2),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f248])).
% 1.57/1.49 thf(f248,definition,(
% 1.57/1.49 spl76_2 <=> ((cS @ sK19) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_2])],[avatar_definition])).
% 1.57/1.49 thf(f1134,plain,(
% 1.57/1.49 ~spl76_24 | ~spl76_55),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1133])).
% 1.57/1.49 thf(f1133,plain,(
% 1.57/1.49 $false | (~spl76_24 | ~spl76_55)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f334,f462])).
% 1.57/1.49 thf(f1132,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_88),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1131])).
% 1.57/1.49 thf(f1131,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_88)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1130])).
% 1.57/1.49 thf(f1130,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_88)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f621,f337])).
% 1.57/1.49 thf(f621,plain,(
% 1.57/1.49 ($true = (cS @ sK13)) | ~spl76_88),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f619])).
% 1.57/1.49 thf(f619,definition,(
% 1.57/1.49 spl76_88 <=> ($true = (cS @ sK13))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_88])],[avatar_definition])).
% 1.57/1.49 thf(f1129,plain,(
% 1.57/1.49 ~spl76_55 | ~spl76_68),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1128])).
% 1.57/1.49 thf(f1128,plain,(
% 1.57/1.49 $false | (~spl76_55 | ~spl76_68)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1124])).
% 1.57/1.49 thf(f1124,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_55 | ~spl76_68)),
% 1.57/1.49 inference(superposition,[status(thm)],[f1071,f462])).
% 1.57/1.49 thf(f1071,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cP @ (sK30 @ X4)))) ) | (~spl76_55 | ~spl76_68)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1070])).
% 1.57/1.49 thf(f1070,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cP @ (sK30 @ X4))) | ($false = $true)) ) | (~spl76_55 | ~spl76_68)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f525,f462])).
% 1.57/1.49 thf(f525,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (((cP @ X4) = $false) | ($false = (cP @ (sK30 @ X4)))) ) | ~spl76_68),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f524])).
% 1.57/1.49 thf(f524,definition,(
% 1.57/1.49 spl76_68 <=> ! [X4 : $i] : (($false = (cP @ (sK30 @ X4))) | ((cP @ X4) = $false))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_68])],[avatar_definition])).
% 1.57/1.49 thf(f1123,plain,(
% 1.57/1.49 ~spl76_13 | ~spl76_55),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1122])).
% 1.57/1.49 thf(f1122,plain,(
% 1.57/1.49 $false | (~spl76_13 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1118])).
% 1.57/1.49 thf(f1118,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_13 | ~spl76_55)),
% 1.57/1.49 inference(superposition,[status(thm)],[f1069,f462])).
% 1.57/1.49 thf(f1069,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (((cP @ (sK51 @ X46)) = $false)) ) | (~spl76_13 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1068])).
% 1.57/1.49 thf(f1068,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($false = $true) | ((cP @ (sK51 @ X46)) = $false)) ) | (~spl76_13 | ~spl76_55)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f292,f462])).
% 1.57/1.49 thf(f292,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (((cP @ (sK51 @ X46)) = $false) | ($false = (cP @ X46))) ) | ~spl76_13),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f291])).
% 1.57/1.49 thf(f291,definition,(
% 1.57/1.49 spl76_13 <=> ! [X46 : $i] : (($false = (cP @ X46)) | ((cP @ (sK51 @ X46)) = $false))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_13])],[avatar_definition])).
% 1.57/1.49 thf(f1117,plain,(
% 1.57/1.49 ~spl76_55 | spl76_84),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1116])).
% 1.57/1.49 thf(f1116,plain,(
% 1.57/1.49 $false | (~spl76_55 | spl76_84)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1115])).
% 1.57/1.49 thf(f1115,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_55 | spl76_84)),
% 1.57/1.49 inference(superposition,[status(thm)],[f604,f462])).
% 1.57/1.49 thf(f604,plain,(
% 1.57/1.49 ($true != (cP @ sK11)) | spl76_84),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f602])).
% 1.57/1.49 thf(f602,definition,(
% 1.57/1.49 spl76_84 <=> ($true = (cP @ sK11))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_84])],[avatar_definition])).
% 1.57/1.49 thf(f1101,plain,(
% 1.57/1.49 spl76_48 | ~spl76_55),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1100])).
% 1.57/1.49 thf(f1100,plain,(
% 1.57/1.49 $false | (spl76_48 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1093])).
% 1.57/1.49 thf(f1093,plain,(
% 1.57/1.49 ($true != $true) | (spl76_48 | ~spl76_55)),
% 1.57/1.49 inference(superposition,[status(thm)],[f436,f462])).
% 1.57/1.49 thf(f436,plain,(
% 1.57/1.49 ((cP @ sK16) != $true) | spl76_48),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f434])).
% 1.57/1.49 thf(f434,definition,(
% 1.57/1.49 spl76_48 <=> ((cP @ sK16) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_48])],[avatar_definition])).
% 1.57/1.49 thf(f1099,plain,(
% 1.57/1.49 spl76_3 | ~spl76_55),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1098])).
% 1.57/1.49 thf(f1098,plain,(
% 1.57/1.49 $false | (spl76_3 | ~spl76_55)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1094])).
% 1.57/1.49 thf(f1094,plain,(
% 1.57/1.49 ($true != $true) | (spl76_3 | ~spl76_55)),
% 1.57/1.49 inference(superposition,[status(thm)],[f254,f462])).
% 1.57/1.49 thf(f254,plain,(
% 1.57/1.49 ((cP @ sK20) != $true) | spl76_3),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f252])).
% 1.57/1.49 thf(f252,definition,(
% 1.57/1.49 spl76_3 <=> ((cP @ sK20) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_3])],[avatar_definition])).
% 1.57/1.49 thf(f1078,plain,(
% 1.57/1.49 ~spl76_55 | spl76_87),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1077])).
% 1.57/1.49 thf(f1077,plain,(
% 1.57/1.49 $false | (~spl76_55 | spl76_87)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f617,f462])).
% 1.57/1.49 thf(f617,plain,(
% 1.57/1.49 ((cP @ sK14) != $true) | spl76_87),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f615])).
% 1.57/1.49 thf(f615,definition,(
% 1.57/1.49 spl76_87 <=> ((cP @ sK14) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_87])],[avatar_definition])).
% 1.57/1.49 thf(f1064,plain,(
% 1.57/1.49 ~spl76_62 | ~spl76_65),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1063])).
% 1.57/1.49 thf(f1063,plain,(
% 1.57/1.49 $false | (~spl76_62 | ~spl76_65)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1062])).
% 1.57/1.49 thf(f1062,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_62 | ~spl76_65)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f509,f496])).
% 1.57/1.49 thf(f509,plain,(
% 1.57/1.49 ((cP @ sK55) = $true) | ~spl76_65),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f507])).
% 1.57/1.49 thf(f507,definition,(
% 1.57/1.49 spl76_65 <=> ((cP @ sK55) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_65])],[avatar_definition])).
% 1.57/1.49 thf(f1051,plain,(
% 1.57/1.49 ~spl76_20 | ~spl76_31),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1050])).
% 1.57/1.49 thf(f1050,plain,(
% 1.57/1.49 $false | (~spl76_20 | ~spl76_31)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1046])).
% 1.57/1.49 thf(f1046,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_20 | ~spl76_31)),
% 1.57/1.49 inference(superposition,[status(thm)],[f1020,f318])).
% 1.57/1.49 thf(f1020,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (($false = (cQ @ (sK72 @ X16)))) ) | (~spl76_20 | ~spl76_31)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1019])).
% 1.57/1.49 thf(f1019,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (($false = (cQ @ (sK72 @ X16))) | ($false = $true)) ) | (~spl76_20 | ~spl76_31)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f362,f318])).
% 1.57/1.49 thf(f362,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (($false = (cQ @ (sK72 @ X16))) | ($false = (cQ @ X16))) ) | ~spl76_31),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f361])).
% 1.57/1.49 thf(f361,definition,(
% 1.57/1.49 spl76_31 <=> ! [X16 : $i] : (($false = (cQ @ (sK72 @ X16))) | ($false = (cQ @ X16)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_31])],[avatar_definition])).
% 1.57/1.49 thf(f1013,plain,(
% 1.57/1.49 ~spl76_4 | ~spl76_89),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f1012])).
% 1.57/1.49 thf(f1012,plain,(
% 1.57/1.49 $false | (~spl76_4 | ~spl76_89)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f1008])).
% 1.57/1.49 thf(f1008,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_4 | ~spl76_89)),
% 1.57/1.49 inference(superposition,[status(thm)],[f990,f257])).
% 1.57/1.49 thf(f990,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cR @ (sK15 @ X22)))) ) | (~spl76_4 | ~spl76_89)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f989])).
% 1.57/1.49 thf(f989,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cR @ (sK15 @ X22))) | ($false = $true)) ) | (~spl76_4 | ~spl76_89)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f625,f257])).
% 1.57/1.49 thf(f625,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cR @ (sK15 @ X22))) | ((cR @ X22) = $false)) ) | ~spl76_89),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f624])).
% 1.57/1.49 thf(f624,definition,(
% 1.57/1.49 spl76_89 <=> ! [X22 : $i] : (($false = (cR @ (sK15 @ X22))) | ((cR @ X22) = $false))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_89])],[avatar_definition])).
% 1.57/1.49 thf(f993,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_110),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f992])).
% 1.57/1.49 thf(f992,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_110)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f991])).
% 1.57/1.49 thf(f991,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_110)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f740,f326])).
% 1.57/1.49 thf(f740,plain,(
% 1.57/1.49 ($true = (cQ @ sK49)) | ~spl76_110),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f738])).
% 1.57/1.49 thf(f738,definition,(
% 1.57/1.49 spl76_110 <=> ($true = (cQ @ sK49))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_110])],[avatar_definition])).
% 1.57/1.49 thf(f987,plain,(
% 1.57/1.49 ~spl76_7 | ~spl76_29),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f986])).
% 1.57/1.49 thf(f986,plain,(
% 1.57/1.49 $false | (~spl76_7 | ~spl76_29)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f985])).
% 1.57/1.49 thf(f985,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_7 | ~spl76_29)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f355,f269])).
% 1.57/1.49 thf(f355,plain,(
% 1.57/1.49 ($true = (cR @ sK70)) | ~spl76_29),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f353])).
% 1.57/1.49 thf(f353,definition,(
% 1.57/1.49 spl76_29 <=> ($true = (cR @ sK70))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_29])],[avatar_definition])).
% 1.57/1.49 thf(f973,plain,(
% 1.57/1.49 ~spl76_10 | ~spl76_24),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f972])).
% 1.57/1.49 thf(f972,plain,(
% 1.57/1.49 $false | (~spl76_10 | ~spl76_24)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f971,f334])).
% 1.57/1.49 thf(f971,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl76_10 | ~spl76_24)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f970])).
% 1.57/1.49 thf(f970,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (($true != $true) | ((cP @ X0) = $true)) ) | (~spl76_10 | ~spl76_24)),
% 1.57/1.49 inference(superposition,[status(thm)],[f334,f281])).
% 1.57/1.49 thf(f281,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (((cP @ (sK51 @ X46)) = $true) | ((cP @ X46) = $true)) ) | ~spl76_10),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f280])).
% 1.57/1.49 thf(f280,definition,(
% 1.57/1.49 spl76_10 <=> ! [X46 : $i] : (((cP @ (sK51 @ X46)) = $true) | ((cP @ X46) = $true))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_10])],[avatar_definition])).
% 1.57/1.49 thf(f963,plain,(
% 1.57/1.49 ~spl76_40 | ~spl76_86),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f962])).
% 1.57/1.49 thf(f962,plain,(
% 1.57/1.49 $false | (~spl76_40 | ~spl76_86)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f961,f400])).
% 1.57/1.49 thf(f961,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cR @ X22) = $true)) ) | (~spl76_40 | ~spl76_86)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f613,f400])).
% 1.57/1.49 thf(f613,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($true = (cR @ (sK15 @ X22))) | ((cR @ X22) = $true)) ) | ~spl76_86),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f612])).
% 1.57/1.49 thf(f612,definition,(
% 1.57/1.49 spl76_86 <=> ! [X22 : $i] : (((cR @ X22) = $true) | ($true = (cR @ (sK15 @ X22))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_86])],[avatar_definition])).
% 1.57/1.49 thf(f944,plain,(
% 1.57/1.49 ~spl76_7 | ~spl76_86),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f943])).
% 1.57/1.49 thf(f943,plain,(
% 1.57/1.49 $false | (~spl76_7 | ~spl76_86)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f942])).
% 1.57/1.49 thf(f942,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_7 | ~spl76_86)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f941,f269])).
% 1.57/1.49 thf(f941,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (((cR @ X22) = $true)) ) | (~spl76_7 | ~spl76_86)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f940])).
% 1.57/1.49 thf(f940,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = $true) | ((cR @ X22) = $true)) ) | (~spl76_7 | ~spl76_86)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f613,f269])).
% 1.57/1.49 thf(f938,plain,(
% 1.57/1.49 ~spl76_60 | ~spl76_63),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f937])).
% 1.57/1.49 thf(f937,plain,(
% 1.57/1.49 $false | (~spl76_60 | ~spl76_63)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f936])).
% 1.57/1.49 thf(f936,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_60 | ~spl76_63)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f500,f488])).
% 1.57/1.49 thf(f488,plain,(
% 1.57/1.49 ($false = (cP @ sK46)) | ~spl76_60),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f486])).
% 1.57/1.49 thf(f486,definition,(
% 1.57/1.49 spl76_60 <=> ($false = (cP @ sK46))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_60])],[avatar_definition])).
% 1.57/1.49 thf(f500,plain,(
% 1.57/1.49 ((cP @ sK46) = $true) | ~spl76_63),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f498])).
% 1.57/1.49 thf(f498,definition,(
% 1.57/1.49 spl76_63 <=> ((cP @ sK46) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_63])],[avatar_definition])).
% 1.57/1.49 thf(f931,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_61),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f930])).
% 1.57/1.49 thf(f930,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_61)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f926])).
% 1.57/1.49 thf(f926,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_61)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f492,f326])).
% 1.57/1.49 thf(f492,plain,(
% 1.57/1.49 ((cQ @ sK48) = $true) | ~spl76_61),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f490])).
% 1.57/1.49 thf(f490,definition,(
% 1.57/1.49 spl76_61 <=> ((cQ @ sK48) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_61])],[avatar_definition])).
% 1.57/1.49 thf(f918,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_112),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f917])).
% 1.57/1.49 thf(f917,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_112)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f916])).
% 1.57/1.49 thf(f916,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_112)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f750,f337])).
% 1.57/1.49 thf(f750,plain,(
% 1.57/1.49 ((cS @ sK12) = $true) | ~spl76_112),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f748])).
% 1.57/1.49 thf(f912,plain,(
% 1.57/1.49 ~spl76_83 | ~spl76_85),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f911])).
% 1.57/1.49 thf(f911,plain,(
% 1.57/1.49 $false | (~spl76_83 | ~spl76_85)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f910])).
% 1.57/1.49 thf(f910,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_83 | ~spl76_85)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f600,f609])).
% 1.57/1.49 thf(f609,plain,(
% 1.57/1.49 ($false = (cR @ sK10)) | ~spl76_85),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f607])).
% 1.57/1.49 thf(f607,definition,(
% 1.57/1.49 spl76_85 <=> ($false = (cR @ sK10))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_85])],[avatar_definition])).
% 1.57/1.49 thf(f600,plain,(
% 1.57/1.49 ((cR @ sK10) = $true) | ~spl76_83),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f598])).
% 1.57/1.49 thf(f598,definition,(
% 1.57/1.49 spl76_83 <=> ((cR @ sK10) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_83])],[avatar_definition])).
% 1.57/1.49 thf(f901,plain,(
% 1.57/1.49 ~spl76_7 | ~spl76_18),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f900])).
% 1.57/1.49 thf(f900,plain,(
% 1.57/1.49 $false | (~spl76_7 | ~spl76_18)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f899])).
% 1.57/1.49 thf(f899,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_7 | ~spl76_18)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f312,f269])).
% 1.57/1.49 thf(f312,plain,(
% 1.57/1.49 ((cR @ sK75) = $true) | ~spl76_18),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f310])).
% 1.57/1.49 thf(f310,definition,(
% 1.57/1.49 spl76_18 <=> ((cR @ sK75) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_18])],[avatar_definition])).
% 1.57/1.49 thf(f898,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_95),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f897])).
% 1.57/1.49 thf(f897,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_95)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f896])).
% 1.57/1.49 thf(f896,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_95)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f654,f326])).
% 1.57/1.49 thf(f654,plain,(
% 1.57/1.49 ((cQ @ sK29) = $true) | ~spl76_95),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f652])).
% 1.57/1.49 thf(f652,definition,(
% 1.57/1.49 spl76_95 <=> ((cQ @ sK29) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_95])],[avatar_definition])).
% 1.57/1.49 thf(f888,plain,(
% 1.57/1.49 ~spl76_11 | ~spl76_30),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f887])).
% 1.57/1.49 thf(f887,plain,(
% 1.57/1.49 $false | (~spl76_11 | ~spl76_30)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f886,f284])).
% 1.57/1.49 thf(f886,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (($true = (cQ @ (sK72 @ X16)))) ) | (~spl76_11 | ~spl76_30)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f358,f284])).
% 1.57/1.49 thf(f358,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (($true = (cQ @ (sK72 @ X16))) | ((cQ @ X16) = $true)) ) | ~spl76_30),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f357])).
% 1.57/1.49 thf(f357,definition,(
% 1.57/1.49 spl76_30 <=> ! [X16 : $i] : (($true = (cQ @ (sK72 @ X16))) | ((cQ @ X16) = $true))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_30])],[avatar_definition])).
% 1.57/1.49 thf(f883,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_30),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f882])).
% 1.57/1.49 thf(f882,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_30)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f881])).
% 1.57/1.49 thf(f881,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_30)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f880,f326])).
% 1.57/1.49 thf(f880,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (((cQ @ X16) = $true)) ) | (~spl76_22 | ~spl76_30)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f879])).
% 1.57/1.49 thf(f879,plain,(
% 1.57/1.49 ( ! [X16 : $i] : (((cQ @ X16) = $true) | ($false = $true)) ) | (~spl76_22 | ~spl76_30)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f358,f326])).
% 1.57/1.49 thf(f874,plain,(
% 1.57/1.49 ~spl76_25 | ~spl76_99),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f873])).
% 1.57/1.49 thf(f873,plain,(
% 1.57/1.49 $false | (~spl76_25 | ~spl76_99)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f871])).
% 1.57/1.49 thf(f871,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_25 | ~spl76_99)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f676,f337])).
% 1.57/1.49 thf(f676,plain,(
% 1.57/1.49 ((cS @ sK17) = $true) | ~spl76_99),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f674])).
% 1.57/1.49 thf(f674,definition,(
% 1.57/1.49 spl76_99 <=> ((cS @ sK17) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_99])],[avatar_definition])).
% 1.57/1.49 thf(f863,plain,(
% 1.57/1.49 ~spl76_16 | ~spl76_51),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f862])).
% 1.57/1.49 thf(f862,plain,(
% 1.57/1.49 $false | (~spl76_16 | ~spl76_51)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f861,f303])).
% 1.57/1.49 thf(f861,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (((cS @ X4) = $true)) ) | (~spl76_16 | ~spl76_51)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f447,f303])).
% 1.57/1.49 thf(f447,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (((cS @ (sK54 @ X4)) = $true) | ((cS @ X4) = $true)) ) | ~spl76_51),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f446])).
% 1.57/1.49 thf(f446,definition,(
% 1.57/1.49 spl76_51 <=> ! [X4 : $i] : (((cS @ (sK54 @ X4)) = $true) | ((cS @ X4) = $true))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_51])],[avatar_definition])).
% 1.57/1.49 thf(f858,plain,(
% 1.57/1.49 ~spl76_26 | ~spl76_27),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f857])).
% 1.57/1.49 thf(f857,plain,(
% 1.57/1.49 $false | (~spl76_26 | ~spl76_27)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f856])).
% 1.57/1.49 thf(f856,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_26 | ~spl76_27)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f341,f346])).
% 1.57/1.49 thf(f346,plain,(
% 1.57/1.49 ((cS @ sK57) = $false) | ~spl76_27),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f344])).
% 1.57/1.49 thf(f344,definition,(
% 1.57/1.49 spl76_27 <=> ((cS @ sK57) = $false)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_27])],[avatar_definition])).
% 1.57/1.49 thf(f341,plain,(
% 1.57/1.49 ((cS @ sK57) = $true) | ~spl76_26),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f339])).
% 1.57/1.49 thf(f339,definition,(
% 1.57/1.49 spl76_26 <=> ((cS @ sK57) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_26])],[avatar_definition])).
% 1.57/1.49 thf(f855,plain,(
% 1.57/1.49 ~spl76_18 | ~spl76_40),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f854])).
% 1.57/1.49 thf(f854,plain,(
% 1.57/1.49 $false | (~spl76_18 | ~spl76_40)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f312,f400])).
% 1.57/1.49 thf(f851,plain,(
% 1.57/1.49 ~spl76_6 | ~spl76_8),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f850])).
% 1.57/1.49 thf(f850,plain,(
% 1.57/1.49 $false | (~spl76_6 | ~spl76_8)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f849])).
% 1.57/1.49 thf(f849,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_6 | ~spl76_8)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f273,f265])).
% 1.57/1.49 thf(f265,plain,(
% 1.57/1.49 ($false = (cR @ sK21)) | ~spl76_6),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f263])).
% 1.57/1.49 thf(f263,definition,(
% 1.57/1.49 spl76_6 <=> ($false = (cR @ sK21))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_6])],[avatar_definition])).
% 1.57/1.49 thf(f273,plain,(
% 1.57/1.49 ($true = (cR @ sK21)) | ~spl76_8),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f271])).
% 1.57/1.49 thf(f271,definition,(
% 1.57/1.49 spl76_8 <=> ($true = (cR @ sK21))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_8])],[avatar_definition])).
% 1.57/1.49 thf(f846,plain,(
% 1.57/1.49 ~spl76_40 | ~spl76_49),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f845])).
% 1.57/1.49 thf(f845,plain,(
% 1.57/1.49 $false | (~spl76_40 | ~spl76_49)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f844,f400])).
% 1.57/1.49 thf(f844,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (((cR @ (sK18 @ X28)) = $true)) ) | (~spl76_40 | ~spl76_49)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f439,f400])).
% 1.57/1.49 thf(f439,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($true = (cR @ X28)) | ((cR @ (sK18 @ X28)) = $true)) ) | ~spl76_49),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f438])).
% 1.57/1.49 thf(f438,definition,(
% 1.57/1.49 spl76_49 <=> ! [X28 : $i] : (((cR @ (sK18 @ X28)) = $true) | ($true = (cR @ X28)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_49])],[avatar_definition])).
% 1.57/1.49 thf(f836,plain,(
% 1.57/1.49 ~spl76_62 | ~spl76_102),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f835])).
% 1.57/1.49 thf(f835,plain,(
% 1.57/1.49 $false | (~spl76_62 | ~spl76_102)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f833])).
% 1.57/1.49 thf(f833,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_62 | ~spl76_102)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f692,f496])).
% 1.57/1.49 thf(f692,plain,(
% 1.57/1.49 ((cP @ sK53) = $true) | ~spl76_102),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f690])).
% 1.57/1.49 thf(f690,definition,(
% 1.57/1.49 spl76_102 <=> ((cP @ sK53) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_102])],[avatar_definition])).
% 1.57/1.49 thf(f829,plain,(
% 1.57/1.49 ~spl76_4 | ~spl76_40),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f828])).
% 1.57/1.49 thf(f828,plain,(
% 1.57/1.49 $false | (~spl76_4 | ~spl76_40)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f400,f257])).
% 1.57/1.49 thf(f827,plain,(
% 1.57/1.49 ~spl76_19 | ~spl76_53),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f826])).
% 1.57/1.49 thf(f826,plain,(
% 1.57/1.49 $false | (~spl76_19 | ~spl76_53)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f823])).
% 1.57/1.49 thf(f823,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_19 | ~spl76_53)),
% 1.57/1.49 inference(superposition,[status(thm)],[f315,f821])).
% 1.57/1.49 thf(f821,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cS @ (sK54 @ X4)))) ) | (~spl76_19 | ~spl76_53)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f820])).
% 1.57/1.49 thf(f820,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cS @ (sK54 @ X4))) | ($false = $true)) ) | (~spl76_19 | ~spl76_53)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f455,f315])).
% 1.57/1.49 thf(f455,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($false = (cS @ (sK54 @ X4))) | ((cS @ X4) = $false)) ) | ~spl76_53),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f454])).
% 1.57/1.49 thf(f454,definition,(
% 1.57/1.49 spl76_53 <=> ! [X4 : $i] : (((cS @ X4) = $false) | ($false = (cS @ (sK54 @ X4))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_53])],[avatar_definition])).
% 1.57/1.49 thf(f819,plain,(
% 1.57/1.49 ~spl76_24 | ~spl76_67),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f818])).
% 1.57/1.49 thf(f818,plain,(
% 1.57/1.49 $false | (~spl76_24 | ~spl76_67)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f817,f334])).
% 1.57/1.49 thf(f817,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | (~spl76_24 | ~spl76_67)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f816])).
% 1.57/1.49 thf(f816,plain,(
% 1.57/1.49 ( ! [X0 : $i] : (((cP @ X0) = $true) | ($true != $true)) ) | (~spl76_24 | ~spl76_67)),
% 1.57/1.49 inference(superposition,[status(thm)],[f334,f521])).
% 1.57/1.49 thf(f521,plain,(
% 1.57/1.49 ( ! [X4 : $i] : (($true = (cP @ (sK30 @ X4))) | ((cP @ X4) = $true)) ) | ~spl76_67),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f520])).
% 1.57/1.49 thf(f520,definition,(
% 1.57/1.49 spl76_67 <=> ! [X4 : $i] : (((cP @ X4) = $true) | ($true = (cP @ (sK30 @ X4))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_67])],[avatar_definition])).
% 1.57/1.49 thf(f815,plain,(
% 1.57/1.49 ~spl76_4 | ~spl76_50),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f814])).
% 1.57/1.49 thf(f814,plain,(
% 1.57/1.49 $false | (~spl76_4 | ~spl76_50)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f810])).
% 1.57/1.49 thf(f810,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_4 | ~spl76_50)),
% 1.57/1.49 inference(superposition,[status(thm)],[f768,f257])).
% 1.57/1.49 thf(f768,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($false = (cR @ (sK18 @ X28)))) ) | (~spl76_4 | ~spl76_50)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f767])).
% 1.57/1.49 thf(f767,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($false = (cR @ (sK18 @ X28))) | ($false = $true)) ) | (~spl76_4 | ~spl76_50)),
% 1.57/1.49 inference(backward_demodulation,[status(thm)],[f443,f257])).
% 1.57/1.49 thf(f443,plain,(
% 1.57/1.49 ( ! [X28 : $i] : (($false = (cR @ (sK18 @ X28))) | ($false = (cR @ X28))) ) | ~spl76_50),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f442])).
% 1.57/1.49 thf(f442,definition,(
% 1.57/1.49 spl76_50 <=> ! [X28 : $i] : (($false = (cR @ X28)) | ($false = (cR @ (sK18 @ X28))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_50])],[avatar_definition])).
% 1.57/1.49 thf(f809,plain,(
% 1.57/1.49 ~spl76_4 | spl76_111),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f808])).
% 1.57/1.49 thf(f808,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_111)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f807])).
% 1.57/1.49 thf(f807,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_4 | spl76_111)),
% 1.57/1.49 inference(superposition,[status(thm)],[f744,f257])).
% 1.57/1.49 thf(f744,plain,(
% 1.57/1.49 ($true != (cR @ sK50)) | spl76_111),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f742])).
% 1.57/1.49 thf(f742,definition,(
% 1.57/1.49 spl76_111 <=> ($true = (cR @ sK50))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_111])],[avatar_definition])).
% 1.57/1.49 thf(f806,plain,(
% 1.57/1.49 ~spl76_24 | ~spl76_102),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f805])).
% 1.57/1.49 thf(f805,plain,(
% 1.57/1.49 $false | (~spl76_24 | ~spl76_102)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f804])).
% 1.57/1.49 thf(f804,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_24 | ~spl76_102)),
% 1.57/1.49 inference(superposition,[status(thm)],[f334,f692])).
% 1.57/1.49 thf(f803,plain,(
% 1.57/1.49 ~spl76_4 | spl76_77),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f802])).
% 1.57/1.49 thf(f802,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_77)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f801])).
% 1.57/1.49 thf(f801,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_4 | spl76_77)),
% 1.57/1.49 inference(superposition,[status(thm)],[f570,f257])).
% 1.57/1.49 thf(f570,plain,(
% 1.57/1.49 ($true != (cR @ sK47)) | spl76_77),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f568])).
% 1.57/1.49 thf(f568,definition,(
% 1.57/1.49 spl76_77 <=> ($true = (cR @ sK47))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_77])],[avatar_definition])).
% 1.57/1.49 thf(f799,plain,(
% 1.57/1.49 ~spl76_20 | spl76_64),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f798])).
% 1.57/1.49 thf(f798,plain,(
% 1.57/1.49 $false | (~spl76_20 | spl76_64)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f797])).
% 1.57/1.49 thf(f797,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_20 | spl76_64)),
% 1.57/1.49 inference(superposition,[status(thm)],[f505,f318])).
% 1.57/1.49 thf(f505,plain,(
% 1.57/1.49 ($true != (cQ @ sK56)) | spl76_64),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f503])).
% 1.57/1.49 thf(f503,definition,(
% 1.57/1.49 spl76_64 <=> ($true = (cQ @ sK56))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_64])],[avatar_definition])).
% 1.57/1.49 thf(f795,plain,(
% 1.57/1.49 ~spl76_20 | spl76_52),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f794])).
% 1.57/1.49 thf(f794,plain,(
% 1.57/1.49 $false | (~spl76_20 | spl76_52)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f451,f318])).
% 1.57/1.49 thf(f451,plain,(
% 1.57/1.49 ((cQ @ sK52) != $true) | spl76_52),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f449])).
% 1.57/1.49 thf(f449,definition,(
% 1.57/1.49 spl76_52 <=> ((cQ @ sK52) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_52])],[avatar_definition])).
% 1.57/1.49 thf(f791,plain,(
% 1.57/1.49 ~spl76_11 | ~spl76_20),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f790])).
% 1.57/1.49 thf(f790,plain,(
% 1.57/1.49 $false | (~spl76_11 | ~spl76_20)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f318,f284])).
% 1.57/1.49 thf(f788,plain,(
% 1.57/1.49 ~spl76_21 | ~spl76_23),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f787])).
% 1.57/1.49 thf(f787,plain,(
% 1.57/1.49 $false | (~spl76_21 | ~spl76_23)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f786])).
% 1.57/1.49 thf(f786,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_21 | ~spl76_23)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f330,f322])).
% 1.57/1.49 thf(f322,plain,(
% 1.57/1.49 ($false = (cQ @ sK73)) | ~spl76_21),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f320])).
% 1.57/1.49 thf(f320,definition,(
% 1.57/1.49 spl76_21 <=> ($false = (cQ @ sK73))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_21])],[avatar_definition])).
% 1.57/1.49 thf(f330,plain,(
% 1.57/1.49 ($true = (cQ @ sK73)) | ~spl76_23),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f328])).
% 1.57/1.49 thf(f328,definition,(
% 1.57/1.49 spl76_23 <=> ($true = (cQ @ sK73))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_23])],[avatar_definition])).
% 1.57/1.49 thf(f784,plain,(
% 1.57/1.49 ~spl76_72 | ~spl76_74),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f783])).
% 1.57/1.49 thf(f783,plain,(
% 1.57/1.49 $false | (~spl76_72 | ~spl76_74)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f782])).
% 1.57/1.49 thf(f782,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_72 | ~spl76_74)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f544,f553])).
% 1.57/1.49 thf(f553,plain,(
% 1.57/1.49 ($false = (cP @ sK33)) | ~spl76_74),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f551])).
% 1.57/1.49 thf(f551,definition,(
% 1.57/1.49 spl76_74 <=> ($false = (cP @ sK33))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_74])],[avatar_definition])).
% 1.57/1.49 thf(f544,plain,(
% 1.57/1.49 ((cP @ sK33) = $true) | ~spl76_72),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f542])).
% 1.57/1.49 thf(f542,definition,(
% 1.57/1.49 spl76_72 <=> ((cP @ sK33) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_72])],[avatar_definition])).
% 1.57/1.49 thf(f781,plain,(
% 1.57/1.49 ~spl76_22 | ~spl76_71),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f780])).
% 1.57/1.49 thf(f780,plain,(
% 1.57/1.49 $false | (~spl76_22 | ~spl76_71)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f779])).
% 1.57/1.49 thf(f779,plain,(
% 1.57/1.49 ($false = $true) | (~spl76_22 | ~spl76_71)),
% 1.57/1.49 inference(forward_demodulation,[status(thm)],[f540,f326])).
% 1.57/1.49 thf(f540,plain,(
% 1.57/1.49 ((cQ @ sK31) = $true) | ~spl76_71),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f538])).
% 1.57/1.49 thf(f538,definition,(
% 1.57/1.49 spl76_71 <=> ((cQ @ sK31) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_71])],[avatar_definition])).
% 1.57/1.49 thf(f778,plain,(
% 1.57/1.49 ~spl76_4 | spl76_73),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f777])).
% 1.57/1.49 thf(f777,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_73)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f776])).
% 1.57/1.49 thf(f776,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_4 | spl76_73)),
% 1.57/1.49 inference(superposition,[status(thm)],[f548,f257])).
% 1.57/1.49 thf(f548,plain,(
% 1.57/1.49 ($true != (cR @ sK32)) | spl76_73),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f546])).
% 1.57/1.49 thf(f546,definition,(
% 1.57/1.49 spl76_73 <=> ($true = (cR @ sK32))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_73])],[avatar_definition])).
% 1.57/1.49 thf(f774,plain,(
% 1.57/1.49 ~spl76_4 | spl76_66),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f773])).
% 1.57/1.49 thf(f773,plain,(
% 1.57/1.49 $false | (~spl76_4 | spl76_66)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f772])).
% 1.57/1.49 thf(f772,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_4 | spl76_66)),
% 1.57/1.49 inference(superposition,[status(thm)],[f518,f257])).
% 1.57/1.49 thf(f518,plain,(
% 1.57/1.49 ($true != (cR @ sK28)) | spl76_66),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f516])).
% 1.57/1.49 thf(f516,definition,(
% 1.57/1.49 spl76_66 <=> ($true = (cR @ sK28))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_66])],[avatar_definition])).
% 1.57/1.49 thf(f771,plain,(
% 1.57/1.49 ~spl76_19 | spl76_28),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f770])).
% 1.57/1.49 thf(f770,plain,(
% 1.57/1.49 $false | (~spl76_19 | spl76_28)),
% 1.57/1.49 inference(trivial_inequality_removal,[status(thm)],[f769])).
% 1.57/1.49 thf(f769,plain,(
% 1.57/1.49 ($true != $true) | (~spl76_19 | spl76_28)),
% 1.57/1.49 inference(superposition,[status(thm)],[f351,f315])).
% 1.57/1.49 thf(f351,plain,(
% 1.57/1.49 ($true != (cS @ sK71)) | spl76_28),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f349])).
% 1.57/1.49 thf(f349,definition,(
% 1.57/1.49 spl76_28 <=> ($true = (cS @ sK71))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_28])],[avatar_definition])).
% 1.57/1.49 thf(f761,plain,(
% 1.57/1.49 ~spl76_19 | spl76_59),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f760])).
% 1.57/1.49 thf(f760,plain,(
% 1.57/1.49 $false | (~spl76_19 | spl76_59)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f479,f315])).
% 1.57/1.49 thf(f479,plain,(
% 1.57/1.49 ((cS @ sK74) != $true) | spl76_59),
% 1.57/1.49 inference(avatar_component_clause,[status(thm)],[f477])).
% 1.57/1.49 thf(f477,definition,(
% 1.57/1.49 spl76_59 <=> ((cS @ sK74) = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_59])],[avatar_definition])).
% 1.57/1.49 thf(f759,plain,(
% 1.57/1.49 ~spl76_16 | ~spl76_19),
% 1.57/1.49 inference(avatar_contradiction_clause,[status(thm)],[f758])).
% 1.57/1.49 thf(f758,plain,(
% 1.57/1.49 $false | (~spl76_16 | ~spl76_19)),
% 1.57/1.49 inference(subsumption_resolution,[status(thm)],[f303,f315])).
% 1.57/1.49 thf(f752,plain,(
% 1.57/1.49 spl76_4 | spl76_112 | spl76_5 | spl76_85 | spl76_55 | spl76_1),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f148,f244,f461,f607,f259,f748,f256])).
% 1.57/1.49 thf(f259,definition,(
% 1.57/1.49 spl76_5 <=> (sP3 = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_5])],[avatar_definition])).
% 1.57/1.49 thf(f244,definition,(
% 1.57/1.49 spl76_1 <=> (sP1 = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_1])],[avatar_definition])).
% 1.57/1.49 thf(f148,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (($false = (cR @ sK10)) | (sP1 = $true) | ($true = (cP @ X16)) | (sP3 = $true) | ($true = (cR @ X13)) | ((cS @ sK12) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.57/1.49 thf(f107,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (((cS @ sK12) = $true) | ($true = (cP @ X16)) | ((cR @ sK10) = (cR @ X13)) | (sP3 = $true) | (sP1 = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f38,plain,(
% 1.57/1.49 ((sP3 = $true) | ((((((($true != (cP @ sK4)) | ! [X1 : $i] : ((cS @ X1) != $true)) & (! [X2 : $i] : ($true = (cP @ X2)) | ((cS @ sK5) = $true))) | ! [X4 : $i] : ((cR @ (sK6 @ X4)) != (cR @ X4))) & (((((cS @ sK7) = $true) | ((cP @ sK8) != $true)) & (! [X8 : $i] : ((cP @ X8) = $true) | ! [X9 : $i] : ($true != (cS @ X9)))) | ! [X11 : $i] : ((cR @ X11) = (cR @ sK9)))) | (sP1 != $true)) & (((! [X13 : $i] : ((cR @ sK10) = (cR @ X13)) | ((($true != (cP @ sK11)) | ! [X15 : $i] : ($true != (cS @ X15))) & (! [X16 : $i] : ($true = (cP @ X16)) | ((cS @ sK12) = $true)))) & (((($true = (cS @ sK13)) | ((cP @ sK14) != $true)) & (! [X20 : $i] : ((cP @ X20) = $true) | ! [X21 : $i] : ((cS @ X21) != $true))) | ! [X22 : $i] : ((cR @ X22) != (cR @ (sK15 @ X22))))) | (sP1 = $true)))) & ((((sP1 = $true) | ((((((cP @ sK16) != $true) | ! [X25 : $i] : ((cS @ X25) != $true)) & (! [X26 : $i] : ((cP @ X26) = $true) | ((cS @ sK17) = $true))) | ! [X28 : $i] : ((cR @ (sK18 @ X28)) != (cR @ X28))) & (((((cS @ sK19) = $true) | ((cP @ sK20) != $true)) & (! [X32 : $i] : ($true = (cP @ X32)) | ! [X33 : $i] : ((cS @ X33) != $true))) | ! [X35 : $i] : ((cR @ X35) = (cR @ sK21))))) & (((! [X37 : $i] : ((cR @ X37) = (cR @ sK22)) | ((($true != (cP @ sK23)) | ! [X39 : $i] : ($true != (cS @ X39))) & (! [X40 : $i] : ((cP @ X40) = $true) | ((cS @ sK24) = $true)))) & (((((cS @ sK25) = $true) | ((cP @ sK26) != $true)) & (! [X44 : $i] : ($true = (cP @ X44)) | ! [X45 : $i] : ((cS @ X45) != $true))) | ! [X46 : $i] : ((cR @ X46) != (cR @ (sK27 @ X46))))) | (sP1 != $true))) | (sP3 != $true))),
% 1.57/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19,sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27])],[f13,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14])).
% 1.57/1.49 thf(f14,plain,(
% 1.57/1.49 ? [X0 : $i] : ((cP @ X0) != $true) => ($true != (cP @ sK4))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f15,plain,(
% 1.57/1.49 ? [X3 : $i] : ((cS @ X3) = $true) => ((cS @ sK5) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f16,plain,(
% 1.57/1.49 ! [X4 : $i] : (? [X5 : $i] : ((cR @ X5) != (cR @ X4)) => ((cR @ (sK6 @ X4)) != (cR @ X4)))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f17,plain,(
% 1.57/1.49 ? [X6 : $i] : ($true = (cS @ X6)) => ((cS @ sK7) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f18,plain,(
% 1.57/1.49 ? [X7 : $i] : ($true != (cP @ X7)) => ((cP @ sK8) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f19,plain,(
% 1.57/1.49 ? [X10 : $i] : ! [X11 : $i] : ((cR @ X11) = (cR @ X10)) => ! [X11 : $i] : ((cR @ X11) = (cR @ sK9))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f20,plain,(
% 1.57/1.49 ? [X12 : $i] : ! [X13 : $i] : ((cR @ X12) = (cR @ X13)) => ! [X13 : $i] : ((cR @ sK10) = (cR @ X13))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f21,plain,(
% 1.57/1.49 ? [X14 : $i] : ($true != (cP @ X14)) => ($true != (cP @ sK11))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f22,plain,(
% 1.57/1.49 ? [X17 : $i] : ($true = (cS @ X17)) => ((cS @ sK12) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f23,plain,(
% 1.57/1.49 ? [X18 : $i] : ($true = (cS @ X18)) => ($true = (cS @ sK13))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f24,plain,(
% 1.57/1.49 ? [X19 : $i] : ((cP @ X19) != $true) => ((cP @ sK14) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f25,plain,(
% 1.57/1.49 ! [X22 : $i] : (? [X23 : $i] : ((cR @ X22) != (cR @ X23)) => ((cR @ X22) != (cR @ (sK15 @ X22))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f26,plain,(
% 1.57/1.49 ? [X24 : $i] : ((cP @ X24) != $true) => ((cP @ sK16) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f27,plain,(
% 1.57/1.49 ? [X27 : $i] : ($true = (cS @ X27)) => ((cS @ sK17) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f28,plain,(
% 1.57/1.49 ! [X28 : $i] : (? [X29 : $i] : ((cR @ X29) != (cR @ X28)) => ((cR @ (sK18 @ X28)) != (cR @ X28)))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f29,plain,(
% 1.57/1.49 ? [X30 : $i] : ((cS @ X30) = $true) => ((cS @ sK19) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f30,plain,(
% 1.57/1.49 ? [X31 : $i] : ($true != (cP @ X31)) => ((cP @ sK20) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f31,plain,(
% 1.57/1.49 ? [X34 : $i] : ! [X35 : $i] : ((cR @ X35) = (cR @ X34)) => ! [X35 : $i] : ((cR @ X35) = (cR @ sK21))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f32,plain,(
% 1.57/1.49 ? [X36 : $i] : ! [X37 : $i] : ((cR @ X37) = (cR @ X36)) => ! [X37 : $i] : ((cR @ X37) = (cR @ sK22))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f33,plain,(
% 1.57/1.49 ? [X38 : $i] : ((cP @ X38) != $true) => ($true != (cP @ sK23))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f34,plain,(
% 1.57/1.49 ? [X41 : $i] : ((cS @ X41) = $true) => ((cS @ sK24) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f35,plain,(
% 1.57/1.49 ? [X42 : $i] : ((cS @ X42) = $true) => ((cS @ sK25) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f36,plain,(
% 1.57/1.49 ? [X43 : $i] : ($true != (cP @ X43)) => ((cP @ sK26) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f37,plain,(
% 1.57/1.49 ! [X46 : $i] : (? [X47 : $i] : ((cR @ X46) != (cR @ X47)) => ((cR @ X46) != (cR @ (sK27 @ X46))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f13,plain,(
% 1.57/1.49 ((sP3 = $true) | ((((((? [X0 : $i] : ((cP @ X0) != $true) | ! [X1 : $i] : ((cS @ X1) != $true)) & (! [X2 : $i] : ($true = (cP @ X2)) | ? [X3 : $i] : ((cS @ X3) = $true))) | ! [X4 : $i] : ? [X5 : $i] : ((cR @ X5) != (cR @ X4))) & (((? [X6 : $i] : ($true = (cS @ X6)) | ? [X7 : $i] : ($true != (cP @ X7))) & (! [X8 : $i] : ((cP @ X8) = $true) | ! [X9 : $i] : ($true != (cS @ X9)))) | ? [X10 : $i] : ! [X11 : $i] : ((cR @ X11) = (cR @ X10)))) | (sP1 != $true)) & (((? [X12 : $i] : ! [X13 : $i] : ((cR @ X12) = (cR @ X13)) | ((? [X14 : $i] : ($true != (cP @ X14)) | ! [X15 : $i] : ($true != (cS @ X15))) & (! [X16 : $i] : ($true = (cP @ X16)) | ? [X17 : $i] : ($true = (cS @ X17))))) & (((? [X18 : $i] : ($true = (cS @ X18)) | ? [X19 : $i] : ((cP @ X19) != $true)) & (! [X20 : $i] : ((cP @ X20) = $true) | ! [X21 : $i] : ((cS @ X21) != $true))) | ! [X22 : $i] : ? [X23 : $i] : ((cR @ X22) != (cR @ X23)))) | (sP1 = $true)))) & ((((sP1 = $true) | ((((? [X24 : $i] : ((cP @ X24) != $true) | ! [X25 : $i] : ((cS @ X25) != $true)) & (! [X26 : $i] : ((cP @ X26) = $true) | ? [X27 : $i] : ($true = (cS @ X27)))) | ! [X28 : $i] : ? [X29 : $i] : ((cR @ X29) != (cR @ X28))) & (((? [X30 : $i] : ((cS @ X30) = $true) | ? [X31 : $i] : ($true != (cP @ X31))) & (! [X32 : $i] : ($true = (cP @ X32)) | ! [X33 : $i] : ((cS @ X33) != $true))) | ? [X34 : $i] : ! [X35 : $i] : ((cR @ X35) = (cR @ X34))))) & (((? [X36 : $i] : ! [X37 : $i] : ((cR @ X37) = (cR @ X36)) | ((? [X38 : $i] : ((cP @ X38) != $true) | ! [X39 : $i] : ($true != (cS @ X39))) & (! [X40 : $i] : ((cP @ X40) = $true) | ? [X41 : $i] : ((cS @ X41) = $true)))) & (((? [X42 : $i] : ((cS @ X42) = $true) | ? [X43 : $i] : ($true != (cP @ X43))) & (! [X44 : $i] : ($true = (cP @ X44)) | ! [X45 : $i] : ((cS @ X45) != $true))) | ! [X46 : $i] : ? [X47 : $i] : ((cR @ X46) != (cR @ X47)))) | (sP1 != $true))) | (sP3 != $true))),
% 1.57/1.49 inference(rectify,[status(thm)],[f12])).
% 1.57/1.49 thf(f12,plain,(
% 1.57/1.49 ((sP3 = $true) | ((((((? [X3 : $i] : ($true != (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true)) & (! [X3 : $i] : ($true = (cP @ X3)) | ? [X2 : $i] : ((cS @ X2) = $true))) | ! [X0 : $i] : ? [X1 : $i] : ((cR @ X1) != (cR @ X0))) & (((? [X2 : $i] : ((cS @ X2) = $true) | ? [X3 : $i] : ($true != (cP @ X3))) & (! [X3 : $i] : ($true = (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true))) | ? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0)))) | (sP1 != $true)) & (((? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0)) | ((? [X3 : $i] : ($true != (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true)) & (! [X3 : $i] : ($true = (cP @ X3)) | ? [X2 : $i] : ((cS @ X2) = $true)))) & (((? [X2 : $i] : ((cS @ X2) = $true) | ? [X3 : $i] : ($true != (cP @ X3))) & (! [X3 : $i] : ($true = (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true))) | ! [X0 : $i] : ? [X1 : $i] : ((cR @ X1) != (cR @ X0)))) | (sP1 = $true)))) & ((((sP1 = $true) | ((((? [X3 : $i] : ($true != (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true)) & (! [X3 : $i] : ($true = (cP @ X3)) | ? [X2 : $i] : ((cS @ X2) = $true))) | ! [X0 : $i] : ? [X1 : $i] : ((cR @ X1) != (cR @ X0))) & (((? [X2 : $i] : ((cS @ X2) = $true) | ? [X3 : $i] : ($true != (cP @ X3))) & (! [X3 : $i] : ($true = (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true))) | ? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0))))) & (((? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0)) | ((? [X3 : $i] : ($true != (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true)) & (! [X3 : $i] : ($true = (cP @ X3)) | ? [X2 : $i] : ((cS @ X2) = $true)))) & (((? [X2 : $i] : ((cS @ X2) = $true) | ? [X3 : $i] : ($true != (cP @ X3))) & (! [X3 : $i] : ($true = (cP @ X3)) | ! [X2 : $i] : ((cS @ X2) != $true))) | ! [X0 : $i] : ? [X1 : $i] : ((cR @ X1) != (cR @ X0)))) | (sP1 != $true))) | (sP3 != $true))),
% 1.57/1.49 inference(nnf_transformation,[status(thm)],[f10])).
% 1.57/1.49 thf(f10,plain,(
% 1.57/1.49 (sP3 = $true) <=> ((sP1 = $true) <=> (? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0)) <=> (? [X2 : $i] : ((cS @ X2) = $true) <=> ! [X3 : $i] : ($true = (cP @ X3)))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.57/1.49 thf(f751,plain,(
% 1.57/1.49 spl76_5 | spl76_112 | spl76_7 | spl76_55 | spl76_1 | spl76_83),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f147,f598,f244,f461,f268,f748,f259])).
% 1.57/1.49 thf(f147,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (($true = (cP @ X16)) | ((cR @ sK10) = $true) | ($false = (cR @ X13)) | (sP1 = $true) | (sP3 = $true) | ((cS @ sK12) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f107])).
% 1.57/1.49 thf(f746,plain,(
% 1.57/1.49 ~spl76_9 | spl76_13 | ~spl76_12 | spl76_110 | ~spl76_111),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f150,f742,f738,f286,f291,f276])).
% 1.57/1.49 thf(f276,definition,(
% 1.57/1.49 spl76_9 <=> ($true = sP0)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_9])],[avatar_definition])).
% 1.57/1.49 thf(f286,definition,(
% 1.57/1.49 spl76_12 <=> (sP2 = $true)),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[spl76_12])],[avatar_definition])).
% 1.57/1.49 thf(f150,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($true = (cQ @ sK49)) | ($true != (cR @ sK50)) | (sP2 != $true) | ($true != sP0) | ($false = (cP @ X46)) | ((cP @ (sK51 @ X46)) = $false)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.57/1.49 thf(f114,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($true = (cQ @ sK49)) | ((cP @ (sK51 @ X46)) != (cP @ X46)) | ($true != sP0) | ($true != (cR @ sK50)) | (sP2 != $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f65,plain,(
% 1.57/1.49 ((sP2 = $true) | ((((((($true != (cR @ sK28)) | ! [X1 : $i] : ((cQ @ X1) != $true)) & (! [X2 : $i] : ($true = (cR @ X2)) | ((cQ @ sK29) = $true))) | ! [X4 : $i] : ((cP @ X4) != (cP @ (sK30 @ X4)))) & (((((cQ @ sK31) = $true) | ($true != (cR @ sK32))) & (! [X8 : $i] : ((cR @ X8) = $true) | ! [X9 : $i] : ($true != (cQ @ X9)))) | ! [X11 : $i] : ((cP @ sK33) = (cP @ X11)))) | ($true != sP0)) & (((! [X13 : $i] : ((cP @ sK34) = (cP @ X13)) | ((((cR @ sK35) != $true) | ! [X15 : $i] : ((cQ @ X15) != $true)) & (! [X16 : $i] : ($true = (cR @ X16)) | ($true = (cQ @ sK36))))) & (((((cQ @ sK37) = $true) | ($true != (cR @ sK38))) & (! [X20 : $i] : ($true = (cR @ X20)) | ! [X21 : $i] : ($true != (cQ @ X21)))) | ! [X22 : $i] : ((cP @ (sK39 @ X22)) != (cP @ X22)))) | ($true = sP0)))) & (((($true = sP0) | ((((((cR @ sK40) != $true) | ! [X25 : $i] : ($true != (cQ @ X25))) & (! [X26 : $i] : ((cR @ X26) = $true) | ((cQ @ sK41) = $true))) | ! [X28 : $i] : ((cP @ X28) != (cP @ (sK42 @ X28)))) & (((((cQ @ sK43) = $true) | ($true != (cR @ sK44))) & (! [X32 : $i] : ($true = (cR @ X32)) | ! [X33 : $i] : ($true != (cQ @ X33)))) | ! [X35 : $i] : ((cP @ X35) = (cP @ sK45))))) & (((! [X37 : $i] : ((cP @ X37) = (cP @ sK46)) | ((($true != (cR @ sK47)) | ! [X39 : $i] : ((cQ @ X39) != $true)) & (! [X40 : $i] : ($true = (cR @ X40)) | ((cQ @ sK48) = $true)))) & (((($true = (cQ @ sK49)) | ($true != (cR @ sK50))) & (! [X44 : $i] : ((cR @ X44) = $true) | ! [X45 : $i] : ($true != (cQ @ X45)))) | ! [X46 : $i] : ((cP @ (sK51 @ X46)) != (cP @ X46)))) | ($true != sP0))) | (sP2 != $true))),
% 1.57/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35,sK36,sK37,sK38,sK39,sK40,sK41,sK42,sK43,sK44,sK45,sK46,sK47,sK48,sK49,sK50,sK51])],[f40,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41])).
% 1.57/1.49 thf(f41,plain,(
% 1.57/1.49 ? [X0 : $i] : ((cR @ X0) != $true) => ($true != (cR @ sK28))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f42,plain,(
% 1.57/1.49 ? [X3 : $i] : ((cQ @ X3) = $true) => ((cQ @ sK29) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f43,plain,(
% 1.57/1.49 ! [X4 : $i] : (? [X5 : $i] : ((cP @ X4) != (cP @ X5)) => ((cP @ X4) != (cP @ (sK30 @ X4))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f44,plain,(
% 1.57/1.49 ? [X6 : $i] : ($true = (cQ @ X6)) => ((cQ @ sK31) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f45,plain,(
% 1.57/1.49 ? [X7 : $i] : ((cR @ X7) != $true) => ($true != (cR @ sK32))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f46,plain,(
% 1.57/1.49 ? [X10 : $i] : ! [X11 : $i] : ((cP @ X10) = (cP @ X11)) => ! [X11 : $i] : ((cP @ sK33) = (cP @ X11))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f47,plain,(
% 1.57/1.49 ? [X12 : $i] : ! [X13 : $i] : ((cP @ X12) = (cP @ X13)) => ! [X13 : $i] : ((cP @ sK34) = (cP @ X13))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f48,plain,(
% 1.57/1.49 ? [X14 : $i] : ((cR @ X14) != $true) => ((cR @ sK35) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f49,plain,(
% 1.57/1.49 ? [X17 : $i] : ($true = (cQ @ X17)) => ($true = (cQ @ sK36))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f50,plain,(
% 1.57/1.49 ? [X18 : $i] : ((cQ @ X18) = $true) => ((cQ @ sK37) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f51,plain,(
% 1.57/1.49 ? [X19 : $i] : ((cR @ X19) != $true) => ($true != (cR @ sK38))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f52,plain,(
% 1.57/1.49 ! [X22 : $i] : (? [X23 : $i] : ((cP @ X23) != (cP @ X22)) => ((cP @ (sK39 @ X22)) != (cP @ X22)))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f53,plain,(
% 1.57/1.49 ? [X24 : $i] : ((cR @ X24) != $true) => ((cR @ sK40) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f54,plain,(
% 1.57/1.49 ? [X27 : $i] : ((cQ @ X27) = $true) => ((cQ @ sK41) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f55,plain,(
% 1.57/1.49 ! [X28 : $i] : (? [X29 : $i] : ((cP @ X29) != (cP @ X28)) => ((cP @ X28) != (cP @ (sK42 @ X28))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f56,plain,(
% 1.57/1.49 ? [X30 : $i] : ((cQ @ X30) = $true) => ((cQ @ sK43) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f57,plain,(
% 1.57/1.49 ? [X31 : $i] : ((cR @ X31) != $true) => ($true != (cR @ sK44))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f58,plain,(
% 1.57/1.49 ? [X34 : $i] : ! [X35 : $i] : ((cP @ X35) = (cP @ X34)) => ! [X35 : $i] : ((cP @ X35) = (cP @ sK45))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f59,plain,(
% 1.57/1.49 ? [X36 : $i] : ! [X37 : $i] : ((cP @ X37) = (cP @ X36)) => ! [X37 : $i] : ((cP @ X37) = (cP @ sK46))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f60,plain,(
% 1.57/1.49 ? [X38 : $i] : ((cR @ X38) != $true) => ($true != (cR @ sK47))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f61,plain,(
% 1.57/1.49 ? [X41 : $i] : ((cQ @ X41) = $true) => ((cQ @ sK48) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f62,plain,(
% 1.57/1.49 ? [X42 : $i] : ((cQ @ X42) = $true) => ($true = (cQ @ sK49))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f63,plain,(
% 1.57/1.49 ? [X43 : $i] : ($true != (cR @ X43)) => ($true != (cR @ sK50))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f64,plain,(
% 1.57/1.49 ! [X46 : $i] : (? [X47 : $i] : ((cP @ X47) != (cP @ X46)) => ((cP @ (sK51 @ X46)) != (cP @ X46)))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f40,plain,(
% 1.57/1.49 ((sP2 = $true) | ((((((? [X0 : $i] : ((cR @ X0) != $true) | ! [X1 : $i] : ((cQ @ X1) != $true)) & (! [X2 : $i] : ($true = (cR @ X2)) | ? [X3 : $i] : ((cQ @ X3) = $true))) | ! [X4 : $i] : ? [X5 : $i] : ((cP @ X4) != (cP @ X5))) & (((? [X6 : $i] : ($true = (cQ @ X6)) | ? [X7 : $i] : ((cR @ X7) != $true)) & (! [X8 : $i] : ((cR @ X8) = $true) | ! [X9 : $i] : ($true != (cQ @ X9)))) | ? [X10 : $i] : ! [X11 : $i] : ((cP @ X10) = (cP @ X11)))) | ($true != sP0)) & (((? [X12 : $i] : ! [X13 : $i] : ((cP @ X12) = (cP @ X13)) | ((? [X14 : $i] : ((cR @ X14) != $true) | ! [X15 : $i] : ((cQ @ X15) != $true)) & (! [X16 : $i] : ($true = (cR @ X16)) | ? [X17 : $i] : ($true = (cQ @ X17))))) & (((? [X18 : $i] : ((cQ @ X18) = $true) | ? [X19 : $i] : ((cR @ X19) != $true)) & (! [X20 : $i] : ($true = (cR @ X20)) | ! [X21 : $i] : ($true != (cQ @ X21)))) | ! [X22 : $i] : ? [X23 : $i] : ((cP @ X23) != (cP @ X22)))) | ($true = sP0)))) & (((($true = sP0) | ((((? [X24 : $i] : ((cR @ X24) != $true) | ! [X25 : $i] : ($true != (cQ @ X25))) & (! [X26 : $i] : ((cR @ X26) = $true) | ? [X27 : $i] : ((cQ @ X27) = $true))) | ! [X28 : $i] : ? [X29 : $i] : ((cP @ X29) != (cP @ X28))) & (((? [X30 : $i] : ((cQ @ X30) = $true) | ? [X31 : $i] : ((cR @ X31) != $true)) & (! [X32 : $i] : ($true = (cR @ X32)) | ! [X33 : $i] : ($true != (cQ @ X33)))) | ? [X34 : $i] : ! [X35 : $i] : ((cP @ X35) = (cP @ X34))))) & (((? [X36 : $i] : ! [X37 : $i] : ((cP @ X37) = (cP @ X36)) | ((? [X38 : $i] : ((cR @ X38) != $true) | ! [X39 : $i] : ((cQ @ X39) != $true)) & (! [X40 : $i] : ($true = (cR @ X40)) | ? [X41 : $i] : ((cQ @ X41) = $true)))) & (((? [X42 : $i] : ((cQ @ X42) = $true) | ? [X43 : $i] : ($true != (cR @ X43))) & (! [X44 : $i] : ((cR @ X44) = $true) | ! [X45 : $i] : ($true != (cQ @ X45)))) | ! [X46 : $i] : ? [X47 : $i] : ((cP @ X47) != (cP @ X46)))) | ($true != sP0))) | (sP2 != $true))),
% 1.57/1.49 inference(rectify,[status(thm)],[f39])).
% 1.57/1.49 thf(f39,plain,(
% 1.57/1.49 ((sP2 = $true) | ((((((? [X12 : $i] : ((cR @ X12) != $true) | ! [X13 : $i] : ($true != (cQ @ X13))) & (! [X12 : $i] : ((cR @ X12) = $true) | ? [X13 : $i] : ($true = (cQ @ X13)))) | ! [X14 : $i] : ? [X15 : $i] : ((cP @ X15) != (cP @ X14))) & (((? [X13 : $i] : ($true = (cQ @ X13)) | ? [X12 : $i] : ((cR @ X12) != $true)) & (! [X12 : $i] : ((cR @ X12) = $true) | ! [X13 : $i] : ($true != (cQ @ X13)))) | ? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14)))) | ($true != sP0)) & (((? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14)) | ((? [X12 : $i] : ((cR @ X12) != $true) | ! [X13 : $i] : ($true != (cQ @ X13))) & (! [X12 : $i] : ((cR @ X12) = $true) | ? [X13 : $i] : ($true = (cQ @ X13))))) & (((? [X13 : $i] : ($true = (cQ @ X13)) | ? [X12 : $i] : ((cR @ X12) != $true)) & (! [X12 : $i] : ((cR @ X12) = $true) | ! [X13 : $i] : ($true != (cQ @ X13)))) | ! [X14 : $i] : ? [X15 : $i] : ((cP @ X15) != (cP @ X14)))) | ($true = sP0)))) & (((($true = sP0) | ((((? [X12 : $i] : ((cR @ X12) != $true) | ! [X13 : $i] : ($true != (cQ @ X13))) & (! [X12 : $i] : ((cR @ X12) = $true) | ? [X13 : $i] : ($true = (cQ @ X13)))) | ! [X14 : $i] : ? [X15 : $i] : ((cP @ X15) != (cP @ X14))) & (((? [X13 : $i] : ($true = (cQ @ X13)) | ? [X12 : $i] : ((cR @ X12) != $true)) & (! [X12 : $i] : ((cR @ X12) = $true) | ! [X13 : $i] : ($true != (cQ @ X13)))) | ? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14))))) & (((? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14)) | ((? [X12 : $i] : ((cR @ X12) != $true) | ! [X13 : $i] : ($true != (cQ @ X13))) & (! [X12 : $i] : ((cR @ X12) = $true) | ? [X13 : $i] : ($true = (cQ @ X13))))) & (((? [X13 : $i] : ($true = (cQ @ X13)) | ? [X12 : $i] : ((cR @ X12) != $true)) & (! [X12 : $i] : ((cR @ X12) = $true) | ! [X13 : $i] : ($true != (cQ @ X13)))) | ! [X14 : $i] : ? [X15 : $i] : ((cP @ X15) != (cP @ X14)))) | ($true != sP0))) | (sP2 != $true))),
% 1.57/1.49 inference(nnf_transformation,[status(thm)],[f9])).
% 1.57/1.49 thf(f9,plain,(
% 1.57/1.49 (sP2 = $true) <=> (($true = sP0) <=> (? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14)) <=> (? [X13 : $i] : ($true = (cQ @ X13)) <=> ! [X12 : $i] : ((cR @ X12) = $true))))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.57/1.49 thf(f745,plain,(
% 1.57/1.49 spl76_110 | ~spl76_111 | ~spl76_12 | spl76_10 | ~spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f149,f276,f280,f286,f742,f738])).
% 1.57/1.49 thf(f149,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (($true = (cQ @ sK49)) | ($true != sP0) | ((cP @ X46) = $true) | ((cP @ (sK51 @ X46)) = $true) | (sP2 != $true) | ($true != (cR @ sK50))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.57/1.49 thf(f736,plain,(
% 1.57/1.49 spl76_43 | ~spl76_1 | spl76_109 | spl76_19 | spl76_20),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f152,f317,f314,f732,f244,f413])).
% 1.57/1.49 thf(f152,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (((cP @ sK60) = $true) | (sP1 != $true) | ($true = (cS @ X13)) | ((cQ @ X16) = $true) | ((cS @ sK58) = $false)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.57/1.49 thf(f131,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (((cQ @ X16) = $true) | ((cP @ sK60) = $true) | ((cS @ sK58) = (cS @ X13)) | (sP1 != $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.49 thf(f80,plain,(
% 1.57/1.49 ((sP1 = $true) | ((((((cQ @ sK52) != $true) | ! [X1 : $i] : ((cP @ X1) != $true)) & (! [X2 : $i] : ($true = (cQ @ X2)) | ((cP @ sK53) = $true))) | ! [X4 : $i] : ((cS @ X4) != (cS @ (sK54 @ X4)))) & (((((cP @ sK55) = $true) | ($true != (cQ @ sK56))) & (! [X8 : $i] : ($true = (cQ @ X8)) | ! [X9 : $i] : ((cP @ X9) != $true))) | ! [X11 : $i] : ((cS @ sK57) = (cS @ X11))))) & (((! [X13 : $i] : ((cS @ sK58) = (cS @ X13)) | ((((cQ @ sK59) != $true) | ! [X15 : $i] : ($true != (cP @ X15))) & (! [X16 : $i] : ((cQ @ X16) = $true) | ((cP @ sK60) = $true)))) & (((($true = (cP @ sK61)) | ($true != (cQ @ sK62))) & (! [X20 : $i] : ((cQ @ X20) = $true) | ! [X21 : $i] : ((cP @ X21) != $true))) | ! [X22 : $i] : ((cS @ (sK63 @ X22)) != (cS @ X22)))) | (sP1 != $true))),
% 1.57/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53,sK54,sK55,sK56,sK57,sK58,sK59,sK60,sK61,sK62,sK63])],[f67,f79,f78,f77,f76,f75,f74,f73,f72,f71,f70,f69,f68])).
% 1.57/1.49 thf(f68,plain,(
% 1.57/1.49 ? [X0 : $i] : ((cQ @ X0) != $true) => ((cQ @ sK52) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f69,plain,(
% 1.57/1.49 ? [X3 : $i] : ($true = (cP @ X3)) => ((cP @ sK53) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f70,plain,(
% 1.57/1.49 ! [X4 : $i] : (? [X5 : $i] : ((cS @ X4) != (cS @ X5)) => ((cS @ X4) != (cS @ (sK54 @ X4))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f71,plain,(
% 1.57/1.49 ? [X6 : $i] : ($true = (cP @ X6)) => ((cP @ sK55) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f72,plain,(
% 1.57/1.49 ? [X7 : $i] : ((cQ @ X7) != $true) => ($true != (cQ @ sK56))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f73,plain,(
% 1.57/1.49 ? [X10 : $i] : ! [X11 : $i] : ((cS @ X11) = (cS @ X10)) => ! [X11 : $i] : ((cS @ sK57) = (cS @ X11))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f74,plain,(
% 1.57/1.49 ? [X12 : $i] : ! [X13 : $i] : ((cS @ X12) = (cS @ X13)) => ! [X13 : $i] : ((cS @ sK58) = (cS @ X13))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f75,plain,(
% 1.57/1.49 ? [X14 : $i] : ($true != (cQ @ X14)) => ((cQ @ sK59) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f76,plain,(
% 1.57/1.49 ? [X17 : $i] : ((cP @ X17) = $true) => ((cP @ sK60) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f77,plain,(
% 1.57/1.49 ? [X18 : $i] : ($true = (cP @ X18)) => ($true = (cP @ sK61))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f78,plain,(
% 1.57/1.49 ? [X19 : $i] : ($true != (cQ @ X19)) => ($true != (cQ @ sK62))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f79,plain,(
% 1.57/1.49 ! [X22 : $i] : (? [X23 : $i] : ((cS @ X23) != (cS @ X22)) => ((cS @ (sK63 @ X22)) != (cS @ X22)))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f67,plain,(
% 1.57/1.49 ((sP1 = $true) | ((((? [X0 : $i] : ((cQ @ X0) != $true) | ! [X1 : $i] : ((cP @ X1) != $true)) & (! [X2 : $i] : ($true = (cQ @ X2)) | ? [X3 : $i] : ($true = (cP @ X3)))) | ! [X4 : $i] : ? [X5 : $i] : ((cS @ X4) != (cS @ X5))) & (((? [X6 : $i] : ($true = (cP @ X6)) | ? [X7 : $i] : ((cQ @ X7) != $true)) & (! [X8 : $i] : ($true = (cQ @ X8)) | ! [X9 : $i] : ((cP @ X9) != $true))) | ? [X10 : $i] : ! [X11 : $i] : ((cS @ X11) = (cS @ X10))))) & (((? [X12 : $i] : ! [X13 : $i] : ((cS @ X12) = (cS @ X13)) | ((? [X14 : $i] : ($true != (cQ @ X14)) | ! [X15 : $i] : ($true != (cP @ X15))) & (! [X16 : $i] : ((cQ @ X16) = $true) | ? [X17 : $i] : ((cP @ X17) = $true)))) & (((? [X18 : $i] : ($true = (cP @ X18)) | ? [X19 : $i] : ($true != (cQ @ X19))) & (! [X20 : $i] : ((cQ @ X20) = $true) | ! [X21 : $i] : ((cP @ X21) != $true))) | ! [X22 : $i] : ? [X23 : $i] : ((cS @ X23) != (cS @ X22)))) | (sP1 != $true))),
% 1.57/1.49 inference(rectify,[status(thm)],[f66])).
% 1.57/1.49 thf(f66,plain,(
% 1.57/1.49 ((sP1 = $true) | ((((? [X5 : $i] : ((cQ @ X5) != $true) | ! [X4 : $i] : ((cP @ X4) != $true)) & (! [X5 : $i] : ((cQ @ X5) = $true) | ? [X4 : $i] : ((cP @ X4) = $true))) | ! [X6 : $i] : ? [X7 : $i] : ((cS @ X7) != (cS @ X6))) & (((? [X4 : $i] : ((cP @ X4) = $true) | ? [X5 : $i] : ((cQ @ X5) != $true)) & (! [X5 : $i] : ((cQ @ X5) = $true) | ! [X4 : $i] : ((cP @ X4) != $true))) | ? [X6 : $i] : ! [X7 : $i] : ((cS @ X7) = (cS @ X6))))) & (((? [X6 : $i] : ! [X7 : $i] : ((cS @ X7) = (cS @ X6)) | ((? [X5 : $i] : ((cQ @ X5) != $true) | ! [X4 : $i] : ((cP @ X4) != $true)) & (! [X5 : $i] : ((cQ @ X5) = $true) | ? [X4 : $i] : ((cP @ X4) = $true)))) & (((? [X4 : $i] : ((cP @ X4) = $true) | ? [X5 : $i] : ((cQ @ X5) != $true)) & (! [X5 : $i] : ((cQ @ X5) = $true) | ! [X4 : $i] : ((cP @ X4) != $true))) | ! [X6 : $i] : ? [X7 : $i] : ((cS @ X7) != (cS @ X6)))) | (sP1 != $true))),
% 1.57/1.49 inference(nnf_transformation,[status(thm)],[f8])).
% 1.57/1.49 thf(f8,plain,(
% 1.57/1.49 (sP1 = $true) <=> (? [X6 : $i] : ! [X7 : $i] : ((cS @ X7) = (cS @ X6)) <=> (? [X4 : $i] : ((cP @ X4) = $true) <=> ! [X5 : $i] : ((cQ @ X5) = $true)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.57/1.49 thf(f735,plain,(
% 1.57/1.49 spl76_41 | spl76_109 | spl76_25 | spl76_20 | ~spl76_1),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f151,f244,f317,f336,f732,f404])).
% 1.57/1.49 thf(f151,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (($false = (cS @ X13)) | (sP1 != $true) | ((cQ @ X16) = $true) | ((cS @ sK58) = $true) | ((cP @ sK60) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f131])).
% 1.57/1.49 thf(f730,plain,(
% 1.57/1.49 spl76_55 | spl76_11 | spl76_106 | spl76_12 | ~spl76_108 | spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f154,f276,f726,f286,f715,f283,f461])).
% 1.57/1.49 thf(f154,plain,(
% 1.57/1.49 ( ! [X15 : $i,X13 : $i] : (($true = (cP @ X13)) | ($true = sP0) | ((cR @ sK35) != $true) | (sP2 = $true) | ((cQ @ X15) != $true) | ((cP @ sK34) = $false)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.57/1.49 thf(f124,plain,(
% 1.57/1.49 ( ! [X15 : $i,X13 : $i] : (((cR @ sK35) != $true) | (sP2 = $true) | ((cQ @ X15) != $true) | ($true = sP0) | ((cP @ sK34) = (cP @ X13))) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f729,plain,(
% 1.57/1.49 spl76_11 | ~spl76_108 | spl76_104 | spl76_12 | spl76_9 | spl76_62),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f153,f495,f276,f286,f706,f726,f283])).
% 1.57/1.49 thf(f153,plain,(
% 1.57/1.49 ( ! [X15 : $i,X13 : $i] : (($true = sP0) | ((cR @ sK35) != $true) | (sP2 = $true) | ((cP @ sK34) = $true) | ($false = (cP @ X13)) | ((cQ @ X15) != $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f124])).
% 1.57/1.49 thf(f724,plain,(
% 1.57/1.49 spl76_7 | ~spl76_1 | spl76_80 | spl76_107 | spl76_55 | ~spl76_5),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f156,f259,f461,f720,f583,f244,f268])).
% 1.57/1.49 thf(f156,plain,(
% 1.57/1.49 ( ! [X40 : $i,X37 : $i] : (((cP @ X40) = $true) | ((cR @ X37) = $false) | ($true = (cR @ sK22)) | ((cS @ sK24) = $true) | (sP1 != $true) | (sP3 != $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.57/1.49 thf(f99,plain,(
% 1.57/1.49 ( ! [X40 : $i,X37 : $i] : ((sP1 != $true) | ((cR @ X37) = (cR @ sK22)) | ((cP @ X40) = $true) | ((cS @ sK24) = $true) | (sP3 != $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f723,plain,(
% 1.57/1.49 spl76_4 | spl76_107 | spl76_55 | ~spl76_5 | spl76_79 | ~spl76_1),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f155,f244,f578,f259,f461,f720,f256])).
% 1.57/1.49 thf(f155,plain,(
% 1.57/1.49 ( ! [X40 : $i,X37 : $i] : (($false = (cR @ sK22)) | (sP3 != $true) | (sP1 != $true) | ((cS @ sK24) = $true) | ((cP @ X40) = $true) | ((cR @ X37) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f99])).
% 1.57/1.49 thf(f718,plain,(
% 1.57/1.49 spl76_105 | spl76_4 | spl76_55 | spl76_106 | spl76_9 | spl76_12),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f158,f286,f276,f715,f461,f256,f710])).
% 1.57/1.49 thf(f158,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (($true = (cP @ X13)) | ((cP @ sK34) = $false) | ($true = sP0) | ($true = (cQ @ sK36)) | ($true = (cR @ X16)) | (sP2 = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.57/1.49 thf(f123,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (($true = (cQ @ sK36)) | ($true = (cR @ X16)) | ($true = sP0) | ((cP @ sK34) = (cP @ X13)) | (sP2 = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f713,plain,(
% 1.57/1.49 spl76_62 | spl76_104 | spl76_9 | spl76_12 | spl76_4 | spl76_105),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f157,f710,f256,f286,f276,f706,f495])).
% 1.57/1.49 thf(f157,plain,(
% 1.57/1.49 ( ! [X16 : $i,X13 : $i] : (($true = (cQ @ sK36)) | ($true = (cR @ X16)) | ((cP @ sK34) = $true) | ($false = (cP @ X13)) | (sP2 = $true) | ($true = sP0)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f123])).
% 1.57/1.49 thf(f704,plain,(
% 1.57/1.49 ~spl76_9 | spl76_19 | spl76_40 | spl76_31),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f160,f361,f399,f314,f276])).
% 1.57/1.49 thf(f160,plain,(
% 1.57/1.49 ( ! [X16 : $i,X12 : $i,X13 : $i] : (($true != (cR @ X13)) | ((cS @ X12) = $true) | ($false = (cQ @ X16)) | ($true != sP0) | ($false = (cQ @ (sK72 @ X16)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.57/1.49 thf(f140,plain,(
% 1.57/1.49 ( ! [X16 : $i,X12 : $i,X13 : $i] : (($true != sP0) | ($true != (cR @ X13)) | ((cQ @ X16) != (cQ @ (sK72 @ X16))) | ((cS @ X12) = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.49 thf(f95,plain,(
% 1.57/1.49 (($true = sP0) | ((! [X0 : $i] : ((cQ @ X0) != (cQ @ (sK64 @ X0))) | ((! [X2 : $i] : ($true != (cR @ X2)) | ($true != (cS @ sK65))) & (($true = (cR @ sK66)) | ! [X5 : $i] : ((cS @ X5) = $true)))) & (! [X7 : $i] : ((cQ @ sK67) = (cQ @ X7)) | ((! [X8 : $i] : ((cS @ X8) = $true) | ! [X9 : $i] : ((cR @ X9) != $true)) & (((cR @ sK68) = $true) | ($true != (cS @ sK69))))))) & (((((! [X12 : $i] : ((cS @ X12) = $true) | ! [X13 : $i] : ($true != (cR @ X13))) & (($true = (cR @ sK70)) | ($true != (cS @ sK71)))) | ! [X16 : $i] : ((cQ @ X16) != (cQ @ (sK72 @ X16)))) & (! [X19 : $i] : ((cQ @ X19) = (cQ @ sK73)) | ((! [X20 : $i] : ($true != (cR @ X20)) | ((cS @ sK74) != $true)) & (((cR @ sK75) = $true) | ! [X23 : $i] : ((cS @ X23) = $true))))) | ($true != sP0))),
% 1.57/1.49 inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65,sK66,sK67,sK68,sK69,sK70,sK71,sK72,sK73,sK74,sK75])],[f82,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83])).
% 1.57/1.49 thf(f83,plain,(
% 1.57/1.49 ! [X0 : $i] : (? [X1 : $i] : ((cQ @ X0) != (cQ @ X1)) => ((cQ @ X0) != (cQ @ (sK64 @ X0))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f84,plain,(
% 1.57/1.49 ? [X3 : $i] : ((cS @ X3) != $true) => ($true != (cS @ sK65))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f85,plain,(
% 1.57/1.49 ? [X4 : $i] : ($true = (cR @ X4)) => ($true = (cR @ sK66))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f86,plain,(
% 1.57/1.49 ? [X6 : $i] : ! [X7 : $i] : ((cQ @ X7) = (cQ @ X6)) => ! [X7 : $i] : ((cQ @ sK67) = (cQ @ X7))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f87,plain,(
% 1.57/1.49 ? [X10 : $i] : ($true = (cR @ X10)) => ((cR @ sK68) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f88,plain,(
% 1.57/1.49 ? [X11 : $i] : ((cS @ X11) != $true) => ($true != (cS @ sK69))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f89,plain,(
% 1.57/1.49 ? [X14 : $i] : ((cR @ X14) = $true) => ($true = (cR @ sK70))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f90,plain,(
% 1.57/1.49 ? [X15 : $i] : ($true != (cS @ X15)) => ($true != (cS @ sK71))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f91,plain,(
% 1.57/1.49 ! [X16 : $i] : (? [X17 : $i] : ((cQ @ X16) != (cQ @ X17)) => ((cQ @ X16) != (cQ @ (sK72 @ X16))))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f92,plain,(
% 1.57/1.49 ? [X18 : $i] : ! [X19 : $i] : ((cQ @ X18) = (cQ @ X19)) => ! [X19 : $i] : ((cQ @ X19) = (cQ @ sK73))),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f93,plain,(
% 1.57/1.49 ? [X21 : $i] : ((cS @ X21) != $true) => ((cS @ sK74) != $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f94,plain,(
% 1.57/1.49 ? [X22 : $i] : ((cR @ X22) = $true) => ((cR @ sK75) = $true)),
% 1.57/1.49 introduced(definition,[],[choice_axiom])).
% 1.57/1.49 thf(f82,plain,(
% 1.57/1.49 (($true = sP0) | ((! [X0 : $i] : ? [X1 : $i] : ((cQ @ X0) != (cQ @ X1)) | ((! [X2 : $i] : ($true != (cR @ X2)) | ? [X3 : $i] : ((cS @ X3) != $true)) & (? [X4 : $i] : ($true = (cR @ X4)) | ! [X5 : $i] : ((cS @ X5) = $true)))) & (? [X6 : $i] : ! [X7 : $i] : ((cQ @ X7) = (cQ @ X6)) | ((! [X8 : $i] : ((cS @ X8) = $true) | ! [X9 : $i] : ((cR @ X9) != $true)) & (? [X10 : $i] : ($true = (cR @ X10)) | ? [X11 : $i] : ((cS @ X11) != $true)))))) & (((((! [X12 : $i] : ((cS @ X12) = $true) | ! [X13 : $i] : ($true != (cR @ X13))) & (? [X14 : $i] : ((cR @ X14) = $true) | ? [X15 : $i] : ($true != (cS @ X15)))) | ! [X16 : $i] : ? [X17 : $i] : ((cQ @ X16) != (cQ @ X17))) & (? [X18 : $i] : ! [X19 : $i] : ((cQ @ X18) = (cQ @ X19)) | ((! [X20 : $i] : ($true != (cR @ X20)) | ? [X21 : $i] : ((cS @ X21) != $true)) & (? [X22 : $i] : ((cR @ X22) = $true) | ! [X23 : $i] : ((cS @ X23) = $true))))) | ($true != sP0))),
% 1.57/1.49 inference(rectify,[status(thm)],[f81])).
% 1.57/1.49 thf(f81,plain,(
% 1.57/1.49 (($true = sP0) | ((! [X8 : $i] : ? [X9 : $i] : ((cQ @ X9) != (cQ @ X8)) | ((! [X10 : $i] : ($true != (cR @ X10)) | ? [X11 : $i] : ((cS @ X11) != $true)) & (? [X10 : $i] : ($true = (cR @ X10)) | ! [X11 : $i] : ((cS @ X11) = $true)))) & (? [X8 : $i] : ! [X9 : $i] : ((cQ @ X9) = (cQ @ X8)) | ((! [X11 : $i] : ((cS @ X11) = $true) | ! [X10 : $i] : ($true != (cR @ X10))) & (? [X10 : $i] : ($true = (cR @ X10)) | ? [X11 : $i] : ((cS @ X11) != $true)))))) & (((((! [X11 : $i] : ((cS @ X11) = $true) | ! [X10 : $i] : ($true != (cR @ X10))) & (? [X10 : $i] : ($true = (cR @ X10)) | ? [X11 : $i] : ((cS @ X11) != $true))) | ! [X8 : $i] : ? [X9 : $i] : ((cQ @ X9) != (cQ @ X8))) & (? [X8 : $i] : ! [X9 : $i] : ((cQ @ X9) = (cQ @ X8)) | ((! [X10 : $i] : ($true != (cR @ X10)) | ? [X11 : $i] : ((cS @ X11) != $true)) & (? [X10 : $i] : ($true = (cR @ X10)) | ! [X11 : $i] : ((cS @ X11) = $true))))) | ($true != sP0))),
% 1.57/1.49 inference(nnf_transformation,[status(thm)],[f7])).
% 1.57/1.49 thf(f7,plain,(
% 1.57/1.49 ($true = sP0) <=> ((! [X11 : $i] : ((cS @ X11) = $true) <=> ? [X10 : $i] : ($true = (cR @ X10))) <=> ? [X8 : $i] : ! [X9 : $i] : ((cQ @ X9) = (cQ @ X8)))),
% 1.57/1.49 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.57/1.49 thf(f703,plain,(
% 1.57/1.49 spl76_30 | spl76_19 | spl76_40 | ~spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f159,f276,f399,f314,f357])).
% 1.57/1.49 thf(f159,plain,(
% 1.57/1.49 ( ! [X16 : $i,X12 : $i,X13 : $i] : (((cQ @ X16) = $true) | ((cS @ X12) = $true) | ($true = (cQ @ (sK72 @ X16))) | ($true != (cR @ X13)) | ($true != sP0)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 1.57/1.49 thf(f702,plain,(
% 1.57/1.49 spl76_11 | spl76_62 | ~spl76_12 | spl76_4 | spl76_9 | spl76_94),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f162,f647,f276,f256,f286,f495,f283])).
% 1.57/1.49 thf(f162,plain,(
% 1.57/1.49 ( ! [X35 : $i,X32 : $i,X33 : $i] : (($true = (cR @ X32)) | (sP2 != $true) | ($true != (cQ @ X33)) | ((cP @ X35) = $false) | ($true = (cP @ sK45)) | ($true = sP0)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.57/1.49 thf(f117,plain,(
% 1.57/1.49 ( ! [X35 : $i,X32 : $i,X33 : $i] : ((sP2 != $true) | ($true != (cQ @ X33)) | ($true = sP0) | ($true = (cR @ X32)) | ((cP @ X35) = (cP @ sK45))) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f701,plain,(
% 1.57/1.49 spl76_4 | spl76_9 | spl76_55 | spl76_93 | ~spl76_12 | spl76_11),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f161,f283,f286,f642,f461,f276,f256])).
% 1.57/1.49 thf(f161,plain,(
% 1.57/1.49 ( ! [X35 : $i,X32 : $i,X33 : $i] : (((cP @ X35) = $true) | ($true = (cR @ X32)) | (sP2 != $true) | ($true != (cQ @ X33)) | ($false = (cP @ sK45)) | ($true = sP0)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f117])).
% 1.57/1.49 thf(f700,plain,(
% 1.57/1.49 spl76_98 | spl76_103 | spl76_4 | ~spl76_12 | spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f164,f276,f286,f256,f696,f666])).
% 1.57/1.49 thf(f164,plain,(
% 1.57/1.49 ( ! [X28 : $i,X26 : $i] : ((sP2 != $true) | ((cR @ X26) = $true) | ($false = (cP @ X28)) | ($true = sP0) | ((cQ @ sK41) = $true) | ($false = (cP @ (sK42 @ X28)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.57/1.49 thf(f119,plain,(
% 1.57/1.49 ( ! [X28 : $i,X26 : $i] : (((cP @ X28) != (cP @ (sK42 @ X28))) | ($true = sP0) | ((cQ @ sK41) = $true) | (sP2 != $true) | ((cR @ X26) = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f699,plain,(
% 1.57/1.49 spl76_4 | spl76_103 | spl76_97 | ~spl76_12 | spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f163,f276,f286,f662,f696,f256])).
% 1.57/1.49 thf(f163,plain,(
% 1.57/1.49 ( ! [X28 : $i,X26 : $i] : (($true = sP0) | ($true = (cP @ (sK42 @ X28))) | ((cQ @ sK41) = $true) | ((cR @ X26) = $true) | (sP2 != $true) | ($true = (cP @ X28))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f119])).
% 1.57/1.49 thf(f694,plain,(
% 1.57/1.49 spl76_1 | spl76_20 | spl76_102 | spl76_53),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f166,f454,f690,f317,f244])).
% 1.57/1.49 thf(f166,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : (((cP @ sK53) = $true) | (sP1 = $true) | ($false = (cS @ (sK54 @ X4))) | ((cS @ X4) = $false) | ($true = (cQ @ X2))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.57/1.49 thf(f135,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : ((sP1 = $true) | ((cS @ X4) != (cS @ (sK54 @ X4))) | ($true = (cQ @ X2)) | ((cP @ sK53) = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.49 thf(f693,plain,(
% 1.57/1.49 spl76_51 | spl76_20 | spl76_1 | spl76_102),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f165,f690,f244,f317,f446])).
% 1.57/1.49 thf(f165,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : (((cS @ X4) = $true) | (sP1 = $true) | ($true = (cQ @ X2)) | ((cP @ sK53) = $true) | ((cS @ (sK54 @ X4)) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 1.57/1.49 thf(f688,plain,(
% 1.57/1.49 ~spl76_1 | spl76_56 | ~spl76_5 | spl76_101 | ~spl76_100),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f168,f680,f684,f259,f465,f244])).
% 1.57/1.49 thf(f168,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (((cP @ sK26) != $true) | (sP1 != $true) | (sP3 != $true) | ((cR @ X46) = $false) | ($false = (cR @ (sK27 @ X46))) | ((cS @ sK25) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.57/1.49 thf(f98,plain,(
% 1.57/1.49 ( ! [X46 : $i] : (((cS @ sK25) = $true) | (sP3 != $true) | (sP1 != $true) | ((cR @ X46) != (cR @ (sK27 @ X46))) | ((cP @ sK26) != $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f687,plain,(
% 1.57/1.49 ~spl76_1 | ~spl76_100 | ~spl76_5 | spl76_54 | spl76_101),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f167,f684,f458,f259,f680,f244])).
% 1.57/1.49 thf(f167,plain,(
% 1.57/1.49 ( ! [X46 : $i] : ((sP1 != $true) | (sP3 != $true) | ((cR @ X46) = $true) | ((cS @ sK25) = $true) | ((cP @ sK26) != $true) | ((cR @ (sK27 @ X46)) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f98])).
% 1.57/1.49 thf(f678,plain,(
% 1.57/1.49 spl76_99 | ~spl76_5 | spl76_55 | spl76_50 | spl76_1),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f170,f244,f442,f461,f259,f674])).
% 1.57/1.49 thf(f170,plain,(
% 1.57/1.49 ( ! [X28 : $i,X26 : $i] : (((cP @ X26) = $true) | ($false = (cR @ X28)) | (sP1 = $true) | (sP3 != $true) | ((cS @ sK17) = $true) | ($false = (cR @ (sK18 @ X28)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.57/1.49 thf(f103,plain,(
% 1.57/1.49 ( ! [X28 : $i,X26 : $i] : ((sP3 != $true) | ((cR @ (sK18 @ X28)) != (cR @ X28)) | (sP1 = $true) | ((cP @ X26) = $true) | ((cS @ sK17) = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f677,plain,(
% 1.57/1.49 spl76_55 | spl76_1 | ~spl76_5 | spl76_99 | spl76_49),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f169,f438,f674,f259,f244,f461])).
% 1.57/1.49 thf(f169,plain,(
% 1.57/1.49 ( ! [X28 : $i,X26 : $i] : (((cP @ X26) = $true) | (sP1 = $true) | ($true = (cR @ X28)) | ((cS @ sK17) = $true) | (sP3 != $true) | ((cR @ (sK18 @ X28)) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.57/1.49 thf(f672,plain,(
% 1.57/1.49 spl76_12 | spl76_4 | spl76_55 | ~spl76_9 | spl76_11 | spl76_74),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f172,f551,f283,f276,f461,f256,f286])).
% 1.57/1.49 thf(f172,plain,(
% 1.57/1.49 ( ! [X11 : $i,X8 : $i,X9 : $i] : ((sP2 = $true) | ($true != sP0) | ($true = (cP @ X11)) | ($false = (cP @ sK33)) | ($true != (cQ @ X9)) | ((cR @ X8) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.57/1.49 thf(f125,plain,(
% 1.57/1.49 ( ! [X11 : $i,X8 : $i,X9 : $i] : (((cP @ sK33) = (cP @ X11)) | ($true != sP0) | ($true != (cQ @ X9)) | (sP2 = $true) | ((cR @ X8) = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f671,plain,(
% 1.57/1.49 spl76_72 | spl76_4 | spl76_62 | ~spl76_9 | spl76_11 | spl76_12),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f171,f286,f283,f276,f495,f256,f542])).
% 1.57/1.49 thf(f171,plain,(
% 1.57/1.49 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($false = (cP @ X11)) | ($true != sP0) | ((cR @ X8) = $true) | ((cP @ sK33) = $true) | (sP2 = $true) | ($true != (cQ @ X9))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f125])).
% 1.57/1.49 thf(f670,plain,(
% 1.57/1.49 spl76_16 | spl76_1 | spl76_5 | spl76_55 | spl76_89),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f174,f624,f461,f259,f244,f302])).
% 1.57/1.49 thf(f174,plain,(
% 1.57/1.49 ( ! [X21 : $i,X22 : $i,X20 : $i] : (((cR @ X22) = $false) | (sP1 = $true) | (sP3 = $true) | ((cS @ X21) != $true) | ((cP @ X20) = $true) | ($false = (cR @ (sK15 @ X22)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.57/1.49 thf(f105,plain,(
% 1.57/1.49 ( ! [X21 : $i,X22 : $i,X20 : $i] : (((cS @ X21) != $true) | ((cR @ X22) != (cR @ (sK15 @ X22))) | ((cP @ X20) = $true) | (sP1 = $true) | (sP3 = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f669,plain,(
% 1.57/1.49 spl76_5 | spl76_86 | spl76_1 | spl76_55 | spl76_16),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f173,f302,f461,f244,f612,f259])).
% 1.57/1.49 thf(f173,plain,(
% 1.57/1.49 ( ! [X21 : $i,X22 : $i,X20 : $i] : (((cR @ X22) = $true) | (sP1 = $true) | (sP3 = $true) | ((cS @ X21) != $true) | ((cP @ X20) = $true) | ($true = (cR @ (sK15 @ X22)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f105])).
% 1.57/1.49 thf(f668,plain,(
% 1.57/1.49 spl76_11 | spl76_9 | spl76_98 | ~spl76_12 | ~spl76_96),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f176,f658,f286,f666,f276,f283])).
% 1.57/1.49 thf(f176,plain,(
% 1.57/1.49 ( ! [X28 : $i,X25 : $i] : (($true != (cQ @ X25)) | ($false = (cP @ (sK42 @ X28))) | (sP2 != $true) | ($true = sP0) | ($false = (cP @ X28)) | ((cR @ sK40) != $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.57/1.49 thf(f120,plain,(
% 1.57/1.49 ( ! [X28 : $i,X25 : $i] : ((sP2 != $true) | ((cP @ X28) != (cP @ (sK42 @ X28))) | ($true != (cQ @ X25)) | ($true = sP0) | ((cR @ sK40) != $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f664,plain,(
% 1.57/1.49 ~spl76_96 | spl76_11 | ~spl76_12 | spl76_97 | spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f175,f276,f662,f286,f283,f658])).
% 1.57/1.49 thf(f175,plain,(
% 1.57/1.49 ( ! [X28 : $i,X25 : $i] : (($true = sP0) | ($true = (cP @ (sK42 @ X28))) | ($true != (cQ @ X25)) | ($true = (cP @ X28)) | ((cR @ sK40) != $true) | (sP2 != $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f120])).
% 1.57/1.49 thf(f656,plain,(
% 1.57/1.49 spl76_12 | spl76_95 | ~spl76_9 | spl76_4 | spl76_68),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f178,f524,f256,f276,f652,f286])).
% 1.57/1.49 thf(f178,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : (($true != sP0) | ((cP @ X4) = $false) | (sP2 = $true) | ($true = (cR @ X2)) | ((cQ @ sK29) = $true) | ($false = (cP @ (sK30 @ X4)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.57/1.49 thf(f127,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : (((cP @ X4) != (cP @ (sK30 @ X4))) | ($true != sP0) | ($true = (cR @ X2)) | ((cQ @ sK29) = $true) | (sP2 = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f655,plain,(
% 1.57/1.49 spl76_95 | spl76_4 | spl76_67 | spl76_12 | ~spl76_9),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f177,f276,f286,f520,f256,f652])).
% 1.57/1.49 thf(f177,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : (($true != sP0) | ($true = (cR @ X2)) | ((cQ @ sK29) = $true) | ($true = (cP @ (sK30 @ X4))) | (sP2 = $true) | ((cP @ X4) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f127])).
% 1.57/1.49 thf(f650,plain,(
% 1.57/1.49 spl76_62 | spl76_9 | ~spl76_91 | spl76_92 | spl76_94 | ~spl76_12),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f180,f286,f647,f638,f634,f276,f495])).
% 1.57/1.49 thf(f180,plain,(
% 1.57/1.49 ( ! [X35 : $i] : (((cQ @ sK43) = $true) | ($true != (cR @ sK44)) | ((cP @ X35) = $false) | ($true = (cP @ sK45)) | (sP2 != $true) | ($true = sP0)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.57/1.49 thf(f118,plain,(
% 1.57/1.49 ( ! [X35 : $i] : (($true != (cR @ sK44)) | ((cQ @ sK43) = $true) | (sP2 != $true) | ((cP @ X35) = (cP @ sK45)) | ($true = sP0)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.49 thf(f645,plain,(
% 1.57/1.49 ~spl76_91 | spl76_55 | spl76_92 | ~spl76_12 | spl76_9 | spl76_93),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f179,f642,f276,f286,f638,f461,f634])).
% 1.57/1.49 thf(f179,plain,(
% 1.57/1.49 ( ! [X35 : $i] : ((sP2 != $true) | ((cQ @ sK43) = $true) | ((cP @ X35) = $true) | ($false = (cP @ sK45)) | ($true != (cR @ sK44)) | ($true = sP0)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f118])).
% 1.57/1.49 thf(f632,plain,(
% 1.57/1.49 spl76_17 | spl76_90 | spl76_5 | ~spl76_1 | spl76_55),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f182,f461,f244,f259,f628,f306])).
% 1.57/1.49 thf(f182,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : ((sP1 != $true) | ($true = (cP @ X2)) | ($false = (cR @ X4)) | (sP3 = $true) | ((cS @ sK5) = $true) | ($false = (cR @ (sK6 @ X4)))) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.57/1.49 thf(f111,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : (($true = (cP @ X2)) | (sP3 = $true) | ((cR @ (sK6 @ X4)) != (cR @ X4)) | (sP1 != $true) | ((cS @ sK5) = $true)) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f631,plain,(
% 1.57/1.49 ~spl76_1 | spl76_55 | spl76_5 | spl76_90 | spl76_15),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f181,f299,f628,f259,f461,f244])).
% 1.57/1.49 thf(f181,plain,(
% 1.57/1.49 ( ! [X2 : $i,X4 : $i] : ((sP3 = $true) | ((cS @ sK5) = $true) | ($true = (cP @ X2)) | ($true = (cR @ X4)) | (sP1 != $true) | ((cR @ (sK6 @ X4)) = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f111])).
% 1.57/1.49 thf(f626,plain,(
% 1.57/1.49 ~spl76_87 | spl76_88 | spl76_5 | spl76_89 | spl76_1),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f184,f244,f624,f259,f619,f615])).
% 1.57/1.49 thf(f184,plain,(
% 1.57/1.49 ( ! [X22 : $i] : (($false = (cR @ (sK15 @ X22))) | (sP3 = $true) | ((cR @ X22) = $false) | ($true = (cS @ sK13)) | ((cP @ sK14) != $true) | (sP1 = $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.57/1.49 thf(f106,plain,(
% 1.57/1.49 ( ! [X22 : $i] : ((sP1 = $true) | (sP3 = $true) | ((cP @ sK14) != $true) | ($true = (cS @ sK13)) | ((cR @ X22) != (cR @ (sK15 @ X22)))) )),
% 1.57/1.49 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.49 thf(f622,plain,(
% 1.57/1.49 spl76_1 | spl76_86 | spl76_5 | ~spl76_87 | spl76_88),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f183,f619,f615,f259,f612,f244])).
% 1.57/1.49 thf(f183,plain,(
% 1.57/1.49 ( ! [X22 : $i] : ((sP1 = $true) | (sP3 = $true) | ((cR @ X22) = $true) | ($true = (cS @ sK13)) | ($true = (cR @ (sK15 @ X22))) | ((cP @ sK14) != $true)) )),
% 1.57/1.49 inference(binary_proxy_clausification,[status(thm)],[f106])).
% 1.57/1.49 thf(f610,plain,(
% 1.57/1.49 spl76_85 | ~spl76_84 | spl76_1 | spl76_4 | spl76_16 | spl76_5),
% 1.57/1.49 inference(avatar_split_clause,[status(thm)],[f186,f259,f302,f256,f244,f602,f607])).
% 1.57/1.50 thf(f186,plain,(
% 1.57/1.50 ( ! [X15 : $i,X13 : $i] : ((sP1 = $true) | ($false = (cR @ sK10)) | ($true != (cP @ sK11)) | (sP3 = $true) | ($true = (cR @ X13)) | ($true != (cS @ X15))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.57/1.50 thf(f108,plain,(
% 1.57/1.50 ( ! [X15 : $i,X13 : $i] : (($true != (cP @ sK11)) | ($true != (cS @ X15)) | ((cR @ sK10) = (cR @ X13)) | (sP1 = $true) | (sP3 = $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f605,plain,(
% 1.57/1.50 spl76_16 | spl76_83 | spl76_7 | ~spl76_84 | spl76_1 | spl76_5),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f185,f259,f244,f602,f268,f598,f302])).
% 1.57/1.50 thf(f185,plain,(
% 1.57/1.50 ( ! [X15 : $i,X13 : $i] : ((sP3 = $true) | ($false = (cR @ X13)) | (sP1 = $true) | ($true != (cP @ sK11)) | ($true != (cS @ X15)) | ((cR @ sK10) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f108])).
% 1.57/1.50 thf(f596,plain,(
% 1.57/1.50 spl76_76 | ~spl76_82 | spl76_7 | ~spl76_1 | spl76_81 | spl76_5),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f188,f259,f588,f244,f268,f592,f561])).
% 1.57/1.50 thf(f188,plain,(
% 1.57/1.50 ( ! [X11 : $i] : ((sP1 != $true) | ($true = (cR @ sK9)) | ((cS @ sK7) = $true) | (sP3 = $true) | ((cP @ sK8) != $true) | ((cR @ X11) = $false)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.57/1.50 thf(f110,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (((cR @ X11) = (cR @ sK9)) | ((cP @ sK8) != $true) | ((cS @ sK7) = $true) | (sP3 = $true) | (sP1 != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f595,plain,(
% 1.57/1.50 spl76_81 | ~spl76_1 | spl76_75 | spl76_5 | spl76_4 | ~spl76_82),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f187,f592,f256,f259,f556,f244,f588])).
% 1.57/1.50 thf(f187,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (((cR @ X11) = $true) | ($false = (cR @ sK9)) | (sP3 = $true) | ((cS @ sK7) = $true) | (sP1 != $true) | ((cP @ sK8) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f110])).
% 1.57/1.50 thf(f586,plain,(
% 1.57/1.50 ~spl76_78 | spl76_80 | spl76_7 | ~spl76_5 | spl76_16 | ~spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f190,f244,f302,f259,f268,f583,f574])).
% 1.57/1.50 thf(f190,plain,(
% 1.57/1.50 ( ! [X39 : $i,X37 : $i] : ((sP1 != $true) | ((cR @ X37) = $false) | (sP3 != $true) | ($true = (cR @ sK22)) | ($true != (cS @ X39)) | ($true != (cP @ sK23))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.57/1.50 thf(f100,plain,(
% 1.57/1.50 ( ! [X39 : $i,X37 : $i] : ((sP3 != $true) | ((cR @ X37) = (cR @ sK22)) | (sP1 != $true) | ($true != (cP @ sK23)) | ($true != (cS @ X39))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f581,plain,(
% 1.57/1.50 ~spl76_5 | ~spl76_78 | spl76_16 | ~spl76_1 | spl76_79 | spl76_4),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f189,f256,f578,f244,f302,f574,f259])).
% 1.57/1.50 thf(f189,plain,(
% 1.57/1.50 ( ! [X39 : $i,X37 : $i] : (($true != (cS @ X39)) | ($true != (cP @ sK23)) | ($false = (cR @ sK22)) | ((cR @ X37) = $true) | (sP1 != $true) | (sP3 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.57/1.50 thf(f572,plain,(
% 1.57/1.50 spl76_11 | ~spl76_77 | spl76_63 | spl76_62 | ~spl76_12 | ~spl76_9),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f192,f276,f286,f495,f498,f568,f283])).
% 1.57/1.50 thf(f192,plain,(
% 1.57/1.50 ( ! [X39 : $i,X37 : $i] : ((sP2 != $true) | ((cP @ X37) = $false) | ((cP @ sK46) = $true) | ($true != sP0) | ($true != (cR @ sK47)) | ((cQ @ X39) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.57/1.50 thf(f116,plain,(
% 1.57/1.50 ( ! [X39 : $i,X37 : $i] : (($true != sP0) | ((cQ @ X39) != $true) | ($true != (cR @ sK47)) | (sP2 != $true) | ((cP @ X37) = (cP @ sK46))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f571,plain,(
% 1.57/1.50 ~spl76_9 | spl76_60 | spl76_11 | ~spl76_77 | ~spl76_12 | spl76_55),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f191,f461,f286,f568,f283,f486,f276])).
% 1.57/1.50 thf(f191,plain,(
% 1.57/1.50 ( ! [X39 : $i,X37 : $i] : (((cP @ X37) = $true) | ((cQ @ X39) != $true) | ($true != sP0) | ($false = (cP @ sK46)) | ($true != (cR @ sK47)) | (sP2 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f116])).
% 1.57/1.50 thf(f566,plain,(
% 1.57/1.50 spl76_47 | spl76_4 | spl76_11 | spl76_9 | spl76_12),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f194,f286,f276,f283,f256,f430])).
% 1.57/1.50 thf(f194,plain,(
% 1.57/1.50 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true != (cQ @ X21)) | ($false = (cP @ (sK39 @ X22))) | ($true = (cR @ X20)) | (sP2 = $true) | ($false = (cP @ X22)) | ($true = sP0)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.57/1.50 thf(f121,plain,(
% 1.57/1.50 ( ! [X21 : $i,X22 : $i,X20 : $i] : (($true != (cQ @ X21)) | ($true = (cR @ X20)) | ($true = sP0) | (sP2 = $true) | ((cP @ (sK39 @ X22)) != (cP @ X22))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f565,plain,(
% 1.57/1.50 spl76_44 | spl76_12 | spl76_9 | spl76_11 | spl76_4),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f193,f256,f283,f276,f286,f418])).
% 1.57/1.50 thf(f193,plain,(
% 1.57/1.50 ( ! [X21 : $i,X22 : $i,X20 : $i] : ((sP2 = $true) | ((cP @ (sK39 @ X22)) = $true) | ($true != (cQ @ X21)) | ($true = (cR @ X20)) | ($true = sP0) | ($true = (cP @ X22))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f121])).
% 1.57/1.50 thf(f564,plain,(
% 1.57/1.50 spl76_5 | ~spl76_1 | spl76_76 | spl76_7 | spl76_55 | spl76_16),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f196,f302,f461,f268,f561,f244,f259])).
% 1.57/1.50 thf(f196,plain,(
% 1.57/1.50 ( ! [X11 : $i,X8 : $i,X9 : $i] : (((cR @ X11) = $false) | ($true != (cS @ X9)) | (sP3 = $true) | (sP1 != $true) | ((cP @ X8) = $true) | ($true = (cR @ sK9))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.57/1.50 thf(f109,plain,(
% 1.57/1.50 ( ! [X11 : $i,X8 : $i,X9 : $i] : (((cP @ X8) = $true) | ($true != (cS @ X9)) | (sP3 = $true) | (sP1 != $true) | ((cR @ X11) = (cR @ sK9))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f559,plain,(
% 1.57/1.50 spl76_75 | spl76_16 | spl76_5 | ~spl76_1 | spl76_4 | spl76_55),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f195,f461,f256,f244,f259,f302,f556])).
% 1.57/1.50 thf(f195,plain,(
% 1.57/1.50 ( ! [X11 : $i,X8 : $i,X9 : $i] : (($false = (cR @ sK9)) | (sP3 = $true) | ($true != (cS @ X9)) | ((cR @ X11) = $true) | (sP1 != $true) | ((cP @ X8) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f109])).
% 1.57/1.50 thf(f554,plain,(
% 1.57/1.50 ~spl76_73 | spl76_74 | spl76_12 | ~spl76_9 | spl76_71 | spl76_55),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f198,f461,f538,f276,f286,f551,f546])).
% 1.57/1.50 thf(f198,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (($false = (cP @ sK33)) | ($true != (cR @ sK32)) | ($true != sP0) | (sP2 = $true) | ((cQ @ sK31) = $true) | ($true = (cP @ X11))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.57/1.50 thf(f126,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (($true != sP0) | ((cQ @ sK31) = $true) | ((cP @ sK33) = (cP @ X11)) | (sP2 = $true) | ($true != (cR @ sK32))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f549,plain,(
% 1.57/1.50 spl76_62 | ~spl76_9 | spl76_71 | spl76_12 | spl76_72 | ~spl76_73),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f197,f546,f542,f286,f538,f276,f495])).
% 1.57/1.50 thf(f197,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (($true != (cR @ sK32)) | ($true != sP0) | ($false = (cP @ X11)) | ((cQ @ sK31) = $true) | (sP2 = $true) | ((cP @ sK33) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f126])).
% 1.57/1.50 thf(f536,plain,(
% 1.57/1.50 spl76_70 | ~spl76_69 | spl76_58 | ~spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f200,f244,f473,f528,f532])).
% 1.57/1.50 thf(f200,plain,(
% 1.57/1.50 ( ! [X22 : $i] : ((sP1 != $true) | ($false = (cS @ X22)) | ((cS @ (sK63 @ X22)) = $false) | ($true = (cP @ sK61)) | ($true != (cQ @ sK62))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.57/1.50 thf(f130,plain,(
% 1.57/1.50 ( ! [X22 : $i] : (((cS @ (sK63 @ X22)) != (cS @ X22)) | ($true != (cQ @ sK62)) | (sP1 != $true) | ($true = (cP @ sK61))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.50 thf(f535,plain,(
% 1.57/1.50 ~spl76_69 | ~spl76_1 | spl76_70 | spl76_57),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f199,f469,f532,f244,f528])).
% 1.57/1.50 thf(f199,plain,(
% 1.57/1.50 ( ! [X22 : $i] : ((sP1 != $true) | ($true != (cQ @ sK62)) | ((cS @ (sK63 @ X22)) = $true) | ($true = (cS @ X22)) | ($true = (cP @ sK61))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f130])).
% 1.57/1.50 thf(f526,plain,(
% 1.57/1.50 spl76_11 | spl76_12 | ~spl76_9 | spl76_68 | ~spl76_66),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f202,f516,f524,f276,f286,f283])).
% 1.57/1.50 thf(f202,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (($true != (cR @ sK28)) | ($false = (cP @ (sK30 @ X4))) | (sP2 = $true) | ($true != sP0) | ((cP @ X4) = $false) | ((cQ @ X1) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.57/1.50 thf(f128,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (((cQ @ X1) != $true) | ($true != (cR @ sK28)) | ((cP @ X4) != (cP @ (sK30 @ X4))) | (sP2 = $true) | ($true != sP0)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f522,plain,(
% 1.57/1.50 ~spl76_9 | spl76_12 | ~spl76_66 | spl76_11 | spl76_67),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f201,f520,f283,f516,f286,f276])).
% 1.57/1.50 thf(f201,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : ((sP2 = $true) | ((cP @ X4) = $true) | ((cQ @ X1) != $true) | ($true = (cP @ (sK30 @ X4))) | ($true != sP0) | ($true != (cR @ sK28))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.57/1.50 thf(f514,plain,(
% 1.57/1.50 spl76_12 | spl76_5),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f145,f259,f286])).
% 1.57/1.50 thf(f145,plain,(
% 1.57/1.50 (sP3 = $true) | (sP2 = $true)),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f96])).
% 1.57/1.50 thf(f96,plain,(
% 1.57/1.50 ((sP3 != $true) | (sP2 != $true)) & ((sP3 = $true) | (sP2 = $true))),
% 1.57/1.50 inference(nnf_transformation,[status(thm)],[f11])).
% 1.57/1.50 thf(f11,plain,(
% 1.57/1.50 (sP2 = $true) <~> (sP3 = $true)),
% 1.57/1.50 inference(definition_folding,[status(thm)],[f6,f10,f9,f8,f7])).
% 1.57/1.50 thf(f6,plain,(
% 1.57/1.50 (((! [X11 : $i] : ((cS @ X11) = $true) <=> ? [X10 : $i] : ($true = (cR @ X10))) <=> ? [X8 : $i] : ! [X9 : $i] : ((cQ @ X9) = (cQ @ X8))) <=> (? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14)) <=> (? [X13 : $i] : ($true = (cQ @ X13)) <=> ! [X12 : $i] : ((cR @ X12) = $true)))) <~> ((? [X6 : $i] : ! [X7 : $i] : ((cS @ X7) = (cS @ X6)) <=> (? [X4 : $i] : ((cP @ X4) = $true) <=> ! [X5 : $i] : ((cQ @ X5) = $true))) <=> (? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0)) <=> (? [X2 : $i] : ((cS @ X2) = $true) <=> ! [X3 : $i] : ($true = (cP @ X3)))))),
% 1.57/1.50 inference(ennf_transformation,[status(thm)],[f5])).
% 1.57/1.50 thf(f5,plain,(
% 1.57/1.50 ~(((? [X6 : $i] : ! [X7 : $i] : ((cS @ X7) = (cS @ X6)) <=> (? [X4 : $i] : ((cP @ X4) = $true) <=> ! [X5 : $i] : ((cQ @ X5) = $true))) <=> (? [X0 : $i] : ! [X1 : $i] : ((cR @ X1) = (cR @ X0)) <=> (? [X2 : $i] : ((cS @ X2) = $true) <=> ! [X3 : $i] : ($true = (cP @ X3))))) <=> (((! [X11 : $i] : ((cS @ X11) = $true) <=> ? [X10 : $i] : ($true = (cR @ X10))) <=> ? [X8 : $i] : ! [X9 : $i] : ((cQ @ X9) = (cQ @ X8))) <=> (? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) = (cP @ X14)) <=> (? [X13 : $i] : ($true = (cQ @ X13)) <=> ! [X12 : $i] : ((cR @ X12) = $true)))))),
% 1.57/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.50 thf(f4,plain,(
% 1.57/1.50 ~(((? [X0 : $i] : ! [X1 : $i] : ((cR @ X0) <=> (cR @ X1)) <=> (? [X2 : $i] : (cS @ X2) <=> ! [X3 : $i] : (cP @ X3))) <=> ((? [X4 : $i] : (cP @ X4) <=> ! [X5 : $i] : (cQ @ X5)) <=> ? [X6 : $i] : ! [X7 : $i] : ((cS @ X7) <=> (cS @ X6)))) <=> ((? [X8 : $i] : ! [X9 : $i] : ((cQ @ X9) <=> (cQ @ X8)) <=> (? [X10 : $i] : (cR @ X10) <=> ! [X11 : $i] : (cS @ X11))) <=> ((! [X12 : $i] : (cR @ X12) <=> ? [X13 : $i] : (cQ @ X13)) <=> ? [X14 : $i] : ! [X15 : $i] : ((cP @ X15) <=> (cP @ X14)))))),
% 1.57/1.50 inference(rectify,[status(thm)],[f2])).
% 1.57/1.50 thf(f2,negated_conjecture,(
% 1.57/1.50 ~(((? [X0 : $i] : ! [X1 : $i] : ((cR @ X0) <=> (cR @ X1)) <=> (? [X0 : $i] : (cS @ X0) <=> ! [X1 : $i] : (cP @ X1))) <=> ((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cQ @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cS @ X1) <=> (cS @ X0)))) <=> ((? [X0 : $i] : ! [X1 : $i] : ((cQ @ X1) <=> (cQ @ X0)) <=> (? [X0 : $i] : (cR @ X0) <=> ! [X1 : $i] : (cS @ X1))) <=> ((! [X1 : $i] : (cR @ X1) <=> ? [X0 : $i] : (cQ @ X0)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1) <=> (cP @ X0)))))),
% 1.57/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.50 thf(f1,conjecture,(
% 1.57/1.50 ((? [X0 : $i] : ! [X1 : $i] : ((cR @ X0) <=> (cR @ X1)) <=> (? [X0 : $i] : (cS @ X0) <=> ! [X1 : $i] : (cP @ X1))) <=> ((? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cQ @ X1)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cS @ X1) <=> (cS @ X0)))) <=> ((? [X0 : $i] : ! [X1 : $i] : ((cQ @ X1) <=> (cQ @ X0)) <=> (? [X0 : $i] : (cR @ X0) <=> ! [X1 : $i] : (cS @ X1))) <=> ((! [X1 : $i] : (cR @ X1) <=> ? [X0 : $i] : (cQ @ X0)) <=> ? [X0 : $i] : ! [X1 : $i] : ((cP @ X1) <=> (cP @ X0))))),
% 1.57/1.50 file('/export/starexec/sandbox2/tmp/tmp.DDLV6Zgj3R/DTF2THF_10908.p',cTHM138)).
% 1.57/1.50 thf(f513,plain,(
% 1.57/1.50 spl76_8 | spl76_55 | spl76_7 | spl76_16 | ~spl76_5 | spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f204,f244,f259,f302,f268,f461,f271])).
% 1.57/1.50 thf(f204,plain,(
% 1.57/1.50 ( ! [X35 : $i,X32 : $i,X33 : $i] : (($false = (cR @ X35)) | ($true = (cR @ sK21)) | ($true = (cP @ X32)) | (sP1 = $true) | ((cS @ X33) != $true) | (sP3 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.57/1.50 thf(f101,plain,(
% 1.57/1.50 ( ! [X35 : $i,X32 : $i,X33 : $i] : (((cS @ X33) != $true) | ($true = (cP @ X32)) | (sP1 = $true) | ((cR @ X35) = (cR @ sK21)) | (sP3 != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f512,plain,(
% 1.57/1.50 spl76_6 | spl76_55 | spl76_4 | ~spl76_5 | spl76_16 | spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f203,f244,f302,f259,f256,f461,f263])).
% 1.57/1.50 thf(f203,plain,(
% 1.57/1.50 ( ! [X35 : $i,X32 : $i,X33 : $i] : (($false = (cR @ sK21)) | ((cR @ X35) = $true) | (sP3 != $true) | ((cS @ X33) != $true) | ($true = (cP @ X32)) | (sP1 = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f101])).
% 1.57/1.50 thf(f511,plain,(
% 1.57/1.50 spl76_27 | spl76_65 | spl76_19 | ~spl76_64 | spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f206,f244,f503,f314,f507,f344])).
% 1.57/1.50 thf(f206,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (((cS @ sK57) = $false) | ((cS @ X11) = $true) | (sP1 = $true) | ($true != (cQ @ sK56)) | ((cP @ sK55) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.57/1.50 thf(f134,plain,(
% 1.57/1.50 ( ! [X11 : $i] : (($true != (cQ @ sK56)) | (sP1 = $true) | ((cP @ sK55) = $true) | ((cS @ sK57) = (cS @ X11))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.50 thf(f510,plain,(
% 1.57/1.50 ~spl76_64 | spl76_65 | spl76_1 | spl76_25 | spl76_26),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f205,f339,f336,f244,f507,f503])).
% 1.57/1.50 thf(f205,plain,(
% 1.57/1.50 ( ! [X11 : $i] : ((sP1 = $true) | ((cP @ sK55) = $true) | ($true != (cQ @ sK56)) | ((cS @ sK57) = $true) | ((cS @ X11) = $false)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.57/1.50 thf(f501,plain,(
% 1.57/1.50 ~spl76_9 | ~spl76_12 | spl76_62 | spl76_61 | spl76_4 | spl76_63),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f208,f498,f256,f490,f495,f286,f276])).
% 1.57/1.50 thf(f208,plain,(
% 1.57/1.50 ( ! [X40 : $i,X37 : $i] : ((sP2 != $true) | ((cP @ sK46) = $true) | ((cP @ X37) = $false) | ((cQ @ sK48) = $true) | ($true != sP0) | ($true = (cR @ X40))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.57/1.50 thf(f115,plain,(
% 1.57/1.50 ( ! [X40 : $i,X37 : $i] : (($true != sP0) | (sP2 != $true) | ((cP @ X37) = (cP @ sK46)) | ((cQ @ sK48) = $true) | ($true = (cR @ X40))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f493,plain,(
% 1.57/1.50 ~spl76_12 | spl76_4 | spl76_60 | spl76_61 | ~spl76_9 | spl76_55),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f207,f461,f276,f490,f486,f256,f286])).
% 1.57/1.50 thf(f207,plain,(
% 1.57/1.50 ( ! [X40 : $i,X37 : $i] : (($true != sP0) | ((cP @ X37) = $true) | ($false = (cP @ sK46)) | ($true = (cR @ X40)) | ((cQ @ sK48) = $true) | (sP2 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f115])).
% 1.57/1.50 thf(f484,plain,(
% 1.57/1.50 spl76_20 | spl76_19 | spl76_35 | spl76_9 | spl76_40),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f210,f399,f276,f378,f314,f317])).
% 1.57/1.50 thf(f210,plain,(
% 1.57/1.50 ( ! [X8 : $i,X9 : $i,X7 : $i] : (((cS @ X8) = $true) | ((cQ @ X7) = $true) | ((cQ @ sK67) = $false) | ($true = sP0) | ((cR @ X9) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.57/1.50 thf(f142,plain,(
% 1.57/1.50 ( ! [X8 : $i,X9 : $i,X7 : $i] : (((cQ @ sK67) = (cQ @ X7)) | ((cR @ X9) != $true) | ($true = sP0) | ((cS @ X8) = $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f483,plain,(
% 1.57/1.50 spl76_9 | spl76_40 | spl76_22 | spl76_32 | spl76_19),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f209,f314,f365,f325,f399,f276])).
% 1.57/1.50 thf(f209,plain,(
% 1.57/1.50 ( ! [X8 : $i,X9 : $i,X7 : $i] : (($true = sP0) | ((cS @ X8) = $true) | ((cR @ X9) != $true) | ((cQ @ X7) = $false) | ((cQ @ sK67) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f142])).
% 1.57/1.50 thf(f482,plain,(
% 1.57/1.50 ~spl76_5 | ~spl76_12),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f146,f286,f259])).
% 1.57/1.50 thf(f146,plain,(
% 1.57/1.50 (sP2 != $true) | (sP3 != $true)),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f96])).
% 1.57/1.50 thf(f481,plain,(
% 1.57/1.50 spl76_23 | ~spl76_9 | ~spl76_59 | spl76_40 | spl76_22),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f212,f325,f399,f477,f276,f328])).
% 1.57/1.50 thf(f212,plain,(
% 1.57/1.50 ( ! [X19 : $i,X20 : $i] : (((cS @ sK74) != $true) | ($true = (cQ @ sK73)) | ($false = (cQ @ X19)) | ($true != (cR @ X20)) | ($true != sP0)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f138])).
% 1.57/1.50 thf(f138,plain,(
% 1.57/1.50 ( ! [X19 : $i,X20 : $i] : (((cQ @ X19) = (cQ @ sK73)) | ($true != sP0) | ($true != (cR @ X20)) | ((cS @ sK74) != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f480,plain,(
% 1.57/1.50 ~spl76_59 | spl76_21 | ~spl76_9 | spl76_40 | spl76_20),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f211,f317,f399,f276,f320,f477])).
% 1.57/1.50 thf(f211,plain,(
% 1.57/1.50 ( ! [X19 : $i,X20 : $i] : (($true != (cR @ X20)) | ((cS @ sK74) != $true) | ($true != sP0) | ($true = (cQ @ X19)) | ($false = (cQ @ sK73))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f138])).
% 1.57/1.50 thf(f475,plain,(
% 1.57/1.50 spl76_24 | ~spl76_1 | spl76_58 | spl76_20),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f214,f317,f473,f244,f333])).
% 1.57/1.50 thf(f214,plain,(
% 1.57/1.50 ( ! [X21 : $i,X22 : $i,X20 : $i] : (((cS @ (sK63 @ X22)) = $false) | (sP1 != $true) | ($false = (cS @ X22)) | ((cP @ X21) != $true) | ((cQ @ X20) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.57/1.50 thf(f129,plain,(
% 1.57/1.50 ( ! [X21 : $i,X22 : $i,X20 : $i] : (((cP @ X21) != $true) | ((cS @ (sK63 @ X22)) != (cS @ X22)) | ((cQ @ X20) = $true) | (sP1 != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.50 thf(f471,plain,(
% 1.57/1.50 spl76_57 | spl76_20 | ~spl76_1 | spl76_24),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f213,f333,f244,f317,f469])).
% 1.57/1.50 thf(f213,plain,(
% 1.57/1.50 ( ! [X21 : $i,X22 : $i,X20 : $i] : (((cP @ X21) != $true) | ((cQ @ X20) = $true) | ((cS @ (sK63 @ X22)) = $true) | ($true = (cS @ X22)) | (sP1 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f129])).
% 1.57/1.50 thf(f467,plain,(
% 1.57/1.50 spl76_55 | ~spl76_1 | spl76_16 | ~spl76_5 | spl76_56),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f216,f465,f259,f302,f244,f461])).
% 1.57/1.50 thf(f216,plain,(
% 1.57/1.50 ( ! [X46 : $i,X44 : $i,X45 : $i] : (($false = (cR @ (sK27 @ X46))) | (sP1 != $true) | ((cR @ X46) = $false) | ($true = (cP @ X44)) | ((cS @ X45) != $true) | (sP3 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.57/1.50 thf(f97,plain,(
% 1.57/1.50 ( ! [X46 : $i,X44 : $i,X45 : $i] : (((cR @ X46) != (cR @ (sK27 @ X46))) | ((cS @ X45) != $true) | ($true = (cP @ X44)) | (sP3 != $true) | (sP1 != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f463,plain,(
% 1.57/1.50 spl76_54 | spl76_16 | ~spl76_1 | ~spl76_5 | spl76_55),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f215,f461,f259,f244,f302,f458])).
% 1.57/1.50 thf(f215,plain,(
% 1.57/1.50 ( ! [X46 : $i,X44 : $i,X45 : $i] : (((cS @ X45) != $true) | ((cR @ X46) = $true) | (sP3 != $true) | ($true = (cP @ X44)) | (sP1 != $true) | ((cR @ (sK27 @ X46)) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.57/1.50 thf(f456,plain,(
% 1.57/1.50 spl76_53 | ~spl76_52 | spl76_1 | spl76_24),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f218,f333,f244,f449,f454])).
% 1.57/1.50 thf(f218,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : ((sP1 = $true) | ((cP @ X1) != $true) | ((cS @ X4) = $false) | ($false = (cS @ (sK54 @ X4))) | ((cQ @ sK52) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.57/1.50 thf(f136,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (((cS @ X4) != (cS @ (sK54 @ X4))) | ((cQ @ sK52) != $true) | (sP1 = $true) | ((cP @ X1) != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.50 thf(f452,plain,(
% 1.57/1.50 spl76_24 | spl76_51 | spl76_1 | ~spl76_52),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f217,f449,f244,f446,f333])).
% 1.57/1.50 thf(f217,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (((cQ @ sK52) != $true) | (sP1 = $true) | ((cS @ (sK54 @ X4)) = $true) | ((cS @ X4) = $true) | ((cP @ X1) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f136])).
% 1.57/1.50 thf(f444,plain,(
% 1.57/1.50 spl76_50 | spl76_16 | ~spl76_48 | ~spl76_5 | spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f220,f244,f259,f434,f302,f442])).
% 1.57/1.50 thf(f220,plain,(
% 1.57/1.50 ( ! [X28 : $i,X25 : $i] : (($false = (cR @ X28)) | (sP3 != $true) | ((cP @ sK16) != $true) | ($false = (cR @ (sK18 @ X28))) | ((cS @ X25) != $true) | (sP1 = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.57/1.50 thf(f104,plain,(
% 1.57/1.50 ( ! [X28 : $i,X25 : $i] : ((sP1 = $true) | (sP3 != $true) | ((cS @ X25) != $true) | ((cP @ sK16) != $true) | ((cR @ (sK18 @ X28)) != (cR @ X28))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f440,plain,(
% 1.57/1.50 ~spl76_48 | spl76_16 | spl76_1 | spl76_49 | ~spl76_5),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f219,f259,f438,f244,f302,f434])).
% 1.57/1.50 thf(f219,plain,(
% 1.57/1.50 ( ! [X28 : $i,X25 : $i] : (((cR @ (sK18 @ X28)) = $true) | ($true = (cR @ X28)) | ((cS @ X25) != $true) | ((cP @ sK16) != $true) | (sP3 != $true) | (sP1 = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.57/1.50 thf(f432,plain,(
% 1.57/1.50 spl76_9 | spl76_47 | spl76_12 | ~spl76_46 | spl76_45),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f222,f421,f425,f286,f430,f276])).
% 1.57/1.50 thf(f222,plain,(
% 1.57/1.50 ( ! [X22 : $i] : (((cQ @ sK37) = $true) | ($false = (cP @ X22)) | ($true = sP0) | (sP2 = $true) | ($false = (cP @ (sK39 @ X22))) | ($true != (cR @ sK38))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.57/1.50 thf(f122,plain,(
% 1.57/1.50 ( ! [X22 : $i] : ((sP2 = $true) | ($true != (cR @ sK38)) | ((cQ @ sK37) = $true) | ((cP @ (sK39 @ X22)) != (cP @ X22)) | ($true = sP0)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f428,plain,(
% 1.57/1.50 spl76_44 | spl76_9 | spl76_45 | ~spl76_46 | spl76_12),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f221,f286,f425,f421,f276,f418])).
% 1.57/1.50 thf(f221,plain,(
% 1.57/1.50 ( ! [X22 : $i] : (($true != (cR @ sK38)) | ($true = (cP @ X22)) | ($true = sP0) | ((cP @ (sK39 @ X22)) = $true) | ((cQ @ sK37) = $true) | (sP2 = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f122])).
% 1.57/1.50 thf(f416,plain,(
% 1.57/1.50 spl76_19 | spl76_24 | spl76_43 | ~spl76_1 | ~spl76_42),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f224,f408,f244,f413,f333,f314])).
% 1.57/1.50 thf(f224,plain,(
% 1.57/1.50 ( ! [X15 : $i,X13 : $i] : (($true != (cP @ X15)) | ((cS @ sK58) = $false) | (sP1 != $true) | ((cQ @ sK59) != $true) | ($true = (cS @ X13))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.57/1.50 thf(f132,plain,(
% 1.57/1.50 ( ! [X15 : $i,X13 : $i] : ((sP1 != $true) | ((cS @ sK58) = (cS @ X13)) | ($true != (cP @ X15)) | ((cQ @ sK59) != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.50 thf(f411,plain,(
% 1.57/1.50 spl76_41 | ~spl76_42 | spl76_25 | ~spl76_1 | spl76_24),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f223,f333,f244,f336,f408,f404])).
% 1.57/1.50 thf(f223,plain,(
% 1.57/1.50 ( ! [X15 : $i,X13 : $i] : (((cS @ sK58) = $true) | ($false = (cS @ X13)) | (sP1 != $true) | ($true != (cP @ X15)) | ((cQ @ sK59) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f132])).
% 1.57/1.50 thf(f402,plain,(
% 1.57/1.50 spl76_9 | ~spl76_39 | spl76_38 | spl76_40),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f226,f399,f391,f395,f276])).
% 1.57/1.50 thf(f226,plain,(
% 1.57/1.50 ( ! [X2 : $i,X0 : $i] : (($true != (cS @ sK65)) | ($false = (cQ @ (sK64 @ X0))) | ($true = sP0) | ($true != (cR @ X2)) | ((cQ @ X0) = $false)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.57/1.50 thf(f144,plain,(
% 1.57/1.50 ( ! [X2 : $i,X0 : $i] : (((cQ @ X0) != (cQ @ (sK64 @ X0))) | ($true = sP0) | ($true != (cR @ X2)) | ($true != (cS @ sK65))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f401,plain,(
% 1.57/1.50 spl76_9 | ~spl76_39 | spl76_36 | spl76_40),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f225,f399,f383,f395,f276])).
% 1.57/1.50 thf(f225,plain,(
% 1.57/1.50 ( ! [X2 : $i,X0 : $i] : (($true != (cS @ sK65)) | ($true = sP0) | ($true = (cQ @ (sK64 @ X0))) | ((cQ @ X0) = $true) | ($true != (cR @ X2))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f144])).
% 1.57/1.50 thf(f393,plain,(
% 1.57/1.50 spl76_9 | spl76_38 | spl76_19 | spl76_37),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f228,f386,f314,f391,f276])).
% 1.57/1.50 thf(f228,plain,(
% 1.57/1.50 ( ! [X0 : $i,X5 : $i] : (($false = (cQ @ (sK64 @ X0))) | ($true = sP0) | ($true = (cR @ sK66)) | ((cQ @ X0) = $false) | ((cS @ X5) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.57/1.50 thf(f143,plain,(
% 1.57/1.50 ( ! [X0 : $i,X5 : $i] : (($true = (cR @ sK66)) | ((cS @ X5) = $true) | ((cQ @ X0) != (cQ @ (sK64 @ X0))) | ($true = sP0)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f389,plain,(
% 1.57/1.50 spl76_36 | spl76_9 | spl76_19 | spl76_37),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f227,f386,f314,f276,f383])).
% 1.57/1.50 thf(f227,plain,(
% 1.57/1.50 ( ! [X0 : $i,X5 : $i] : (($true = (cR @ sK66)) | ((cQ @ X0) = $true) | ($true = (cQ @ (sK64 @ X0))) | ((cS @ X5) = $true) | ($true = sP0)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.57/1.50 thf(f381,plain,(
% 1.57/1.50 spl76_33 | spl76_20 | ~spl76_34 | spl76_35 | spl76_9),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f230,f276,f378,f373,f317,f369])).
% 1.57/1.50 thf(f230,plain,(
% 1.57/1.50 ( ! [X7 : $i] : (($true = sP0) | ($true != (cS @ sK69)) | ((cQ @ sK67) = $false) | ((cR @ sK68) = $true) | ((cQ @ X7) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.57/1.50 thf(f141,plain,(
% 1.57/1.50 ( ! [X7 : $i] : (($true = sP0) | ((cQ @ sK67) = (cQ @ X7)) | ($true != (cS @ sK69)) | ((cR @ sK68) = $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f376,plain,(
% 1.57/1.50 spl76_32 | spl76_33 | spl76_22 | ~spl76_34 | spl76_9),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f229,f276,f373,f325,f369,f365])).
% 1.57/1.50 thf(f229,plain,(
% 1.57/1.50 ( ! [X7 : $i] : (((cR @ sK68) = $true) | ($true = sP0) | ((cQ @ sK67) = $true) | ((cQ @ X7) = $false) | ($true != (cS @ sK69))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f141])).
% 1.57/1.50 thf(f363,plain,(
% 1.57/1.50 ~spl76_28 | spl76_31 | ~spl76_9 | spl76_29),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f232,f353,f276,f361,f349])).
% 1.57/1.50 thf(f232,plain,(
% 1.57/1.50 ( ! [X16 : $i] : (($false = (cQ @ (sK72 @ X16))) | ($true != sP0) | ($true != (cS @ sK71)) | ($true = (cR @ sK70)) | ($false = (cQ @ X16))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.57/1.50 thf(f139,plain,(
% 1.57/1.50 ( ! [X16 : $i] : (($true != sP0) | ($true = (cR @ sK70)) | ((cQ @ X16) != (cQ @ (sK72 @ X16))) | ($true != (cS @ sK71))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f359,plain,(
% 1.57/1.50 ~spl76_28 | spl76_29 | spl76_30 | ~spl76_9),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f231,f276,f357,f353,f349])).
% 1.57/1.50 thf(f231,plain,(
% 1.57/1.50 ( ! [X16 : $i] : (($true != sP0) | ($true = (cQ @ (sK72 @ X16))) | ($true != (cS @ sK71)) | ((cQ @ X16) = $true) | ($true = (cR @ sK70))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.57/1.50 thf(f347,plain,(
% 1.57/1.50 spl76_24 | spl76_20 | spl76_27 | spl76_1 | spl76_19),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f234,f314,f244,f344,f317,f333])).
% 1.57/1.50 thf(f234,plain,(
% 1.57/1.50 ( ! [X11 : $i,X8 : $i,X9 : $i] : (((cS @ X11) = $true) | ((cS @ sK57) = $false) | ((cP @ X9) != $true) | ($true = (cQ @ X8)) | (sP1 = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f133])).
% 1.57/1.50 thf(f133,plain,(
% 1.57/1.50 ( ! [X11 : $i,X8 : $i,X9 : $i] : (((cP @ X9) != $true) | ($true = (cQ @ X8)) | ((cS @ sK57) = (cS @ X11)) | (sP1 = $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f80])).
% 1.57/1.50 thf(f342,plain,(
% 1.57/1.50 spl76_20 | spl76_24 | spl76_25 | spl76_1 | spl76_26),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f233,f339,f244,f336,f333,f317])).
% 1.57/1.50 thf(f233,plain,(
% 1.57/1.50 ( ! [X11 : $i,X8 : $i,X9 : $i] : (((cS @ sK57) = $true) | (sP1 = $true) | ((cS @ X11) = $false) | ($true = (cQ @ X8)) | ((cP @ X9) != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f133])).
% 1.57/1.50 thf(f331,plain,(
% 1.57/1.50 spl76_22 | spl76_19 | spl76_23 | spl76_18 | ~spl76_9),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f236,f276,f310,f328,f314,f325])).
% 1.57/1.50 thf(f236,plain,(
% 1.57/1.50 ( ! [X19 : $i,X23 : $i] : (((cR @ sK75) = $true) | ($true != sP0) | ($false = (cQ @ X19)) | ($true = (cQ @ sK73)) | ((cS @ X23) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.57/1.50 thf(f137,plain,(
% 1.57/1.50 ( ! [X19 : $i,X23 : $i] : (($true != sP0) | ((cR @ sK75) = $true) | ((cQ @ X19) = (cQ @ sK73)) | ((cS @ X23) = $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f95])).
% 1.57/1.50 thf(f323,plain,(
% 1.57/1.50 spl76_18 | spl76_19 | spl76_20 | ~spl76_9 | spl76_21),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f235,f320,f276,f317,f314,f310])).
% 1.57/1.50 thf(f235,plain,(
% 1.57/1.50 ( ! [X19 : $i,X23 : $i] : (($true != sP0) | ($true = (cQ @ X19)) | ($false = (cQ @ sK73)) | ((cS @ X23) = $true) | ((cR @ sK75) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.57/1.50 thf(f308,plain,(
% 1.57/1.50 spl76_5 | ~spl76_14 | spl76_17 | spl76_16 | ~spl76_1),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f238,f244,f302,f306,f295,f259])).
% 1.57/1.50 thf(f238,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (($false = (cR @ X4)) | ($false = (cR @ (sK6 @ X4))) | (sP3 = $true) | ((cS @ X1) != $true) | ($true != (cP @ sK4)) | (sP1 != $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.57/1.50 thf(f112,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (((cR @ (sK6 @ X4)) != (cR @ X4)) | ((cS @ X1) != $true) | (sP1 != $true) | ($true != (cP @ sK4)) | (sP3 = $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f304,plain,(
% 1.57/1.50 ~spl76_14 | ~spl76_1 | spl76_15 | spl76_16 | spl76_5),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f237,f259,f302,f299,f244,f295])).
% 1.57/1.50 thf(f237,plain,(
% 1.57/1.50 ( ! [X1 : $i,X4 : $i] : (((cR @ (sK6 @ X4)) = $true) | ($true != (cP @ sK4)) | ((cS @ X1) != $true) | (sP3 = $true) | (sP1 != $true) | ($true = (cR @ X4))) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.57/1.50 thf(f293,plain,(
% 1.57/1.50 ~spl76_9 | spl76_13 | spl76_4 | spl76_11 | ~spl76_12),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f240,f286,f283,f256,f291,f276])).
% 1.57/1.50 thf(f240,plain,(
% 1.57/1.50 ( ! [X46 : $i,X44 : $i,X45 : $i] : (((cR @ X44) = $true) | ($true != (cQ @ X45)) | (sP2 != $true) | ($true != sP0) | ($false = (cP @ X46)) | ((cP @ (sK51 @ X46)) = $false)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.57/1.50 thf(f113,plain,(
% 1.57/1.50 ( ! [X46 : $i,X44 : $i,X45 : $i] : (((cR @ X44) = $true) | (sP2 != $true) | ($true != (cQ @ X45)) | ($true != sP0) | ((cP @ (sK51 @ X46)) != (cP @ X46))) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f65])).
% 1.57/1.50 thf(f289,plain,(
% 1.57/1.50 ~spl76_9 | spl76_10 | spl76_4 | spl76_11 | ~spl76_12),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f239,f286,f283,f256,f280,f276])).
% 1.57/1.50 thf(f239,plain,(
% 1.57/1.50 ( ! [X46 : $i,X44 : $i,X45 : $i] : (((cP @ (sK51 @ X46)) = $true) | ((cP @ X46) = $true) | ($true != (cQ @ X45)) | ($true != sP0) | (sP2 != $true) | ((cR @ X44) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.57/1.50 thf(f274,plain,(
% 1.57/1.50 ~spl76_3 | ~spl76_5 | spl76_7 | spl76_1 | spl76_2 | spl76_8),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f242,f271,f248,f244,f268,f259,f252])).
% 1.57/1.50 thf(f242,plain,(
% 1.57/1.50 ( ! [X35 : $i] : (((cS @ sK19) = $true) | ((cP @ sK20) != $true) | ($false = (cR @ X35)) | ($true = (cR @ sK21)) | (sP3 != $true) | (sP1 = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.57/1.50 thf(f102,plain,(
% 1.57/1.50 ( ! [X35 : $i] : (((cR @ X35) = (cR @ sK21)) | (sP3 != $true) | (sP1 = $true) | ((cS @ sK19) = $true) | ((cP @ sK20) != $true)) )),
% 1.57/1.50 inference(cnf_transformation,[status(thm)],[f38])).
% 1.57/1.50 thf(f266,plain,(
% 1.57/1.50 spl76_1 | spl76_2 | ~spl76_3 | spl76_4 | ~spl76_5 | spl76_6),
% 1.57/1.50 inference(avatar_split_clause,[status(thm)],[f241,f263,f259,f256,f252,f248,f244])).
% 1.57/1.50 thf(f241,plain,(
% 1.57/1.50 ( ! [X35 : $i] : ((sP3 != $true) | ((cP @ sK20) != $true) | ((cR @ X35) = $true) | (sP1 = $true) | ($false = (cR @ sK21)) | ((cS @ sK19) = $true)) )),
% 1.57/1.50 inference(binary_proxy_clausification,[status(thm)],[f102])).
% 1.57/1.50 % SZS output end Proof for DTF2THF_10908
% 1.57/1.50 % (11027)------------------------------
% 1.57/1.50 % (11027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.50 % (11027)Termination reason: Refutation
% 1.57/1.50
% 1.57/1.50 % (11027)Memory used [KB]: 6524
% 1.57/1.50 % (11027)Time elapsed: 0.107 s
% 1.57/1.50 % (11027)Instructions burned: 168 (million)
% 1.57/1.50 % (11027)------------------------------
% 1.57/1.50 % (11027)------------------------------
% 1.57/1.50 % (11006)Success in time 0.173 s
%------------------------------------------------------------------------------