LEO-II---2.3.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SEV617+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Oct  7 10:50:19 AM UTC 2026

% Result   : Theorem 211.96s 42.71s
% Output   : CNFRefutation 211.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :  189
% Syntax   : Number of formulae    : 2926 (1341 unt;   0 typ;   0 def)
%            Number of atoms       : 26106 (6473 equ;   0 cnn)
%            Maximal formula atoms :    9 (   8 avg)
%            Number of connectives : 62210 (7974   ~;9690   |; 226   &;43494   @)
%                                         ( 104 <=>; 722  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 2028 (2025 usr; 930 con; 0-23 aty)
%            Number of variables   : 11067 (   0   ^;11067   !;   0   ?;11067   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_cA,type,
    cA: $i ).

thf(tp_cCoq_2eArith_2eBetween_2eP__nth,type,
    cCoq_2eArith_2eBetween_2eP__nth: $i ).

thf(tp_cCoq_2eArith_2eBetween_2eP__nth___24a5,type,
    cCoq_2eArith_2eBetween_2eP__nth___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eArith_2eBetween_2ebetween,type,
    cCoq_2eArith_2eBetween_2ebetween: $i ).

thf(tp_cCoq_2eArith_2eBetween_2ebetween___24a3,type,
    cCoq_2eArith_2eBetween_2ebetween___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eArith_2eBetween_2eexists__between,type,
    cCoq_2eArith_2eBetween_2eexists__between: $i ).

thf(tp_cCoq_2eArith_2eBetween_2eexists__between___24a3,type,
    cCoq_2eArith_2eBetween_2eexists__between___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eArith_2eEqNat_2eeq__nat,type,
    cCoq_2eArith_2eEqNat_2eeq__nat: $i ).

thf(tp_cCoq_2eArith_2eEqNat_2eeq__nat___24a2,type,
    cCoq_2eArith_2eEqNat_2eeq__nat___24a2: $i > $i > $o ).

thf(tp_cCoq_2eArith_2eEven_2eeven,type,
    cCoq_2eArith_2eEven_2eeven: $i ).

thf(tp_cCoq_2eArith_2eEven_2eeven___24a1,type,
    cCoq_2eArith_2eEven_2eeven___24a1: $i > $o ).

thf(tp_cCoq_2eArith_2eEven_2eodd,type,
    cCoq_2eArith_2eEven_2eodd: $i ).

thf(tp_cCoq_2eArith_2eEven_2eodd___24a1,type,
    cCoq_2eArith_2eEven_2eodd___24a1: $i > $o ).

thf(tp_cCoq_2eArith_2ePeanoNat_2eNat_2ele,type,
    cCoq_2eArith_2ePeanoNat_2eNat_2ele: $i ).

thf(tp_cCoq_2eArith_2ePeanoNat_2eNat_2elt,type,
    cCoq_2eArith_2ePeanoNat_2eNat_2elt: $i ).

thf(tp_cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,type,
    cCoq_2eArith_2ePeanoNat_2eNat_2erecursion: $i ).

thf(tp_cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1,type,
    cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1: $i > $i ).

thf(tp_cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4,type,
    cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eBool_2eBool_2eIs__true,type,
    cCoq_2eBool_2eBool_2eIs__true: $i ).

thf(tp_cCoq_2eBool_2eBool_2eIs__true___24a1,type,
    cCoq_2eBool_2eBool_2eIs__true___24a1: $i > $o ).

thf(tp_cCoq_2eBool_2eBool_2eReflectF,type,
    cCoq_2eBool_2eBool_2eReflectF: $i ).

thf(tp_cCoq_2eBool_2eBool_2eReflectF___24a1,type,
    cCoq_2eBool_2eBool_2eReflectF___24a1: $i > $i ).

thf(tp_cCoq_2eBool_2eBool_2eReflectT,type,
    cCoq_2eBool_2eBool_2eReflectT: $i ).

thf(tp_cCoq_2eBool_2eBool_2eReflectT___24a1,type,
    cCoq_2eBool_2eBool_2eReflectT___24a1: $i > $i ).

thf(tp_cCoq_2eBool_2eBool_2eeqb,type,
    cCoq_2eBool_2eBool_2eeqb: $i ).

thf(tp_cCoq_2eBool_2eBool_2eeqb___24a2,type,
    cCoq_2eBool_2eBool_2eeqb___24a2: $i > $i > $i ).

thf(tp_cCoq_2eBool_2eBool_2eifb,type,
    cCoq_2eBool_2eBool_2eifb: $i ).

thf(tp_cCoq_2eBool_2eBool_2eifb___24a3,type,
    cCoq_2eBool_2eBool_2eifb___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eBool_2eBool_2ereflect,type,
    cCoq_2eBool_2eBool_2ereflect: $i ).

thf(tp_cCoq_2eBool_2eBool_2ereflect___24a2,type,
    cCoq_2eBool_2eBool_2ereflect___24a2: $i > $i > $i ).

thf(tp_cCoq_2eBool_2eBool_2ereflect___24t,type,
    cCoq_2eBool_2eBool_2ereflect___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eMorphisms_2eProper,type,
    cCoq_2eClasses_2eMorphisms_2eProper: $i ).

thf(tp_cCoq_2eClasses_2eMorphisms_2eProper___24a3,type,
    cCoq_2eClasses_2eMorphisms_2eProper___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eMorphisms_2erespectful,type,
    cCoq_2eClasses_2eMorphisms_2erespectful: $i ).

thf(tp_cCoq_2eClasses_2eMorphisms_2erespectful___24a4,type,
    cCoq_2eClasses_2eMorphisms_2erespectful___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eEquivalence,type,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence: $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2,type,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2: $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2ePreOrder,type,
    cCoq_2eClasses_2eRelationClasses_2ePreOrder: $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2,type,
    cCoq_2eClasses_2eRelationClasses_2ePreOrder___24a2: $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eReflexive,type,
    cCoq_2eClasses_2eRelationClasses_2eReflexive: $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2,type,
    cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2: $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eRewriteRelation,type,
    cCoq_2eClasses_2eRelationClasses_2eRewriteRelation: $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2,type,
    cCoq_2eClasses_2eRelationClasses_2eRewriteRelation___24a2: $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eSymmetric,type,
    cCoq_2eClasses_2eRelationClasses_2eSymmetric: $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2,type,
    cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2: $i > $i > $o ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eTransitive,type,
    cCoq_2eClasses_2eRelationClasses_2eTransitive: $i ).

thf(tp_cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2,type,
    cCoq_2eClasses_2eRelationClasses_2eTransitive___24a2: $i > $i > $o ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2: $i > $i > $o ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t: $i > $o ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2: $i > $i > $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t: $i > $o ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree: $i ).

thf(tp_cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t,type,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eByte_2ebyte,type,
    cCoq_2eInit_2eByte_2ebyte: $i ).

thf(tp_cCoq_2eInit_2eByte_2ebyte___24t,type,
    cCoq_2eInit_2eByte_2ebyte___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eByte_2ex00,type,
    cCoq_2eInit_2eByte_2ex00: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex01,type,
    cCoq_2eInit_2eByte_2ex01: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex02,type,
    cCoq_2eInit_2eByte_2ex02: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex03,type,
    cCoq_2eInit_2eByte_2ex03: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex04,type,
    cCoq_2eInit_2eByte_2ex04: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex05,type,
    cCoq_2eInit_2eByte_2ex05: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex06,type,
    cCoq_2eInit_2eByte_2ex06: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex07,type,
    cCoq_2eInit_2eByte_2ex07: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex08,type,
    cCoq_2eInit_2eByte_2ex08: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex09,type,
    cCoq_2eInit_2eByte_2ex09: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex0a,type,
    cCoq_2eInit_2eByte_2ex0a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex0b,type,
    cCoq_2eInit_2eByte_2ex0b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex0c,type,
    cCoq_2eInit_2eByte_2ex0c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex0d,type,
    cCoq_2eInit_2eByte_2ex0d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex0e,type,
    cCoq_2eInit_2eByte_2ex0e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex0f,type,
    cCoq_2eInit_2eByte_2ex0f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex10,type,
    cCoq_2eInit_2eByte_2ex10: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex11,type,
    cCoq_2eInit_2eByte_2ex11: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex12,type,
    cCoq_2eInit_2eByte_2ex12: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex13,type,
    cCoq_2eInit_2eByte_2ex13: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex14,type,
    cCoq_2eInit_2eByte_2ex14: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex15,type,
    cCoq_2eInit_2eByte_2ex15: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex16,type,
    cCoq_2eInit_2eByte_2ex16: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex17,type,
    cCoq_2eInit_2eByte_2ex17: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex18,type,
    cCoq_2eInit_2eByte_2ex18: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex19,type,
    cCoq_2eInit_2eByte_2ex19: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex1a,type,
    cCoq_2eInit_2eByte_2ex1a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex1b,type,
    cCoq_2eInit_2eByte_2ex1b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex1c,type,
    cCoq_2eInit_2eByte_2ex1c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex1d,type,
    cCoq_2eInit_2eByte_2ex1d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex1e,type,
    cCoq_2eInit_2eByte_2ex1e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex1f,type,
    cCoq_2eInit_2eByte_2ex1f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex20,type,
    cCoq_2eInit_2eByte_2ex20: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex21,type,
    cCoq_2eInit_2eByte_2ex21: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex22,type,
    cCoq_2eInit_2eByte_2ex22: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex23,type,
    cCoq_2eInit_2eByte_2ex23: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex24,type,
    cCoq_2eInit_2eByte_2ex24: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex25,type,
    cCoq_2eInit_2eByte_2ex25: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex26,type,
    cCoq_2eInit_2eByte_2ex26: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex27,type,
    cCoq_2eInit_2eByte_2ex27: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex28,type,
    cCoq_2eInit_2eByte_2ex28: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex29,type,
    cCoq_2eInit_2eByte_2ex29: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex2a,type,
    cCoq_2eInit_2eByte_2ex2a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex2b,type,
    cCoq_2eInit_2eByte_2ex2b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex2c,type,
    cCoq_2eInit_2eByte_2ex2c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex2d,type,
    cCoq_2eInit_2eByte_2ex2d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex2e,type,
    cCoq_2eInit_2eByte_2ex2e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex2f,type,
    cCoq_2eInit_2eByte_2ex2f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex30,type,
    cCoq_2eInit_2eByte_2ex30: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex31,type,
    cCoq_2eInit_2eByte_2ex31: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex32,type,
    cCoq_2eInit_2eByte_2ex32: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex33,type,
    cCoq_2eInit_2eByte_2ex33: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex34,type,
    cCoq_2eInit_2eByte_2ex34: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex35,type,
    cCoq_2eInit_2eByte_2ex35: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex36,type,
    cCoq_2eInit_2eByte_2ex36: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex37,type,
    cCoq_2eInit_2eByte_2ex37: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex38,type,
    cCoq_2eInit_2eByte_2ex38: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex39,type,
    cCoq_2eInit_2eByte_2ex39: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex3a,type,
    cCoq_2eInit_2eByte_2ex3a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex3b,type,
    cCoq_2eInit_2eByte_2ex3b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex3c,type,
    cCoq_2eInit_2eByte_2ex3c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex3d,type,
    cCoq_2eInit_2eByte_2ex3d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex3e,type,
    cCoq_2eInit_2eByte_2ex3e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex3f,type,
    cCoq_2eInit_2eByte_2ex3f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex40,type,
    cCoq_2eInit_2eByte_2ex40: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex41,type,
    cCoq_2eInit_2eByte_2ex41: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex42,type,
    cCoq_2eInit_2eByte_2ex42: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex43,type,
    cCoq_2eInit_2eByte_2ex43: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex44,type,
    cCoq_2eInit_2eByte_2ex44: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex45,type,
    cCoq_2eInit_2eByte_2ex45: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex46,type,
    cCoq_2eInit_2eByte_2ex46: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex47,type,
    cCoq_2eInit_2eByte_2ex47: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex48,type,
    cCoq_2eInit_2eByte_2ex48: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex49,type,
    cCoq_2eInit_2eByte_2ex49: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex4a,type,
    cCoq_2eInit_2eByte_2ex4a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex4b,type,
    cCoq_2eInit_2eByte_2ex4b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex4c,type,
    cCoq_2eInit_2eByte_2ex4c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex4d,type,
    cCoq_2eInit_2eByte_2ex4d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex4e,type,
    cCoq_2eInit_2eByte_2ex4e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex4f,type,
    cCoq_2eInit_2eByte_2ex4f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex50,type,
    cCoq_2eInit_2eByte_2ex50: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex51,type,
    cCoq_2eInit_2eByte_2ex51: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex52,type,
    cCoq_2eInit_2eByte_2ex52: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex53,type,
    cCoq_2eInit_2eByte_2ex53: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex54,type,
    cCoq_2eInit_2eByte_2ex54: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex55,type,
    cCoq_2eInit_2eByte_2ex55: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex56,type,
    cCoq_2eInit_2eByte_2ex56: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex57,type,
    cCoq_2eInit_2eByte_2ex57: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex58,type,
    cCoq_2eInit_2eByte_2ex58: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex59,type,
    cCoq_2eInit_2eByte_2ex59: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex5a,type,
    cCoq_2eInit_2eByte_2ex5a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex5b,type,
    cCoq_2eInit_2eByte_2ex5b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex5c,type,
    cCoq_2eInit_2eByte_2ex5c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex5d,type,
    cCoq_2eInit_2eByte_2ex5d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex5e,type,
    cCoq_2eInit_2eByte_2ex5e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex5f,type,
    cCoq_2eInit_2eByte_2ex5f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex60,type,
    cCoq_2eInit_2eByte_2ex60: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex61,type,
    cCoq_2eInit_2eByte_2ex61: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex62,type,
    cCoq_2eInit_2eByte_2ex62: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex63,type,
    cCoq_2eInit_2eByte_2ex63: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex64,type,
    cCoq_2eInit_2eByte_2ex64: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex65,type,
    cCoq_2eInit_2eByte_2ex65: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex66,type,
    cCoq_2eInit_2eByte_2ex66: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex67,type,
    cCoq_2eInit_2eByte_2ex67: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex68,type,
    cCoq_2eInit_2eByte_2ex68: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex69,type,
    cCoq_2eInit_2eByte_2ex69: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex6a,type,
    cCoq_2eInit_2eByte_2ex6a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex6b,type,
    cCoq_2eInit_2eByte_2ex6b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex6c,type,
    cCoq_2eInit_2eByte_2ex6c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex6d,type,
    cCoq_2eInit_2eByte_2ex6d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex6e,type,
    cCoq_2eInit_2eByte_2ex6e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex6f,type,
    cCoq_2eInit_2eByte_2ex6f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex70,type,
    cCoq_2eInit_2eByte_2ex70: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex71,type,
    cCoq_2eInit_2eByte_2ex71: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex72,type,
    cCoq_2eInit_2eByte_2ex72: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex73,type,
    cCoq_2eInit_2eByte_2ex73: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex74,type,
    cCoq_2eInit_2eByte_2ex74: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex75,type,
    cCoq_2eInit_2eByte_2ex75: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex76,type,
    cCoq_2eInit_2eByte_2ex76: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex77,type,
    cCoq_2eInit_2eByte_2ex77: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex78,type,
    cCoq_2eInit_2eByte_2ex78: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex79,type,
    cCoq_2eInit_2eByte_2ex79: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex7a,type,
    cCoq_2eInit_2eByte_2ex7a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex7b,type,
    cCoq_2eInit_2eByte_2ex7b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex7c,type,
    cCoq_2eInit_2eByte_2ex7c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex7d,type,
    cCoq_2eInit_2eByte_2ex7d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex7e,type,
    cCoq_2eInit_2eByte_2ex7e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex7f,type,
    cCoq_2eInit_2eByte_2ex7f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex80,type,
    cCoq_2eInit_2eByte_2ex80: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex81,type,
    cCoq_2eInit_2eByte_2ex81: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex82,type,
    cCoq_2eInit_2eByte_2ex82: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex83,type,
    cCoq_2eInit_2eByte_2ex83: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex84,type,
    cCoq_2eInit_2eByte_2ex84: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex85,type,
    cCoq_2eInit_2eByte_2ex85: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex86,type,
    cCoq_2eInit_2eByte_2ex86: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex87,type,
    cCoq_2eInit_2eByte_2ex87: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex88,type,
    cCoq_2eInit_2eByte_2ex88: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex89,type,
    cCoq_2eInit_2eByte_2ex89: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex8a,type,
    cCoq_2eInit_2eByte_2ex8a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex8b,type,
    cCoq_2eInit_2eByte_2ex8b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex8c,type,
    cCoq_2eInit_2eByte_2ex8c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex8d,type,
    cCoq_2eInit_2eByte_2ex8d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex8e,type,
    cCoq_2eInit_2eByte_2ex8e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex8f,type,
    cCoq_2eInit_2eByte_2ex8f: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex90,type,
    cCoq_2eInit_2eByte_2ex90: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex91,type,
    cCoq_2eInit_2eByte_2ex91: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex92,type,
    cCoq_2eInit_2eByte_2ex92: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex93,type,
    cCoq_2eInit_2eByte_2ex93: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex94,type,
    cCoq_2eInit_2eByte_2ex94: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex95,type,
    cCoq_2eInit_2eByte_2ex95: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex96,type,
    cCoq_2eInit_2eByte_2ex96: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex97,type,
    cCoq_2eInit_2eByte_2ex97: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex98,type,
    cCoq_2eInit_2eByte_2ex98: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex99,type,
    cCoq_2eInit_2eByte_2ex99: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex9a,type,
    cCoq_2eInit_2eByte_2ex9a: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex9b,type,
    cCoq_2eInit_2eByte_2ex9b: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex9c,type,
    cCoq_2eInit_2eByte_2ex9c: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex9d,type,
    cCoq_2eInit_2eByte_2ex9d: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex9e,type,
    cCoq_2eInit_2eByte_2ex9e: $i ).

thf(tp_cCoq_2eInit_2eByte_2ex9f,type,
    cCoq_2eInit_2eByte_2ex9f: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa0,type,
    cCoq_2eInit_2eByte_2exa0: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa1,type,
    cCoq_2eInit_2eByte_2exa1: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa2,type,
    cCoq_2eInit_2eByte_2exa2: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa3,type,
    cCoq_2eInit_2eByte_2exa3: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa4,type,
    cCoq_2eInit_2eByte_2exa4: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa5,type,
    cCoq_2eInit_2eByte_2exa5: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa6,type,
    cCoq_2eInit_2eByte_2exa6: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa7,type,
    cCoq_2eInit_2eByte_2exa7: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa8,type,
    cCoq_2eInit_2eByte_2exa8: $i ).

thf(tp_cCoq_2eInit_2eByte_2exa9,type,
    cCoq_2eInit_2eByte_2exa9: $i ).

thf(tp_cCoq_2eInit_2eByte_2exaa,type,
    cCoq_2eInit_2eByte_2exaa: $i ).

thf(tp_cCoq_2eInit_2eByte_2exab,type,
    cCoq_2eInit_2eByte_2exab: $i ).

thf(tp_cCoq_2eInit_2eByte_2exac,type,
    cCoq_2eInit_2eByte_2exac: $i ).

thf(tp_cCoq_2eInit_2eByte_2exad,type,
    cCoq_2eInit_2eByte_2exad: $i ).

thf(tp_cCoq_2eInit_2eByte_2exae,type,
    cCoq_2eInit_2eByte_2exae: $i ).

thf(tp_cCoq_2eInit_2eByte_2exaf,type,
    cCoq_2eInit_2eByte_2exaf: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb0,type,
    cCoq_2eInit_2eByte_2exb0: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb1,type,
    cCoq_2eInit_2eByte_2exb1: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb2,type,
    cCoq_2eInit_2eByte_2exb2: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb3,type,
    cCoq_2eInit_2eByte_2exb3: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb4,type,
    cCoq_2eInit_2eByte_2exb4: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb5,type,
    cCoq_2eInit_2eByte_2exb5: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb6,type,
    cCoq_2eInit_2eByte_2exb6: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb7,type,
    cCoq_2eInit_2eByte_2exb7: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb8,type,
    cCoq_2eInit_2eByte_2exb8: $i ).

thf(tp_cCoq_2eInit_2eByte_2exb9,type,
    cCoq_2eInit_2eByte_2exb9: $i ).

thf(tp_cCoq_2eInit_2eByte_2exba,type,
    cCoq_2eInit_2eByte_2exba: $i ).

thf(tp_cCoq_2eInit_2eByte_2exbb,type,
    cCoq_2eInit_2eByte_2exbb: $i ).

thf(tp_cCoq_2eInit_2eByte_2exbc,type,
    cCoq_2eInit_2eByte_2exbc: $i ).

thf(tp_cCoq_2eInit_2eByte_2exbd,type,
    cCoq_2eInit_2eByte_2exbd: $i ).

thf(tp_cCoq_2eInit_2eByte_2exbe,type,
    cCoq_2eInit_2eByte_2exbe: $i ).

thf(tp_cCoq_2eInit_2eByte_2exbf,type,
    cCoq_2eInit_2eByte_2exbf: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc0,type,
    cCoq_2eInit_2eByte_2exc0: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc1,type,
    cCoq_2eInit_2eByte_2exc1: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc2,type,
    cCoq_2eInit_2eByte_2exc2: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc3,type,
    cCoq_2eInit_2eByte_2exc3: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc4,type,
    cCoq_2eInit_2eByte_2exc4: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc5,type,
    cCoq_2eInit_2eByte_2exc5: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc6,type,
    cCoq_2eInit_2eByte_2exc6: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc7,type,
    cCoq_2eInit_2eByte_2exc7: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc8,type,
    cCoq_2eInit_2eByte_2exc8: $i ).

thf(tp_cCoq_2eInit_2eByte_2exc9,type,
    cCoq_2eInit_2eByte_2exc9: $i ).

thf(tp_cCoq_2eInit_2eByte_2exca,type,
    cCoq_2eInit_2eByte_2exca: $i ).

thf(tp_cCoq_2eInit_2eByte_2excb,type,
    cCoq_2eInit_2eByte_2excb: $i ).

thf(tp_cCoq_2eInit_2eByte_2excc,type,
    cCoq_2eInit_2eByte_2excc: $i ).

thf(tp_cCoq_2eInit_2eByte_2excd,type,
    cCoq_2eInit_2eByte_2excd: $i ).

thf(tp_cCoq_2eInit_2eByte_2exce,type,
    cCoq_2eInit_2eByte_2exce: $i ).

thf(tp_cCoq_2eInit_2eByte_2excf,type,
    cCoq_2eInit_2eByte_2excf: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd0,type,
    cCoq_2eInit_2eByte_2exd0: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd1,type,
    cCoq_2eInit_2eByte_2exd1: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd2,type,
    cCoq_2eInit_2eByte_2exd2: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd3,type,
    cCoq_2eInit_2eByte_2exd3: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd4,type,
    cCoq_2eInit_2eByte_2exd4: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd5,type,
    cCoq_2eInit_2eByte_2exd5: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd6,type,
    cCoq_2eInit_2eByte_2exd6: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd7,type,
    cCoq_2eInit_2eByte_2exd7: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd8,type,
    cCoq_2eInit_2eByte_2exd8: $i ).

thf(tp_cCoq_2eInit_2eByte_2exd9,type,
    cCoq_2eInit_2eByte_2exd9: $i ).

thf(tp_cCoq_2eInit_2eByte_2exda,type,
    cCoq_2eInit_2eByte_2exda: $i ).

thf(tp_cCoq_2eInit_2eByte_2exdb,type,
    cCoq_2eInit_2eByte_2exdb: $i ).

thf(tp_cCoq_2eInit_2eByte_2exdc,type,
    cCoq_2eInit_2eByte_2exdc: $i ).

thf(tp_cCoq_2eInit_2eByte_2exdd,type,
    cCoq_2eInit_2eByte_2exdd: $i ).

thf(tp_cCoq_2eInit_2eByte_2exde,type,
    cCoq_2eInit_2eByte_2exde: $i ).

thf(tp_cCoq_2eInit_2eByte_2exdf,type,
    cCoq_2eInit_2eByte_2exdf: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe0,type,
    cCoq_2eInit_2eByte_2exe0: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe1,type,
    cCoq_2eInit_2eByte_2exe1: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe2,type,
    cCoq_2eInit_2eByte_2exe2: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe3,type,
    cCoq_2eInit_2eByte_2exe3: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe4,type,
    cCoq_2eInit_2eByte_2exe4: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe5,type,
    cCoq_2eInit_2eByte_2exe5: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe6,type,
    cCoq_2eInit_2eByte_2exe6: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe7,type,
    cCoq_2eInit_2eByte_2exe7: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe8,type,
    cCoq_2eInit_2eByte_2exe8: $i ).

thf(tp_cCoq_2eInit_2eByte_2exe9,type,
    cCoq_2eInit_2eByte_2exe9: $i ).

thf(tp_cCoq_2eInit_2eByte_2exea,type,
    cCoq_2eInit_2eByte_2exea: $i ).

thf(tp_cCoq_2eInit_2eByte_2exeb,type,
    cCoq_2eInit_2eByte_2exeb: $i ).

thf(tp_cCoq_2eInit_2eByte_2exec,type,
    cCoq_2eInit_2eByte_2exec: $i ).

thf(tp_cCoq_2eInit_2eByte_2exed,type,
    cCoq_2eInit_2eByte_2exed: $i ).

thf(tp_cCoq_2eInit_2eByte_2exee,type,
    cCoq_2eInit_2eByte_2exee: $i ).

thf(tp_cCoq_2eInit_2eByte_2exef,type,
    cCoq_2eInit_2eByte_2exef: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf0,type,
    cCoq_2eInit_2eByte_2exf0: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf1,type,
    cCoq_2eInit_2eByte_2exf1: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf2,type,
    cCoq_2eInit_2eByte_2exf2: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf3,type,
    cCoq_2eInit_2eByte_2exf3: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf4,type,
    cCoq_2eInit_2eByte_2exf4: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf5,type,
    cCoq_2eInit_2eByte_2exf5: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf6,type,
    cCoq_2eInit_2eByte_2exf6: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf7,type,
    cCoq_2eInit_2eByte_2exf7: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf8,type,
    cCoq_2eInit_2eByte_2exf8: $i ).

thf(tp_cCoq_2eInit_2eByte_2exf9,type,
    cCoq_2eInit_2eByte_2exf9: $i ).

thf(tp_cCoq_2eInit_2eByte_2exfa,type,
    cCoq_2eInit_2eByte_2exfa: $i ).

thf(tp_cCoq_2eInit_2eByte_2exfb,type,
    cCoq_2eInit_2eByte_2exfb: $i ).

thf(tp_cCoq_2eInit_2eByte_2exfc,type,
    cCoq_2eInit_2eByte_2exfc: $i ).

thf(tp_cCoq_2eInit_2eByte_2exfd,type,
    cCoq_2eInit_2eByte_2exfd: $i ).

thf(tp_cCoq_2eInit_2eByte_2exfe,type,
    cCoq_2eInit_2eByte_2exfe: $i ).

thf(tp_cCoq_2eInit_2eByte_2exff,type,
    cCoq_2eInit_2eByte_2exff: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eBoolSpec,type,
    cCoq_2eInit_2eDatatypes_2eBoolSpec: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3,type,
    cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompEqT,type,
    cCoq_2eInit_2eDatatypes_2eCompEqT: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompEqT___24a3,type,
    cCoq_2eInit_2eDatatypes_2eCompEqT___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompGtT,type,
    cCoq_2eInit_2eDatatypes_2eCompGtT: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompGtT___24a3,type,
    cCoq_2eInit_2eDatatypes_2eCompGtT___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompLtT,type,
    cCoq_2eInit_2eDatatypes_2eCompLtT: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompLtT___24a3,type,
    cCoq_2eInit_2eDatatypes_2eCompLtT___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompareSpec,type,
    cCoq_2eInit_2eDatatypes_2eCompareSpec: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompareSpecT,type,
    cCoq_2eInit_2eDatatypes_2eCompareSpecT: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4,type,
    cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t,type,
    cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4,type,
    cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2eEmpty__set,type,
    cCoq_2eInit_2eDatatypes_2eEmpty__set: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eEq,type,
    cCoq_2eInit_2eDatatypes_2eEq: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eGt,type,
    cCoq_2eInit_2eDatatypes_2eGt: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eID,type,
    cCoq_2eInit_2eDatatypes_2eID: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eIDProp,type,
    cCoq_2eInit_2eDatatypes_2eIDProp: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eID___24t,type,
    cCoq_2eInit_2eDatatypes_2eID___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2eLt,type,
    cCoq_2eInit_2eDatatypes_2eLt: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eNone,type,
    cCoq_2eInit_2eDatatypes_2eNone: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eNone___24a1,type,
    cCoq_2eInit_2eDatatypes_2eNone___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eO,type,
    cCoq_2eInit_2eDatatypes_2eO: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eS,type,
    cCoq_2eInit_2eDatatypes_2eS: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eS___24a1,type,
    cCoq_2eInit_2eDatatypes_2eS___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eSome,type,
    cCoq_2eInit_2eDatatypes_2eSome: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eSome___24a2,type,
    cCoq_2eInit_2eDatatypes_2eSome___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eandb,type,
    cCoq_2eInit_2eDatatypes_2eandb: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eandb___24a2,type,
    cCoq_2eInit_2eDatatypes_2eandb___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eapp,type,
    cCoq_2eInit_2eDatatypes_2eapp: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eapp___24a3,type,
    cCoq_2eInit_2eDatatypes_2eapp___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2ebool,type,
    cCoq_2eInit_2eDatatypes_2ebool: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2ebool___24t,type,
    cCoq_2eInit_2eDatatypes_2ebool___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2ecomparison,type,
    cCoq_2eInit_2eDatatypes_2ecomparison: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2ecomparison___24t,type,
    cCoq_2eInit_2eDatatypes_2ecomparison___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2econs,type,
    cCoq_2eInit_2eDatatypes_2econs: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2econs___24a3,type,
    cCoq_2eInit_2eDatatypes_2econs___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eeq__true,type,
    cCoq_2eInit_2eDatatypes_2eeq__true: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eeq__true___24a1,type,
    cCoq_2eInit_2eDatatypes_2eeq__true___24a1: $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2efalse,type,
    cCoq_2eInit_2eDatatypes_2efalse: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eidentity,type,
    cCoq_2eInit_2eDatatypes_2eidentity: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eidentity___24a3,type,
    cCoq_2eInit_2eDatatypes_2eidentity___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2einl,type,
    cCoq_2eInit_2eDatatypes_2einl: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2einl___24a3,type,
    cCoq_2eInit_2eDatatypes_2einl___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2einr,type,
    cCoq_2eInit_2eDatatypes_2einr: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2einr___24a3,type,
    cCoq_2eInit_2eDatatypes_2einr___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2elist,type,
    cCoq_2eInit_2eDatatypes_2elist: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2elist___24a1,type,
    cCoq_2eInit_2eDatatypes_2elist___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2elist___24t,type,
    cCoq_2eInit_2eDatatypes_2elist___24t: $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2enat,type,
    cCoq_2eInit_2eDatatypes_2enat: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2enat___24t,type,
    cCoq_2eInit_2eDatatypes_2enat___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2enat__rect,type,
    cCoq_2eInit_2eDatatypes_2enat__rect: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2enat__rect___24a1,type,
    cCoq_2eInit_2eDatatypes_2enat__rect___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2enegb,type,
    cCoq_2eInit_2eDatatypes_2enegb: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2enegb___24a1,type,
    cCoq_2eInit_2eDatatypes_2enegb___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2enil,type,
    cCoq_2eInit_2eDatatypes_2enil: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2enil___24a1,type,
    cCoq_2eInit_2eDatatypes_2enil___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eoption,type,
    cCoq_2eInit_2eDatatypes_2eoption: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eoption___24a1,type,
    cCoq_2eInit_2eDatatypes_2eoption___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eoption___24t,type,
    cCoq_2eInit_2eDatatypes_2eoption___24t: $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2eorb,type,
    cCoq_2eInit_2eDatatypes_2eorb: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eorb___24a2,type,
    cCoq_2eInit_2eDatatypes_2eorb___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2epair,type,
    cCoq_2eInit_2eDatatypes_2epair: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2epair___24a4,type,
    cCoq_2eInit_2eDatatypes_2epair___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eprod,type,
    cCoq_2eInit_2eDatatypes_2eprod: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eprod___24a2,type,
    cCoq_2eInit_2eDatatypes_2eprod___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eprod___24t,type,
    cCoq_2eInit_2eDatatypes_2eprod___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2esum,type,
    cCoq_2eInit_2eDatatypes_2esum: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2esum___24a2,type,
    cCoq_2eInit_2eDatatypes_2esum___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2esum___24t,type,
    cCoq_2eInit_2eDatatypes_2esum___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2etrue,type,
    cCoq_2eInit_2eDatatypes_2etrue: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2ett,type,
    cCoq_2eInit_2eDatatypes_2ett: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eunit,type,
    cCoq_2eInit_2eDatatypes_2eunit: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2eunit___24t,type,
    cCoq_2eInit_2eDatatypes_2eunit___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDatatypes_2exorb,type,
    cCoq_2eInit_2eDatatypes_2exorb: $i ).

thf(tp_cCoq_2eInit_2eDatatypes_2exorb___24a2,type,
    cCoq_2eInit_2eDatatypes_2exorb___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD0,type,
    cCoq_2eInit_2eDecimal_2eD0: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD0___24a1,type,
    cCoq_2eInit_2eDecimal_2eD0___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD1,type,
    cCoq_2eInit_2eDecimal_2eD1: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD1___24a1,type,
    cCoq_2eInit_2eDecimal_2eD1___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD2,type,
    cCoq_2eInit_2eDecimal_2eD2: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD2___24a1,type,
    cCoq_2eInit_2eDecimal_2eD2___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD3,type,
    cCoq_2eInit_2eDecimal_2eD3: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD3___24a1,type,
    cCoq_2eInit_2eDecimal_2eD3___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD4,type,
    cCoq_2eInit_2eDecimal_2eD4: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD4___24a1,type,
    cCoq_2eInit_2eDecimal_2eD4___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD5,type,
    cCoq_2eInit_2eDecimal_2eD5: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD5___24a1,type,
    cCoq_2eInit_2eDecimal_2eD5___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD6,type,
    cCoq_2eInit_2eDecimal_2eD6: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD6___24a1,type,
    cCoq_2eInit_2eDecimal_2eD6___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD7,type,
    cCoq_2eInit_2eDecimal_2eD7: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD7___24a1,type,
    cCoq_2eInit_2eDecimal_2eD7___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD8,type,
    cCoq_2eInit_2eDecimal_2eD8: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD8___24a1,type,
    cCoq_2eInit_2eDecimal_2eD8___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD9,type,
    cCoq_2eInit_2eDecimal_2eD9: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eD9___24a1,type,
    cCoq_2eInit_2eDecimal_2eD9___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eDecimal,type,
    cCoq_2eInit_2eDecimal_2eDecimal: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eDecimalExp,type,
    cCoq_2eInit_2eDecimal_2eDecimalExp: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eDecimalExp___24a3,type,
    cCoq_2eInit_2eDecimal_2eDecimalExp___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eDecimal___24a2,type,
    cCoq_2eInit_2eDecimal_2eDecimal___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eNeg,type,
    cCoq_2eInit_2eDecimal_2eNeg: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eNeg___24a1,type,
    cCoq_2eInit_2eDecimal_2eNeg___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eNil,type,
    cCoq_2eInit_2eDecimal_2eNil: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2ePos,type,
    cCoq_2eInit_2eDecimal_2ePos: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2ePos___24a1,type,
    cCoq_2eInit_2eDecimal_2ePos___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eDecimal_2edecimal,type,
    cCoq_2eInit_2eDecimal_2edecimal: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2edecimal___24t,type,
    cCoq_2eInit_2eDecimal_2edecimal___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDecimal_2eint,type,
    cCoq_2eInit_2eDecimal_2eint: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2eint___24t,type,
    cCoq_2eInit_2eDecimal_2eint___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eDecimal_2euint,type,
    cCoq_2eInit_2eDecimal_2euint: $i ).

thf(tp_cCoq_2eInit_2eDecimal_2euint___24t,type,
    cCoq_2eInit_2eDecimal_2euint___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eLogic_2eFalse__rec,type,
    cCoq_2eInit_2eLogic_2eFalse__rec: $i ).

thf(tp_cCoq_2eInit_2eLogic_2eeq__rect,type,
    cCoq_2eInit_2eLogic_2eeq__rect: $i ).

thf(tp_cCoq_2eInit_2eLogic_2eeq__rect___24a5,type,
    cCoq_2eInit_2eLogic_2eeq__rect___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eLogic_2eex,type,
    cCoq_2eInit_2eLogic_2eex: $i ).

thf(tp_cCoq_2eInit_2eLogic_2eex2,type,
    cCoq_2eInit_2eLogic_2eex2: $i ).

thf(tp_cCoq_2eInit_2eLogic_2eex2___24a3,type,
    cCoq_2eInit_2eLogic_2eex2___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eLogic_2eex___24a2,type,
    cCoq_2eInit_2eLogic_2eex___24a2: $i > $i > $o ).

thf(tp_cCoq_2eInit_2eLogic_2eunique,type,
    cCoq_2eInit_2eLogic_2eunique: $i ).

thf(tp_cCoq_2eInit_2eLogic_2eunique___24a2,type,
    cCoq_2eInit_2eLogic_2eunique___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eLogic__Type_2enotT,type,
    cCoq_2eInit_2eLogic__Type_2enotT: $i ).

thf(tp_cCoq_2eInit_2eLogic__Type_2enotT___24a1,type,
    cCoq_2eInit_2eLogic__Type_2enotT___24a1: $i > $o ).

thf(tp_cCoq_2eInit_2eNat_2eadd,type,
    cCoq_2eInit_2eNat_2eadd: $i ).

thf(tp_cCoq_2eInit_2eNat_2eadd___24a2,type,
    cCoq_2eInit_2eNat_2eadd___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eNat_2emax,type,
    cCoq_2eInit_2eNat_2emax: $i ).

thf(tp_cCoq_2eInit_2eNat_2emax___24a2,type,
    cCoq_2eInit_2eNat_2emax___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eNat_2emin,type,
    cCoq_2eInit_2eNat_2emin: $i ).

thf(tp_cCoq_2eInit_2eNat_2emin___24a2,type,
    cCoq_2eInit_2eNat_2emin___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eNat_2emul,type,
    cCoq_2eInit_2eNat_2emul: $i ).

thf(tp_cCoq_2eInit_2eNat_2emul___24a2,type,
    cCoq_2eInit_2eNat_2emul___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eNat_2epred,type,
    cCoq_2eInit_2eNat_2epred: $i ).

thf(tp_cCoq_2eInit_2eNat_2epred___24a1,type,
    cCoq_2eInit_2eNat_2epred___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eNat_2esub,type,
    cCoq_2eInit_2eNat_2esub: $i ).

thf(tp_cCoq_2eInit_2eNat_2esub___24a2,type,
    cCoq_2eInit_2eNat_2esub___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eNat_2et,type,
    cCoq_2eInit_2eNat_2et: $i ).

thf(tp_cCoq_2eInit_2eNat_2et___24t,type,
    cCoq_2eInit_2eNat_2et___24t: $i > $o ).

thf(tp_cCoq_2eInit_2eNat_2ezero,type,
    cCoq_2eInit_2eNat_2ezero: $i ).

thf(tp_cCoq_2eInit_2ePeano_2eIsSucc,type,
    cCoq_2eInit_2ePeano_2eIsSucc: $i ).

thf(tp_cCoq_2eInit_2ePeano_2eIsSucc___24a1,type,
    cCoq_2eInit_2ePeano_2eIsSucc___24a1: $i > $o ).

thf(tp_cCoq_2eInit_2ePeano_2egt,type,
    cCoq_2eInit_2ePeano_2egt: $i ).

thf(tp_cCoq_2eInit_2ePeano_2egt___24a2,type,
    cCoq_2eInit_2ePeano_2egt___24a2: $i > $i > $o ).

thf(tp_cCoq_2eInit_2ePeano_2ele,type,
    cCoq_2eInit_2ePeano_2ele: $i ).

thf(tp_cCoq_2eInit_2ePeano_2ele___24a2,type,
    cCoq_2eInit_2ePeano_2ele___24a2: $i > $i > $o ).

thf(tp_cCoq_2eInit_2ePeano_2elt,type,
    cCoq_2eInit_2ePeano_2elt: $i ).

thf(tp_cCoq_2eInit_2ePeano_2elt___24a2,type,
    cCoq_2eInit_2ePeano_2elt___24a2: $i > $i > $o ).

thf(tp_cCoq_2eInit_2eSpecif_2eexcept,type,
    cCoq_2eInit_2eSpecif_2eexcept: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexist,type,
    cCoq_2eInit_2eSpecif_2eexist: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexist2,type,
    cCoq_2eInit_2eSpecif_2eexist2: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexist2___24a4,type,
    cCoq_2eInit_2eSpecif_2eexist2___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexistT,type,
    cCoq_2eInit_2eSpecif_2eexistT: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexistT2,type,
    cCoq_2eInit_2eSpecif_2eexistT2: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexistT2___24a6,type,
    cCoq_2eInit_2eSpecif_2eexistT2___24a6: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexistT___24a4,type,
    cCoq_2eInit_2eSpecif_2eexistT___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eexist___24a3,type,
    cCoq_2eInit_2eSpecif_2eexist___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2einleft,type,
    cCoq_2eInit_2eSpecif_2einleft: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2einleft___24a3,type,
    cCoq_2eInit_2eSpecif_2einleft___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2einright,type,
    cCoq_2eInit_2eSpecif_2einright: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2einright___24a2,type,
    cCoq_2eInit_2eSpecif_2einright___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eleft,type,
    cCoq_2eInit_2eSpecif_2eleft: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eleft___24a2,type,
    cCoq_2eInit_2eSpecif_2eleft___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eright,type,
    cCoq_2eInit_2eSpecif_2eright: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2eright___24a2,type,
    cCoq_2eInit_2eSpecif_2eright___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esig,type,
    cCoq_2eInit_2eSpecif_2esig: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esig2,type,
    cCoq_2eInit_2eSpecif_2esig2: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esig2___24a3,type,
    cCoq_2eInit_2eSpecif_2esig2___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esig2___24t,type,
    cCoq_2eInit_2eSpecif_2esig2___24t: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eSpecif_2esigT,type,
    cCoq_2eInit_2eSpecif_2esigT: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esigT2,type,
    cCoq_2eInit_2eSpecif_2esigT2: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esigT2___24a3,type,
    cCoq_2eInit_2eSpecif_2esigT2___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esigT2___24t,type,
    cCoq_2eInit_2eSpecif_2esigT2___24t: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eSpecif_2esigT___24a2,type,
    cCoq_2eInit_2eSpecif_2esigT___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esigT___24t,type,
    cCoq_2eInit_2eSpecif_2esigT___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eSpecif_2esig___24a2,type,
    cCoq_2eInit_2eSpecif_2esig___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esig___24t,type,
    cCoq_2eInit_2eSpecif_2esig___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eSpecif_2esumbool,type,
    cCoq_2eInit_2eSpecif_2esumbool: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esumbool___24a2,type,
    cCoq_2eInit_2eSpecif_2esumbool___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esumbool___24t,type,
    cCoq_2eInit_2eSpecif_2esumbool___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eSpecif_2esumor,type,
    cCoq_2eInit_2eSpecif_2esumor: $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esumor___24a2,type,
    cCoq_2eInit_2eSpecif_2esumor___24a2: $i > $i > $i ).

thf(tp_cCoq_2eInit_2eSpecif_2esumor___24t,type,
    cCoq_2eInit_2eSpecif_2esumor___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eWf_2eAcc,type,
    cCoq_2eInit_2eWf_2eAcc: $i ).

thf(tp_cCoq_2eInit_2eWf_2eAcc___24a3,type,
    cCoq_2eInit_2eWf_2eAcc___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eInit_2eWf_2ewell__founded,type,
    cCoq_2eInit_2eWf_2ewell__founded: $i ).

thf(tp_cCoq_2eInit_2eWf_2ewell__founded___24a1,type,
    cCoq_2eInit_2eWf_2ewell__founded___24a1: $i > $i ).

thf(tp_cCoq_2eInit_2eWf_2ewell__founded___24a2,type,
    cCoq_2eInit_2eWf_2ewell__founded___24a2: $i > $i > $i ).

thf(tp_cCoq_2eLists_2eList_2eExists,type,
    cCoq_2eLists_2eList_2eExists: $i ).

thf(tp_cCoq_2eLists_2eList_2eExists___24a3,type,
    cCoq_2eLists_2eList_2eExists___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eList_2eForall,type,
    cCoq_2eLists_2eList_2eForall: $i ).

thf(tp_cCoq_2eLists_2eList_2eForall2,type,
    cCoq_2eLists_2eList_2eForall2: $i ).

thf(tp_cCoq_2eLists_2eList_2eForall2___24a5,type,
    cCoq_2eLists_2eList_2eForall2___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eList_2eForallOrdPairs,type,
    cCoq_2eLists_2eList_2eForallOrdPairs: $i ).

thf(tp_cCoq_2eLists_2eList_2eForallOrdPairs___24a3,type,
    cCoq_2eLists_2eList_2eForallOrdPairs___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eList_2eForall___24a3,type,
    cCoq_2eLists_2eList_2eForall___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eList_2eIn,type,
    cCoq_2eLists_2eList_2eIn: $i ).

thf(tp_cCoq_2eLists_2eList_2eIn___24a1,type,
    cCoq_2eLists_2eList_2eIn___24a1: $i > $i ).

thf(tp_cCoq_2eLists_2eList_2eIn___24a3,type,
    cCoq_2eLists_2eList_2eIn___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eList_2eNoDup,type,
    cCoq_2eLists_2eList_2eNoDup: $i ).

thf(tp_cCoq_2eLists_2eList_2eNoDup___24a2,type,
    cCoq_2eLists_2eList_2eNoDup___24a2: $i > $i > $o ).

thf(tp_cCoq_2eLists_2eList_2efold__right,type,
    cCoq_2eLists_2eList_2efold__right: $i ).

thf(tp_cCoq_2eLists_2eList_2efold__right___24a5,type,
    cCoq_2eLists_2eList_2efold__right___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2eInA,type,
    cCoq_2eLists_2eSetoidList_2eInA: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2eInA___24a4,type,
    cCoq_2eLists_2eSetoidList_2eInA___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eSetoidList_2eNoDupA,type,
    cCoq_2eLists_2eSetoidList_2eNoDupA: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2eNoDupA___24a3,type,
    cCoq_2eLists_2eSetoidList_2eNoDupA___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eSetoidList_2eeqlistA,type,
    cCoq_2eLists_2eSetoidList_2eeqlistA: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2eeqlistA___24a4,type,
    cCoq_2eLists_2eSetoidList_2eeqlistA___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose,type,
    cCoq_2eLists_2eSetoidList_2etranspose: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose2,type,
    cCoq_2eLists_2eSetoidList_2etranspose2: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose2___24a4,type,
    cCoq_2eLists_2eSetoidList_2etranspose2___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose___24a4,type,
    cCoq_2eLists_2eSetoidList_2etranspose___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose__restr,type,
    cCoq_2eLists_2eSetoidList_2etranspose__restr: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose__restr2,type,
    cCoq_2eLists_2eSetoidList_2etranspose__restr2: $i ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5,type,
    cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5,type,
    cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on,type,
    cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on: $i ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2,type,
    cCoq_2eLogic_2eChoiceFacts_2eDependentFunctionalChoice__on___24a2: $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on,type,
    cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on: $i ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2,type,
    cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on___24a2: $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel,type,
    cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel: $i ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3,type,
    cCoq_2eLogic_2eChoiceFacts_2eFunctionalChoice__on__rel___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on,type,
    cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on: $i ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1,type,
    cCoq_2eLogic_2eChoiceFacts_2eFunctionalCountableChoice__on___24a1: $i > $o ).

thf(tp_cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance,type,
    cCoq_2eLogic_2eChoiceFacts_2eProofIrrelevance: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eBoolP,type,
    cCoq_2eLogic_2eClassicalFacts_2eBoolP: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox,type,
    cCoq_2eLogic_2eClassicalFacts_2eDrinkerParadox: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eGodelDummett,type,
    cCoq_2eLogic_2eClassicalFacts_2eGodelDummett: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises,type,
    cCoq_2eLogic_2eClassicalFacts_2eIndependenceOfGeneralPremises: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction,type,
    cCoq_2eLogic_2eClassicalFacts_2eRightDistributivityImplicationOverDisjunction: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eboolP,type,
    cCoq_2eLogic_2eClassicalFacts_2eboolP: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle,type,
    cCoq_2eLogic_2eClassicalFacts_2eexcluded__middle: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle,type,
    cCoq_2eLogic_2eClassicalFacts_2egeneralized__excluded__middle: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint,type,
    cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1,type,
    cCoq_2eLogic_2eClassicalFacts_2ehas__fixpoint___24a1: $i > $o ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance,type,
    cCoq_2eLogic_2eClassicalFacts_2eproof__irrelevance: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eretract,type,
    cCoq_2eLogic_2eClassicalFacts_2eretract: $i ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eretract___24a2,type,
    cCoq_2eLogic_2eClassicalFacts_2eretract___24a2: $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle,type,
    cCoq_2eLogic_2eClassicalFacts_2eweak__generalized__excluded__middle: $i ).

thf(tp_cCoq_2eLogic_2eDecidable_2edecidable,type,
    cCoq_2eLogic_2eDecidable_2edecidable: $i ).

thf(tp_cCoq_2eLogic_2eDecidable_2edecidable___24a1,type,
    cCoq_2eLogic_2eDecidable_2edecidable___24a1: $i > $o ).

thf(tp_cCoq_2eLogic_2eEqdepFacts_2eeq__dep,type,
    cCoq_2eLogic_2eEqdepFacts_2eeq__dep: $i ).

thf(tp_cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,type,
    cCoq_2eLogic_2eEqdepFacts_2eeq__dep1: $i ).

thf(tp_cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6,type,
    cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6,type,
    cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eFinFun_2eBijective,type,
    cCoq_2eLogic_2eFinFun_2eBijective: $i ).

thf(tp_cCoq_2eLogic_2eFinFun_2eBijective___24a3,type,
    cCoq_2eLogic_2eFinFun_2eBijective___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eFinFun_2eInjective,type,
    cCoq_2eLogic_2eFinFun_2eInjective: $i ).

thf(tp_cCoq_2eLogic_2eFinFun_2eInjective___24a3,type,
    cCoq_2eLogic_2eFinFun_2eInjective___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eLogic_2eFinFun_2eSurjective,type,
    cCoq_2eLogic_2eFinFun_2eSurjective: $i ).

thf(tp_cCoq_2eLogic_2eFinFun_2eSurjective___24a3,type,
    cCoq_2eLogic_2eFinFun_2eSurjective___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2eadd,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2eadd: $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2: $i > $i > $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2ecompare: $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2: $i > $i > $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2esucc,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2esucc: $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1: $i > $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2et,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2et: $i ).

thf(tp_cCoq_2eNArith_2eBinNatDef_2eN_2et___24t,type,
    cCoq_2eNArith_2eBinNatDef_2eN_2et___24t: $i > $o ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2ele,type,
    cCoq_2eNArith_2eBinNat_2eN_2ele: $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2ele___24a2,type,
    cCoq_2eNArith_2eBinNat_2eN_2ele___24a2: $i > $i > $o ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2elt,type,
    cCoq_2eNArith_2eBinNat_2eN_2elt: $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2elt___24a2,type,
    cCoq_2eNArith_2eBinNat_2eN_2elt___24a2: $i > $i > $o ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,type,
    cCoq_2eNArith_2eBinNat_2eN_2epeano__rect: $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1,type,
    cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1: $i > $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4,type,
    cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2erecursion,type,
    cCoq_2eNArith_2eBinNat_2eN_2erecursion: $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1,type,
    cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1: $i > $i ).

thf(tp_cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4,type,
    cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eN,type,
    cCoq_2eNumbers_2eBinNums_2eN: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eN0,type,
    cCoq_2eNumbers_2eBinNums_2eN0: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eN___24t,type,
    cCoq_2eNumbers_2eBinNums_2eN___24t: $i > $o ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eNpos,type,
    cCoq_2eNumbers_2eBinNums_2eNpos: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eNpos___24a1,type,
    cCoq_2eNumbers_2eBinNums_2eNpos___24a1: $i > $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZ,type,
    cCoq_2eNumbers_2eBinNums_2eZ: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZ0,type,
    cCoq_2eNumbers_2eBinNums_2eZ0: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZ___24t,type,
    cCoq_2eNumbers_2eBinNums_2eZ___24t: $i > $o ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZneg,type,
    cCoq_2eNumbers_2eBinNums_2eZneg: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZneg___24a1,type,
    cCoq_2eNumbers_2eBinNums_2eZneg___24a1: $i > $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZpos,type,
    cCoq_2eNumbers_2eBinNums_2eZpos: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2eZpos___24a1,type,
    cCoq_2eNumbers_2eBinNums_2eZpos___24a1: $i > $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2epositive,type,
    cCoq_2eNumbers_2eBinNums_2epositive: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2epositive___24t,type,
    cCoq_2eNumbers_2eBinNums_2epositive___24t: $i > $o ).

thf(tp_cCoq_2eNumbers_2eBinNums_2exH,type,
    cCoq_2eNumbers_2eBinNums_2exH: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2exI,type,
    cCoq_2eNumbers_2eBinNums_2exI: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2exI___24a1,type,
    cCoq_2eNumbers_2eBinNums_2exI___24a1: $i > $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2exO,type,
    cCoq_2eNumbers_2eBinNums_2exO: $i ).

thf(tp_cCoq_2eNumbers_2eBinNums_2exO___24a1,type,
    cCoq_2eNumbers_2eBinNums_2exO___24a1: $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1: $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eadd: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2: $i > $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1: $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eiter: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2emask,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t: $i > $o ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2emul,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emul: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2: $i > $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1: $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2esucc: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1: $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2et,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2et: $i ).

thf(tp_cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t,type,
    cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t: $i > $o ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne,type,
    cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne: $i ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,type,
    cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc: $i ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2,type,
    cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2: $i > $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,type,
    cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView: $i ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1,type,
    cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1: $i > $i ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t,type,
    cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t: $i > $i > $o ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect,type,
    cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect: $i ).

thf(tp_cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4,type,
    cCoq_2ePArith_2eBinPos_2ePos_2epeano__rect___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eProgram_2eBasics_2eflip,type,
    cCoq_2eProgram_2eBasics_2eflip: $i ).

thf(tp_cCoq_2eProgram_2eBasics_2eflip___24a4,type,
    cCoq_2eProgram_2eBasics_2eflip___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eProgram_2eBasics_2eflip___24a6,type,
    cCoq_2eProgram_2eBasics_2eflip___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eProgram_2eBasics_2eimpl,type,
    cCoq_2eProgram_2eBasics_2eimpl: $i ).

thf(tp_cCoq_2eProgram_2eBasics_2eimpl___24a2,type,
    cCoq_2eProgram_2eBasics_2eimpl___24a2: $i > $i > $o ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQ,type,
    cCoq_2eQArith_2eQArith__base_2eQ: $i ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQ___24t,type,
    cCoq_2eQArith_2eQArith__base_2eQ___24t: $i > $o ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQden,type,
    cCoq_2eQArith_2eQArith__base_2eQden: $i ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQden___24a1,type,
    cCoq_2eQArith_2eQArith__base_2eQden___24a1: $i > $i ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQmake,type,
    cCoq_2eQArith_2eQArith__base_2eQmake: $i ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQmake___24a2,type,
    cCoq_2eQArith_2eQArith__base_2eQmake___24a2: $i > $i > $i ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQnum,type,
    cCoq_2eQArith_2eQArith__base_2eQnum: $i ).

thf(tp_cCoq_2eQArith_2eQArith__base_2eQnum___24a1,type,
    cCoq_2eQArith_2eQArith__base_2eQnum___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknegreal,type,
    cCoq_2eReals_2eRIneq_2emknegreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknegreal___24a1,type,
    cCoq_2eReals_2eRIneq_2emknegreal___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknonnegreal,type,
    cCoq_2eReals_2eRIneq_2emknonnegreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknonnegreal___24a1,type,
    cCoq_2eReals_2eRIneq_2emknonnegreal___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknonposreal,type,
    cCoq_2eReals_2eRIneq_2emknonposreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknonposreal___24a1,type,
    cCoq_2eReals_2eRIneq_2emknonposreal___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknonzeroreal,type,
    cCoq_2eReals_2eRIneq_2emknonzeroreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1,type,
    cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emkposreal,type,
    cCoq_2eReals_2eRIneq_2emkposreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2emkposreal___24a1,type,
    cCoq_2eReals_2eRIneq_2emkposreal___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRIneq_2enegreal,type,
    cCoq_2eReals_2eRIneq_2enegreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2enegreal___24t,type,
    cCoq_2eReals_2eRIneq_2enegreal___24t: $i > $o ).

thf(tp_cCoq_2eReals_2eRIneq_2enonnegreal,type,
    cCoq_2eReals_2eRIneq_2enonnegreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2enonnegreal___24t,type,
    cCoq_2eReals_2eRIneq_2enonnegreal___24t: $i > $o ).

thf(tp_cCoq_2eReals_2eRIneq_2enonposreal,type,
    cCoq_2eReals_2eRIneq_2enonposreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2enonposreal___24t,type,
    cCoq_2eReals_2eRIneq_2enonposreal___24t: $i > $o ).

thf(tp_cCoq_2eReals_2eRIneq_2enonzeroreal,type,
    cCoq_2eReals_2eRIneq_2enonzeroreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2enonzeroreal___24t,type,
    cCoq_2eReals_2eRIneq_2enonzeroreal___24t: $i > $o ).

thf(tp_cCoq_2eReals_2eRIneq_2eposreal,type,
    cCoq_2eReals_2eRIneq_2eposreal: $i ).

thf(tp_cCoq_2eReals_2eRIneq_2eposreal___24t,type,
    cCoq_2eReals_2eRIneq_2eposreal___24t: $i > $o ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eIZR,type,
    cCoq_2eReals_2eRdefinitions_2eIZR: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eIZR___24a1,type,
    cCoq_2eReals_2eRdefinitions_2eIZR___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eR,type,
    cCoq_2eReals_2eRdefinitions_2eR: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eR0,type,
    cCoq_2eReals_2eRdefinitions_2eR0: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eR1,type,
    cCoq_2eReals_2eRdefinitions_2eR1: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eR___24t,type,
    cCoq_2eReals_2eRdefinitions_2eR___24t: $i > $o ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRinv,type,
    cCoq_2eReals_2eRdefinitions_2eRinv: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRle,type,
    cCoq_2eReals_2eRdefinitions_2eRle: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRle___24a2,type,
    cCoq_2eReals_2eRdefinitions_2eRle___24a2: $i > $i > $o ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRlt,type,
    cCoq_2eReals_2eRdefinitions_2eRlt: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRlt___24a2,type,
    cCoq_2eReals_2eRdefinitions_2eRlt___24a2: $i > $i > $o ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRmult,type,
    cCoq_2eReals_2eRdefinitions_2eRmult: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRopp,type,
    cCoq_2eReals_2eRdefinitions_2eRopp: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eRplus,type,
    cCoq_2eReals_2eRdefinitions_2eRplus: $i ).

thf(tp_cCoq_2eReals_2eRdefinitions_2eup,type,
    cCoq_2eReals_2eRdefinitions_2eup: $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZ__spec,type,
    cCoq_2eReals_2eRfunctions_2eZ__spec: $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZ__spec___24a2,type,
    cCoq_2eReals_2eRfunctions_2eZ__spec___24a2: $i > $i > $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZ__spec___24t,type,
    cCoq_2eReals_2eRfunctions_2eZ__spec___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZintNeg,type,
    cCoq_2eReals_2eRfunctions_2eZintNeg: $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZintNeg___24a2,type,
    cCoq_2eReals_2eRfunctions_2eZintNeg___24a2: $i > $i > $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZintNull,type,
    cCoq_2eReals_2eRfunctions_2eZintNull: $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZintNull___24a1,type,
    cCoq_2eReals_2eRfunctions_2eZintNull___24a1: $i > $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZintPos,type,
    cCoq_2eReals_2eRfunctions_2eZintPos: $i ).

thf(tp_cCoq_2eReals_2eRfunctions_2eZintPos___24a2,type,
    cCoq_2eReals_2eRfunctions_2eZintPos___24a2: $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2ePER,type,
    cCoq_2eRelations_2eRelation__Definitions_2ePER: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,type,
    cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2ecommut,type,
    cCoq_2eRelations_2eRelation__Definitions_2ecommut: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3,type,
    cCoq_2eRelations_2eRelation__Definitions_2ecommut___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eequiv,type,
    cCoq_2eRelations_2eRelation__Definitions_2eequiv: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2eequiv___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eequivalence,type,
    cCoq_2eRelations_2eRelation__Definitions_2eequivalence: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2einclusion,type,
    cCoq_2eRelations_2eRelation__Definitions_2einclusion: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1,type,
    cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3,type,
    cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eorder,type,
    cCoq_2eRelations_2eRelation__Definitions_2eorder: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2epreorder,type,
    cCoq_2eRelations_2eRelation__Definitions_2epreorder: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2ereflexive,type,
    cCoq_2eRelations_2eRelation__Definitions_2ereflexive: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2erelation,type,
    cCoq_2eRelations_2eRelation__Definitions_2erelation: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1,type,
    cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2erelation___24t,type,
    cCoq_2eRelations_2eRelation__Definitions_2erelation___24t: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2esame__relation,type,
    cCoq_2eRelations_2eRelation__Definitions_2esame__relation: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1,type,
    cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3,type,
    cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2esymmetric,type,
    cCoq_2eRelations_2eRelation__Definitions_2esymmetric: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2etransitive,type,
    cCoq_2eRelations_2eRelation__Definitions_2etransitive: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a1,type,
    cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2,type,
    cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2: $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eDesc,type,
    cCoq_2eRelations_2eRelation__Operators_2eDesc: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3,type,
    cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eLtl,type,
    cCoq_2eRelations_2eRelation__Operators_2eLtl: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a2: $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2: $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2: $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2: $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2etransp,type,
    cCoq_2eRelations_2eRelation__Operators_2etransp: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2etransp___24a1,type,
    cCoq_2eRelations_2eRelation__Operators_2etransp___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2etransp___24a2,type,
    cCoq_2eRelations_2eRelation__Operators_2etransp___24a2: $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2etransp___24a4,type,
    cCoq_2eRelations_2eRelation__Operators_2etransp___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eunion,type,
    cCoq_2eRelations_2eRelation__Operators_2eunion: $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eunion___24a1,type,
    cCoq_2eRelations_2eRelation__Operators_2eunion___24a1: $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eunion___24a3,type,
    cCoq_2eRelations_2eRelation__Operators_2eunion___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2eRelations_2eRelation__Operators_2eunion___24a5,type,
    cCoq_2eRelations_2eRelation__Operators_2eunion___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,type,
    cCoq_2eSetoids_2eSetoid_2eSetoid__Theory: $i ).

thf(tp_cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2,type,
    cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2: $i > $i > $o ).

thf(tp_cCoq_2eSets_2eRelations__1_2eRelation,type,
    cCoq_2eSets_2eRelations__1_2eRelation: $i ).

thf(tp_cCoq_2eSets_2eRelations__1_2eRelation___24a1,type,
    cCoq_2eSets_2eRelations__1_2eRelation___24a1: $i > $i ).

thf(tp_cCoq_2eSorting_2ePermutation_2ePermutation,type,
    cCoq_2eSorting_2ePermutation_2ePermutation: $i ).

thf(tp_cCoq_2eSorting_2ePermutation_2ePermutation___24a1,type,
    cCoq_2eSorting_2ePermutation_2ePermutation___24a1: $i > $i ).

thf(tp_cCoq_2eSorting_2ePermutation_2ePermutation___24a3,type,
    cCoq_2eSorting_2ePermutation_2ePermutation___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eSorting_2eSorted_2eHdRel,type,
    cCoq_2eSorting_2eSorted_2eHdRel: $i ).

thf(tp_cCoq_2eSorting_2eSorted_2eHdRel___24a4,type,
    cCoq_2eSorting_2eSorted_2eHdRel___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eSorting_2eSorted_2eLocallySorted,type,
    cCoq_2eSorting_2eSorted_2eLocallySorted: $i ).

thf(tp_cCoq_2eSorting_2eSorted_2eLocallySorted___24a3,type,
    cCoq_2eSorting_2eSorted_2eLocallySorted___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eSorting_2eSorted_2eSorted,type,
    cCoq_2eSorting_2eSorted_2eSorted: $i ).

thf(tp_cCoq_2eSorting_2eSorted_2eSorted___24a3,type,
    cCoq_2eSorting_2eSorted_2eSorted___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eSorting_2eSorted_2eStronglySorted,type,
    cCoq_2eSorting_2eSorted_2eStronglySorted: $i ).

thf(tp_cCoq_2eSorting_2eSorted_2eStronglySorted___24a3,type,
    cCoq_2eSorting_2eSorted_2eStronglySorted___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eStrings_2eAscii_2eAscii,type,
    cCoq_2eStrings_2eAscii_2eAscii: $i ).

thf(tp_cCoq_2eStrings_2eAscii_2eAscii___24a8,type,
    cCoq_2eStrings_2eAscii_2eAscii___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eStrings_2eAscii_2eascii,type,
    cCoq_2eStrings_2eAscii_2eascii: $i ).

thf(tp_cCoq_2eStrings_2eAscii_2eascii___24t,type,
    cCoq_2eStrings_2eAscii_2eascii___24t: $i > $o ).

thf(tp_cCoq_2eStrings_2eAscii_2enat__of__ascii,type,
    cCoq_2eStrings_2eAscii_2enat__of__ascii: $i ).

thf(tp_cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1,type,
    cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1: $i > $i ).

thf(tp_cCoq_2eStrings_2eString_2eEmptyString,type,
    cCoq_2eStrings_2eString_2eEmptyString: $i ).

thf(tp_cCoq_2eStrings_2eString_2eString,type,
    cCoq_2eStrings_2eString_2eString: $i ).

thf(tp_cCoq_2eStrings_2eString_2eString___24a2,type,
    cCoq_2eStrings_2eString_2eString___24a2: $i > $i > $i ).

thf(tp_cCoq_2eStrings_2eString_2estring,type,
    cCoq_2eStrings_2eString_2estring: $i ).

thf(tp_cCoq_2eStrings_2eString_2estring___24t,type,
    cCoq_2eStrings_2eString_2estring___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2elt: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2elt: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2: $i > $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t,type,
    cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2: $i > $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et: $i ).

thf(tp_cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t,type,
    cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t: $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eCompare,type,
    cCoq_2eStructures_2eOrderedType_2eCompare: $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eCompare___24a5,type,
    cCoq_2eStructures_2eOrderedType_2eCompare___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eCompare___24t,type,
    cCoq_2eStructures_2eOrderedType_2eCompare___24t: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eEQ,type,
    cCoq_2eStructures_2eOrderedType_2eEQ: $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eEQ___24a5,type,
    cCoq_2eStructures_2eOrderedType_2eEQ___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eGT,type,
    cCoq_2eStructures_2eOrderedType_2eGT: $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eGT___24a5,type,
    cCoq_2eStructures_2eOrderedType_2eGT___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eLT,type,
    cCoq_2eStructures_2eOrderedType_2eLT: $i ).

thf(tp_cCoq_2eStructures_2eOrderedType_2eLT___24a5,type,
    cCoq_2eStructures_2eOrderedType_2eLT___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eStructures_2eOrdersTac_2eOEQ,type,
    cCoq_2eStructures_2eOrdersTac_2eOEQ: $i ).

thf(tp_cCoq_2eStructures_2eOrdersTac_2eOLE,type,
    cCoq_2eStructures_2eOrdersTac_2eOLE: $i ).

thf(tp_cCoq_2eStructures_2eOrdersTac_2eOLT,type,
    cCoq_2eStructures_2eOrdersTac_2eOLT: $i ).

thf(tp_cCoq_2eStructures_2eOrdersTac_2eord,type,
    cCoq_2eStructures_2eOrdersTac_2eord: $i ).

thf(tp_cCoq_2eStructures_2eOrdersTac_2eord___24t,type,
    cCoq_2eStructures_2eOrdersTac_2eord___24t: $i > $o ).

thf(tp_cCoq_2eVectors_2eFin_2eF1,type,
    cCoq_2eVectors_2eFin_2eF1: $i ).

thf(tp_cCoq_2eVectors_2eFin_2eF1___24a1,type,
    cCoq_2eVectors_2eFin_2eF1___24a1: $i > $i ).

thf(tp_cCoq_2eVectors_2eFin_2eFS,type,
    cCoq_2eVectors_2eFin_2eFS: $i ).

thf(tp_cCoq_2eVectors_2eFin_2eFS___24a2,type,
    cCoq_2eVectors_2eFin_2eFS___24a2: $i > $i > $i ).

thf(tp_cCoq_2eVectors_2eFin_2et,type,
    cCoq_2eVectors_2eFin_2et: $i ).

thf(tp_cCoq_2eVectors_2eFin_2et___24a1,type,
    cCoq_2eVectors_2eFin_2et___24a1: $i > $i ).

thf(tp_cCoq_2eVectors_2eFin_2et___24t,type,
    cCoq_2eVectors_2eFin_2et___24t: $i > $i > $o ).

thf(tp_cCoq_2eVectors_2eVectorDef_2econs,type,
    cCoq_2eVectors_2eVectorDef_2econs: $i ).

thf(tp_cCoq_2eVectors_2eVectorDef_2econs___24a4,type,
    cCoq_2eVectors_2eVectorDef_2econs___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eVectors_2eVectorDef_2enil,type,
    cCoq_2eVectors_2eVectorDef_2enil: $i ).

thf(tp_cCoq_2eVectors_2eVectorDef_2enil___24a1,type,
    cCoq_2eVectors_2eVectorDef_2enil___24a1: $i > $i ).

thf(tp_cCoq_2eVectors_2eVectorDef_2et,type,
    cCoq_2eVectors_2eVectorDef_2et: $i ).

thf(tp_cCoq_2eVectors_2eVectorDef_2et___24a2,type,
    cCoq_2eVectors_2eVectorDef_2et___24a2: $i > $i > $i ).

thf(tp_cCoq_2eVectors_2eVectorDef_2et___24t,type,
    cCoq_2eVectors_2eVectorDef_2et___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eabs: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1: $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eadd: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2emul,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2emul: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1: $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eopp: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1: $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2esub,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2esub: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2esucc,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2esucc: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1: $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2et,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2et: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t: $i > $o ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos: $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1: $i > $i ).

thf(tp_cCoq_2eZArith_2eBinIntDef_2eZ_2ezero,type,
    cCoq_2eZArith_2eBinIntDef_2eZ_2ezero: $i ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2edivide,type,
    cCoq_2eZArith_2eBinInt_2eZ_2edivide: $i ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2,type,
    cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2: $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2eeq,type,
    cCoq_2eZArith_2eBinInt_2eZ_2eeq: $i ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2ege,type,
    cCoq_2eZArith_2eBinInt_2eZ_2ege: $i ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2,type,
    cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2: $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2ele,type,
    cCoq_2eZArith_2eBinInt_2eZ_2ele: $i ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2,type,
    cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2: $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2elt,type,
    cCoq_2eZArith_2eBinInt_2eZ_2elt: $i ).

thf(tp_cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2,type,
    cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2: $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eZeven_2eZeven,type,
    cCoq_2eZArith_2eZeven_2eZeven: $i ).

thf(tp_cCoq_2eZArith_2eZeven_2eZeven___24a1,type,
    cCoq_2eZArith_2eZeven_2eZeven___24a1: $i > $o ).

thf(tp_cCoq_2eZArith_2eZeven_2eZodd,type,
    cCoq_2eZArith_2eZeven_2eZodd: $i ).

thf(tp_cCoq_2eZArith_2eZeven_2eZodd___24a1,type,
    cCoq_2eZArith_2eZeven_2eZodd___24a1: $i > $o ).

thf(tp_cCoq_2eZArith_2eZlogarithm_2eIs__power,type,
    cCoq_2eZArith_2eZlogarithm_2eIs__power: $i ).

thf(tp_cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1,type,
    cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1: $i > $o ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eBezout,type,
    cCoq_2eZArith_2eZnumtheory_2eBezout: $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eBezout___24a3,type,
    cCoq_2eZArith_2eZnumtheory_2eBezout___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eEuclid,type,
    cCoq_2eZArith_2eZnumtheory_2eEuclid: $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2,type,
    cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eEuclid___24t,type,
    cCoq_2eZArith_2eZnumtheory_2eEuclid___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,type,
    cCoq_2eZArith_2eZnumtheory_2eEuclid__intro: $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5,type,
    cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eZis__gcd,type,
    cCoq_2eZArith_2eZnumtheory_2eZis__gcd: $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3,type,
    cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eprime,type,
    cCoq_2eZArith_2eZnumtheory_2eprime: $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2eprime___24a1,type,
    cCoq_2eZArith_2eZnumtheory_2eprime___24a1: $i > $o ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2erel__prime,type,
    cCoq_2eZArith_2eZnumtheory_2erel__prime: $i ).

thf(tp_cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2,type,
    cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2: $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,type,
    cCoq_2eZArith_2eZpower_2eZdiv__rest__proof: $i ).

thf(tp_cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4,type,
    cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,type,
    cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs: $i ).

thf(tp_cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2,type,
    cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2: $i > $i > $i ).

thf(tp_cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t,type,
    cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t: $i > $i > $i > $o ).

thf(tp_cCoq_2eZArith_2eZpower_2etwo__power__pos,type,
    cCoq_2eZArith_2eZpower_2etwo__power__pos: $i ).

thf(tp_cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1,type,
    cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,type,
    cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant: $i ).

thf(tp_cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2,type,
    cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eDeclConstant_2eGT,type,
    cCoq_2emicromega_2eDeclConstant_2eGT: $i ).

thf(tp_cCoq_2emicromega_2eDeclConstant_2eGT___24a2,type,
    cCoq_2emicromega_2eDeclConstant_2eGT___24a2: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eEnvRing_2eMon,type,
    cCoq_2emicromega_2eEnvRing_2eMon: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2eMon___24t,type,
    cCoq_2emicromega_2eEnvRing_2eMon___24t: $i > $o ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEX,type,
    cCoq_2emicromega_2eEnvRing_2ePEX: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEX___24a2,type,
    cCoq_2emicromega_2eEnvRing_2ePEX___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEadd,type,
    cCoq_2emicromega_2eEnvRing_2ePEadd: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEadd___24a3,type,
    cCoq_2emicromega_2eEnvRing_2ePEadd___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEc,type,
    cCoq_2emicromega_2eEnvRing_2ePEc: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEc___24a2,type,
    cCoq_2emicromega_2eEnvRing_2ePEc___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEmul,type,
    cCoq_2emicromega_2eEnvRing_2ePEmul: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEmul___24a3,type,
    cCoq_2emicromega_2eEnvRing_2ePEmul___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEopp,type,
    cCoq_2emicromega_2eEnvRing_2ePEopp: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEopp___24a2,type,
    cCoq_2emicromega_2eEnvRing_2ePEopp___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEpow,type,
    cCoq_2emicromega_2eEnvRing_2ePEpow: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEpow___24a3,type,
    cCoq_2emicromega_2eEnvRing_2ePEpow___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEsub,type,
    cCoq_2emicromega_2eEnvRing_2ePEsub: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePEsub___24a3,type,
    cCoq_2emicromega_2eEnvRing_2ePEsub___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePExpr,type,
    cCoq_2emicromega_2eEnvRing_2ePExpr: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePExpr___24a1,type,
    cCoq_2emicromega_2eEnvRing_2ePExpr___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePExpr___24t,type,
    cCoq_2emicromega_2eEnvRing_2ePExpr___24t: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePX,type,
    cCoq_2emicromega_2eEnvRing_2ePX: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePX___24a4,type,
    cCoq_2emicromega_2eEnvRing_2ePX___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePc,type,
    cCoq_2emicromega_2eEnvRing_2ePc: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePc___24a2,type,
    cCoq_2emicromega_2eEnvRing_2ePc___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePinj,type,
    cCoq_2emicromega_2eEnvRing_2ePinj: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePinj___24a3,type,
    cCoq_2emicromega_2eEnvRing_2ePinj___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePol,type,
    cCoq_2emicromega_2eEnvRing_2ePol: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePol___24a1,type,
    cCoq_2emicromega_2eEnvRing_2ePol___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ePol___24t,type,
    cCoq_2emicromega_2eEnvRing_2ePol___24t: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eEnvRing_2emon0,type,
    cCoq_2emicromega_2eEnvRing_2emon0: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2evmon,type,
    cCoq_2emicromega_2eEnvRing_2evmon: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2evmon___24a2,type,
    cCoq_2emicromega_2eEnvRing_2evmon___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ezmon,type,
    cCoq_2emicromega_2eEnvRing_2ezmon: $i ).

thf(tp_cCoq_2emicromega_2eEnvRing_2ezmon___24a2,type,
    cCoq_2emicromega_2eEnvRing_2ezmon___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eEnv_2eEnv,type,
    cCoq_2emicromega_2eEnv_2eEnv: $i ).

thf(tp_cCoq_2emicromega_2eEnv_2eEnv___24a1,type,
    cCoq_2emicromega_2eEnv_2eEnv___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eOrderedRing_2eSOR,type,
    cCoq_2emicromega_2eOrderedRing_2eSOR: $i ).

thf(tp_cCoq_2emicromega_2eOrderedRing_2eSOR___24a10,type,
    cCoq_2emicromega_2eOrderedRing_2eSOR___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eC0,type,
    cCoq_2emicromega_2eRMicromega_2eC0: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eC1,type,
    cCoq_2emicromega_2eRMicromega_2eC1: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCInv,type,
    cCoq_2emicromega_2eRMicromega_2eCInv: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCInv___24a1,type,
    cCoq_2emicromega_2eRMicromega_2eCInv___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCMinus,type,
    cCoq_2emicromega_2eRMicromega_2eCMinus: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCMinus___24a2,type,
    cCoq_2emicromega_2eRMicromega_2eCMinus___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCMult,type,
    cCoq_2emicromega_2eRMicromega_2eCMult: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCMult___24a2,type,
    cCoq_2emicromega_2eRMicromega_2eCMult___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCOpp,type,
    cCoq_2emicromega_2eRMicromega_2eCOpp: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCOpp___24a1,type,
    cCoq_2emicromega_2eRMicromega_2eCOpp___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCPlus,type,
    cCoq_2emicromega_2eRMicromega_2eCPlus: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCPlus___24a2,type,
    cCoq_2emicromega_2eRMicromega_2eCPlus___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCPow,type,
    cCoq_2emicromega_2eRMicromega_2eCPow: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCPow___24a2,type,
    cCoq_2emicromega_2eRMicromega_2eCPow___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCQ,type,
    cCoq_2emicromega_2eRMicromega_2eCQ: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCQ___24a1,type,
    cCoq_2emicromega_2eRMicromega_2eCQ___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCZ,type,
    cCoq_2emicromega_2eRMicromega_2eCZ: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eCZ___24a1,type,
    cCoq_2emicromega_2eRMicromega_2eCZ___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eRcst,type,
    cCoq_2emicromega_2eRMicromega_2eRcst: $i ).

thf(tp_cCoq_2emicromega_2eRMicromega_2eRcst___24t,type,
    cCoq_2emicromega_2eRMicromega_2eRcst___24t: $i > $o ).

thf(tp_cCoq_2emicromega_2eRefl_2emake__conj,type,
    cCoq_2emicromega_2eRefl_2emake__conj: $i ).

thf(tp_cCoq_2emicromega_2eRefl_2emake__conj___24a3,type,
    cCoq_2emicromega_2eRefl_2emake__conj___24a3: $i > $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,type,
    cCoq_2emicromega_2eRingMicromega_2eBuild__Formula: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4,type,
    cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eEqual,type,
    cCoq_2emicromega_2eRingMicromega_2eEqual: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eFormula,type,
    cCoq_2emicromega_2eRingMicromega_2eFormula: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eFormula___24a1,type,
    cCoq_2emicromega_2eRingMicromega_2eFormula___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eFormula___24t,type,
    cCoq_2emicromega_2eRingMicromega_2eFormula___24t: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eNonEqual,type,
    cCoq_2emicromega_2eRingMicromega_2eNonEqual: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eNonStrict,type,
    cCoq_2emicromega_2eRingMicromega_2eNonStrict: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOp1,type,
    cCoq_2emicromega_2eRingMicromega_2eOp1: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOp1___24t,type,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t: $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOp2,type,
    cCoq_2emicromega_2eRingMicromega_2eOp2: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOp2___24t,type,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t: $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOpEq,type,
    cCoq_2emicromega_2eRingMicromega_2eOpEq: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOpGe,type,
    cCoq_2emicromega_2eRingMicromega_2eOpGe: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOpGt,type,
    cCoq_2emicromega_2eRingMicromega_2eOpGt: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOpLe,type,
    cCoq_2emicromega_2eRingMicromega_2eOpLe: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOpLt,type,
    cCoq_2emicromega_2eRingMicromega_2eOpLt: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eOpNEq,type,
    cCoq_2emicromega_2eRingMicromega_2eOpNEq: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePolC,type,
    cCoq_2emicromega_2eRingMicromega_2ePolC: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePolC___24a1,type,
    cCoq_2emicromega_2eRingMicromega_2ePolC___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePolC___24t,type,
    cCoq_2emicromega_2eRingMicromega_2ePolC___24t: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePolEnv,type,
    cCoq_2emicromega_2eRingMicromega_2ePolEnv: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1,type,
    cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatz,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatz: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzAdd: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzC,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzC: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzIn,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzIn: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzMulC,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzMulC: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzMulE: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzSquare: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzZ,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzZ: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2ePsatz___24t,type,
    cCoq_2emicromega_2eRingMicromega_2ePsatz___24t: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eSORaddon,type,
    cCoq_2emicromega_2eRingMicromega_2eSORaddon: $i ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22,type,
    cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eRingMicromega_2eStrict,type,
    cCoq_2emicromega_2eRingMicromega_2eStrict: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eA,type,
    cCoq_2emicromega_2eTauto_2eA: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eA___24a6,type,
    cCoq_2emicromega_2eTauto_2eA___24a6: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eCj,type,
    cCoq_2emicromega_2eTauto_2eCj: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eCj___24a6,type,
    cCoq_2emicromega_2eTauto_2eCj___24a6: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eD,type,
    cCoq_2emicromega_2eTauto_2eD: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eD___24a6,type,
    cCoq_2emicromega_2eTauto_2eD___24a6: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eFF,type,
    cCoq_2emicromega_2eTauto_2eFF: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eFF___24a4,type,
    cCoq_2emicromega_2eTauto_2eFF___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eGFormula,type,
    cCoq_2emicromega_2eTauto_2eGFormula: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eGFormula___24a4,type,
    cCoq_2emicromega_2eTauto_2eGFormula___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eGFormula___24t,type,
    cCoq_2emicromega_2eTauto_2eGFormula___24t: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eTauto_2eI,type,
    cCoq_2emicromega_2eTauto_2eI: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eI___24a7,type,
    cCoq_2emicromega_2eTauto_2eI___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eN,type,
    cCoq_2emicromega_2eTauto_2eN: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eN___24a5,type,
    cCoq_2emicromega_2eTauto_2eN___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eTT,type,
    cCoq_2emicromega_2eTauto_2eTT: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eTT___24a4,type,
    cCoq_2emicromega_2eTauto_2eTT___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eX,type,
    cCoq_2emicromega_2eTauto_2eX: $i ).

thf(tp_cCoq_2emicromega_2eTauto_2eX___24a5,type,
    cCoq_2emicromega_2eTauto_2eX___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2eBranch,type,
    cCoq_2emicromega_2eVarMap_2eBranch: $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2eBranch___24a4,type,
    cCoq_2emicromega_2eVarMap_2eBranch___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2eElt,type,
    cCoq_2emicromega_2eVarMap_2eElt: $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2eElt___24a2,type,
    cCoq_2emicromega_2eVarMap_2eElt___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2eEmpty,type,
    cCoq_2emicromega_2eVarMap_2eEmpty: $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2eEmpty___24a1,type,
    cCoq_2emicromega_2eVarMap_2eEmpty___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2et,type,
    cCoq_2emicromega_2eVarMap_2et: $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2et___24a1,type,
    cCoq_2emicromega_2eVarMap_2et___24a1: $i > $i ).

thf(tp_cCoq_2emicromega_2eVarMap_2et___24t,type,
    cCoq_2emicromega_2eVarMap_2et___24t: $i > $i > $o ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eCutProof,type,
    cCoq_2emicromega_2eZMicromega_2eCutProof: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eCutProof___24a2,type,
    cCoq_2emicromega_2eZMicromega_2eCutProof___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eDoneProof,type,
    cCoq_2emicromega_2eZMicromega_2eDoneProof: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eEnumProof,type,
    cCoq_2emicromega_2eZMicromega_2eEnumProof: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3,type,
    cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eRatProof,type,
    cCoq_2emicromega_2eZMicromega_2eRatProof: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eRatProof___24a2,type,
    cCoq_2emicromega_2eZMicromega_2eRatProof___24a2: $i > $i > $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,type,
    cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1,type,
    cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1: $i > $o ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,type,
    cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1,type,
    cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1: $i > $o ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eZArithProof,type,
    cCoq_2emicromega_2eZMicromega_2eZArithProof: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eZArithProof___24t,type,
    cCoq_2emicromega_2eZMicromega_2eZArithProof___24t: $i > $o ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eZWitness,type,
    cCoq_2emicromega_2eZMicromega_2eZWitness: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eZWitness___24t,type,
    cCoq_2emicromega_2eZMicromega_2eZWitness___24t: $i > $o ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,type,
    cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt: $i ).

thf(tp_cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4,type,
    cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4: $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEI,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEI: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEO,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEO: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEX,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEX: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEadd,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEadd: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEc,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEc: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEdiv,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEdiv: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEinv,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEinv: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEmul,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEmul: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEopp,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEopp: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEpow,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEpow: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEsub,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEsub: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3,type,
    cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFExpr,type,
    cCoq_2esetoid__ring_2eField__theory_2eFExpr: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1,type,
    cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t,type,
    cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t: $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,type,
    cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10,type,
    cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2efield__theory,type,
    cCoq_2esetoid__ring_2eField__theory_2efield__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10,type,
    cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2elinear,type,
    cCoq_2esetoid__ring_2eField__theory_2elinear: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2elinear___24a1,type,
    cCoq_2esetoid__ring_2eField__theory_2elinear___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2elinear___24t,type,
    cCoq_2esetoid__ring_2eField__theory_2elinear___24t: $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2emk__linear,type,
    cCoq_2esetoid__ring_2eField__theory_2emk__linear: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4,type,
    cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,type,
    cCoq_2esetoid__ring_2eField__theory_2emk__rsplit: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4,type,
    cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2ersplit,type,
    cCoq_2esetoid__ring_2eField__theory_2ersplit: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1,type,
    cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2ersplit___24t,type,
    cCoq_2esetoid__ring_2eField__theory_2ersplit___24t: $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory,type,
    cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8,type,
    cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,type,
    cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS: $i ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,type,
    cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1: $i ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5,type,
    cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5,type,
    cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2ehypo,type,
    cCoq_2esetoid__ring_2eInitialRing_2ehypo: $i ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t,type,
    cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t: $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2emkhypo,type,
    cCoq_2esetoid__ring_2eInitialRing_2emkhypo: $i ).

thf(tp_cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2,type,
    cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2eMon,type,
    cCoq_2esetoid__ring_2eRing__polynom_2eMon: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t,type,
    cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t: $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEI,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEI: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEO,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEO: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEX,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEX: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEadd: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEc,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEc: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEmul,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEmul: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEopp: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEpow: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEsub: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePExpr: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t: $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePX,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePX: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePc,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePc: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePinj,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePinj: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePol,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePol: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t: $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow,type,
    cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5,type,
    cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2emon0,type,
    cCoq_2esetoid__ring_2eRing__polynom_2emon0: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2evmon,type,
    cCoq_2esetoid__ring_2eRing__polynom_2evmon: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2,type,
    cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ezmon,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ezmon: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2,type,
    cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eAbstract,type,
    cCoq_2esetoid__ring_2eRing__theory_2eAbstract: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eComputational,type,
    cCoq_2esetoid__ring_2eRing__theory_2eComputational: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3,type,
    cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3: $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eIDphi,type,
    cCoq_2esetoid__ring_2eRing__theory_2eIDphi: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2,type,
    cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eMorphism,type,
    cCoq_2esetoid__ring_2eRing__theory_2eMorphism: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17,type,
    cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eSRopp,type,
    cCoq_2esetoid__ring_2eRing__theory_2eSRopp: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2,type,
    cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2: $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,type,
    cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8,type,
    cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,type,
    cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1,type,
    cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1: $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2epow__N,type,
    cCoq_2esetoid__ring_2eRing__theory_2epow__N: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5,type,
    cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2epow__pos,type,
    cCoq_2esetoid__ring_2eRing__theory_2epow__pos: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4,type,
    cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4: $i > $i > $i > $i > $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2epower__theory,type,
    cCoq_2esetoid__ring_2eRing__theory_2epower__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7,type,
    cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7: $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__kind,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__kind: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t: $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__morph,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__morph: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__theory,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8,type,
    cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,type,
    cCoq_2esetoid__ring_2eRing__theory_2esemi__morph: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13,type,
    cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,type,
    cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6,type,
    cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,type,
    cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext: $i ).

thf(tp_cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4,type,
    cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4: $i > $i > $i > $i > $o ).

thf(tp_cHammer_2eTactics_2eReconstr_2eAllHyps,type,
    cHammer_2eTactics_2eReconstr_2eAllHyps: $i ).

thf(tp_cHammer_2eTactics_2eReconstr_2eEmpty,type,
    cHammer_2eTactics_2eReconstr_2eEmpty: $i ).

thf(tp_cHammer_2eTactics_2eReconstr_2eReconstrT,type,
    cHammer_2eTactics_2eReconstr_2eReconstrT: $i ).

thf(tp_cHammer_2eTactics_2eReconstr_2eReconstrT___24t,type,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t: $i > $o ).

thf(tp_cHammer_2eTactics_2eReconstr_2erdone,type,
    cHammer_2eTactics_2eReconstr_2erdone: $i ).

thf(tp_cHammer_2eTactics_2eReconstr_2erdone___24a2,type,
    cHammer_2eTactics_2eReconstr_2erdone___24a2: $i > $i > $o ).

thf(tp_cHammer_2eTactics_2eTactics_2erdone,type,
    cHammer_2eTactics_2eTactics_2erdone: $i ).

thf(tp_cHammer_2eTactics_2eTactics_2erdone___24a2,type,
    cHammer_2eTactics_2eTactics_2erdone___24a2: $i > $i > $o ).

thf(tp_cProp,type,
    cProp: $i ).

thf(tp_cProp___24t,type,
    cProp___24t: $i > $o ).

thf(tp_cType,type,
    cType: $i ).

thf(tp_cType___24t,type,
    cType___24t: $i > $o ).

thf(tp_c_24False,type,
    c_24False: $i ).

thf(tp_c_24Proof,type,
    c_24Proof: $i ).

thf(tp_c_24True,type,
    c_24True: $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916,type,
    c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916: $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916___24a6,type,
    c_24__case__Coq_2eInit_2eDatatypes_2elist_2433916___24a6: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003,type,
    c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003: $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3,type,
    c_24__case__Coq_2eInit_2eDatatypes_2elist_2434003___24a3: $i > $i > $i > $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170,type,
    c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170: $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170___24a3,type,
    c_24__case__Coq_2eInit_2eDatatypes_2enat_2434170___24a3: $i > $i > $i > $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192,type,
    c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192: $i ).

thf(tp_c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1,type,
    c_24__case__Coq_2eInit_2eDatatypes_2enat_2434192___24a1: $i > $i ).

thf(tp_c_24__case__Coq_2eNumbers_2eBinNums_2eN_245393,type,
    c_24__case__Coq_2eNumbers_2eBinNums_2eN_245393: $i ).

thf(tp_c_24__case__Coq_2eNumbers_2eBinNums_2eN_245393___24a4,type,
    c_24__case__Coq_2eNumbers_2eBinNums_2eN_245393___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187,type,
    c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187: $i ).

thf(tp_c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3,type,
    c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2434187___24a3: $i > $i > $i > $i ).

thf(tp_c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458,type,
    c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458: $i ).

thf(tp_c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2,type,
    c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435458___24a2: $i > $i > $i ).

thf(tp_c_24__fix__34048__v__CANONICAL__1,type,
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thf(tp_c_24__fix__34048__v__CANONICAL__1___24a3,type,
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thf(tp_c_24__fix__35474__v__CANONICAL__0,type,
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thf(tp_c_24__fix__35474__v__CANONICAL__0___24a1,type,
    c_24__fix__35474__v__CANONICAL__0___24a1: $i > $i ).

thf(tp_c_24__lam__10882,type,
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thf(tp_c_24__lam__10882___24a1,type,
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thf(tp_c_24__lam__10882___24a2,type,
    c_24__lam__10882___24a2: $i > $i > $i ).

thf(tp_c_24__lam__10990,type,
    c_24__lam__10990: $i ).

thf(tp_c_24__lam__10990___24a1,type,
    c_24__lam__10990___24a1: $i > $i ).

thf(tp_c_24__lam__10990___24a2,type,
    c_24__lam__10990___24a2: $i > $i > $i ).

thf(tp_c_24__lam__16,type,
    c_24__lam__16: $i ).

thf(tp_c_24__lam__16___24a4,type,
    c_24__lam__16___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__16___24a5,type,
    c_24__lam__16___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__33077,type,
    c_24__lam__33077: $i ).

thf(tp_c_24__lam__33077___24a3,type,
    c_24__lam__33077___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__33077___24a4,type,
    c_24__lam__33077___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__33085,type,
    c_24__lam__33085: $i ).

thf(tp_c_24__lam__33085___24a3,type,
    c_24__lam__33085___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__33085___24a4,type,
    c_24__lam__33085___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__35673,type,
    c_24__lam__35673: $i ).

thf(tp_c_24__lam__35673___24a2,type,
    c_24__lam__35673___24a2: $i > $i > $o ).

thf(tp_c_24__lam__3955,type,
    c_24__lam__3955: $i ).

thf(tp_c_24__lam__3955___24a1,type,
    c_24__lam__3955___24a1: $i > $i ).

thf(tp_c_24__lam__3955___24a2,type,
    c_24__lam__3955___24a2: $i > $i > $o ).

thf(tp_c_24__lam__3963,type,
    c_24__lam__3963: $i ).

thf(tp_c_24__lam__3963___24a3,type,
    c_24__lam__3963___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__3963___24a5,type,
    c_24__lam__3963___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__3971,type,
    c_24__lam__3971: $i ).

thf(tp_c_24__lam__3971___24a3,type,
    c_24__lam__3971___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__3971___24a5,type,
    c_24__lam__3971___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__40479,type,
    c_24__lam__40479: $i ).

thf(tp_c_24__lam__40479___24a4,type,
    c_24__lam__40479___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__40479___24a5,type,
    c_24__lam__40479___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__40489,type,
    c_24__lam__40489: $i ).

thf(tp_c_24__lam__40489___24a4,type,
    c_24__lam__40489___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__40489___24a5,type,
    c_24__lam__40489___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__40507,type,
    c_24__lam__40507: $i ).

thf(tp_c_24__lam__40507___24a1,type,
    c_24__lam__40507___24a1: $i > $i ).

thf(tp_c_24__lam__40507___24a3,type,
    c_24__lam__40507___24a3: $i > $i > $i > $o ).

thf(tp_c_24__lam__40532,type,
    c_24__lam__40532: $i ).

thf(tp_c_24__lam__40532___24a3,type,
    c_24__lam__40532___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__40532___24a4,type,
    c_24__lam__40532___24a4: $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__45572,type,
    c_24__lam__45572: $i ).

thf(tp_c_24__lam__45572___24a4,type,
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thf(tp_c_24__lam__45572___24a5,type,
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thf(tp_c_24__lam__45583,type,
    c_24__lam__45583: $i ).

thf(tp_c_24__lam__45583___24a4,type,
    c_24__lam__45583___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__45583___24a5,type,
    c_24__lam__45583___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__45594,type,
    c_24__lam__45594: $i ).

thf(tp_c_24__lam__45594___24a4,type,
    c_24__lam__45594___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__45594___24a5,type,
    c_24__lam__45594___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__45609,type,
    c_24__lam__45609: $i ).

thf(tp_c_24__lam__45609___24a4,type,
    c_24__lam__45609___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__45609___24a5,type,
    c_24__lam__45609___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__45623,type,
    c_24__lam__45623: $i ).

thf(tp_c_24__lam__45623___24a2,type,
    c_24__lam__45623___24a2: $i > $i > $i ).

thf(tp_c_24__lam__45623___24a4,type,
    c_24__lam__45623___24a4: $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__7587,type,
    c_24__lam__7587: $i ).

thf(tp_c_24__lam__7587___24a3,type,
    c_24__lam__7587___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__7587___24a4,type,
    c_24__lam__7587___24a4: $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__7591,type,
    c_24__lam__7591: $i ).

thf(tp_c_24__lam__7591___24a3,type,
    c_24__lam__7591___24a3: $i > $i > $i > $i ).

thf(tp_c_24__lam__7591___24a4,type,
    c_24__lam__7591___24a4: $i > $i > $i > $i > $o ).

thf(tp_c_24__lam__7800,type,
    c_24__lam__7800: $i ).

thf(tp_c_24__lam__7800___24a4,type,
    c_24__lam__7800___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__lam__7800___24a6,type,
    c_24__lam__7800___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__let__4__P_27__5379,type,
    c_24__let__4__P_27__5379: $i ).

thf(tp_c_24__let__4__P_27__5379___24a1,type,
    c_24__let__4__P_27__5379___24a1: $i > $i ).

thf(tp_c_24__let__4__P_27__5379___24a2,type,
    c_24__let__4__P_27__5379___24a2: $i > $i > $i ).

thf(tp_c_24__let__5__f_27__5380,type,
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thf(tp_c_24__let__5__f_27__5380___24a2,type,
    c_24__let__5__f_27__5380___24a2: $i > $i > $i ).

thf(tp_c_24__let__5__f_27__5380___24a3,type,
    c_24__let__5__f_27__5380___24a3: $i > $i > $i > $i ).

thf(tp_c_24__let__var__6__p__22915__22918,type,
    c_24__let__var__6__p__22915__22918: $i ).

thf(tp_c_24__let__var__6__p__22915__22918___24a4,type,
    c_24__let__var__6__p__22915__22918___24a4: $i > $i > $i > $i > $i ).

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thf(tp_c_24__let__var__6__p__22917__22919___24a4,type,
    c_24__let__var__6__p__22917__22919___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__prop__35352,type,
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thf(tp_c_24__prop__35352___24a4,type,
    c_24__prop__35352___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__prop__35353,type,
    c_24__prop__35353: $i ).

thf(tp_c_24__prop__35353___24a3,type,
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thf(tp_c_24__prop__35354,type,
    c_24__prop__35354: $i ).

thf(tp_c_24__prop__35354___24a3,type,
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thf(tp_c_24__prop__35355,type,
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thf(tp_c_24__prop__35355___24a3,type,
    c_24__prop__35355___24a3: $i > $i > $i > $i ).

thf(tp_c_24__prop__35356,type,
    c_24__prop__35356: $i ).

thf(tp_c_24__prop__35356___24a3,type,
    c_24__prop__35356___24a3: $i > $i > $i > $i ).

thf(tp_c_24__prop__35357,type,
    c_24__prop__35357: $i ).

thf(tp_c_24__prop__35357___24a3,type,
    c_24__prop__35357___24a3: $i > $i > $i > $i ).

thf(tp_c_24__prop__35358,type,
    c_24__prop__35358: $i ).

thf(tp_c_24__prop__35358___24a2,type,
    c_24__prop__35358___24a2: $i > $i > $i ).

thf(tp_c_24__prop__35372,type,
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thf(tp_c_24__prop__35372___24a2,type,
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thf(tp_c_24__prop__35373,type,
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thf(tp_c_24__prop__35373___24a3,type,
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thf(tp_c_24__prop__35374,type,
    c_24__prop__35374: $i ).

thf(tp_c_24__prop__35374___24a3,type,
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thf(tp_c_24__type__10127,type,
    c_24__type__10127: $i ).

thf(tp_c_24__type__10127___24t,type,
    c_24__type__10127___24t: $i > $o ).

thf(tp_c_24__type__10166,type,
    c_24__type__10166: $i ).

thf(tp_c_24__type__10166___24t,type,
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thf(tp_c_24__type__102___24a1,type,
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thf(tp_c_24__type__102___24t,type,
    c_24__type__102___24t: $i > $i > $o ).

thf(tp_c_24__type__1030___24a10,type,
    c_24__type__1030___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

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thf(tp_c_24__type__10727___24a3,type,
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thf(tp_c_24__type__10727___24t,type,
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thf(tp_c_24__type__10755,type,
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thf(tp_c_24__type__10755___24t,type,
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thf(tp_c_24__type__10826,type,
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thf(tp_c_24__type__10826___24t,type,
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thf(tp_c_24__type__10867,type,
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thf(tp_c_24__type__10867___24t,type,
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thf(tp_c_24__type__10877___24t,type,
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thf(tp_c_24__type__10894,type,
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thf(tp_c_24__type__10894___24t,type,
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thf(tp_c_24__type__10899___24t,type,
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thf(tp_c_24__type__10912___24t,type,
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thf(tp_c_24__type__10923___24a1,type,
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thf(tp_c_24__type__10923___24t,type,
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thf(tp_c_24__type__10932___24a1,type,
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thf(tp_c_24__type__10932___24t,type,
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thf(tp_c_24__type__11002,type,
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thf(tp_c_24__type__11002___24t,type,
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thf(tp_c_24__type__11691___24t,type,
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    c_24__type__1194___24t: $i > $i > $o ).

thf(tp_c_24__type__1199___24a1,type,
    c_24__type__1199___24a1: $i > $i ).

thf(tp_c_24__type__1199___24t,type,
    c_24__type__1199___24t: $i > $i > $o ).

thf(tp_c_24__type__12172,type,
    c_24__type__12172: $i ).

thf(tp_c_24__type__12172___24t,type,
    c_24__type__12172___24t: $i > $o ).

thf(tp_c_24__type__12203___24a6,type,
    c_24__type__12203___24a6: $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__12203___24t,type,
    c_24__type__12203___24t: $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__12227,type,
    c_24__type__12227: $i ).

thf(tp_c_24__type__12227___24t,type,
    c_24__type__12227___24t: $i > $o ).

thf(tp_c_24__type__12273,type,
    c_24__type__12273: $i ).

thf(tp_c_24__type__12273___24t,type,
    c_24__type__12273___24t: $i > $o ).

thf(tp_c_24__type__1233,type,
    c_24__type__1233: $i ).

thf(tp_c_24__type__12337,type,
    c_24__type__12337: $i ).

thf(tp_c_24__type__12337___24t,type,
    c_24__type__12337___24t: $i > $o ).

thf(tp_c_24__type__1233___24t,type,
    c_24__type__1233___24t: $i > $o ).

thf(tp_c_24__type__12344___24a2,type,
    c_24__type__12344___24a2: $i > $i > $i ).

thf(tp_c_24__type__12344___24t,type,
    c_24__type__12344___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__12398___24a3,type,
    c_24__type__12398___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__12398___24t,type,
    c_24__type__12398___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__12422___24a3,type,
    c_24__type__12422___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__12422___24t,type,
    c_24__type__12422___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__12470___24a5,type,
    c_24__type__12470___24a5: $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__12470___24t,type,
    c_24__type__12470___24t: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__12505___24a3,type,
    c_24__type__12505___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__12505___24t,type,
    c_24__type__12505___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__12720,type,
    c_24__type__12720: $i ).

thf(tp_c_24__type__12720___24t,type,
    c_24__type__12720___24t: $i > $o ).

thf(tp_c_24__type__12752,type,
    c_24__type__12752: $i ).

thf(tp_c_24__type__12752___24t,type,
    c_24__type__12752___24t: $i > $o ).

thf(tp_c_24__type__13288___24a22,type,
    c_24__type__13288___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__13288___24t,type,
    c_24__type__13288___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__13634___24a22,type,
    c_24__type__13634___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__13634___24t,type,
    c_24__type__13634___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__13980___24a22,type,
    c_24__type__13980___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__13980___24t,type,
    c_24__type__13980___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__14303___24a22,type,
    c_24__type__14303___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__14303___24t,type,
    c_24__type__14303___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__14649___24a22,type,
    c_24__type__14649___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__14649___24t,type,
    c_24__type__14649___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1479___24a8,type,
    c_24__type__1479___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__1479___24t,type,
    c_24__type__1479___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__14995___24a22,type,
    c_24__type__14995___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__14995___24t,type,
    c_24__type__14995___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__15341___24a22,type,
    c_24__type__15341___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__15341___24t,type,
    c_24__type__15341___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1542___24a8,type,
    c_24__type__1542___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__1542___24t,type,
    c_24__type__1542___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__15687___24a22,type,
    c_24__type__15687___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__15687___24t,type,
    c_24__type__15687___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__16033___24a22,type,
    c_24__type__16033___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__16033___24t,type,
    c_24__type__16033___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1605___24a8,type,
    c_24__type__1605___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__1605___24t,type,
    c_24__type__1605___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__16356___24a22,type,
    c_24__type__16356___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__16356___24t,type,
    c_24__type__16356___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1659___24a8,type,
    c_24__type__1659___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__1659___24t,type,
    c_24__type__1659___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__16702___24a22,type,
    c_24__type__16702___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__16702___24t,type,
    c_24__type__16702___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__17048___24a22,type,
    c_24__type__17048___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__17048___24t,type,
    c_24__type__17048___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1722___24a8,type,
    c_24__type__1722___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__1722___24t,type,
    c_24__type__1722___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__17371___24a22,type,
    c_24__type__17371___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__17371___24t,type,
    c_24__type__17371___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1754,type,
    c_24__type__1754: $i ).

thf(tp_c_24__type__1754___24t,type,
    c_24__type__1754___24t: $i > $o ).

thf(tp_c_24__type__1767,type,
    c_24__type__1767: $i ).

thf(tp_c_24__type__1767___24t,type,
    c_24__type__1767___24t: $i > $o ).

thf(tp_c_24__type__17694___24a22,type,
    c_24__type__17694___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__17694___24t,type,
    c_24__type__17694___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__1777,type,
    c_24__type__1777: $i ).

thf(tp_c_24__type__1777___24t,type,
    c_24__type__1777___24t: $i > $o ).

thf(tp_c_24__type__18040___24a22,type,
    c_24__type__18040___24a22: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__18040___24t,type,
    c_24__type__18040___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18200___24a3,type,
    c_24__type__18200___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__18200___24t,type,
    c_24__type__18200___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18254___24a4,type,
    c_24__type__18254___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__type__18254___24t,type,
    c_24__type__18254___24t: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18297___24a3,type,
    c_24__type__18297___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__18297___24t,type,
    c_24__type__18297___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18336___24a4,type,
    c_24__type__18336___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__type__18336___24t,type,
    c_24__type__18336___24t: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18371___24a3,type,
    c_24__type__18371___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__18371___24t,type,
    c_24__type__18371___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18397___24a3,type,
    c_24__type__18397___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__18397___24t,type,
    c_24__type__18397___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18405___24a3,type,
    c_24__type__18405___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__18405___24t,type,
    c_24__type__18405___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__18413,type,
    c_24__type__18413: $i ).

thf(tp_c_24__type__18413___24t,type,
    c_24__type__18413___24t: $i > $o ).

thf(tp_c_24__type__18715,type,
    c_24__type__18715: $i ).

thf(tp_c_24__type__18715___24t,type,
    c_24__type__18715___24t: $i > $o ).

thf(tp_c_24__type__1892___24a1,type,
    c_24__type__1892___24a1: $i > $i ).

thf(tp_c_24__type__1892___24t,type,
    c_24__type__1892___24t: $i > $i > $o ).

thf(tp_c_24__type__19670___24a1,type,
    c_24__type__19670___24a1: $i > $i ).

thf(tp_c_24__type__19670___24t,type,
    c_24__type__19670___24t: $i > $i > $o ).

thf(tp_c_24__type__20702,type,
    c_24__type__20702: $i ).

thf(tp_c_24__type__20702___24t,type,
    c_24__type__20702___24t: $i > $o ).

thf(tp_c_24__type__2080___24a1,type,
    c_24__type__2080___24a1: $i > $i ).

thf(tp_c_24__type__2080___24t,type,
    c_24__type__2080___24t: $i > $i > $o ).

thf(tp_c_24__type__21408___24a2,type,
    c_24__type__21408___24a2: $i > $i > $i ).

thf(tp_c_24__type__21408___24t,type,
    c_24__type__21408___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__21422___24a2,type,
    c_24__type__21422___24a2: $i > $i > $i ).

thf(tp_c_24__type__21422___24t,type,
    c_24__type__21422___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__21429___24a2,type,
    c_24__type__21429___24a2: $i > $i > $i ).

thf(tp_c_24__type__21429___24t,type,
    c_24__type__21429___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__21___24a2,type,
    c_24__type__21___24a2: $i > $i > $i ).

thf(tp_c_24__type__21___24t,type,
    c_24__type__21___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__22885,type,
    c_24__type__22885: $i ).

thf(tp_c_24__type__22885___24t,type,
    c_24__type__22885___24t: $i > $o ).

thf(tp_c_24__type__22929,type,
    c_24__type__22929: $i ).

thf(tp_c_24__type__22929___24t,type,
    c_24__type__22929___24t: $i > $o ).

thf(tp_c_24__type__23183___24a8,type,
    c_24__type__23183___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23183___24t,type,
    c_24__type__23183___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__23246___24a8,type,
    c_24__type__23246___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23246___24t,type,
    c_24__type__23246___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__23309___24a8,type,
    c_24__type__23309___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23309___24t,type,
    c_24__type__23309___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__23363___24a8,type,
    c_24__type__23363___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23363___24t,type,
    c_24__type__23363___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__2340,type,
    c_24__type__2340: $i ).

thf(tp_c_24__type__2340___24t,type,
    c_24__type__2340___24t: $i > $o ).

thf(tp_c_24__type__23426___24a8,type,
    c_24__type__23426___24a8: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23426___24t,type,
    c_24__type__23426___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__2345,type,
    c_24__type__2345: $i ).

thf(tp_c_24__type__2345___24t,type,
    c_24__type__2345___24t: $i > $o ).

thf(tp_c_24__type__23562___24a4,type,
    c_24__type__23562___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23562___24t,type,
    c_24__type__23562___24t: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__23585___24a4,type,
    c_24__type__23585___24a4: $i > $i > $i > $i > $i ).

thf(tp_c_24__type__23585___24t,type,
    c_24__type__23585___24t: $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__23608___24a4,type,
    c_24__type__23608___24a4: $i > $i > $i > $i > $i ).

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thf(tp_c_24__type__23675___24t,type,
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thf(tp_c_24__type__23857___24t,type,
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thf(tp_c_24__type__23887___24t,type,
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thf(tp_c_24__type__23974___24t,type,
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thf(tp_c_24__type__23998___24t,type,
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thf(tp_c_24__type__27156___24t,type,
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thf(tp_c_24__type__27369___24a17,type,
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thf(tp_c_24__type__27369___24t,type,
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thf(tp_c_24__type__28027___24t,type,
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thf(tp_c_24__type__28130___24t,type,
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thf(tp_c_24__type__28140___24t,type,
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thf(tp_c_24__type__28181___24a3,type,
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thf(tp_c_24__type__28181___24t,type,
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thf(tp_c_24__type__28___24t,type,
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thf(tp_c_24__type__29851,type,
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thf(tp_c_24__type__3019,type,
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thf(tp_c_24__type__3019___24t,type,
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thf(tp_c_24__type__30495___24a3,type,
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thf(tp_c_24__type__30495___24t,type,
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thf(tp_c_24__type__30516___24a3,type,
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thf(tp_c_24__type__30516___24t,type,
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thf(tp_c_24__type__30551___24a5,type,
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thf(tp_c_24__type__30551___24t,type,
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thf(tp_c_24__type__30559___24a5,type,
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thf(tp_c_24__type__30559___24t,type,
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thf(tp_c_24__type__30564,type,
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thf(tp_c_24__type__30580,type,
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thf(tp_c_24__type__30580___24t,type,
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thf(tp_c_24__type__30593___24a2,type,
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thf(tp_c_24__type__30593___24t,type,
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thf(tp_c_24__type__30600___24a2,type,
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thf(tp_c_24__type__30600___24t,type,
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thf(tp_c_24__type__30604,type,
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thf(tp_c_24__type__30604___24t,type,
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thf(tp_c_24__type__30610___24a1,type,
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thf(tp_c_24__type__30610___24t,type,
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thf(tp_c_24__type__30797___24a6,type,
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thf(tp_c_24__type__30797___24t,type,
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thf(tp_c_24__type__30993___24a10,type,
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thf(tp_c_24__type__30993___24t,type,
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thf(tp_c_24__type__31436___24t,type,
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thf(tp_c_24__type__7224,type,
    c_24__type__7224: $i ).

thf(tp_c_24__type__7224___24t,type,
    c_24__type__7224___24t: $i > $o ).

thf(tp_c_24__type__7233,type,
    c_24__type__7233: $i ).

thf(tp_c_24__type__7233___24t,type,
    c_24__type__7233___24t: $i > $o ).

thf(tp_c_24__type__7246,type,
    c_24__type__7246: $i ).

thf(tp_c_24__type__7246___24t,type,
    c_24__type__7246___24t: $i > $o ).

thf(tp_c_24__type__7254,type,
    c_24__type__7254: $i ).

thf(tp_c_24__type__7254___24t,type,
    c_24__type__7254___24t: $i > $o ).

thf(tp_c_24__type__7264,type,
    c_24__type__7264: $i ).

thf(tp_c_24__type__7264___24t,type,
    c_24__type__7264___24t: $i > $o ).

thf(tp_c_24__type__7272,type,
    c_24__type__7272: $i ).

thf(tp_c_24__type__7272___24t,type,
    c_24__type__7272___24t: $i > $o ).

thf(tp_c_24__type__7286,type,
    c_24__type__7286: $i ).

thf(tp_c_24__type__7286___24t,type,
    c_24__type__7286___24t: $i > $o ).

thf(tp_c_24__type__7302,type,
    c_24__type__7302: $i ).

thf(tp_c_24__type__7302___24t,type,
    c_24__type__7302___24t: $i > $o ).

thf(tp_c_24__type__7327___24a2,type,
    c_24__type__7327___24a2: $i > $i > $i ).

thf(tp_c_24__type__7327___24t,type,
    c_24__type__7327___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__7331___24a2,type,
    c_24__type__7331___24a2: $i > $i > $i ).

thf(tp_c_24__type__7331___24t,type,
    c_24__type__7331___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__7354,type,
    c_24__type__7354: $i ).

thf(tp_c_24__type__7354___24t,type,
    c_24__type__7354___24t: $i > $o ).

thf(tp_c_24__type__738___24a10,type,
    c_24__type__738___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__738___24t,type,
    c_24__type__738___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__7394,type,
    c_24__type__7394: $i ).

thf(tp_c_24__type__7394___24t,type,
    c_24__type__7394___24t: $i > $o ).

thf(tp_c_24__type__7411,type,
    c_24__type__7411: $i ).

thf(tp_c_24__type__7411___24t,type,
    c_24__type__7411___24t: $i > $o ).

thf(tp_c_24__type__7473,type,
    c_24__type__7473: $i ).

thf(tp_c_24__type__7473___24t,type,
    c_24__type__7473___24t: $i > $o ).

thf(tp_c_24__type__7484,type,
    c_24__type__7484: $i ).

thf(tp_c_24__type__7484___24t,type,
    c_24__type__7484___24t: $i > $o ).

thf(tp_c_24__type__7489,type,
    c_24__type__7489: $i ).

thf(tp_c_24__type__7489___24t,type,
    c_24__type__7489___24t: $i > $o ).

thf(tp_c_24__type__7494,type,
    c_24__type__7494: $i ).

thf(tp_c_24__type__7494___24t,type,
    c_24__type__7494___24t: $i > $o ).

thf(tp_c_24__type__7544,type,
    c_24__type__7544: $i ).

thf(tp_c_24__type__7544___24t,type,
    c_24__type__7544___24t: $i > $o ).

thf(tp_c_24__type__7547,type,
    c_24__type__7547: $i ).

thf(tp_c_24__type__7547___24t,type,
    c_24__type__7547___24t: $i > $o ).

thf(tp_c_24__type__80,type,
    c_24__type__80: $i ).

thf(tp_c_24__type__8060___24a3,type,
    c_24__type__8060___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__8060___24t,type,
    c_24__type__8060___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__8068___24a3,type,
    c_24__type__8068___24a3: $i > $i > $i > $i ).

thf(tp_c_24__type__8068___24t,type,
    c_24__type__8068___24t: $i > $i > $i > $i > $o ).

thf(tp_c_24__type__8076,type,
    c_24__type__8076: $i ).

thf(tp_c_24__type__8076___24t,type,
    c_24__type__8076___24t: $i > $o ).

thf(tp_c_24__type__80___24t,type,
    c_24__type__80___24t: $i > $o ).

thf(tp_c_24__type__8128___24a2,type,
    c_24__type__8128___24a2: $i > $i > $i ).

thf(tp_c_24__type__8128___24t,type,
    c_24__type__8128___24t: $i > $i > $i > $o ).

thf(tp_c_24__type__8132,type,
    c_24__type__8132: $i ).

thf(tp_c_24__type__8132___24t,type,
    c_24__type__8132___24t: $i > $o ).

thf(tp_c_24__type__828___24a10,type,
    c_24__type__828___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__828___24t,type,
    c_24__type__828___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__85,type,
    c_24__type__85: $i ).

thf(tp_c_24__type__85___24t,type,
    c_24__type__85___24t: $i > $o ).

thf(tp_c_24__type__90,type,
    c_24__type__90: $i ).

thf(tp_c_24__type__90___24t,type,
    c_24__type__90___24t: $i > $o ).

thf(tp_c_24__type__929___24a10,type,
    c_24__type__929___24a10: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_c_24__type__929___24t,type,
    c_24__type__929___24t: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).

thf(tp_c_24__type__96,type,
    c_24__type__96: $i ).

thf(tp_c_24__type__96___24t,type,
    c_24__type__96___24t: $i > $o ).

thf(tp_c_24__type__99,type,
    c_24__type__99: $i ).

thf(tp_c_24__type__99___24t,type,
    c_24__type__99___24t: $i > $o ).

thf(tp_c_3c_3d_3e,type,
    c_3c_3d_3e: $i ).

thf(tp_c_3d___24a1,type,
    c_3d___24a1: $i > $i ).

thf(tp_c_3d___24a2,type,
    c_3d___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2eMixin,type,
    chahn_2eHahnBase_2eEquality_2eMixin: $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2eMixin___24a3,type,
    chahn_2eHahnBase_2eEquality_2eMixin___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2ePack,type,
    chahn_2eHahnBase_2eEquality_2ePack: $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2ePack___24a3,type,
    chahn_2eHahnBase_2eEquality_2ePack___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2eaxiom___24a2,type,
    chahn_2eHahnBase_2eEquality_2eaxiom___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2eaxiom___24t,type,
    chahn_2eHahnBase_2eEquality_2eaxiom___24t: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnBase_2eEquality_2emixin__of,type,
    chahn_2eHahnBase_2eEquality_2emixin__of: $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2emixin__of___24a1,type,
    chahn_2eHahnBase_2eEquality_2emixin__of___24a1: $i > $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2emixin__of___24t,type,
    chahn_2eHahnBase_2eEquality_2emixin__of___24t: $i > $i > $o ).

thf(tp_chahn_2eHahnBase_2eEquality_2etype,type,
    chahn_2eHahnBase_2eEquality_2etype: $i ).

thf(tp_chahn_2eHahnBase_2eEquality_2etype___24t,type,
    chahn_2eHahnBase_2eEquality_2etype___24t: $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eacyclic,type,
    chahn_2eHahnRelationsBasic_2eacyclic: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eacyclic___24a1,type,
    chahn_2eHahnRelationsBasic_2eacyclic___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eacyclic___24a2,type,
    chahn_2eHahnRelationsBasic_2eacyclic___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ebunion,type,
    chahn_2eHahnRelationsBasic_2ebunion: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ebunion___24a2,type,
    chahn_2eHahnRelationsBasic_2ebunion___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ebunion___24a4,type,
    chahn_2eHahnRelationsBasic_2ebunion___24a4: $i > $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ebunion___24a6,type,
    chahn_2eHahnRelationsBasic_2ebunion___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__refl,type,
    chahn_2eHahnRelationsBasic_2eclos__refl: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__refl___24a1,type,
    chahn_2eHahnRelationsBasic_2eclos__refl___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__refl___24a2,type,
    chahn_2eHahnRelationsBasic_2eclos__refl___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__refl___24a4,type,
    chahn_2eHahnRelationsBasic_2eclos__refl___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__refl__sym,type,
    chahn_2eHahnRelationsBasic_2eclos__refl__sym: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4,type,
    chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__sym,type,
    chahn_2eHahnRelationsBasic_2eclos__sym: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eclos__sym___24a4,type,
    chahn_2eHahnRelationsBasic_2eclos__sym___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2ecodom__rel,type,
    chahn_2eHahnRelationsBasic_2ecodom__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecodom__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2ecodom__rel___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2ecollect__rel,type,
    chahn_2eHahnRelationsBasic_2ecollect__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecollect__rel___24a2,type,
    chahn_2eHahnRelationsBasic_2ecollect__rel___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecollect__rel___24a4,type,
    chahn_2eHahnRelationsBasic_2ecollect__rel___24a4: $i > $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecollect__rel___24a6,type,
    chahn_2eHahnRelationsBasic_2ecollect__rel___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2ecross__rel,type,
    chahn_2eHahnRelationsBasic_2ecross__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecross__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2ecross__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecross__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2ecross__rel___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2ecross__rel___24a5,type,
    chahn_2eHahnRelationsBasic_2ecross__rel___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2edom__rel,type,
    chahn_2eHahnRelationsBasic_2edom__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2edom__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2edom__rel___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eeq__rel,type,
    chahn_2eHahnRelationsBasic_2eeq__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeq__rel___24a5,type,
    chahn_2eHahnRelationsBasic_2eeq__rel___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__dom__rel,type,
    chahn_2eHahnRelationsBasic_2eeqv__dom__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a2,type,
    chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a4,type,
    chahn_2eHahnRelationsBasic_2eeqv__dom__rel___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__rel,type,
    chahn_2eHahnRelationsBasic_2eeqv__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2eeqv__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__rel___24a2,type,
    chahn_2eHahnRelationsBasic_2eeqv__rel___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eeqv__rel___24a4,type,
    chahn_2eHahnRelationsBasic_2eeqv__rel___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2efunctional,type,
    chahn_2eHahnRelationsBasic_2efunctional: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2efunctional___24a1,type,
    chahn_2eHahnRelationsBasic_2efunctional___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2efunctional___24a2,type,
    chahn_2eHahnRelationsBasic_2efunctional___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eimmediate,type,
    chahn_2eHahnRelationsBasic_2eimmediate: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eimmediate___24a1,type,
    chahn_2eHahnRelationsBasic_2eimmediate___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eimmediate___24a2,type,
    chahn_2eHahnRelationsBasic_2eimmediate___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eimmediate___24a4,type,
    chahn_2eHahnRelationsBasic_2eimmediate___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2einter__rel,type,
    chahn_2eHahnRelationsBasic_2einter__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2einter__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2einter__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2einter__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2einter__rel___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2einter__rel___24a5,type,
    chahn_2eHahnRelationsBasic_2einter__rel___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eirreflexive,type,
    chahn_2eHahnRelationsBasic_2eirreflexive: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eirreflexive___24a1,type,
    chahn_2eHahnRelationsBasic_2eirreflexive___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eirreflexive___24a2,type,
    chahn_2eHahnRelationsBasic_2eirreflexive___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eis__total,type,
    chahn_2eHahnRelationsBasic_2eis__total: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eis__total___24a1,type,
    chahn_2eHahnRelationsBasic_2eis__total___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eis__total___24a3,type,
    chahn_2eHahnRelationsBasic_2eis__total___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2emap__rel,type,
    chahn_2eHahnRelationsBasic_2emap__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2emap__rel___24a2,type,
    chahn_2eHahnRelationsBasic_2emap__rel___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2emap__rel___24a4,type,
    chahn_2eHahnRelationsBasic_2emap__rel___24a4: $i > $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2emap__rel___24a6,type,
    chahn_2eHahnRelationsBasic_2emap__rel___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eminus__rel,type,
    chahn_2eHahnRelationsBasic_2eminus__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eminus__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2eminus__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eminus__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2eminus__rel___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eminus__rel___24a5,type,
    chahn_2eHahnRelationsBasic_2eminus__rel___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2epow__rel,type,
    chahn_2eHahnRelationsBasic_2epow__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2epow__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2epow__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2epow__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2epow__rel___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__eq__rel,type,
    chahn_2eHahnRelationsBasic_2erestr__eq__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a2,type,
    chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a2: $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4,type,
    chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a4: $i > $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6,type,
    chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6: $i > $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__rel,type,
    chahn_2eHahnRelationsBasic_2erestr__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__rel___24a1,type,
    chahn_2eHahnRelationsBasic_2erestr__rel___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__rel___24a3,type,
    chahn_2eHahnRelationsBasic_2erestr__rel___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__rel___24a5,type,
    chahn_2eHahnRelationsBasic_2erestr__rel___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__subset,type,
    chahn_2eHahnRelationsBasic_2erestr__subset: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2erestr__subset___24a4,type,
    chahn_2eHahnRelationsBasic_2erestr__subset___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eseq,type,
    chahn_2eHahnRelationsBasic_2eseq: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eseq___24a1,type,
    chahn_2eHahnRelationsBasic_2eseq___24a1: $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eseq___24a3,type,
    chahn_2eHahnRelationsBasic_2eseq___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eseq___24a5,type,
    chahn_2eHahnRelationsBasic_2eseq___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2esingl__rel,type,
    chahn_2eHahnRelationsBasic_2esingl__rel: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2esingl__rel___24a5,type,
    chahn_2eHahnRelationsBasic_2esingl__rel___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2estrict__partial__order,type,
    chahn_2eHahnRelationsBasic_2estrict__partial__order: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2,type,
    chahn_2eHahnRelationsBasic_2estrict__partial__order___24a2: $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2estrict__total__order,type,
    chahn_2eHahnRelationsBasic_2estrict__total__order: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2estrict__total__order___24a3,type,
    chahn_2eHahnRelationsBasic_2estrict__total__order___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnRelationsBasic_2eupward__closed,type,
    chahn_2eHahnRelationsBasic_2eupward__closed: $i ).

thf(tp_chahn_2eHahnRelationsBasic_2eupward__closed___24a3,type,
    chahn_2eHahnRelationsBasic_2eupward__closed___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__bunion,type,
    chahn_2eHahnSets_2eset__bunion: $i ).

thf(tp_chahn_2eHahnSets_2eset__bunion___24a5,type,
    chahn_2eHahnSets_2eset__bunion___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__collect,type,
    chahn_2eHahnSets_2eset__collect: $i ).

thf(tp_chahn_2eHahnSets_2eset__collect___24a5,type,
    chahn_2eHahnSets_2eset__collect___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__compl,type,
    chahn_2eHahnSets_2eset__compl: $i ).

thf(tp_chahn_2eHahnSets_2eset__compl___24a3,type,
    chahn_2eHahnSets_2eset__compl___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__disjoint,type,
    chahn_2eHahnSets_2eset__disjoint: $i ).

thf(tp_chahn_2eHahnSets_2eset__disjoint___24a3,type,
    chahn_2eHahnSets_2eset__disjoint___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__empty,type,
    chahn_2eHahnSets_2eset__empty: $i ).

thf(tp_chahn_2eHahnSets_2eset__empty___24a1,type,
    chahn_2eHahnSets_2eset__empty___24a1: $i > $i ).

thf(tp_chahn_2eHahnSets_2eset__empty___24a2,type,
    chahn_2eHahnSets_2eset__empty___24a2: $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__equiv,type,
    chahn_2eHahnSets_2eset__equiv: $i ).

thf(tp_chahn_2eHahnSets_2eset__equiv___24a1,type,
    chahn_2eHahnSets_2eset__equiv___24a1: $i > $i ).

thf(tp_chahn_2eHahnSets_2eset__equiv___24a3,type,
    chahn_2eHahnSets_2eset__equiv___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__full,type,
    chahn_2eHahnSets_2eset__full: $i ).

thf(tp_chahn_2eHahnSets_2eset__full___24a2,type,
    chahn_2eHahnSets_2eset__full___24a2: $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__inter,type,
    chahn_2eHahnSets_2eset__inter: $i ).

thf(tp_chahn_2eHahnSets_2eset__inter___24a3,type,
    chahn_2eHahnSets_2eset__inter___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnSets_2eset__inter___24a4,type,
    chahn_2eHahnSets_2eset__inter___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__map,type,
    chahn_2eHahnSets_2eset__map: $i ).

thf(tp_chahn_2eHahnSets_2eset__map___24a5,type,
    chahn_2eHahnSets_2eset__map___24a5: $i > $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__minus,type,
    chahn_2eHahnSets_2eset__minus: $i ).

thf(tp_chahn_2eHahnSets_2eset__minus___24a4,type,
    chahn_2eHahnSets_2eset__minus___24a4: $i > $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__subset,type,
    chahn_2eHahnSets_2eset__subset: $i ).

thf(tp_chahn_2eHahnSets_2eset__subset___24a1,type,
    chahn_2eHahnSets_2eset__subset___24a1: $i > $i ).

thf(tp_chahn_2eHahnSets_2eset__subset___24a3,type,
    chahn_2eHahnSets_2eset__subset___24a3: $i > $i > $i > $o ).

thf(tp_chahn_2eHahnSets_2eset__union,type,
    chahn_2eHahnSets_2eset__union: $i ).

thf(tp_chahn_2eHahnSets_2eset__union___24a3,type,
    chahn_2eHahnSets_2eset__union___24a3: $i > $i > $i > $i ).

thf(tp_chahn_2eHahnSets_2eset__union___24a4,type,
    chahn_2eHahnSets_2eset__union___24a4: $i > $i > $i > $i > $o ).

thf(tp_cr,type,
    cr: $i ).

thf(tp_cr_27,type,
    cr_27: $i ).

thf(tp_happ,type,
    happ: $i > $i > $i ).

thf(tp_p,type,
    p: $i > $o ).

thf(tp_sK10_SY476,type,
    sK10_SY476: $i > $i ).

thf(tp_sK11_SY478,type,
    sK11_SY478: $i > $i ).

thf(tp_sK12_Vv__CANONICAL__0,type,
    sK12_Vv__CANONICAL__0: $i > $i ).

thf(tp_sK13_Vv__CANONICAL__1,type,
    sK13_Vv__CANONICAL__1: $i > $i > $i ).

thf(tp_sK14_SY479,type,
    sK14_SY479: $i > $i > $i ).

thf(tp_sK15_Vv__CANONICAL__2,type,
    sK15_Vv__CANONICAL__2: $i > $i > $i > $i ).

thf(tp_sK16_Vv__CANONICAL__1,type,
    sK16_Vv__CANONICAL__1: $i > $i > $i ).

thf(tp_sK17_Vv__CANONICAL__2,type,
    sK17_Vv__CANONICAL__2: $i > $i > $i > $i ).

thf(tp_sK18_V3__x,type,
    sK18_V3__x: $i > $i > $i > $i ).

thf(tp_sK19_SY480,type,
    sK19_SY480: $i > $i > $i > $i ).

thf(tp_sK1_Vv__CANONICAL__0,type,
    sK1_Vv__CANONICAL__0: $i > $i ).

thf(tp_sK2_SY468,type,
    sK2_SY468: $i > $i ).

thf(tp_sK3_Vv__CANONICAL__0,type,
    sK3_Vv__CANONICAL__0: $i > $i ).

thf(tp_sK4_SY469,type,
    sK4_SY469: $i > $i ).

thf(tp_sK5_SY471,type,
    sK5_SY471: $i > $i ).

thf(tp_sK6_Vv__CANONICAL__0,type,
    sK6_Vv__CANONICAL__0: $i > $i ).

thf(tp_sK7_SY472,type,
    sK7_SY472: $i > $i ).

thf(tp_sK8_Vv__CANONICAL__0,type,
    sK8_Vv__CANONICAL__0: $i > $i ).

thf(tp_sK9_SY473,type,
    sK9_SY473: $i > $i ).

thf(tp_t,type,
    t: $i > $i > $o ).

thf(464,axiom,
    ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
      ( ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2einclusion @ V_24X1 ) @ V_24X2 ) @ V_24X3 )
      = ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Coq.Relations.Relation_Definitions.inclusion_$a3') ).

thf(569,axiom,
    ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
      ( ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) )
    <=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_Coq.Relations.Relation_Definitions.same_relation_$a3') ).

thf(645,axiom,
    ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
      ( ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 )
      = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_hahn.HahnRelationsBasic.minus_rel_$a3') ).

thf(663,axiom,
    ! [V_24X1: $i,V_24X2: $i,V_24X3: $i,V_24X4: $i,V_24X5: $i] :
      ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 )
      = ( c_24__lam__45594___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_45594_$a5') ).

thf(724,axiom,
    ! [V_24X1: $i,V_24X2: $i,V_24X3: $i,V_24X4: $i,V_24X5: $i] :
      ( ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 ) )
    <=> ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_hahn.HahnRelationsBasic.minus_rel_$a5') ).

thf(733,axiom,
    ! [V_24X1: $i,V_24X2: $i] :
      ( ( p @ ( happ @ ( happ @ c_24__lam__35673 @ V_24X1 ) @ V_24X2 ) )
    <=> ( c_24__lam__35673___24a2 @ V_24X1 @ V_24X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_$_lam_35673_$a2') ).

thf(736,axiom,
    ! [V_24X1: $i] :
      ( ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 )
      = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a1 @ V_24X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$adef_hahn.HahnRelationsBasic.minus_rel_$a1') ).

thf(904,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V1__r ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.same_relation_refl2') ).

thf(920,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__r_27 ) )
                 => ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__r ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.irreflexive_inclusion') ).

thf(921,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_r2_search') ).

thf(922,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_r2') ).

thf(923,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_r1_search') ).

thf(924,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_r1') ).

thf(925,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_r') ).

thf(926,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__s: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                 => ! [V4__s_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__s ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_mon') ).

thf(927,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_minus') ).

thf(928,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                   => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                     => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_union_l') ).

thf(930,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_t_t2') ).

thf(931,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_t_t') ).

thf(936,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_step_t') ).

thf(937,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_step_rt') ).

thf(938,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_step_cr') ).

thf(943,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__s: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                 => ! [V4__s_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_seq_mon') ).

thf(945,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_rt_rt2') ).

thf(946,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_rt_rt') ).

thf(954,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V1__r ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_refl2') ).

thf(957,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__r ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_r_cr') ).

thf(958,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_minus_rel') ).

thf(959,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__s: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                 => ! [V4__s_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__s_27 @ V3__s ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_minus_mon') ).

thf(960,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__s: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__s ) )
                  <=> ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__s ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_minus_l') ).

thf(961,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                     => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_inter_r') ).

thf(962,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__s: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                 => ! [V4__s_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_inter_mon') ).

thf(963,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_inter_l2_search') ).

thf(964,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_inter_l2') ).

thf(965,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_inter_l1_search') ).

thf(966,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_inter_l1') ).

thf(975,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__r_27 ) )
                 => ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__r ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.inclusion_acyclic') ).

thf(980,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ V1__r ) )
               => ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.functional_minus') ).

thf(985,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V1__r ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.eq_in_r') ).

thf(986,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','hahn.HahnRelationsBasic.eq_in_l') ).

thf(1000,axiom,
    p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ cA @ cr @ cr_27 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','SUB') ).

thf(1004,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V1__x ) )
                <=> ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.well_founded_more') ).

thf(1006,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.union_mori') ).

thf(1008,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.union_more') ).

thf(1011,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V2__r_27 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.union_absorb_r') ).

thf(1012,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.union_absorb_l') ).

thf(1013,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.unionK') ).

thf(1014,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
         => ! [V2__r2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.unionC') ).

thf(1015,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.unionAC') ).

thf(1016,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
         => ! [V2__r2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
             => ! [V3__r3: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.unionA') ).

thf(1018,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.transp_mori') ).

thf(1020,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.transp_more') ).

thf(1022,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V1__x )
                <=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V2__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.transitive_more') ).

thf(1026,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.seq_mori') ).

thf(1028,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.seq_more') ).

thf(1040,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
         => ! [V2__r2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
             => ! [V3__r3: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.seqA') ).

thf(1044,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
               => ! [V4__x: $i] :
                    ( ( t @ V4__x @ V0__A )
                   => ! [V5__y: $i] :
                        ( ( t @ V5__y @ V0__A )
                       => ( ( p @ ( happ @ ( happ @ V1__r @ V4__x ) @ V5__y ) )
                        <=> ( p @ ( happ @ ( happ @ V2__r_27 @ V4__x ) @ V5__y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.same_relation_exp') ).

thf(1062,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
         => ! [V2__r2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
             => ! [V3__r: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r1 @ V3__r ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r2 @ V3__r ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.minus_union_l') ).

thf(1066,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.minus_rel_more') ).

thf(1078,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__x ) )
                <=> ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.irreflexive_more') ).

thf(1083,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.inter_rel_mori') ).

thf(1085,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.inter_rel_more') ).

thf(1086,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__i: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__i )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__i ) @ V1__r ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.inter_inclusion') ).

thf(1089,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.inter_absorb_r') ).

thf(1090,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V1__r ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.inter_absorb_l') ).

thf(1091,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.interK') ).

thf(1092,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
         => ! [V2__r2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.interC') ).

thf(1093,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
         => ! [V2__r_27: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
             => ! [V3__r_27_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.interAC') ).

thf(1094,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__r1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
         => ! [V2__r2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
             => ! [V3__r3: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.interA') ).

thf(1101,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ! [V4__x: $i] :
                    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                   => ! [V5__y: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                       => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                         => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V4__x ) )
                          <=> ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.inclusion_more') ).

thf(1103,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V2__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.immediate_more') ).

thf(1124,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.clos_trans_mori') ).

thf(1126,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.clos_trans_more') ).

thf(1128,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.clos_relf_more') ).

thf(1130,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.clos_refl_trans_mori') ).

thf(1132,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.clos_refl_trans_more') ).

thf(1134,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
               => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.clos_refl_mori') ).

thf(1149,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__x: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
         => ! [V2__y: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
             => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
               => ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__x ) )
                <=> ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.acyclic_more') ).

thf(1150,axiom,
    ! [V0__r: $i] :
      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ c_24__lam__35673 ) @ V0__r ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.PropertiesMinus.minus_false_r') ).

thf(1151,axiom,
    ! [V0__r: $i] :
      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ V0__r ) @ c_24__lam__35673 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.PropertiesMinus.minus_false_l') ).

thf(1152,axiom,
    ! [V0__r: $i] :
      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ V0__r ) @ c_24__lam__35673 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','HahnEquational.PropertiesMinus.minusK') ).

thf(1240,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__R: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Operators_Properties.clos_rt_idempotent') ).

thf(1252,axiom,
    ! [V0__A: $i] :
      ( ( cType___24t @ V0__A )
     => ! [V1__R: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Relations.Operators_Properties.clos_rst_idempotent') ).

thf(1282,axiom,
    ! [V0__P: $i] :
      ( ( cProp___24t @ V0__P )
     => ! [V1__Q: $i] :
          ( ( cProp___24t @ V1__Q )
         => ( ~ ( ( p @ V0__P )
               => ( p @ V1__Q ) )
           => ( p @ V0__P ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Classical_Prop.not_imply_elim') ).

thf(1283,axiom,
    ! [V0__P: $i] :
      ( ( cProp___24t @ V0__P )
     => ! [V1__Q: $i] :
          ( ( cProp___24t @ V1__Q )
         => ! [V2__R: $i] :
              ( ( cProp___24t @ V2__R )
             => ( ( ( p @ V0__P )
                 => ( p @ V1__Q ) )
               => ( ( ( p @ V0__P )
                    | ( p @ V2__R ) )
                 => ( ( p @ V1__Q )
                    | ( p @ V2__R ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Classical_Prop.imply_and_or2') ).

thf(1284,axiom,
    ! [V0__P: $i] :
      ( ( cProp___24t @ V0__P )
     => ! [V1__Q: $i] :
          ( ( cProp___24t @ V1__Q )
         => ( ( ( p @ V0__P )
             => ( p @ V1__Q ) )
           => ( ( ( p @ V0__P )
                | ( p @ V1__Q ) )
             => ( p @ V1__Q ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Classical_Prop.imply_and_or') ).

thf(1285,axiom,
    ! [V0__P: $i] :
      ( ( cProp___24t @ V0__P )
     => ( ( p @ V0__P )
        | ~ ( p @ V0__P ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Classical_Prop.classic') ).

thf(1287,axiom,
    ! [V0__p: $i] :
      ( ( cProp___24t @ V0__p )
     => ( ~ ~ ( p @ V0__p )
       => ( p @ V0__p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.Classical_Prop.NNPP') ).

thf(1289,axiom,
    ! [V0__A: $i] :
      ( ( cProp___24t @ V0__A )
     => ! [V1__B: $i] :
          ( ( cProp___24t @ V1__B )
         => ( ( ( p @ V0__A )
              & ( p @ V1__B ) )
           => ( p @ V0__A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Logic.ChoiceFacts.proj1_inf') ).

thf(1311,axiom,
    cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ cr_27,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_r\'') ).

thf(1312,axiom,
    cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ cr,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_r') ).

thf(1334,axiom,
    c_24__type__90___24t @ chahn_2eHahnRelationsBasic_2eminus__rel,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_hahn.HahnRelationsBasic.minus_rel') ).

thf(1353,axiom,
    cType___24t @ chahn_2eHahnBase_2eEquality_2etype,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_hahn.HahnBase.Equality.type') ).

thf(1357,axiom,
    cType___24t @ cHammer_2eTactics_2eReconstr_2eReconstrT,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Hammer.Tactics.Reconstr.ReconstrT') ).

thf(1358,axiom,
    cType___24t @ cCoq_2esetoid__ring_2eRing__theory_2ering__kind,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.setoid_ring.Ring_theory.ring_kind') ).

thf(1371,axiom,
    cType___24t @ cCoq_2esetoid__ring_2eRing__polynom_2eMon,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.setoid_ring.Ring_polynom.Mon') ).

thf(1372,axiom,
    cType___24t @ cCoq_2esetoid__ring_2eInitialRing_2ehypo,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.setoid_ring.InitialRing.hypo') ).

thf(1378,axiom,
    cType___24t @ cCoq_2emicromega_2eZMicromega_2eZArithProof,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.micromega.ZMicromega.ZArithProof') ).

thf(1391,axiom,
    cType___24t @ cCoq_2emicromega_2eRingMicromega_2eOp2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.micromega.RingMicromega.Op2') ).

thf(1392,axiom,
    cType___24t @ cCoq_2emicromega_2eRingMicromega_2eOp1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.micromega.RingMicromega.Op1') ).

thf(1398,axiom,
    cType___24t @ cCoq_2emicromega_2eRMicromega_2eRcst,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.micromega.RMicromega.Rcst') ).

thf(1403,axiom,
    cType___24t @ cCoq_2emicromega_2eEnvRing_2eMon,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.micromega.EnvRing.Mon') ).

thf(1412,axiom,
    cType___24t @ cCoq_2eZArith_2eBinIntDef_2eZ_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.ZArith.BinIntDef.Z.t') ).

thf(1424,axiom,
    cType___24t @ cCoq_2eStructures_2eOrdersTac_2eord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrdersTac.ord') ).

thf(1428,axiom,
    cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t') ).

thf(1430,axiom,
    cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t') ).

thf(1431,axiom,
    cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t') ).

thf(1432,axiom,
    cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t') ).

thf(1435,axiom,
    cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.t') ).

thf(1438,axiom,
    cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.t') ).

thf(1441,axiom,
    cType___24t @ cCoq_2eStrings_2eString_2estring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Strings.String.string') ).

thf(1443,axiom,
    cType___24t @ cCoq_2eStrings_2eAscii_2eascii,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Strings.Ascii.ascii') ).

thf(1466,axiom,
    cType___24t @ cCoq_2eReals_2eRdefinitions_2eR,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Reals.Rdefinitions.R') ).

thf(1467,axiom,
    cType___24t @ cCoq_2eReals_2eRIneq_2eposreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Reals.RIneq.posreal') ).

thf(1468,axiom,
    cType___24t @ cCoq_2eReals_2eRIneq_2enonzeroreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Reals.RIneq.nonzeroreal') ).

thf(1469,axiom,
    cType___24t @ cCoq_2eReals_2eRIneq_2enonposreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Reals.RIneq.nonposreal') ).

thf(1470,axiom,
    cType___24t @ cCoq_2eReals_2eRIneq_2enonnegreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Reals.RIneq.nonnegreal') ).

thf(1471,axiom,
    cType___24t @ cCoq_2eReals_2eRIneq_2enegreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Reals.RIneq.negreal') ).

thf(1475,axiom,
    cType___24t @ cCoq_2eQArith_2eQArith__base_2eQ,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.QArith.QArith_base.Q') ).

thf(1476,axiom,
    cType___24t @ cCoq_2ePArith_2eBinPosDef_2ePos_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.PArith.BinPosDef.Pos.t') ).

thf(1477,axiom,
    cType___24t @ cCoq_2ePArith_2eBinPosDef_2ePos_2emask,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.PArith.BinPosDef.Pos.mask') ).

thf(1488,axiom,
    cType___24t @ cCoq_2eNumbers_2eBinNums_2epositive,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Numbers.BinNums.positive') ).

thf(1492,axiom,
    cType___24t @ cCoq_2eNumbers_2eBinNums_2eZ,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Numbers.BinNums.Z') ).

thf(1495,axiom,
    cType___24t @ cCoq_2eNumbers_2eBinNums_2eN,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Numbers.BinNums.N') ).

thf(1496,axiom,
    cType___24t @ cCoq_2eNArith_2eBinNatDef_2eN_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.NArith.BinNatDef.N.t') ).

thf(1540,axiom,
    cType___24t @ cCoq_2eInit_2eNat_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Nat.t') ).

thf(1548,axiom,
    cType___24t @ cCoq_2eInit_2eDecimal_2euint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Decimal.uint') ).

thf(1549,axiom,
    cType___24t @ cCoq_2eInit_2eDecimal_2eint,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Decimal.int') ).

thf(1550,axiom,
    cType___24t @ cCoq_2eInit_2eDecimal_2edecimal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Decimal.decimal') ).

thf(1552,axiom,
    cType___24t @ cCoq_2eInit_2eDatatypes_2eunit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.unit') ).

thf(1562,axiom,
    cType___24t @ cCoq_2eInit_2eDatatypes_2enat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.nat') ).

thf(1566,axiom,
    cType___24t @ cCoq_2eInit_2eDatatypes_2ecomparison,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.comparison') ).

thf(1567,axiom,
    cType___24t @ cCoq_2eInit_2eDatatypes_2ebool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.bool') ).

thf(1575,axiom,
    cType___24t @ cCoq_2eInit_2eDatatypes_2eID,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.ID') ).

thf(1578,axiom,
    cType___24t @ cCoq_2eInit_2eDatatypes_2eEmpty__set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.Empty_set') ).

thf(1836,axiom,
    cType___24t @ cCoq_2eInit_2eByte_2ebyte,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Byte.byte') ).

thf(1837,axiom,
    cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree') ).

thf(1838,axiom,
    cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.FSets.FSetPositive.PositiveSet.t') ).

thf(1839,axiom,
    cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt') ).

thf(1849,axiom,
    cType___24t @ cA,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_A') ).

thf(1851,axiom,
    ! [Vvar__97: $i] :
      ( ( c_24__type__96___24t @ Vvar__97 )
    <=> ! [Vv__CANONICAL__0: $i] :
          ( ( cType___24t @ Vv__CANONICAL__0 )
         => ! [Vv__CANONICAL__1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__97 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_96') ).

thf(1853,axiom,
    ! [Vvar__91: $i] :
      ( ( c_24__type__90___24t @ Vvar__91 )
    <=> ! [Vv__CANONICAL__0: $i] :
          ( ( cType___24t @ Vv__CANONICAL__0 )
         => ! [Vv__CANONICAL__1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
             => ! [Vv__CANONICAL__2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ ( happ @ Vvar__91 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_90') ).

thf(1908,axiom,
    ! [Vvar__53: $i] :
      ( ( c_24__type__52___24t @ Vvar__53 )
    <=> ! [Vv__CANONICAL__0: $i] :
          ( ( cType___24t @ Vv__CANONICAL__0 )
         => ! [Vv__CANONICAL__1: $i] :
              ( ( cType___24t @ Vv__CANONICAL__1 )
             => ( cType___24t @ ( happ @ ( happ @ Vvar__53 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_52') ).

thf(1909,axiom,
    ! [Vvar__4734: $i] :
      ( ( c_24__type__4733___24t @ Vvar__4734 )
    <=> ! [Vv__CANONICAL__0: $i] :
          ( ( cType___24t @ Vv__CANONICAL__0 )
         => ! [Vv__CANONICAL__1: $i] :
              ( ( cType___24t @ Vv__CANONICAL__1 )
             => ! [Vv__CANONICAL__2: $i] :
                  ( ( cType___24t @ Vv__CANONICAL__2 )
                 => ! [Vv__CANONICAL__3: $i] :
                      ( ( cType___24t @ Vv__CANONICAL__3 )
                     => ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ Vvar__4734 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_4733') ).

thf(1999,axiom,
    ! [Vvar__29: $i] :
      ( ( c_24__type__28___24t @ Vvar__29 )
    <=> ! [Vv__CANONICAL__0: $i] :
          ( ( cType___24t @ Vv__CANONICAL__0 )
         => ( cType___24t @ ( happ @ Vvar__29 @ Vv__CANONICAL__0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_28') ).

thf(2104,axiom,
    ! [Vv__CANONICAL__0: $i,Vvar__11830: $i] :
      ( ( c_24__type__11829___24t @ Vv__CANONICAL__0 @ Vvar__11830 )
    <=> ! [Vv__CANONICAL__1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
         => ! [Vv__CANONICAL__2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__11830 @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_11829') ).

thf(2107,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vvar__11788: $i] :
      ( ( c_24__type__11787___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11788 )
    <=> ! [Vv__CANONICAL__2: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 )
         => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11788 @ Vv__CANONICAL__2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_11787') ).

thf(2110,axiom,
    ! [Vv__CANONICAL__0: $i,Vvar__11749: $i] :
      ( ( c_24__type__11748___24t @ Vv__CANONICAL__0 @ Vvar__11749 )
    <=> ! [Vv__CANONICAL__1: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
         => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11749 @ Vv__CANONICAL__1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_11748') ).

thf(2116,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vvar__11700: $i] :
      ( ( c_24__type__11699___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11700 )
    <=> ! [Vv__CANONICAL__2: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
         => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( happ @ Vvar__11700 @ Vv__CANONICAL__2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_type_11699') ).

thf(2143,axiom,
    ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35350: $i] :
      ( ( p @ ( c_24__prop__35358___24a2 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35350 ) )
    <=> ~ ( p @ Vvar__0__P__35350 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_35358') ).

thf(2144,axiom,
    ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35345: $i,Vvar__1__Q__35346: $i] :
      ( ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) )
    <=> ( ( p @ Vvar__0__P__35345 )
       => ( p @ Vvar__1__Q__35346 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_35357') ).

thf(2145,axiom,
    ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35341: $i,Vvar__1__Q__35342: $i] :
      ( ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) )
    <=> ( ( p @ Vvar__0__P__35341 )
        | ( p @ Vvar__1__Q__35342 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_35356') ).

thf(2146,axiom,
    ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35337: $i,Vvar__1__Q__35338: $i] :
      ( ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) )
    <=> ( ( p @ Vvar__0__P__35337 )
        & ( p @ Vvar__1__Q__35338 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_35355') ).

thf(2148,axiom,
    ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__x__35333: $i,Vvar__1__y__35334: $i] :
      ( ( p @ ( c_24__prop__35353___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__x__35333 @ Vvar__1__y__35334 ) )
    <=> ( Vvar__0__x__35333 = Vvar__1__y__35334 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_35353') ).

thf(2149,axiom,
    ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__S__35330: $i,Vvar__1__x__35331: $i,Vvar__2__y__35332: $i] :
      ( ( p @ ( c_24__prop__35352___24a4 @ Vvar__0___24Anonymous__35328 @ Vvar__0__S__35330 @ Vvar__1__x__35331 @ Vvar__2__y__35332 ) )
    <=> ( Vvar__1__x__35331 = Vvar__2__y__35332 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_prop_35352') ).

thf(2150,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i,Vv__CANONICAL__5: $i] :
      ( ( c_24__lam__7800___24a6 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 @ Vv__CANONICAL__5 )
    <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__3 @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__4 ) ) @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_7800') ).

thf(2151,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
      ( ( c_24__lam__7591___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
    <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_7591') ).

thf(2152,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
      ( ( c_24__lam__7587___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
    <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_7587') ).

thf(2155,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
      ( ( c_24__lam__45594___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
      = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ Vv__CANONICAL__1 @ ( happ @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) @ Vv__CANONICAL__2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_45594') ).

thf(2158,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
      ( ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
    <=> ( ( p @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) )
        & ( p @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_40532') ).

thf(2162,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
      ( ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
    <=> ( ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
        | ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_3971') ).

thf(2166,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
      ( ( c_24__lam__33085___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
      = ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_33085') ).

thf(2167,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
      ( ( c_24__lam__33077___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
      = ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_33077') ).

thf(2168,axiom,
    ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
      ( ( c_24__lam__16___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
    <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_lam_16') ).

thf(2483,axiom,
    ! [V0__A: $i,V1__s: $i,V2__s_27: $i,V3__x: $i] :
      ( ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
    <=> ( ( p @ ( happ @ V1__s @ V3__x ) )
        | ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnSets.set_union') ).

thf(2485,axiom,
    ! [V0__A: $i,V1__s: $i,V2__s_27: $i,V3__x: $i] :
      ( ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
    <=> ( ( p @ ( happ @ V1__s @ V3__x ) )
        & ~ ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnSets.set_minus') ).

thf(2486,axiom,
    ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__d: $i,V4__x: $i] :
      ( ( chahn_2eHahnSets_2eset__map___24a5 @ V0__A @ V1__B @ V2__f @ V3__d @ V4__x )
    <=> ( p @ ( happ @ V3__d @ ( happ @ V2__f @ V4__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnSets.set_map') ).

thf(2487,axiom,
    ! [V0__A: $i,V1__s: $i,V2__s_27: $i,V3__x: $i] :
      ( ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
    <=> ( ( p @ ( happ @ V1__s @ V3__x ) )
        & ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnSets.set_inter') ).

thf(2492,axiom,
    ! [V0__A: $i,V1__s: $i,V2__x: $i] :
      ( ( chahn_2eHahnSets_2eset__compl___24a3 @ V0__A @ V1__s @ V2__x )
    <=> ~ ( p @ ( happ @ V1__s @ V2__x ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnSets.set_compl') ).

thf(2501,axiom,
    ! [V0__A: $i,V1__cond: $i,V2__r: $i,V3__x: $i,V4__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
    <=> ( ( p @ ( happ @ ( happ @ V2__r @ V3__x ) @ V4__y ) )
        & ( p @ ( happ @ V1__cond @ V3__x ) )
        & ( p @ ( happ @ V1__cond @ V4__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.restr_rel') ).

thf(2502,axiom,
    ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r: $i,V4__x: $i,V5__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y )
    <=> ( ( p @ ( happ @ ( happ @ V3__r @ V4__x ) @ V5__y ) )
        & ( ( happ @ V2__f @ V4__x )
          = ( happ @ V2__f @ V5__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.restr_eq_rel') ).

thf(2504,axiom,
    ! [V0__A: $i,V1__r: $i,V2__r_27: $i,V3__x: $i,V4__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
    <=> ( ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
        & ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.minus_rel') ).

thf(2505,axiom,
    ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r_27_27: $i,V4__x: $i,V5__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r_27_27 @ V4__x @ V5__y )
    <=> ( p @ ( happ @ ( happ @ V3__r_27_27 @ ( happ @ V2__f @ V4__x ) ) @ ( happ @ V2__f @ V5__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.map_rel') ).

thf(2508,axiom,
    ! [V0__A: $i,V1__r: $i,V2__r_27: $i,V3__x: $i,V4__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
    <=> ( ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
        & ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.inter_rel') ).

thf(2511,axiom,
    ! [V0__A: $i,V1__cond: $i,V2__x: $i,V3__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y )
    <=> ( ( V2__x = V3__y )
        & ( p @ ( happ @ V1__cond @ V2__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.eqv_rel') ).

thf(2513,axiom,
    ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__x: $i,V4__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ V0__A @ V1__B @ V2__f @ V3__x @ V4__y )
    <=> ( ( happ @ V2__f @ V3__x )
        = ( happ @ V2__f @ V4__y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.eq_rel') ).

thf(2515,axiom,
    ! [V0__A: $i,V1__r: $i,V2__r_27: $i,V3__a: $i,V4__b: $i] :
      ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b )
    <=> ( ( p @ ( happ @ V1__r @ V3__a ) )
        & ( p @ ( happ @ V2__r_27 @ V4__b ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.cross_rel') ).

thf(2518,axiom,
    ! [V0__A: $i,V1__r: $i,V2__x: $i,V3__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
    <=> ( ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
        | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.clos_sym') ).

thf(2519,axiom,
    ! [V0__A: $i,V1__r: $i,V2__x: $i,V3__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
    <=> ( ( V2__x = V3__y )
        | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
        | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.clos_refl_sym') ).

thf(2520,axiom,
    ! [V0__A: $i,V1__r: $i,V2__x: $i,V3__y: $i] :
      ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
    <=> ( ( V2__x = V3__y )
        | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_hahn.HahnRelationsBasic.clos_refl') ).

thf(2565,axiom,
    ! [V0__A: $i,V1__R1: $i,V2__R2: $i,V3__x: $i,V4__y: $i] :
      ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y )
    <=> ( ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
        | ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Relations.Relation_Operators.union') ).

thf(2566,axiom,
    ! [V0__A: $i,V1__R: $i,V2__x: $i,V3__y: $i] :
      ( ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ V0__A @ V1__R @ V2__x @ V3__y )
    <=> ( p @ ( happ @ ( happ @ V1__R @ V3__y ) @ V2__x ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Relations.Relation_Operators.transp') ).

thf(2569,axiom,
    ! [V0__A: $i,V1__R1: $i,V2__R2: $i] :
      ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 )
    <=> ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
        & ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__R2 @ V1__R1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Relations.Relation_Definitions.same_relation') ).

thf(2572,axiom,
    ! [V0__A: $i,V1__R1: $i,V2__R2: $i] :
      ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
    <=> ! [V3__x: $i] :
          ( ( t @ V3__x @ V0__A )
         => ! [V4__y: $i] :
              ( ( t @ V4__y @ V0__A )
             => ( ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
               => ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Relations.Relation_Definitions.inclusion') ).

thf(2592,axiom,
    ! [V0__P: $i] :
      ( ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ V0__P )
    <=> ( ( p @ V0__P )
        | ~ ( p @ V0__P ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Logic.Decidable.decidable') ).

thf(2653,axiom,
    cType___24t @ cType,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_COQ_TYPE_TYPE') ).

thf(2654,axiom,
    ~ ( p @ c_24False ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_COQ_FALSE') ).

thf(2655,axiom,
    p @ c_24True,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_COQ_TRUE') ).

thf(2656,conjecture,
    cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ cr @ cr_27 ) @ c_24__lam__35673,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).

thf(2657,negated_conjecture,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ cr @ cr_27 ) @ c_24__lam__35673 )
    = $false ),
    inference(negate_conjecture,[status(cth)],[2656]) ).

thf(2658,plain,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ cr @ cr_27 ) @ c_24__lam__35673 )
    = $false ),
    inference(unfold_def,[status(thm)],[2657]) ).

thf(2659,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2einclusion @ V_24X1 ) @ V_24X2 ) @ V_24X3 )
          = ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[464]) ).

thf(2660,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) )
        <=> ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[569]) ).

thf(2661,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i,V_24X4: $i,V_24X5: $i] :
          ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 )
          = ( c_24__lam__45594___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[663]) ).

thf(2662,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i,V_24X4: $i,V_24X5: $i] :
          ( ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 ) )
        <=> ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[724]) ).

thf(2663,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i] :
          ( ( p @ ( happ @ ( happ @ c_24__lam__35673 @ V_24X1 ) @ V_24X2 ) )
        <=> ( c_24__lam__35673___24a2 @ V_24X1 @ V_24X2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[733]) ).

thf(2664,plain,
    ( ( ! [V_24X1: $i] :
          ( ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 )
          = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a1 @ V_24X1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[736]) ).

thf(2665,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__r_27 ) )
                     => ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__r ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[920]) ).

thf(2666,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                       => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[921]) ).

thf(2667,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[922]) ).

thf(2668,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                       => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[923]) ).

thf(2669,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[924]) ).

thf(2670,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) )
                       => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[925]) ).

thf(2671,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__s: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                     => ! [V4__s_27: $i] :
                          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                         => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__s ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[926]) ).

thf(2672,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[927]) ).

thf(2673,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[928]) ).

thf(2674,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[930]) ).

thf(2675,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[931]) ).

thf(2676,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[936]) ).

thf(2677,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[937]) ).

thf(2678,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[938]) ).

thf(2679,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__s: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                     => ! [V4__s_27: $i] :
                          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                         => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[943]) ).

thf(2680,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[945]) ).

thf(2681,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[946]) ).

thf(2682,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V1__r ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[954]) ).

thf(2683,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__r ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[957]) ).

thf(2684,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[958]) ).

thf(2685,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__s: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                     => ! [V4__s_27: $i] :
                          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                         => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__s_27 @ V3__s ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[959]) ).

thf(2686,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__s: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__s ) )
                      <=> ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__s ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[960]) ).

thf(2687,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                       => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                         => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[961]) ).

thf(2688,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__s: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                     => ! [V4__s_27: $i] :
                          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                         => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[962]) ).

thf(2689,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                       => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[963]) ).

thf(2690,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[964]) ).

thf(2691,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                       => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[965]) ).

thf(2692,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[966]) ).

thf(2693,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__r_27 ) )
                     => ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__r ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[975]) ).

thf(2694,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ V1__r ) )
                   => ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[980]) ).

thf(2695,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V1__r ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[985]) ).

thf(2696,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[986]) ).

thf(2697,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V1__x ) )
                    <=> ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1004]) ).

thf(2698,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1006]) ).

thf(2699,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1008]) ).

thf(2700,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1011]) ).

thf(2701,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1012]) ).

thf(2702,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1013]) ).

thf(2703,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
             => ! [V2__r2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1014]) ).

thf(2704,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1015]) ).

thf(2705,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
             => ! [V2__r2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                 => ! [V3__r3: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1016]) ).

thf(2706,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1018]) ).

thf(2707,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1020]) ).

thf(2708,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V1__x )
                    <=> ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1022]) ).

thf(2709,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1026]) ).

thf(2710,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1028]) ).

thf(2711,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
             => ! [V2__r2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                 => ! [V3__r3: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1040]) ).

thf(2712,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                   => ! [V4__x: $i] :
                        ( ( t @ V4__x @ V0__A )
                       => ! [V5__y: $i] :
                            ( ( t @ V5__y @ V0__A )
                           => ( ( p @ ( happ @ ( happ @ V1__r @ V4__x ) @ V5__y ) )
                            <=> ( p @ ( happ @ ( happ @ V2__r_27 @ V4__x ) @ V5__y ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1044]) ).

thf(2713,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
             => ! [V2__r2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                 => ! [V3__r: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r1 @ V3__r ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r2 @ V3__r ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1062]) ).

thf(2714,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__x ) )
                    <=> ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1078]) ).

thf(2715,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1083]) ).

thf(2716,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1085]) ).

thf(2717,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__i: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__i )
                 => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__i ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1086]) ).

thf(2718,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1089]) ).

thf(2719,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1090]) ).

thf(2720,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1091]) ).

thf(2721,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
             => ! [V2__r2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1092]) ).

thf(2722,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ! [V2__r_27: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                 => ! [V3__r_27_27: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1093]) ).

thf(2723,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
             => ! [V2__r2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                 => ! [V3__r3: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1094]) ).

thf(2724,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                             => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V4__x ) )
                              <=> ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1101]) ).

thf(2725,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1103]) ).

thf(2726,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1124]) ).

thf(2727,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1126]) ).

thf(2728,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1128]) ).

thf(2729,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1130]) ).

thf(2730,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1132]) ).

thf(2731,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                   => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1134]) ).

thf(2732,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__x ) )
                    <=> ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__y ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1149]) ).

thf(2733,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__R: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1240]) ).

thf(2734,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__R: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
             => ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1252]) ).

thf(2735,plain,
    ( ( ! [V0__P: $i] :
          ( ( cProp___24t @ V0__P )
         => ! [V1__Q: $i] :
              ( ( cProp___24t @ V1__Q )
             => ( ~ ( ( p @ V0__P )
                   => ( p @ V1__Q ) )
               => ( p @ V0__P ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1282]) ).

thf(2736,plain,
    ( ( ! [V0__P: $i] :
          ( ( cProp___24t @ V0__P )
         => ! [V1__Q: $i] :
              ( ( cProp___24t @ V1__Q )
             => ! [V2__R: $i] :
                  ( ( cProp___24t @ V2__R )
                 => ( ( ( p @ V0__P )
                     => ( p @ V1__Q ) )
                   => ( ( ( p @ V0__P )
                        | ( p @ V2__R ) )
                     => ( ( p @ V1__Q )
                        | ( p @ V2__R ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1283]) ).

thf(2737,plain,
    ( ( ! [V0__P: $i] :
          ( ( cProp___24t @ V0__P )
         => ! [V1__Q: $i] :
              ( ( cProp___24t @ V1__Q )
             => ( ( ( p @ V0__P )
                 => ( p @ V1__Q ) )
               => ( ( ( p @ V0__P )
                    | ( p @ V1__Q ) )
                 => ( p @ V1__Q ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1284]) ).

thf(2738,plain,
    ( ( ! [V0__P: $i] :
          ( ( cProp___24t @ V0__P )
         => ( ( p @ V0__P )
            | ~ ( p @ V0__P ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1285]) ).

thf(2739,plain,
    ( ( ! [V0__p: $i] :
          ( ( cProp___24t @ V0__p )
         => ( ~ ~ ( p @ V0__p )
           => ( p @ V0__p ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1287]) ).

thf(2740,plain,
    ( ( ! [V0__A: $i] :
          ( ( cProp___24t @ V0__A )
         => ! [V1__B: $i] :
              ( ( cProp___24t @ V1__B )
             => ( ( ( p @ V0__A )
                  & ( p @ V1__B ) )
               => ( p @ V0__A ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1289]) ).

thf(2741,plain,
    ( ( c_24__type__90___24t @ chahn_2eHahnRelationsBasic_2eminus__rel )
    = $true ),
    inference(unfold_def,[status(thm)],[1334]) ).

thf(2742,plain,
    ( ( cType___24t @ chahn_2eHahnBase_2eEquality_2etype )
    = $true ),
    inference(unfold_def,[status(thm)],[1353]) ).

thf(2743,plain,
    ( ( cType___24t @ cHammer_2eTactics_2eReconstr_2eReconstrT )
    = $true ),
    inference(unfold_def,[status(thm)],[1357]) ).

thf(2744,plain,
    ( ( cType___24t @ cCoq_2esetoid__ring_2eRing__theory_2ering__kind )
    = $true ),
    inference(unfold_def,[status(thm)],[1358]) ).

thf(2745,plain,
    ( ( cType___24t @ cCoq_2esetoid__ring_2eRing__polynom_2eMon )
    = $true ),
    inference(unfold_def,[status(thm)],[1371]) ).

thf(2746,plain,
    ( ( cType___24t @ cCoq_2esetoid__ring_2eInitialRing_2ehypo )
    = $true ),
    inference(unfold_def,[status(thm)],[1372]) ).

thf(2747,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eZMicromega_2eZArithProof )
    = $true ),
    inference(unfold_def,[status(thm)],[1378]) ).

thf(2748,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eRingMicromega_2eOp2 )
    = $true ),
    inference(unfold_def,[status(thm)],[1391]) ).

thf(2749,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eRingMicromega_2eOp1 )
    = $true ),
    inference(unfold_def,[status(thm)],[1392]) ).

thf(2750,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eRMicromega_2eRcst )
    = $true ),
    inference(unfold_def,[status(thm)],[1398]) ).

thf(2751,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eEnvRing_2eMon )
    = $true ),
    inference(unfold_def,[status(thm)],[1403]) ).

thf(2752,plain,
    ( ( cType___24t @ cCoq_2eZArith_2eBinIntDef_2eZ_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1412]) ).

thf(2753,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrdersTac_2eord )
    = $true ),
    inference(unfold_def,[status(thm)],[1424]) ).

thf(2754,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1428]) ).

thf(2755,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1430]) ).

thf(2756,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1431]) ).

thf(2757,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1432]) ).

thf(2758,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1435]) ).

thf(2759,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1438]) ).

thf(2760,plain,
    ( ( cType___24t @ cCoq_2eStrings_2eString_2estring )
    = $true ),
    inference(unfold_def,[status(thm)],[1441]) ).

thf(2761,plain,
    ( ( cType___24t @ cCoq_2eStrings_2eAscii_2eascii )
    = $true ),
    inference(unfold_def,[status(thm)],[1443]) ).

thf(2762,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRdefinitions_2eR )
    = $true ),
    inference(unfold_def,[status(thm)],[1466]) ).

thf(2763,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2eposreal )
    = $true ),
    inference(unfold_def,[status(thm)],[1467]) ).

thf(2764,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enonzeroreal )
    = $true ),
    inference(unfold_def,[status(thm)],[1468]) ).

thf(2765,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enonposreal )
    = $true ),
    inference(unfold_def,[status(thm)],[1469]) ).

thf(2766,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enonnegreal )
    = $true ),
    inference(unfold_def,[status(thm)],[1470]) ).

thf(2767,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enegreal )
    = $true ),
    inference(unfold_def,[status(thm)],[1471]) ).

thf(2768,plain,
    ( ( cType___24t @ cCoq_2eQArith_2eQArith__base_2eQ )
    = $true ),
    inference(unfold_def,[status(thm)],[1475]) ).

thf(2769,plain,
    ( ( cType___24t @ cCoq_2ePArith_2eBinPosDef_2ePos_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1476]) ).

thf(2770,plain,
    ( ( cType___24t @ cCoq_2ePArith_2eBinPosDef_2ePos_2emask )
    = $true ),
    inference(unfold_def,[status(thm)],[1477]) ).

thf(2771,plain,
    ( ( cType___24t @ cCoq_2eNumbers_2eBinNums_2epositive )
    = $true ),
    inference(unfold_def,[status(thm)],[1488]) ).

thf(2772,plain,
    ( ( cType___24t @ cCoq_2eNumbers_2eBinNums_2eZ )
    = $true ),
    inference(unfold_def,[status(thm)],[1492]) ).

thf(2773,plain,
    ( ( cType___24t @ cCoq_2eNumbers_2eBinNums_2eN )
    = $true ),
    inference(unfold_def,[status(thm)],[1495]) ).

thf(2774,plain,
    ( ( cType___24t @ cCoq_2eNArith_2eBinNatDef_2eN_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1496]) ).

thf(2775,plain,
    ( ( cType___24t @ cCoq_2eInit_2eNat_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1540]) ).

thf(2776,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDecimal_2euint )
    = $true ),
    inference(unfold_def,[status(thm)],[1548]) ).

thf(2777,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDecimal_2eint )
    = $true ),
    inference(unfold_def,[status(thm)],[1549]) ).

thf(2778,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDecimal_2edecimal )
    = $true ),
    inference(unfold_def,[status(thm)],[1550]) ).

thf(2779,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2eunit )
    = $true ),
    inference(unfold_def,[status(thm)],[1552]) ).

thf(2780,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2enat )
    = $true ),
    inference(unfold_def,[status(thm)],[1562]) ).

thf(2781,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2ecomparison )
    = $true ),
    inference(unfold_def,[status(thm)],[1566]) ).

thf(2782,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2ebool )
    = $true ),
    inference(unfold_def,[status(thm)],[1567]) ).

thf(2783,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2eID )
    = $true ),
    inference(unfold_def,[status(thm)],[1575]) ).

thf(2784,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2eEmpty__set )
    = $true ),
    inference(unfold_def,[status(thm)],[1578]) ).

thf(2785,plain,
    ( ( cType___24t @ cCoq_2eInit_2eByte_2ebyte )
    = $true ),
    inference(unfold_def,[status(thm)],[1836]) ).

thf(2786,plain,
    ( ( cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree )
    = $true ),
    inference(unfold_def,[status(thm)],[1837]) ).

thf(2787,plain,
    ( ( cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et )
    = $true ),
    inference(unfold_def,[status(thm)],[1838]) ).

thf(2788,plain,
    ( ( cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt )
    = $true ),
    inference(unfold_def,[status(thm)],[1839]) ).

thf(2789,plain,
    ( ( ! [Vvar__97: $i] :
          ( ( c_24__type__96___24t @ Vvar__97 )
        <=> ! [Vv__CANONICAL__0: $i] :
              ( ( cType___24t @ Vv__CANONICAL__0 )
             => ! [Vv__CANONICAL__1: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__97 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1851]) ).

thf(2790,plain,
    ( ( ! [Vvar__91: $i] :
          ( ( c_24__type__90___24t @ Vvar__91 )
        <=> ! [Vv__CANONICAL__0: $i] :
              ( ( cType___24t @ Vv__CANONICAL__0 )
             => ! [Vv__CANONICAL__1: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
                 => ! [Vv__CANONICAL__2: $i] :
                      ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ ( happ @ Vvar__91 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1853]) ).

thf(2791,plain,
    ( ( ! [Vvar__53: $i] :
          ( ( c_24__type__52___24t @ Vvar__53 )
        <=> ! [Vv__CANONICAL__0: $i] :
              ( ( cType___24t @ Vv__CANONICAL__0 )
             => ! [Vv__CANONICAL__1: $i] :
                  ( ( cType___24t @ Vv__CANONICAL__1 )
                 => ( cType___24t @ ( happ @ ( happ @ Vvar__53 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1908]) ).

thf(2792,plain,
    ( ( ! [Vvar__4734: $i] :
          ( ( c_24__type__4733___24t @ Vvar__4734 )
        <=> ! [Vv__CANONICAL__0: $i] :
              ( ( cType___24t @ Vv__CANONICAL__0 )
             => ! [Vv__CANONICAL__1: $i] :
                  ( ( cType___24t @ Vv__CANONICAL__1 )
                 => ! [Vv__CANONICAL__2: $i] :
                      ( ( cType___24t @ Vv__CANONICAL__2 )
                     => ! [Vv__CANONICAL__3: $i] :
                          ( ( cType___24t @ Vv__CANONICAL__3 )
                         => ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ Vvar__4734 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1909]) ).

thf(2793,plain,
    ( ( ! [Vvar__29: $i] :
          ( ( c_24__type__28___24t @ Vvar__29 )
        <=> ! [Vv__CANONICAL__0: $i] :
              ( ( cType___24t @ Vv__CANONICAL__0 )
             => ( cType___24t @ ( happ @ Vvar__29 @ Vv__CANONICAL__0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1999]) ).

thf(2794,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vvar__11830: $i] :
          ( ( c_24__type__11829___24t @ Vv__CANONICAL__0 @ Vvar__11830 )
        <=> ! [Vv__CANONICAL__1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
             => ! [Vv__CANONICAL__2: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                 => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__11830 @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2104]) ).

thf(2795,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vvar__11788: $i] :
          ( ( c_24__type__11787___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11788 )
        <=> ! [Vv__CANONICAL__2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11788 @ Vv__CANONICAL__2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2107]) ).

thf(2796,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vvar__11749: $i] :
          ( ( c_24__type__11748___24t @ Vv__CANONICAL__0 @ Vvar__11749 )
        <=> ! [Vv__CANONICAL__1: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11749 @ Vv__CANONICAL__1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2110]) ).

thf(2797,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vvar__11700: $i] :
          ( ( c_24__type__11699___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11700 )
        <=> ! [Vv__CANONICAL__2: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
             => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( happ @ Vvar__11700 @ Vv__CANONICAL__2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2116]) ).

thf(2798,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35350: $i] :
          ( ( p @ ( c_24__prop__35358___24a2 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35350 ) )
        <=> ~ ( p @ Vvar__0__P__35350 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2143]) ).

thf(2799,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35345: $i,Vvar__1__Q__35346: $i] :
          ( ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) )
        <=> ( ( p @ Vvar__0__P__35345 )
           => ( p @ Vvar__1__Q__35346 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2144]) ).

thf(2800,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35341: $i,Vvar__1__Q__35342: $i] :
          ( ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) )
        <=> ( ( p @ Vvar__0__P__35341 )
            | ( p @ Vvar__1__Q__35342 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2145]) ).

thf(2801,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35337: $i,Vvar__1__Q__35338: $i] :
          ( ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) )
        <=> ( ( p @ Vvar__0__P__35337 )
            & ( p @ Vvar__1__Q__35338 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2146]) ).

thf(2802,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__x__35333: $i,Vvar__1__y__35334: $i] :
          ( ( p @ ( c_24__prop__35353___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__x__35333 @ Vvar__1__y__35334 ) )
        <=> ( Vvar__0__x__35333 = Vvar__1__y__35334 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2148]) ).

thf(2803,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__S__35330: $i,Vvar__1__x__35331: $i,Vvar__2__y__35332: $i] :
          ( ( p @ ( c_24__prop__35352___24a4 @ Vvar__0___24Anonymous__35328 @ Vvar__0__S__35330 @ Vvar__1__x__35331 @ Vvar__2__y__35332 ) )
        <=> ( Vvar__1__x__35331 = Vvar__2__y__35332 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2149]) ).

thf(2804,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i,Vv__CANONICAL__5: $i] :
          ( ( c_24__lam__7800___24a6 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 @ Vv__CANONICAL__5 )
        <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__3 @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__4 ) ) @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2150]) ).

thf(2805,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__7591___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
        <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2151]) ).

thf(2806,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__7587___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
        <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2152]) ).

thf(2807,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
        <=> ( ( p @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) )
            & ( p @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2158]) ).

thf(2808,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
          ( ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
        <=> ( ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
            | ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2162]) ).

thf(2809,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__33085___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
          = ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2166]) ).

thf(2810,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__33077___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
          = ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2167]) ).

thf(2811,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
          ( ( c_24__lam__16___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
        <=> ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2168]) ).

thf(2812,plain,
    ( ( ! [V0__A: $i,V1__s: $i,V2__s_27: $i,V3__x: $i] :
          ( ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
        <=> ( ( p @ ( happ @ V1__s @ V3__x ) )
            | ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2483]) ).

thf(2813,plain,
    ( ( ! [V0__A: $i,V1__s: $i,V2__s_27: $i,V3__x: $i] :
          ( ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
        <=> ( ( p @ ( happ @ V1__s @ V3__x ) )
            & ~ ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2485]) ).

thf(2814,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__d: $i,V4__x: $i] :
          ( ( chahn_2eHahnSets_2eset__map___24a5 @ V0__A @ V1__B @ V2__f @ V3__d @ V4__x )
        <=> ( p @ ( happ @ V3__d @ ( happ @ V2__f @ V4__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2486]) ).

thf(2815,plain,
    ( ( ! [V0__A: $i,V1__s: $i,V2__s_27: $i,V3__x: $i] :
          ( ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
        <=> ( ( p @ ( happ @ V1__s @ V3__x ) )
            & ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2487]) ).

thf(2816,plain,
    ( ( ! [V0__A: $i,V1__s: $i,V2__x: $i] :
          ( ( chahn_2eHahnSets_2eset__compl___24a3 @ V0__A @ V1__s @ V2__x )
        <=> ~ ( p @ ( happ @ V1__s @ V2__x ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2492]) ).

thf(2817,plain,
    ( ( ! [V0__A: $i,V1__cond: $i,V2__r: $i,V3__x: $i,V4__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
        <=> ( ( p @ ( happ @ ( happ @ V2__r @ V3__x ) @ V4__y ) )
            & ( p @ ( happ @ V1__cond @ V3__x ) )
            & ( p @ ( happ @ V1__cond @ V4__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2501]) ).

thf(2818,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r: $i,V4__x: $i,V5__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y )
        <=> ( ( p @ ( happ @ ( happ @ V3__r @ V4__x ) @ V5__y ) )
            & ( ( happ @ V2__f @ V4__x )
              = ( happ @ V2__f @ V5__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2502]) ).

thf(2819,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i,V3__x: $i,V4__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
        <=> ( ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
            & ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2504]) ).

thf(2820,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r_27_27: $i,V4__x: $i,V5__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r_27_27 @ V4__x @ V5__y )
        <=> ( p @ ( happ @ ( happ @ V3__r_27_27 @ ( happ @ V2__f @ V4__x ) ) @ ( happ @ V2__f @ V5__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2505]) ).

thf(2821,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i,V3__x: $i,V4__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
        <=> ( ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
            & ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2508]) ).

thf(2822,plain,
    ( ( ! [V0__A: $i,V1__cond: $i,V2__x: $i,V3__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y )
        <=> ( ( V2__x = V3__y )
            & ( p @ ( happ @ V1__cond @ V2__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2511]) ).

thf(2823,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__x: $i,V4__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ V0__A @ V1__B @ V2__f @ V3__x @ V4__y )
        <=> ( ( happ @ V2__f @ V3__x )
            = ( happ @ V2__f @ V4__y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2513]) ).

thf(2824,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i,V3__a: $i,V4__b: $i] :
          ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b )
        <=> ( ( p @ ( happ @ V1__r @ V3__a ) )
            & ( p @ ( happ @ V2__r_27 @ V4__b ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2515]) ).

thf(2825,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__x: $i,V3__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
        <=> ( ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
            | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2518]) ).

thf(2826,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__x: $i,V3__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
        <=> ( ( V2__x = V3__y )
            | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
            | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2519]) ).

thf(2827,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__x: $i,V3__y: $i] :
          ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
        <=> ( ( V2__x = V3__y )
            | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2520]) ).

thf(2828,plain,
    ( ( ! [V0__A: $i,V1__R1: $i,V2__R2: $i,V3__x: $i,V4__y: $i] :
          ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y )
        <=> ( ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
            | ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2565]) ).

thf(2829,plain,
    ( ( ! [V0__A: $i,V1__R: $i,V2__x: $i,V3__y: $i] :
          ( ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ V0__A @ V1__R @ V2__x @ V3__y )
        <=> ( p @ ( happ @ ( happ @ V1__R @ V3__y ) @ V2__x ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2566]) ).

thf(2830,plain,
    ( ( ! [V0__A: $i,V1__R1: $i,V2__R2: $i] :
          ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
        <=> ! [V3__x: $i] :
              ( ( t @ V3__x @ V0__A )
             => ! [V4__y: $i] :
                  ( ( t @ V4__y @ V0__A )
                 => ( ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
                   => ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2572]) ).

thf(2831,plain,
    ( ( ! [V0__P: $i] :
          ( ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ V0__P )
        <=> ( ( p @ V0__P )
            | ~ ( p @ V0__P ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2592]) ).

thf(2832,plain,
    ( ( cType___24t @ cType )
    = $true ),
    inference(unfold_def,[status(thm)],[2653]) ).

thf(2833,plain,
    ( ( ~ ( p @ c_24False ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2654]) ).

thf(2834,plain,
    ( ( p @ c_24True )
    = $true ),
    inference(unfold_def,[status(thm)],[2655]) ).

thf(2835,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 )
          = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[645]) ).

thf(2836,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__r: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V1__r ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[904]) ).

thf(2837,plain,
    ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ cA @ cr @ cr_27 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1000]) ).

thf(2838,plain,
    ( ( ! [V0__A: $i] :
          ( ( cType___24t @ V0__A )
         => ! [V1__x: $i] :
              ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
             => ! [V2__y: $i] :
                  ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                 => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                   => ! [V4__x: $i] :
                        ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                       => ! [V5__y: $i] :
                            ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                           => ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                             => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1066]) ).

thf(2839,plain,
    ( ( ! [V0__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ c_24__lam__35673 ) @ V0__r ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1150]) ).

thf(2840,plain,
    ( ( ! [V0__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ V0__r ) @ c_24__lam__35673 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1151]) ).

thf(2841,plain,
    ( ( ! [V0__r: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
         => ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ V0__r ) @ c_24__lam__35673 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1152]) ).

thf(2842,plain,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ cr_27 )
    = $true ),
    inference(unfold_def,[status(thm)],[1311]) ).

thf(2843,plain,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ cr )
    = $true ),
    inference(unfold_def,[status(thm)],[1312]) ).

thf(2844,plain,
    ( ( cType___24t @ cA )
    = $true ),
    inference(unfold_def,[status(thm)],[1849]) ).

thf(2845,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
          ( ( c_24__lam__45594___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
          = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ Vv__CANONICAL__1 @ ( happ @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) @ Vv__CANONICAL__2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2155]) ).

thf(2846,plain,
    ( ( ! [V0__A: $i,V1__R1: $i,V2__R2: $i] :
          ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 )
        <=> ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
            & ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__R2 @ V1__R1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2569]) ).

thf(2847,plain,
    ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ cr @ cr_27 ) @ c_24__lam__35673 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[2658]) ).

thf(2848,plain,
    ( ( ! [V_24X1: $i] :
          ( ! [V_24X2: $i,V_24X3: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V_24X1 @ V_24X2 @ V_24X3 )
              | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) ) )
          & ! [V_24X2: $i,V_24X3: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2660]) ).

thf(2849,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ! [V_24X4: $i,V_24X5: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 )
              | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 ) ) )
          & ! [V_24X4: $i,V_24X5: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2662]) ).

thf(2850,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i] :
          ( ~ ( c_24__lam__35673___24a2 @ V_24X1 @ V_24X2 )
          | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ V_24X1 ) @ V_24X2 ) ) )
      & ! [V_24X1: $i,V_24X2: $i] :
          ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ V_24X1 ) @ V_24X2 ) )
          | ( c_24__lam__35673___24a2 @ V_24X1 @ V_24X2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2663]) ).

thf(2851,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__r_27 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__r ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2665]) ).

thf(2852,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2666]) ).

thf(2853,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2667]) ).

thf(2854,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2668]) ).

thf(2855,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2669]) ).

thf(2856,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( ! [V3__r_27_27: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) )
                    & ! [V3__r_27_27: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2670]) ).

thf(2857,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__s ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2671]) ).

thf(2858,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2672]) ).

thf(2859,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2673]) ).

thf(2860,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2674]) ).

thf(2861,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2675]) ).

thf(2862,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2676]) ).

thf(2863,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2677]) ).

thf(2864,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2678]) ).

thf(2865,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2679]) ).

thf(2866,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2680]) ).

thf(2867,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2681]) ).

thf(2868,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V1__r ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2682]) ).

thf(2869,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__r ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2683]) ).

thf(2870,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2684]) ).

thf(2871,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__s_27 @ V3__s ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2685]) ).

thf(2872,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( ! [V3__s: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__s ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__s ) ) ) )
                    & ! [V3__s: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__s ) ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__s ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2686]) ).

thf(2873,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2687]) ).

thf(2874,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2688]) ).

thf(2875,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2689]) ).

thf(2876,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2690]) ).

thf(2877,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2691]) ).

thf(2878,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2692]) ).

thf(2879,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__r_27 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__r ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2693]) ).

thf(2880,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ V1__r ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2694]) ).

thf(2881,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V1__r ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2695]) ).

thf(2882,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2696]) ).

thf(2883,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V1__x ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V2__y ) ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V2__y ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V1__x ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2697]) ).

thf(2884,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2698]) ).

thf(2885,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2699]) ).

thf(2886,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V2__r_27 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2700]) ).

thf(2887,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2701]) ).

thf(2888,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2702]) ).

thf(2889,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2703]) ).

thf(2890,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2704]) ).

thf(2891,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2705]) ).

thf(2892,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2706]) ).

thf(2893,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2707]) ).

thf(2894,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V1__x )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V2__y ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V2__y )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V1__x ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2708]) ).

thf(2895,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2709]) ).

thf(2896,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2710]) ).

thf(2897,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2711]) ).

thf(2898,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                  | ! [V4__x: $i] :
                      ( ~ ( t @ V4__x @ V0__A )
                      | ( ! [V5__y: $i] :
                            ( ~ ( t @ V5__y @ V0__A )
                            | ~ ( p @ ( happ @ ( happ @ V1__r @ V4__x ) @ V5__y ) )
                            | ( p @ ( happ @ ( happ @ V2__r_27 @ V4__x ) @ V5__y ) ) )
                        & ! [V5__y: $i] :
                            ( ~ ( t @ V5__y @ V0__A )
                            | ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V4__x ) @ V5__y ) )
                            | ( p @ ( happ @ ( happ @ V1__r @ V4__x ) @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2712]) ).

thf(2899,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r1 @ V3__r ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r2 @ V3__r ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2713]) ).

thf(2900,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__x ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__y ) ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__y ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__x ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2714]) ).

thf(2901,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2715]) ).

thf(2902,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2716]) ).

thf(2903,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__i: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__i )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__i ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2717]) ).

thf(2904,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2718]) ).

thf(2905,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V1__r ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2719]) ).

thf(2906,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2720]) ).

thf(2907,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2721]) ).

thf(2908,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2722]) ).

thf(2909,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2723]) ).

thf(2910,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ( ! [V5__y: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V4__x ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__y @ V5__y ) ) )
                        & ! [V5__y: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__y @ V5__y ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V4__x ) ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2724]) ).

thf(2911,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2725]) ).

thf(2912,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2726]) ).

thf(2913,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2727]) ).

thf(2914,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2728]) ).

thf(2915,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2729]) ).

thf(2916,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2730]) ).

thf(2917,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2731]) ).

thf(2918,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__x ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__y ) ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__y ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__x ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2732]) ).

thf(2919,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__R: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2733]) ).

thf(2920,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__R: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2734]) ).

thf(2921,plain,
    ( ( ! [V0__P: $i] :
          ( ~ ( cProp___24t @ V0__P )
          | ! [V1__Q: $i] :
              ( ~ ( cProp___24t @ V1__Q )
              | ~ ( p @ V0__P )
              | ( p @ V1__Q )
              | ( p @ V0__P ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2735]) ).

thf(2922,plain,
    ( ( ! [V0__P: $i] :
          ( ~ ( cProp___24t @ V0__P )
          | ! [V1__Q: $i] :
              ( ~ ( cProp___24t @ V1__Q )
              | ( ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ( p @ V0__P )
                    | ~ ( p @ V0__P )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) )
                & ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ( p @ V0__P )
                    | ~ ( p @ V2__R )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) )
                & ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ~ ( p @ V1__Q )
                    | ~ ( p @ V0__P )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) )
                & ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ~ ( p @ V1__Q )
                    | ~ ( p @ V2__R )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2736]) ).

thf(2923,plain,
    ( ( ! [V0__P: $i] :
          ( ~ ( cProp___24t @ V0__P )
          | ( ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ( p @ V0__P )
                | ~ ( p @ V0__P )
                | ( p @ V1__Q ) )
            & ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ( p @ V0__P )
                | ~ ( p @ V1__Q )
                | ( p @ V1__Q ) )
            & ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ~ ( p @ V1__Q )
                | ~ ( p @ V0__P )
                | ( p @ V1__Q ) )
            & ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ~ ( p @ V1__Q )
                | ~ ( p @ V1__Q )
                | ( p @ V1__Q ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2737]) ).

thf(2924,plain,
    ( ( ! [V0__P: $i] :
          ~ ( cProp___24t @ V0__P )
      | $true )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2738]) ).

thf(2925,plain,
    ( ( ! [V0__p: $i] :
          ( ~ ( cProp___24t @ V0__p )
          | ~ ( p @ V0__p )
          | ( p @ V0__p ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2739]) ).

thf(2926,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cProp___24t @ V0__A )
          | ! [V1__B: $i] :
              ( ~ ( cProp___24t @ V1__B )
              | ~ ( p @ V0__A )
              | ~ ( p @ V1__B )
              | ( p @ V0__A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2740]) ).

thf(2927,plain,
    ( ( ! [Vvar__97: $i] :
          ( ( ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) @ ( sK2_SY468 @ Vvar__97 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) @ ( happ @ ( happ @ Vvar__97 @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) ) @ ( sK2_SY468 @ Vvar__97 ) ) ) )
          | ( c_24__type__96___24t @ Vvar__97 ) )
      & ! [Vvar__97: $i] :
          ( ~ ( c_24__type__96___24t @ Vvar__97 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__97 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2789]) ).

thf(2928,plain,
    ( ( ! [Vvar__91: $i] :
          ( ( ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) @ ( sK4_SY469 @ Vvar__91 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) @ ( sK5_SY471 @ Vvar__91 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) @ ( happ @ ( happ @ ( happ @ Vvar__91 @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) ) @ ( sK4_SY469 @ Vvar__91 ) ) @ ( sK5_SY471 @ Vvar__91 ) ) ) )
          | ( c_24__type__90___24t @ Vvar__91 ) )
      & ! [Vvar__91: $i] :
          ( ~ ( c_24__type__90___24t @ Vvar__91 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
                  | ! [Vv__CANONICAL__2: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ ( happ @ Vvar__91 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2790]) ).

thf(2929,plain,
    ( ( ! [Vvar__53: $i] :
          ( ( ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ Vvar__53 ) )
            & ( cType___24t @ ( sK7_SY472 @ Vvar__53 ) )
            & ~ ( cType___24t @ ( happ @ ( happ @ Vvar__53 @ ( sK6_Vv__CANONICAL__0 @ Vvar__53 ) ) @ ( sK7_SY472 @ Vvar__53 ) ) ) )
          | ( c_24__type__52___24t @ Vvar__53 ) )
      & ! [Vvar__53: $i] :
          ( ~ ( c_24__type__52___24t @ Vvar__53 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cType___24t @ Vv__CANONICAL__1 )
                  | ( cType___24t @ ( happ @ ( happ @ Vvar__53 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2791]) ).

thf(2930,plain,
    ( ( ! [Vvar__4734: $i] :
          ( ( ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ Vvar__4734 ) )
            & ( cType___24t @ ( sK9_SY473 @ Vvar__4734 ) )
            & ( cType___24t @ ( sK10_SY476 @ Vvar__4734 ) )
            & ( cType___24t @ ( sK11_SY478 @ Vvar__4734 ) )
            & ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ Vvar__4734 @ ( sK8_Vv__CANONICAL__0 @ Vvar__4734 ) ) @ ( sK9_SY473 @ Vvar__4734 ) ) @ ( sK10_SY476 @ Vvar__4734 ) ) @ ( sK11_SY478 @ Vvar__4734 ) ) ) )
          | ( c_24__type__4733___24t @ Vvar__4734 ) )
      & ! [Vvar__4734: $i] :
          ( ~ ( c_24__type__4733___24t @ Vvar__4734 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cType___24t @ Vv__CANONICAL__1 )
                  | ! [Vv__CANONICAL__2: $i] :
                      ( ~ ( cType___24t @ Vv__CANONICAL__2 )
                      | ! [Vv__CANONICAL__3: $i] :
                          ( ~ ( cType___24t @ Vv__CANONICAL__3 )
                          | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ Vvar__4734 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2792]) ).

thf(2931,plain,
    ( ( ! [Vvar__29: $i] :
          ( ( ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ Vvar__29 ) )
            & ~ ( cType___24t @ ( happ @ Vvar__29 @ ( sK12_Vv__CANONICAL__0 @ Vvar__29 ) ) ) )
          | ( c_24__type__28___24t @ Vvar__29 ) )
      & ! [Vvar__29: $i] :
          ( ~ ( c_24__type__28___24t @ Vvar__29 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ( cType___24t @ ( happ @ Vvar__29 @ Vv__CANONICAL__0 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2793]) ).

thf(2932,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vvar__11830: $i] :
          ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK13_Vv__CANONICAL__1 @ Vvar__11830 @ Vv__CANONICAL__0 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK14_SY479 @ Vvar__11830 @ Vv__CANONICAL__0 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__11830 @ ( sK13_Vv__CANONICAL__1 @ Vvar__11830 @ Vv__CANONICAL__0 ) ) @ ( sK14_SY479 @ Vvar__11830 @ Vv__CANONICAL__0 ) ) ) )
          | ( c_24__type__11829___24t @ Vv__CANONICAL__0 @ Vvar__11830 ) )
      & ! [Vv__CANONICAL__0: $i,Vvar__11830: $i] :
          ( ~ ( c_24__type__11829___24t @ Vv__CANONICAL__0 @ Vvar__11830 )
          | ! [Vv__CANONICAL__1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
              | ! [Vv__CANONICAL__2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__11830 @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2794]) ).

thf(2933,plain,
    ( ( ! [Vv__CANONICAL__0: $i] :
          ( ! [Vv__CANONICAL__1: $i,Vvar__11788: $i] :
              ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( sK15_Vv__CANONICAL__2 @ Vvar__11788 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) )
                & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11788 @ ( sK15_Vv__CANONICAL__2 @ Vvar__11788 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) ) ) )
              | ( c_24__type__11787___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11788 ) )
          & ! [Vv__CANONICAL__1: $i,Vvar__11788: $i] :
              ( ~ ( c_24__type__11787___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11788 )
              | ! [Vv__CANONICAL__2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11788 @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2795]) ).

thf(2934,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vvar__11749: $i] :
          ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK16_Vv__CANONICAL__1 @ Vvar__11749 @ Vv__CANONICAL__0 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11749 @ ( sK16_Vv__CANONICAL__1 @ Vvar__11749 @ Vv__CANONICAL__0 ) ) ) )
          | ( c_24__type__11748___24t @ Vv__CANONICAL__0 @ Vvar__11749 ) )
      & ! [Vv__CANONICAL__0: $i,Vvar__11749: $i] :
          ( ~ ( c_24__type__11748___24t @ Vv__CANONICAL__0 @ Vvar__11749 )
          | ! [Vv__CANONICAL__1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11749 @ Vv__CANONICAL__1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2796]) ).

thf(2935,plain,
    ( ( ! [Vv__CANONICAL__0: $i] :
          ( ! [Vv__CANONICAL__1: $i,Vvar__11700: $i] :
              ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK17_Vv__CANONICAL__2 @ Vvar__11700 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) )
                & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( happ @ Vvar__11700 @ ( sK17_Vv__CANONICAL__2 @ Vvar__11700 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) ) ) )
              | ( c_24__type__11699___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11700 ) )
          & ! [Vv__CANONICAL__1: $i,Vvar__11700: $i] :
              ( ~ ( c_24__type__11699___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11700 )
              | ! [Vv__CANONICAL__2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( happ @ Vvar__11700 @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2797]) ).

thf(2936,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35350: $i] :
          ( ~ ( p @ ( c_24__prop__35358___24a2 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35350 ) )
          | ~ ( p @ Vvar__0__P__35350 ) )
      & ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35350: $i] :
          ( ( p @ Vvar__0__P__35350 )
          | ( p @ ( c_24__prop__35358___24a2 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35350 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2798]) ).

thf(2937,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__P__35345: $i] :
              ( ( p @ Vvar__0__P__35345 )
              | ! [Vvar__1__Q__35346: $i] : ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) ) )
          & ! [Vvar__0__P__35345: $i,Vvar__1__Q__35346: $i] :
              ( ~ ( p @ Vvar__1__Q__35346 )
              | ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) ) )
          & ! [Vvar__0__P__35345: $i,Vvar__1__Q__35346: $i] :
              ( ~ ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) )
              | ~ ( p @ Vvar__0__P__35345 )
              | ( p @ Vvar__1__Q__35346 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2799]) ).

thf(2938,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__P__35341: $i,Vvar__1__Q__35342: $i] :
              ( ~ ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) )
              | ( p @ Vvar__0__P__35341 )
              | ( p @ Vvar__1__Q__35342 ) )
          & ! [Vvar__0__P__35341: $i] :
              ( ~ ( p @ Vvar__0__P__35341 )
              | ! [Vvar__1__Q__35342: $i] : ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) ) )
          & ! [Vvar__0__P__35341: $i,Vvar__1__Q__35342: $i] :
              ( ~ ( p @ Vvar__1__Q__35342 )
              | ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2800]) ).

thf(2939,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__P__35337: $i,Vvar__1__Q__35338: $i] :
              ( ~ ( p @ Vvar__0__P__35337 )
              | ~ ( p @ Vvar__1__Q__35338 )
              | ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) ) )
          & ! [Vvar__0__P__35337: $i] :
              ( ! [Vvar__1__Q__35338: $i] :
                  ~ ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) )
              | ( p @ Vvar__0__P__35337 ) )
          & ! [Vvar__0__P__35337: $i,Vvar__1__Q__35338: $i] :
              ( ~ ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) )
              | ( p @ Vvar__1__Q__35338 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2801]) ).

thf(2940,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__x__35333: $i,Vvar__1__y__35334: $i] :
              ( ( Vvar__0__x__35333 != Vvar__1__y__35334 )
              | ( p @ ( c_24__prop__35353___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__x__35333 @ Vvar__1__y__35334 ) ) )
          & ! [Vvar__0__x__35333: $i,Vvar__1__y__35334: $i] :
              ( ~ ( p @ ( c_24__prop__35353___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__x__35333 @ Vvar__1__y__35334 ) )
              | ( Vvar__0__x__35333 = Vvar__1__y__35334 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2802]) ).

thf(2941,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__S__35330: $i] :
          ( ! [Vvar__1__x__35331: $i,Vvar__2__y__35332: $i] :
              ( ( Vvar__1__x__35331 != Vvar__2__y__35332 )
              | ( p @ ( c_24__prop__35352___24a4 @ Vvar__0___24Anonymous__35328 @ Vvar__0__S__35330 @ Vvar__1__x__35331 @ Vvar__2__y__35332 ) ) )
          & ! [Vvar__1__x__35331: $i,Vvar__2__y__35332: $i] :
              ( ~ ( p @ ( c_24__prop__35352___24a4 @ Vvar__0___24Anonymous__35328 @ Vvar__0__S__35330 @ Vvar__1__x__35331 @ Vvar__2__y__35332 ) )
              | ( Vvar__1__x__35331 = Vvar__2__y__35332 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2803]) ).

thf(2942,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ! [Vv__CANONICAL__4: $i,Vv__CANONICAL__5: $i] :
              ( ~ ( c_24__lam__7800___24a6 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 @ Vv__CANONICAL__5 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__3 @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__4 ) ) @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__5 ) ) ) )
          & ! [Vv__CANONICAL__4: $i,Vv__CANONICAL__5: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__3 @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__4 ) ) @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__5 ) ) )
              | ( c_24__lam__7800___24a6 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 @ Vv__CANONICAL__5 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2804]) ).

thf(2943,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i] :
          ( ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__7591___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) )
              | ( c_24__lam__7591___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2805]) ).

thf(2944,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i] :
          ( ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__7587___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__2 ) ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__2 ) )
              | ( c_24__lam__7587___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2806]) ).

thf(2945,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i] :
          ( ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( p @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) )
              | ~ ( p @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) )
              | ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2807]) ).

thf(2946,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i] :
          ( ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) )
          & ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) )
          & ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2808]) ).

thf(2947,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i] :
          ( ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( c_24__lam__16___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) )
          & ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( c_24__lam__16___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2811]) ).

thf(2948,plain,
    ( ( ! [V0__A: $i,V1__s: $i] :
          ( ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V1__s @ V3__x ) )
              | ( p @ ( happ @ V2__s_27 @ V3__x ) ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V1__s @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V2__s_27 @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2812]) ).

thf(2949,plain,
    ( ( ! [V0__A: $i,V1__s: $i] :
          ( ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V1__s @ V3__x ) )
              | ( p @ ( happ @ V2__s_27 @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V1__s @ V3__x ) ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ~ ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2813]) ).

thf(2950,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i] :
          ( ! [V3__d: $i,V4__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ V0__A @ V1__B @ V2__f @ V3__d @ V4__x )
              | ( p @ ( happ @ V3__d @ ( happ @ V2__f @ V4__x ) ) ) )
          & ! [V3__d: $i,V4__x: $i] :
              ( ~ ( p @ ( happ @ V3__d @ ( happ @ V2__f @ V4__x ) ) )
              | ( chahn_2eHahnSets_2eset__map___24a5 @ V0__A @ V1__B @ V2__f @ V3__d @ V4__x ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2814]) ).

thf(2951,plain,
    ( ( ! [V0__A: $i,V1__s: $i] :
          ( ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V1__s @ V3__x ) )
              | ~ ( p @ ( happ @ V2__s_27 @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V1__s @ V3__x ) ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2815]) ).

thf(2952,plain,
    ( ( ! [V0__A: $i] :
          ( ! [V1__s: $i,V2__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ V0__A @ V1__s @ V2__x )
              | ~ ( p @ ( happ @ V1__s @ V2__x ) ) )
          & ! [V1__s: $i,V2__x: $i] :
              ( ( p @ ( happ @ V1__s @ V2__x ) )
              | ( chahn_2eHahnSets_2eset__compl___24a3 @ V0__A @ V1__s @ V2__x ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2816]) ).

thf(2953,plain,
    ( ( ! [V0__A: $i,V1__cond: $i,V2__r: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V2__r @ V3__x ) @ V4__y ) )
              | ~ ( p @ ( happ @ V1__cond @ V3__x ) )
              | ~ ( p @ ( happ @ V1__cond @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V2__r @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i] :
              ( ! [V4__y: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
              | ( p @ ( happ @ V1__cond @ V3__x ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
              | ( p @ ( happ @ V1__cond @ V4__y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2817]) ).

thf(2954,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r: $i] :
          ( ! [V4__x: $i,V5__y: $i] :
              ( ( ( happ @ V2__f @ V4__x )
               != ( happ @ V2__f @ V5__y ) )
              | ~ ( p @ ( happ @ ( happ @ V3__r @ V4__x ) @ V5__y ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y ) )
          & ! [V4__x: $i,V5__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y )
              | ( ( happ @ V2__f @ V4__x )
                = ( happ @ V2__f @ V5__y ) ) )
          & ! [V4__x: $i,V5__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y )
              | ( p @ ( happ @ ( happ @ V3__r @ V4__x ) @ V5__y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2818]) ).

thf(2955,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
              | ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2819]) ).

thf(2956,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r_27_27: $i] :
          ( ! [V4__x: $i,V5__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r_27_27 @ V4__x @ V5__y )
              | ( p @ ( happ @ ( happ @ V3__r_27_27 @ ( happ @ V2__f @ V4__x ) ) @ ( happ @ V2__f @ V5__y ) ) ) )
          & ! [V4__x: $i,V5__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V3__r_27_27 @ ( happ @ V2__f @ V4__x ) ) @ ( happ @ V2__f @ V5__y ) ) )
              | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r_27_27 @ V4__x @ V5__y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2820]) ).

thf(2957,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
              | ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2821]) ).

thf(2958,plain,
    ( ( ! [V0__A: $i,V1__cond: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ( V2__x != V3__y )
              | ~ ( p @ ( happ @ V1__cond @ V2__x ) )
              | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y )
              | ( V2__x = V3__y ) )
          & ! [V2__x: $i] :
              ( ! [V3__y: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y )
              | ( p @ ( happ @ V1__cond @ V2__x ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2822]) ).

thf(2959,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ( ( happ @ V2__f @ V3__x )
               != ( happ @ V2__f @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ V0__A @ V1__B @ V2__f @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ V0__A @ V1__B @ V2__f @ V3__x @ V4__y )
              | ( ( happ @ V2__f @ V3__x )
                = ( happ @ V2__f @ V4__y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2823]) ).

thf(2960,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i] :
          ( ! [V3__a: $i,V4__b: $i] :
              ( ~ ( p @ ( happ @ V1__r @ V3__a ) )
              | ~ ( p @ ( happ @ V2__r_27 @ V4__b ) )
              | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b ) )
          & ! [V3__a: $i] :
              ( ! [V4__b: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b )
              | ( p @ ( happ @ V1__r @ V3__a ) ) )
          & ! [V3__a: $i,V4__b: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b )
              | ( p @ ( happ @ V2__r_27 @ V4__b ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2824]) ).

thf(2961,plain,
    ( ( ! [V0__A: $i,V1__r: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2825]) ).

thf(2962,plain,
    ( ( ! [V0__A: $i,V1__r: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) )
              | ( V2__x = V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ( V2__x != V3__y )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2826]) ).

thf(2963,plain,
    ( ( ! [V0__A: $i,V1__r: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
              | ( V2__x = V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ( V2__x != V3__y )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2827]) ).

thf(2964,plain,
    ( ( ! [V0__A: $i,V1__R1: $i,V2__R2: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
              | ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2828]) ).

thf(2965,plain,
    ( ( ! [V0__A: $i,V1__R: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ V0__A @ V1__R @ V2__x @ V3__y )
              | ( p @ ( happ @ ( happ @ V1__R @ V3__y ) @ V2__x ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__R @ V3__y ) @ V2__x ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ V0__A @ V1__R @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2829]) ).

thf(2966,plain,
    ( ( ! [V0__A: $i] :
          ( ! [V1__R1: $i,V2__R2: $i] :
              ( ( ( t @ ( sK18_V3__x @ V2__R2 @ V1__R1 @ V0__A ) @ V0__A )
                & ( t @ ( sK19_SY480 @ V2__R2 @ V1__R1 @ V0__A ) @ V0__A )
                & ( p @ ( happ @ ( happ @ V1__R1 @ ( sK18_V3__x @ V2__R2 @ V1__R1 @ V0__A ) ) @ ( sK19_SY480 @ V2__R2 @ V1__R1 @ V0__A ) ) )
                & ~ ( p @ ( happ @ ( happ @ V2__R2 @ ( sK18_V3__x @ V2__R2 @ V1__R1 @ V0__A ) ) @ ( sK19_SY480 @ V2__R2 @ V1__R1 @ V0__A ) ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) ) )
          & ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
              | ! [V3__x: $i] :
                  ( ~ ( t @ V3__x @ V0__A )
                  | ! [V4__y: $i] :
                      ( ~ ( t @ V4__y @ V0__A )
                      | ~ ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
                      | ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2830]) ).

thf(2967,plain,
    ( ( ( ! [V0__P: $i] :
            ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ V0__P )
        | $true )
      & ( ~ $true
        | ! [V0__P: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ V0__P ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2831]) ).

thf(2968,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V1__r ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2836]) ).

thf(2969,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2838]) ).

thf(2970,plain,
    ( ( ! [V0__r: $i] :
          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ c_24__lam__35673 ) @ V0__r ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2839]) ).

thf(2971,plain,
    ( ( ! [V0__r: $i] :
          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ V0__r ) @ c_24__lam__35673 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2840]) ).

thf(2972,plain,
    ( ( ! [V0__r: $i] :
          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ V0__r ) @ c_24__lam__35673 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2841]) ).

thf(2973,plain,
    ( ( ! [V0__A: $i] :
          ( ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__R2 @ V1__R1 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
          & ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) ) )
          & ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__R2 @ V1__R1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[2846]) ).

thf(2974,plain,
    ( ( ! [V0__A: $i] :
          ( ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__R2 @ V1__R1 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
          & ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) ) )
          & ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__R1 @ V2__R2 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__R2 @ V1__R1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2973]) ).

thf(2975,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
          ( ( c_24__lam__45594___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
          = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ Vv__CANONICAL__1 @ ( happ @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) @ Vv__CANONICAL__2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2845]) ).

thf(2976,plain,
    ( ( cType___24t @ cA )
    = $true ),
    inference(copy,[status(thm)],[2844]) ).

thf(2977,plain,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ cr )
    = $true ),
    inference(copy,[status(thm)],[2843]) ).

thf(2978,plain,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ cr_27 )
    = $true ),
    inference(copy,[status(thm)],[2842]) ).

thf(2979,plain,
    ( ( ! [V0__r: $i] :
          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ V0__r ) @ c_24__lam__35673 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2972]) ).

thf(2980,plain,
    ( ( ! [V0__r: $i] :
          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ V0__r ) @ c_24__lam__35673 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2971]) ).

thf(2981,plain,
    ( ( ! [V0__r: $i] :
          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ V0__r )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ V0__r @ c_24__lam__35673 ) @ V0__r ) ) )
    = $true ),
    inference(copy,[status(thm)],[2970]) ).

thf(2982,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2969]) ).

thf(2983,plain,
    ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ cA @ cr @ cr_27 ) )
    = $true ),
    inference(copy,[status(thm)],[2837]) ).

thf(2984,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V1__r ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2968]) ).

thf(2985,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 )
          = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2835]) ).

thf(2986,plain,
    ( ( p @ c_24True )
    = $true ),
    inference(copy,[status(thm)],[2834]) ).

thf(2987,plain,
    ( ( ~ ( p @ c_24False ) )
    = $true ),
    inference(copy,[status(thm)],[2833]) ).

thf(2988,plain,
    ( ( cType___24t @ cType )
    = $true ),
    inference(copy,[status(thm)],[2832]) ).

thf(2989,plain,
    ( ( ( ! [V0__P: $i] :
            ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ V0__P )
        | $true )
      & ( ~ $true
        | ! [V0__P: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ V0__P ) ) )
    = $true ),
    inference(copy,[status(thm)],[2967]) ).

thf(2990,plain,
    ( ( ! [V0__A: $i] :
          ( ! [V1__R1: $i,V2__R2: $i] :
              ( ( ( t @ ( sK18_V3__x @ V2__R2 @ V1__R1 @ V0__A ) @ V0__A )
                & ( t @ ( sK19_SY480 @ V2__R2 @ V1__R1 @ V0__A ) @ V0__A )
                & ( p @ ( happ @ ( happ @ V1__R1 @ ( sK18_V3__x @ V2__R2 @ V1__R1 @ V0__A ) ) @ ( sK19_SY480 @ V2__R2 @ V1__R1 @ V0__A ) ) )
                & ~ ( p @ ( happ @ ( happ @ V2__R2 @ ( sK18_V3__x @ V2__R2 @ V1__R1 @ V0__A ) ) @ ( sK19_SY480 @ V2__R2 @ V1__R1 @ V0__A ) ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) ) )
          & ! [V1__R1: $i,V2__R2: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__R1 @ V2__R2 ) )
              | ! [V3__x: $i] :
                  ( ~ ( t @ V3__x @ V0__A )
                  | ! [V4__y: $i] :
                      ( ~ ( t @ V4__y @ V0__A )
                      | ~ ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
                      | ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2966]) ).

thf(2991,plain,
    ( ( ! [V0__A: $i,V1__R: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ V0__A @ V1__R @ V2__x @ V3__y )
              | ( p @ ( happ @ ( happ @ V1__R @ V3__y ) @ V2__x ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__R @ V3__y ) @ V2__x ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ V0__A @ V1__R @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2965]) ).

thf(2992,plain,
    ( ( ! [V0__A: $i,V1__R1: $i,V2__R2: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
              | ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__R1 @ V3__x ) @ V4__y ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V2__R2 @ V3__x ) @ V4__y ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ V0__A @ V1__R1 @ V2__R2 @ V3__x @ V4__y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2964]) ).

thf(2993,plain,
    ( ( ! [V0__A: $i,V1__r: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
              | ( V2__x = V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ( V2__x != V3__y )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2963]) ).

thf(2994,plain,
    ( ( ! [V0__A: $i,V1__r: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) )
              | ( V2__x = V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ( V2__x != V3__y )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2962]) ).

thf(2995,plain,
    ( ( ! [V0__A: $i,V1__r: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V2__x ) @ V3__y ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__y ) @ V2__x ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ V0__A @ V1__r @ V2__x @ V3__y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2961]) ).

thf(2996,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i] :
          ( ! [V3__a: $i,V4__b: $i] :
              ( ~ ( p @ ( happ @ V1__r @ V3__a ) )
              | ~ ( p @ ( happ @ V2__r_27 @ V4__b ) )
              | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b ) )
          & ! [V3__a: $i] :
              ( ! [V4__b: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b )
              | ( p @ ( happ @ V1__r @ V3__a ) ) )
          & ! [V3__a: $i,V4__b: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__a @ V4__b )
              | ( p @ ( happ @ V2__r_27 @ V4__b ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2960]) ).

thf(2997,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ( ( happ @ V2__f @ V3__x )
               != ( happ @ V2__f @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ V0__A @ V1__B @ V2__f @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ V0__A @ V1__B @ V2__f @ V3__x @ V4__y )
              | ( ( happ @ V2__f @ V3__x )
                = ( happ @ V2__f @ V4__y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2959]) ).

thf(2998,plain,
    ( ( ! [V0__A: $i,V1__cond: $i] :
          ( ! [V2__x: $i,V3__y: $i] :
              ( ( V2__x != V3__y )
              | ~ ( p @ ( happ @ V1__cond @ V2__x ) )
              | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y ) )
          & ! [V2__x: $i,V3__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y )
              | ( V2__x = V3__y ) )
          & ! [V2__x: $i] :
              ( ! [V3__y: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ V0__A @ V1__cond @ V2__x @ V3__y )
              | ( p @ ( happ @ V1__cond @ V2__x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2958]) ).

thf(2999,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
              | ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2957]) ).

thf(3000,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r_27_27: $i] :
          ( ! [V4__x: $i,V5__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r_27_27 @ V4__x @ V5__y )
              | ( p @ ( happ @ ( happ @ V3__r_27_27 @ ( happ @ V2__f @ V4__x ) ) @ ( happ @ V2__f @ V5__y ) ) ) )
          & ! [V4__x: $i,V5__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V3__r_27_27 @ ( happ @ V2__f @ V4__x ) ) @ ( happ @ V2__f @ V5__y ) ) )
              | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r_27_27 @ V4__x @ V5__y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2956]) ).

thf(3001,plain,
    ( ( ! [V0__A: $i,V1__r: $i,V2__r_27: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) )
              | ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V1__r @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V0__A @ V1__r @ V2__r_27 @ V3__x @ V4__y )
              | ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V3__x ) @ V4__y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2955]) ).

thf(3002,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i,V3__r: $i] :
          ( ! [V4__x: $i,V5__y: $i] :
              ( ( ( happ @ V2__f @ V4__x )
               != ( happ @ V2__f @ V5__y ) )
              | ~ ( p @ ( happ @ ( happ @ V3__r @ V4__x ) @ V5__y ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y ) )
          & ! [V4__x: $i,V5__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y )
              | ( ( happ @ V2__f @ V4__x )
                = ( happ @ V2__f @ V5__y ) ) )
          & ! [V4__x: $i,V5__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ V0__A @ V1__B @ V2__f @ V3__r @ V4__x @ V5__y )
              | ( p @ ( happ @ ( happ @ V3__r @ V4__x ) @ V5__y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2954]) ).

thf(3003,plain,
    ( ( ! [V0__A: $i,V1__cond: $i,V2__r: $i] :
          ( ! [V3__x: $i,V4__y: $i] :
              ( ~ ( p @ ( happ @ ( happ @ V2__r @ V3__x ) @ V4__y ) )
              | ~ ( p @ ( happ @ V1__cond @ V3__x ) )
              | ~ ( p @ ( happ @ V1__cond @ V4__y ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
              | ( p @ ( happ @ ( happ @ V2__r @ V3__x ) @ V4__y ) ) )
          & ! [V3__x: $i] :
              ( ! [V4__y: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
              | ( p @ ( happ @ V1__cond @ V3__x ) ) )
          & ! [V3__x: $i,V4__y: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ V0__A @ V1__cond @ V2__r @ V3__x @ V4__y )
              | ( p @ ( happ @ V1__cond @ V4__y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2953]) ).

thf(3004,plain,
    ( ( ! [V0__A: $i] :
          ( ! [V1__s: $i,V2__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ V0__A @ V1__s @ V2__x )
              | ~ ( p @ ( happ @ V1__s @ V2__x ) ) )
          & ! [V1__s: $i,V2__x: $i] :
              ( ( p @ ( happ @ V1__s @ V2__x ) )
              | ( chahn_2eHahnSets_2eset__compl___24a3 @ V0__A @ V1__s @ V2__x ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2952]) ).

thf(3005,plain,
    ( ( ! [V0__A: $i,V1__s: $i] :
          ( ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V1__s @ V3__x ) )
              | ~ ( p @ ( happ @ V2__s_27 @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V1__s @ V3__x ) ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2951]) ).

thf(3006,plain,
    ( ( ! [V0__A: $i,V1__B: $i,V2__f: $i] :
          ( ! [V3__d: $i,V4__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ V0__A @ V1__B @ V2__f @ V3__d @ V4__x )
              | ( p @ ( happ @ V3__d @ ( happ @ V2__f @ V4__x ) ) ) )
          & ! [V3__d: $i,V4__x: $i] :
              ( ~ ( p @ ( happ @ V3__d @ ( happ @ V2__f @ V4__x ) ) )
              | ( chahn_2eHahnSets_2eset__map___24a5 @ V0__A @ V1__B @ V2__f @ V3__d @ V4__x ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2950]) ).

thf(3007,plain,
    ( ( ! [V0__A: $i,V1__s: $i] :
          ( ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V1__s @ V3__x ) )
              | ( p @ ( happ @ V2__s_27 @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V1__s @ V3__x ) ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ~ ( p @ ( happ @ V2__s_27 @ V3__x ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2949]) ).

thf(3008,plain,
    ( ( ! [V0__A: $i,V1__s: $i] :
          ( ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x )
              | ( p @ ( happ @ V1__s @ V3__x ) )
              | ( p @ ( happ @ V2__s_27 @ V3__x ) ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V1__s @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) )
          & ! [V2__s_27: $i,V3__x: $i] :
              ( ~ ( p @ ( happ @ V2__s_27 @ V3__x ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ V0__A @ V1__s @ V2__s_27 @ V3__x ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2948]) ).

thf(3009,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i] :
          ( ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( c_24__lam__16___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) )
          & ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( c_24__lam__16___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2947]) ).

thf(3010,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__33077___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
          = ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2810]) ).

thf(3011,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ( c_24__lam__33085___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
          = ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2809]) ).

thf(3012,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i] :
          ( ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) ) )
          & ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) )
          & ! [Vv__CANONICAL__3: $i,Vv__CANONICAL__4: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__4 ) )
              | ( c_24__lam__3971___24a5 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2946]) ).

thf(3013,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i] :
          ( ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( p @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) )
              | ~ ( p @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) )
              | ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2945]) ).

thf(3014,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i] :
          ( ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__7587___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__2 ) ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__3 ) @ Vv__CANONICAL__2 ) )
              | ( c_24__lam__7587___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2944]) ).

thf(3015,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i] :
          ( ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( c_24__lam__7591___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) )
          & ! [Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) )
              | ( c_24__lam__7591___24a4 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2943]) ).

thf(3016,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vv__CANONICAL__1: $i,Vv__CANONICAL__2: $i,Vv__CANONICAL__3: $i] :
          ( ! [Vv__CANONICAL__4: $i,Vv__CANONICAL__5: $i] :
              ( ~ ( c_24__lam__7800___24a6 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 @ Vv__CANONICAL__5 )
              | ( p @ ( happ @ ( happ @ Vv__CANONICAL__3 @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__4 ) ) @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__5 ) ) ) )
          & ! [Vv__CANONICAL__4: $i,Vv__CANONICAL__5: $i] :
              ( ~ ( p @ ( happ @ ( happ @ Vv__CANONICAL__3 @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__4 ) ) @ ( happ @ Vv__CANONICAL__2 @ Vv__CANONICAL__5 ) ) )
              | ( c_24__lam__7800___24a6 @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 @ Vv__CANONICAL__3 @ Vv__CANONICAL__4 @ Vv__CANONICAL__5 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2942]) ).

thf(3017,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__S__35330: $i] :
          ( ! [Vvar__1__x__35331: $i,Vvar__2__y__35332: $i] :
              ( ( Vvar__1__x__35331 != Vvar__2__y__35332 )
              | ( p @ ( c_24__prop__35352___24a4 @ Vvar__0___24Anonymous__35328 @ Vvar__0__S__35330 @ Vvar__1__x__35331 @ Vvar__2__y__35332 ) ) )
          & ! [Vvar__1__x__35331: $i,Vvar__2__y__35332: $i] :
              ( ~ ( p @ ( c_24__prop__35352___24a4 @ Vvar__0___24Anonymous__35328 @ Vvar__0__S__35330 @ Vvar__1__x__35331 @ Vvar__2__y__35332 ) )
              | ( Vvar__1__x__35331 = Vvar__2__y__35332 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2941]) ).

thf(3018,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__x__35333: $i,Vvar__1__y__35334: $i] :
              ( ( Vvar__0__x__35333 != Vvar__1__y__35334 )
              | ( p @ ( c_24__prop__35353___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__x__35333 @ Vvar__1__y__35334 ) ) )
          & ! [Vvar__0__x__35333: $i,Vvar__1__y__35334: $i] :
              ( ~ ( p @ ( c_24__prop__35353___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__x__35333 @ Vvar__1__y__35334 ) )
              | ( Vvar__0__x__35333 = Vvar__1__y__35334 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2940]) ).

thf(3019,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__P__35337: $i,Vvar__1__Q__35338: $i] :
              ( ~ ( p @ Vvar__0__P__35337 )
              | ~ ( p @ Vvar__1__Q__35338 )
              | ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) ) )
          & ! [Vvar__0__P__35337: $i] :
              ( ! [Vvar__1__Q__35338: $i] :
                  ~ ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) )
              | ( p @ Vvar__0__P__35337 ) )
          & ! [Vvar__0__P__35337: $i,Vvar__1__Q__35338: $i] :
              ( ~ ( p @ ( c_24__prop__35355___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35337 @ Vvar__1__Q__35338 ) )
              | ( p @ Vvar__1__Q__35338 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2939]) ).

thf(3020,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__P__35341: $i,Vvar__1__Q__35342: $i] :
              ( ~ ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) )
              | ( p @ Vvar__0__P__35341 )
              | ( p @ Vvar__1__Q__35342 ) )
          & ! [Vvar__0__P__35341: $i] :
              ( ~ ( p @ Vvar__0__P__35341 )
              | ! [Vvar__1__Q__35342: $i] : ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) ) )
          & ! [Vvar__0__P__35341: $i,Vvar__1__Q__35342: $i] :
              ( ~ ( p @ Vvar__1__Q__35342 )
              | ( p @ ( c_24__prop__35356___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35341 @ Vvar__1__Q__35342 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2938]) ).

thf(3021,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i] :
          ( ! [Vvar__0__P__35345: $i] :
              ( ( p @ Vvar__0__P__35345 )
              | ! [Vvar__1__Q__35346: $i] : ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) ) )
          & ! [Vvar__0__P__35345: $i,Vvar__1__Q__35346: $i] :
              ( ~ ( p @ Vvar__1__Q__35346 )
              | ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) ) )
          & ! [Vvar__0__P__35345: $i,Vvar__1__Q__35346: $i] :
              ( ~ ( p @ ( c_24__prop__35357___24a3 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35345 @ Vvar__1__Q__35346 ) )
              | ~ ( p @ Vvar__0__P__35345 )
              | ( p @ Vvar__1__Q__35346 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2937]) ).

thf(3022,plain,
    ( ( ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35350: $i] :
          ( ~ ( p @ ( c_24__prop__35358___24a2 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35350 ) )
          | ~ ( p @ Vvar__0__P__35350 ) )
      & ! [Vvar__0___24Anonymous__35328: $i,Vvar__0__P__35350: $i] :
          ( ( p @ Vvar__0__P__35350 )
          | ( p @ ( c_24__prop__35358___24a2 @ Vvar__0___24Anonymous__35328 @ Vvar__0__P__35350 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2936]) ).

thf(3023,plain,
    ( ( ! [Vv__CANONICAL__0: $i] :
          ( ! [Vv__CANONICAL__1: $i,Vvar__11700: $i] :
              ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK17_Vv__CANONICAL__2 @ Vvar__11700 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) )
                & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( happ @ Vvar__11700 @ ( sK17_Vv__CANONICAL__2 @ Vvar__11700 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) ) ) )
              | ( c_24__type__11699___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11700 ) )
          & ! [Vv__CANONICAL__1: $i,Vvar__11700: $i] :
              ( ~ ( c_24__type__11699___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11700 )
              | ! [Vv__CANONICAL__2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( happ @ Vvar__11700 @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2935]) ).

thf(3024,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vvar__11749: $i] :
          ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK16_Vv__CANONICAL__1 @ Vvar__11749 @ Vv__CANONICAL__0 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11749 @ ( sK16_Vv__CANONICAL__1 @ Vvar__11749 @ Vv__CANONICAL__0 ) ) ) )
          | ( c_24__type__11748___24t @ Vv__CANONICAL__0 @ Vvar__11749 ) )
      & ! [Vv__CANONICAL__0: $i,Vvar__11749: $i] :
          ( ~ ( c_24__type__11748___24t @ Vv__CANONICAL__0 @ Vvar__11749 )
          | ! [Vv__CANONICAL__1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11749 @ Vv__CANONICAL__1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2934]) ).

thf(3025,plain,
    ( ( ! [Vv__CANONICAL__0: $i] :
          ( ! [Vv__CANONICAL__1: $i,Vvar__11788: $i] :
              ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ ( sK15_Vv__CANONICAL__2 @ Vvar__11788 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) )
                & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11788 @ ( sK15_Vv__CANONICAL__2 @ Vvar__11788 @ Vv__CANONICAL__1 @ Vv__CANONICAL__0 ) ) ) )
              | ( c_24__type__11787___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11788 ) )
          & ! [Vv__CANONICAL__1: $i,Vvar__11788: $i] :
              ( ~ ( c_24__type__11787___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 @ Vvar__11788 )
              | ! [Vv__CANONICAL__2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__1 @ Vv__CANONICAL__2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ Vvar__11788 @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2933]) ).

thf(3026,plain,
    ( ( ! [Vv__CANONICAL__0: $i,Vvar__11830: $i] :
          ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK13_Vv__CANONICAL__1 @ Vvar__11830 @ Vv__CANONICAL__0 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( sK14_SY479 @ Vvar__11830 @ Vv__CANONICAL__0 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__11830 @ ( sK13_Vv__CANONICAL__1 @ Vvar__11830 @ Vv__CANONICAL__0 ) ) @ ( sK14_SY479 @ Vvar__11830 @ Vv__CANONICAL__0 ) ) ) )
          | ( c_24__type__11829___24t @ Vv__CANONICAL__0 @ Vvar__11830 ) )
      & ! [Vv__CANONICAL__0: $i,Vvar__11830: $i] :
          ( ~ ( c_24__type__11829___24t @ Vv__CANONICAL__0 @ Vvar__11830 )
          | ! [Vv__CANONICAL__1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
              | ! [Vv__CANONICAL__2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__11830 @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2932]) ).

thf(3027,plain,
    ( ( ! [Vvar__29: $i] :
          ( ( ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ Vvar__29 ) )
            & ~ ( cType___24t @ ( happ @ Vvar__29 @ ( sK12_Vv__CANONICAL__0 @ Vvar__29 ) ) ) )
          | ( c_24__type__28___24t @ Vvar__29 ) )
      & ! [Vvar__29: $i] :
          ( ~ ( c_24__type__28___24t @ Vvar__29 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ( cType___24t @ ( happ @ Vvar__29 @ Vv__CANONICAL__0 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2931]) ).

thf(3028,plain,
    ( ( ! [Vvar__4734: $i] :
          ( ( ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ Vvar__4734 ) )
            & ( cType___24t @ ( sK9_SY473 @ Vvar__4734 ) )
            & ( cType___24t @ ( sK10_SY476 @ Vvar__4734 ) )
            & ( cType___24t @ ( sK11_SY478 @ Vvar__4734 ) )
            & ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ Vvar__4734 @ ( sK8_Vv__CANONICAL__0 @ Vvar__4734 ) ) @ ( sK9_SY473 @ Vvar__4734 ) ) @ ( sK10_SY476 @ Vvar__4734 ) ) @ ( sK11_SY478 @ Vvar__4734 ) ) ) )
          | ( c_24__type__4733___24t @ Vvar__4734 ) )
      & ! [Vvar__4734: $i] :
          ( ~ ( c_24__type__4733___24t @ Vvar__4734 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cType___24t @ Vv__CANONICAL__1 )
                  | ! [Vv__CANONICAL__2: $i] :
                      ( ~ ( cType___24t @ Vv__CANONICAL__2 )
                      | ! [Vv__CANONICAL__3: $i] :
                          ( ~ ( cType___24t @ Vv__CANONICAL__3 )
                          | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ Vvar__4734 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) @ Vv__CANONICAL__3 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2930]) ).

thf(3029,plain,
    ( ( ! [Vvar__53: $i] :
          ( ( ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ Vvar__53 ) )
            & ( cType___24t @ ( sK7_SY472 @ Vvar__53 ) )
            & ~ ( cType___24t @ ( happ @ ( happ @ Vvar__53 @ ( sK6_Vv__CANONICAL__0 @ Vvar__53 ) ) @ ( sK7_SY472 @ Vvar__53 ) ) ) )
          | ( c_24__type__52___24t @ Vvar__53 ) )
      & ! [Vvar__53: $i] :
          ( ~ ( c_24__type__52___24t @ Vvar__53 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cType___24t @ Vv__CANONICAL__1 )
                  | ( cType___24t @ ( happ @ ( happ @ Vvar__53 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2929]) ).

thf(3030,plain,
    ( ( ! [Vvar__91: $i] :
          ( ( ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) @ ( sK4_SY469 @ Vvar__91 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) @ ( sK5_SY471 @ Vvar__91 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) @ ( happ @ ( happ @ ( happ @ Vvar__91 @ ( sK3_Vv__CANONICAL__0 @ Vvar__91 ) ) @ ( sK4_SY469 @ Vvar__91 ) ) @ ( sK5_SY471 @ Vvar__91 ) ) ) )
          | ( c_24__type__90___24t @ Vvar__91 ) )
      & ! [Vvar__91: $i] :
          ( ~ ( c_24__type__90___24t @ Vvar__91 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
                  | ! [Vv__CANONICAL__2: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__2 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ ( happ @ Vvar__91 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) @ Vv__CANONICAL__2 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2928]) ).

thf(3031,plain,
    ( ( ! [Vvar__97: $i] :
          ( ( ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) )
            & ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) @ ( sK2_SY468 @ Vvar__97 ) )
            & ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) @ ( happ @ ( happ @ Vvar__97 @ ( sK1_Vv__CANONICAL__0 @ Vvar__97 ) ) @ ( sK2_SY468 @ Vvar__97 ) ) ) )
          | ( c_24__type__96___24t @ Vvar__97 ) )
      & ! [Vvar__97: $i] :
          ( ~ ( c_24__type__96___24t @ Vvar__97 )
          | ! [Vv__CANONICAL__0: $i] :
              ( ~ ( cType___24t @ Vv__CANONICAL__0 )
              | ! [Vv__CANONICAL__1: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ Vv__CANONICAL__1 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ Vv__CANONICAL__0 @ ( happ @ ( happ @ Vvar__97 @ Vv__CANONICAL__0 ) @ Vv__CANONICAL__1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2927]) ).

thf(3032,plain,
    ( ( cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt )
    = $true ),
    inference(copy,[status(thm)],[2788]) ).

thf(3033,plain,
    ( ( cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et )
    = $true ),
    inference(copy,[status(thm)],[2787]) ).

thf(3034,plain,
    ( ( cType___24t @ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree )
    = $true ),
    inference(copy,[status(thm)],[2786]) ).

thf(3035,plain,
    ( ( cType___24t @ cCoq_2eInit_2eByte_2ebyte )
    = $true ),
    inference(copy,[status(thm)],[2785]) ).

thf(3036,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2eEmpty__set )
    = $true ),
    inference(copy,[status(thm)],[2784]) ).

thf(3037,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2eID )
    = $true ),
    inference(copy,[status(thm)],[2783]) ).

thf(3038,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2ebool )
    = $true ),
    inference(copy,[status(thm)],[2782]) ).

thf(3039,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2ecomparison )
    = $true ),
    inference(copy,[status(thm)],[2781]) ).

thf(3040,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2enat )
    = $true ),
    inference(copy,[status(thm)],[2780]) ).

thf(3041,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDatatypes_2eunit )
    = $true ),
    inference(copy,[status(thm)],[2779]) ).

thf(3042,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDecimal_2edecimal )
    = $true ),
    inference(copy,[status(thm)],[2778]) ).

thf(3043,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDecimal_2eint )
    = $true ),
    inference(copy,[status(thm)],[2777]) ).

thf(3044,plain,
    ( ( cType___24t @ cCoq_2eInit_2eDecimal_2euint )
    = $true ),
    inference(copy,[status(thm)],[2776]) ).

thf(3045,plain,
    ( ( cType___24t @ cCoq_2eInit_2eNat_2et )
    = $true ),
    inference(copy,[status(thm)],[2775]) ).

thf(3046,plain,
    ( ( cType___24t @ cCoq_2eNArith_2eBinNatDef_2eN_2et )
    = $true ),
    inference(copy,[status(thm)],[2774]) ).

thf(3047,plain,
    ( ( cType___24t @ cCoq_2eNumbers_2eBinNums_2eN )
    = $true ),
    inference(copy,[status(thm)],[2773]) ).

thf(3048,plain,
    ( ( cType___24t @ cCoq_2eNumbers_2eBinNums_2eZ )
    = $true ),
    inference(copy,[status(thm)],[2772]) ).

thf(3049,plain,
    ( ( cType___24t @ cCoq_2eNumbers_2eBinNums_2epositive )
    = $true ),
    inference(copy,[status(thm)],[2771]) ).

thf(3050,plain,
    ( ( cType___24t @ cCoq_2ePArith_2eBinPosDef_2ePos_2emask )
    = $true ),
    inference(copy,[status(thm)],[2770]) ).

thf(3051,plain,
    ( ( cType___24t @ cCoq_2ePArith_2eBinPosDef_2ePos_2et )
    = $true ),
    inference(copy,[status(thm)],[2769]) ).

thf(3052,plain,
    ( ( cType___24t @ cCoq_2eQArith_2eQArith__base_2eQ )
    = $true ),
    inference(copy,[status(thm)],[2768]) ).

thf(3053,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enegreal )
    = $true ),
    inference(copy,[status(thm)],[2767]) ).

thf(3054,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enonnegreal )
    = $true ),
    inference(copy,[status(thm)],[2766]) ).

thf(3055,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enonposreal )
    = $true ),
    inference(copy,[status(thm)],[2765]) ).

thf(3056,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2enonzeroreal )
    = $true ),
    inference(copy,[status(thm)],[2764]) ).

thf(3057,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRIneq_2eposreal )
    = $true ),
    inference(copy,[status(thm)],[2763]) ).

thf(3058,plain,
    ( ( cType___24t @ cCoq_2eReals_2eRdefinitions_2eR )
    = $true ),
    inference(copy,[status(thm)],[2762]) ).

thf(3059,plain,
    ( ( cType___24t @ cCoq_2eStrings_2eAscii_2eascii )
    = $true ),
    inference(copy,[status(thm)],[2761]) ).

thf(3060,plain,
    ( ( cType___24t @ cCoq_2eStrings_2eString_2estring )
    = $true ),
    inference(copy,[status(thm)],[2760]) ).

thf(3061,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et )
    = $true ),
    inference(copy,[status(thm)],[2759]) ).

thf(3062,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et )
    = $true ),
    inference(copy,[status(thm)],[2758]) ).

thf(3063,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et )
    = $true ),
    inference(copy,[status(thm)],[2757]) ).

thf(3064,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et )
    = $true ),
    inference(copy,[status(thm)],[2756]) ).

thf(3065,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et )
    = $true ),
    inference(copy,[status(thm)],[2755]) ).

thf(3066,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et )
    = $true ),
    inference(copy,[status(thm)],[2754]) ).

thf(3067,plain,
    ( ( cType___24t @ cCoq_2eStructures_2eOrdersTac_2eord )
    = $true ),
    inference(copy,[status(thm)],[2753]) ).

thf(3068,plain,
    ( ( cType___24t @ cCoq_2eZArith_2eBinIntDef_2eZ_2et )
    = $true ),
    inference(copy,[status(thm)],[2752]) ).

thf(3069,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eEnvRing_2eMon )
    = $true ),
    inference(copy,[status(thm)],[2751]) ).

thf(3070,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eRMicromega_2eRcst )
    = $true ),
    inference(copy,[status(thm)],[2750]) ).

thf(3071,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eRingMicromega_2eOp1 )
    = $true ),
    inference(copy,[status(thm)],[2749]) ).

thf(3072,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eRingMicromega_2eOp2 )
    = $true ),
    inference(copy,[status(thm)],[2748]) ).

thf(3073,plain,
    ( ( cType___24t @ cCoq_2emicromega_2eZMicromega_2eZArithProof )
    = $true ),
    inference(copy,[status(thm)],[2747]) ).

thf(3074,plain,
    ( ( cType___24t @ cCoq_2esetoid__ring_2eInitialRing_2ehypo )
    = $true ),
    inference(copy,[status(thm)],[2746]) ).

thf(3075,plain,
    ( ( cType___24t @ cCoq_2esetoid__ring_2eRing__polynom_2eMon )
    = $true ),
    inference(copy,[status(thm)],[2745]) ).

thf(3076,plain,
    ( ( cType___24t @ cCoq_2esetoid__ring_2eRing__theory_2ering__kind )
    = $true ),
    inference(copy,[status(thm)],[2744]) ).

thf(3077,plain,
    ( ( cType___24t @ cHammer_2eTactics_2eReconstr_2eReconstrT )
    = $true ),
    inference(copy,[status(thm)],[2743]) ).

thf(3078,plain,
    ( ( cType___24t @ chahn_2eHahnBase_2eEquality_2etype )
    = $true ),
    inference(copy,[status(thm)],[2742]) ).

thf(3079,plain,
    ( ( c_24__type__90___24t @ chahn_2eHahnRelationsBasic_2eminus__rel )
    = $true ),
    inference(copy,[status(thm)],[2741]) ).

thf(3080,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cProp___24t @ V0__A )
          | ! [V1__B: $i] :
              ( ~ ( cProp___24t @ V1__B )
              | ~ ( p @ V0__A )
              | ~ ( p @ V1__B )
              | ( p @ V0__A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2926]) ).

thf(3081,plain,
    ( ( ! [V0__p: $i] :
          ( ~ ( cProp___24t @ V0__p )
          | ~ ( p @ V0__p )
          | ( p @ V0__p ) ) )
    = $true ),
    inference(copy,[status(thm)],[2925]) ).

thf(3082,plain,
    ( ( ! [V0__P: $i] :
          ~ ( cProp___24t @ V0__P )
      | $true )
    = $true ),
    inference(copy,[status(thm)],[2924]) ).

thf(3083,plain,
    ( ( ! [V0__P: $i] :
          ( ~ ( cProp___24t @ V0__P )
          | ( ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ( p @ V0__P )
                | ~ ( p @ V0__P )
                | ( p @ V1__Q ) )
            & ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ( p @ V0__P )
                | ~ ( p @ V1__Q )
                | ( p @ V1__Q ) )
            & ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ~ ( p @ V1__Q )
                | ~ ( p @ V0__P )
                | ( p @ V1__Q ) )
            & ! [V1__Q: $i] :
                ( ~ ( cProp___24t @ V1__Q )
                | ~ ( p @ V1__Q )
                | ~ ( p @ V1__Q )
                | ( p @ V1__Q ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2923]) ).

thf(3084,plain,
    ( ( ! [V0__P: $i] :
          ( ~ ( cProp___24t @ V0__P )
          | ! [V1__Q: $i] :
              ( ~ ( cProp___24t @ V1__Q )
              | ( ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ( p @ V0__P )
                    | ~ ( p @ V0__P )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) )
                & ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ( p @ V0__P )
                    | ~ ( p @ V2__R )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) )
                & ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ~ ( p @ V1__Q )
                    | ~ ( p @ V0__P )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) )
                & ! [V2__R: $i] :
                    ( ~ ( cProp___24t @ V2__R )
                    | ~ ( p @ V1__Q )
                    | ~ ( p @ V2__R )
                    | ( p @ V1__Q )
                    | ( p @ V2__R ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2922]) ).

thf(3085,plain,
    ( ( ! [V0__P: $i] :
          ( ~ ( cProp___24t @ V0__P )
          | ! [V1__Q: $i] :
              ( ~ ( cProp___24t @ V1__Q )
              | ~ ( p @ V0__P )
              | ( p @ V1__Q )
              | ( p @ V0__P ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2921]) ).

thf(3086,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__R: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ V0__A @ V1__R ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2920]) ).

thf(3087,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__R: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__R )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__R ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2919]) ).

thf(3088,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__x ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__y ) ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__y ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__x ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2918]) ).

thf(3089,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2917]) ).

thf(3090,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2916]) ).

thf(3091,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2915]) ).

thf(3092,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2914]) ).

thf(3093,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2913]) ).

thf(3094,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2912]) ).

thf(3095,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V1__x ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2911]) ).

thf(3096,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ( ! [V5__y: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V4__x ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__y @ V5__y ) ) )
                        & ! [V5__y: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__y @ V5__y ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V4__x ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2910]) ).

thf(3097,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2909]) ).

thf(3098,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2908]) ).

thf(3099,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2907]) ).

thf(3100,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2906]) ).

thf(3101,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V1__r ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2905]) ).

thf(3102,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2904]) ).

thf(3103,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__i: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__i )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__i ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2903]) ).

thf(3104,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2902]) ).

thf(3105,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2901]) ).

thf(3106,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__x ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__y ) ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__y ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__x ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2900]) ).

thf(3107,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r1 @ V3__r ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r2 @ V3__r ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2899]) ).

thf(3108,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                  | ! [V4__x: $i] :
                      ( ~ ( t @ V4__x @ V0__A )
                      | ( ! [V5__y: $i] :
                            ( ~ ( t @ V5__y @ V0__A )
                            | ~ ( p @ ( happ @ ( happ @ V1__r @ V4__x ) @ V5__y ) )
                            | ( p @ ( happ @ ( happ @ V2__r_27 @ V4__x ) @ V5__y ) ) )
                        & ! [V5__y: $i] :
                            ( ~ ( t @ V5__y @ V0__A )
                            | ~ ( p @ ( happ @ ( happ @ V2__r_27 @ V4__x ) @ V5__y ) )
                            | ( p @ ( happ @ ( happ @ V1__r @ V4__x ) @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2898]) ).

thf(3109,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r1 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2897]) ).

thf(3110,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2896]) ).

thf(3111,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__x @ V4__x ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2895]) ).

thf(3112,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V1__x )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V2__y ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V2__y )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ V0__A @ V1__x ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2894]) ).

thf(3113,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2893]) ).

thf(3114,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V1__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ V0__A @ V2__y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2892]) ).

thf(3115,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ! [V3__r3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ V3__r3 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V3__r3 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2891]) ).

thf(3116,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2890]) ).

thf(3117,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r1 )
              | ! [V2__r2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r1 @ V2__r2 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r2 @ V1__r1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2889]) ).

thf(3118,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V1__r ) @ V1__r ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2888]) ).

thf(3119,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2887]) ).

thf(3120,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V1__r ) @ V2__r_27 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2886]) ).

thf(3121,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V4__x @ V5__y )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2885]) ).

thf(3122,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ! [V2__y: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__x @ V2__y ) )
                  | ! [V4__x: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__x )
                      | ! [V5__y: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V5__y )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__x @ V5__y ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__x @ V4__x ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__y @ V5__y ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2884]) ).

thf(3123,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__x: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__x )
              | ( ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V1__x ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V2__y ) ) )
                & ! [V2__y: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__y )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__x @ V2__y )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V2__y ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ V0__A @ V1__x ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2883]) ).

thf(3124,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2882]) ).

thf(3125,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V0__A @ V1__r @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V1__r ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2881]) ).

thf(3126,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ V1__r ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2880]) ).

thf(3127,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V2__r_27 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ V0__A @ V1__r ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2879]) ).

thf(3128,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2878]) ).

thf(3129,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2877]) ).

thf(3130,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2876]) ).

thf(3131,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2875]) ).

thf(3132,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2874]) ).

thf(3133,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2873]) ).

thf(3134,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( ! [V3__s: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__s ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__s ) ) ) )
                    & ! [V3__s: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__s ) ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__s ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2872]) ).

thf(3135,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V4__s_27 @ V3__s ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2871]) ).

thf(3136,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V1__r ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2870]) ).

thf(3137,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V1__r ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2869]) ).

thf(3138,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V1__r ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2868]) ).

thf(3139,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2867]) ).

thf(3140,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2866]) ).

thf(3141,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V1__r @ V3__s ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2865]) ).

thf(3142,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2864]) ).

thf(3143,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2863]) ).

thf(3144,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2862]) ).

thf(3145,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2861]) ).

thf(3146,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V1__r ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ V0__A @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2860]) ).

thf(3147,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V3__r_27_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2859]) ).

thf(3148,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ V0__A @ V1__r @ V2__r_27 ) @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2858]) ).

thf(3149,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__s: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__s )
                      | ! [V4__s_27: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V4__s_27 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V3__s @ V4__s_27 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V3__s ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V4__s_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2857]) ).

thf(3150,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( ! [V3__r_27_27: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) )
                    & ! [V3__r_27_27: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2856]) ).

thf(3151,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2855]) ).

thf(3152,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2854]) ).

thf(3153,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V2__r_27 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V1__r @ V2__r_27 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2853]) ).

thf(3154,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ! [V3__r_27_27: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V3__r_27_27 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V3__r_27_27 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ V0__A @ V2__r_27 @ V3__r_27_27 ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2852]) ).

thf(3155,plain,
    ( ( ! [V0__A: $i] :
          ( ~ ( cType___24t @ V0__A )
          | ! [V1__r: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V1__r )
              | ! [V2__r_27: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ V0__A @ V2__r_27 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V0__A @ V1__r @ V2__r_27 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V2__r_27 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ V0__A @ V1__r ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2851]) ).

thf(3156,plain,
    ( ( ! [V_24X1: $i] :
          ( ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 )
          = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a1 @ V_24X1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2664]) ).

thf(3157,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i] :
          ( ~ ( c_24__lam__35673___24a2 @ V_24X1 @ V_24X2 )
          | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ V_24X1 ) @ V_24X2 ) ) )
      & ! [V_24X1: $i,V_24X2: $i] :
          ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ V_24X1 ) @ V_24X2 ) )
          | ( c_24__lam__35673___24a2 @ V_24X1 @ V_24X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2850]) ).

thf(3158,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ! [V_24X4: $i,V_24X5: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 )
              | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 ) ) )
          & ! [V_24X4: $i,V_24X5: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2849]) ).

thf(3159,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i,V_24X4: $i,V_24X5: $i] :
          ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) @ V_24X4 ) @ V_24X5 )
          = ( c_24__lam__45594___24a5 @ V_24X1 @ V_24X2 @ V_24X3 @ V_24X4 @ V_24X5 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2661]) ).

thf(3160,plain,
    ( ( ! [V_24X1: $i] :
          ( ! [V_24X2: $i,V_24X3: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V_24X1 @ V_24X2 @ V_24X3 )
              | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) ) )
          & ! [V_24X2: $i,V_24X3: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ V_24X1 ) @ V_24X2 ) @ V_24X3 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[2848]) ).

thf(3161,plain,
    ( ( ! [V_24X1: $i,V_24X2: $i,V_24X3: $i] :
          ( ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2einclusion @ V_24X1 ) @ V_24X2 ) @ V_24X3 )
          = ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ V_24X1 @ V_24X2 @ V_24X3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[2659]) ).

thf(3162,plain,
    ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ cr @ cr_27 ) @ c_24__lam__35673 ) )
    = $true ),
    inference(copy,[status(thm)],[2847]) ).

thf(3163,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cProp___24t @ SX0 )
          | ~ ( ~ ~ ( ~ ! [SX1: $i] :
                          ( ~ ( cProp___24t @ SX1 )
                          | ( p @ SX0 )
                          | ~ ( p @ SX0 )
                          | ( p @ SX1 ) )
                    | ~ ! [SX1: $i] :
                          ( ~ ( cProp___24t @ SX1 )
                          | ( p @ SX0 )
                          | ~ ( p @ SX1 )
                          | ( p @ SX1 ) ) )
              | ~ ~ ( ~ ! [SX1: $i] :
                          ( ~ ( cProp___24t @ SX1 )
                          | ~ ( p @ SX1 )
                          | ~ ( p @ SX0 )
                          | ( p @ SX1 ) )
                    | ~ ! [SX1: $i] :
                          ( ~ ( cProp___24t @ SX1 )
                          | ~ ( p @ SX1 )
                          | ~ ( p @ SX1 )
                          | ( p @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3083]) ).

thf(3164,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) )
                    | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( sK2_SY468 @ SX0 ) )
                          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ SX0 @ ( sK1_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK2_SY468 @ SX0 ) ) ) ) )
                | ( c_24__type__96___24t @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( c_24__type__96___24t @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( cType___24t @ SX1 )
                    | ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3031]) ).

thf(3165,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ~ ( ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SX0 @ SX1 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SX0 @ SX2 ) )
                  | ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SX0 @ SX2 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3112]) ).

thf(3166,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                  | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SX0 ) @ SX1 ) @ SX2 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SX0 ) @ SX1 ) @ SX2 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3160]) ).

thf(3167,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( c_24__lam__35673___24a2 @ SX0 @ SX1 )
                | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) )
                | ( c_24__lam__35673___24a2 @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3157]) ).

thf(3168,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( c_24__lam__3971___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                  | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) )
            | ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                        | ( c_24__lam__3971___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                        | ( c_24__lam__3971___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3012]) ).

thf(3169,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ( ( happ @ SX2 @ SX3 )
                   != ( happ @ SX2 @ SX4 ) )
                  | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
            | ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                  | ( ( happ @ SX2 @ SX3 )
                    = ( happ @ SX2 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2997]) ).

thf(3170,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                  | ! [SX3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                      | ~ ( ~ ! [SX4: $i] :
                                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX4 )
                                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX3 @ SX4 )
                                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX3 ) )
                                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX2 @ SX4 ) ) )
                          | ~ ! [SX4: $i] :
                                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX4 )
                                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX3 @ SX4 )
                                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX2 @ SX4 ) )
                                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX3 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3096]) ).

thf(3171,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( c_24__lam__7591___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) )
                  | ( c_24__lam__7591___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3015]) ).

thf(3172,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ~ ( ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SX0 @ SX1 ) )
                        | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SX0 @ SX2 ) ) )
                  | ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SX0 @ SX2 ) )
                        | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SX0 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3123]) ).

thf(3173,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SX0 ) )
                    | ~ ~ ( cType___24t @ ( happ @ SX0 @ ( sK12_Vv__CANONICAL__0 @ SX0 ) ) ) )
                | ( c_24__type__28___24t @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( c_24__type__28___24t @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( cType___24t @ SX1 )
                    | ( cType___24t @ ( happ @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3027]) ).

thf(3174,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( happ @ SX1 @ SX3 ) )
                  | ( p @ ( happ @ SX2 @ SX3 ) )
                  | ( chahn_2eHahnSets_2eset__minus___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( p @ ( happ @ SX1 @ SX3 ) ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ~ ( p @ ( happ @ SX2 @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3007]) ).

thf(3175,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( c_24__lam__7587___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) )
                  | ( c_24__lam__7587___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3014]) ).

thf(3176,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SX0 @ SX1 @ SX2 )
                  | ~ ( p @ ( happ @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ( p @ ( happ @ SX1 @ SX2 ) )
                  | ( chahn_2eHahnSets_2eset__compl___24a3 @ SX0 @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3004]) ).

thf(3177,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                  | ~ ( ~ ! [SX3: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SX0 @ SX1 @ SX2 ) @ SX3 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SX0 @ SX2 @ SX3 ) ) ) )
                      | ~ ! [SX3: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SX0 @ SX2 @ SX3 ) ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3134]) ).

thf(3178,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                  | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) )
            | ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                        | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                        | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2992]) ).

thf(3179,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cProp___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cProp___24t @ SX1 )
              | ~ ( ~ ~ ( ~ ! [SX2: $i] :
                              ( ~ ( cProp___24t @ SX2 )
                              | ( p @ SX0 )
                              | ~ ( p @ SX0 )
                              | ( p @ SX1 )
                              | ( p @ SX2 ) )
                        | ~ ! [SX2: $i] :
                              ( ~ ( cProp___24t @ SX2 )
                              | ( p @ SX0 )
                              | ~ ( p @ SX2 )
                              | ( p @ SX1 )
                              | ( p @ SX2 ) ) )
                  | ~ ~ ( ~ ! [SX2: $i] :
                              ( ~ ( cProp___24t @ SX2 )
                              | ~ ( p @ SX1 )
                              | ~ ( p @ SX0 )
                              | ( p @ SX1 )
                              | ( p @ SX2 ) )
                        | ~ ! [SX2: $i] :
                              ( ~ ( cProp___24t @ SX2 )
                              | ~ ( p @ SX1 )
                              | ~ ( p @ SX2 )
                              | ( p @ SX1 )
                              | ( p @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3084]) ).

thf(3180,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ SX1 @ SX3 ) )
                  | ~ ( p @ ( happ @ SX2 @ SX4 ) )
                  | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
            | ~ ~ ( ~ ! [SX3: $i] :
                        ( ! [SX4: $i] :
                            ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ( p @ ( happ @ SX1 @ SX3 ) ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ( p @ ( happ @ SX2 @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2996]) ).

thf(3181,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
                    | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) ) )
                | ( c_24__type__11748___24t @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( c_24__type__11748___24t @ SX0 @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3024]) ).

thf(3182,plain,
    ( ( ~ ( ~ ( ! [SX0: $i] :
                  ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 )
              | $true )
          | ~ ( ~ $true
              | ! [SX0: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2989]) ).

thf(3183,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                  | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SX0 ) @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) ) )
            | ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SX0 ) @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) )
                  | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3158]) ).

thf(3184,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX2 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX2 @ SX1 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 ) )
            | ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX2 ) ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX2 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2974]) ).

thf(3185,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) )
                | ~ ( p @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( p @ SX1 )
                | ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3022]) ).

thf(3186,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( happ @ SX1 @ SX3 ) )
                  | ~ ( p @ ( happ @ SX2 @ SX3 ) )
                  | ( c_24__lam__40532___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( c_24__lam__40532___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( p @ ( happ @ SX1 @ SX3 ) ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( c_24__lam__40532___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( p @ ( happ @ SX2 @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3013]) ).

thf(3187,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ~ ( ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SX0 @ SX1 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SX0 @ SX2 ) ) )
                  | ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SX0 @ SX2 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SX0 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3106]) ).

thf(3188,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( SX2 = SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ( SX2 != SX3 )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2993]) ).

thf(3189,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( ~ ( t @ ( sK18_V3__x @ SX2 @ SX1 @ SX0 ) @ SX0 )
                      | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                            | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SX1 @ ( sK18_V3__x @ SX2 @ SX1 @ SX0 ) ) @ ( sK19_SY480 @ SX2 @ SX1 @ SX0 ) ) )
                                  | ~ ~ ( p @ ( happ @ ( happ @ SX2 @ ( sK18_V3__x @ SX2 @ SX1 @ SX0 ) ) @ ( sK19_SY480 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX2 ) )
                  | ! [SX3: $i] :
                      ( ~ ( t @ SX3 @ SX0 )
                      | ! [SX4: $i] :
                          ( ~ ( t @ SX4 @ SX0 )
                          | ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                          | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2990]) ).

thf(3190,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2995]) ).

thf(3191,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                  | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                  | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
            | ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3001]) ).

thf(3192,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK17_Vv__CANONICAL__2 @ SX2 @ SX1 @ SX0 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ SX2 @ ( sK17_Vv__CANONICAL__2 @ SX2 @ SX1 @ SX0 ) ) ) )
                  | ( c_24__type__11699___24t @ SX0 @ SX1 @ SX2 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( c_24__type__11699___24t @ SX0 @ SX1 @ SX2 )
                  | ! [SX3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ SX2 @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3023]) ).

thf(3193,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( c_24__lam__16___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                  | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) )
            | ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                  | ( c_24__lam__16___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3009]) ).

thf(3194,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ ( c_24__prop__35356___24a3 @ SX0 @ SX1 @ SX2 ) )
                  | ( p @ SX1 )
                  | ( p @ SX2 ) )
            | ~ ~ ( ~ ! [SX1: $i] :
                        ( ~ ( p @ SX1 )
                        | ! [SX2: $i] : ( p @ ( c_24__prop__35356___24a3 @ SX0 @ SX1 @ SX2 ) ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( p @ SX2 )
                        | ( p @ ( c_24__prop__35356___24a3 @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3020]) ).

thf(3195,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                  | ~ ( p @ ( happ @ SX1 @ SX3 ) )
                  | ~ ( p @ ( happ @ SX1 @ SX4 ) )
                  | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
            | ~ ~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                              | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) )
                        | ~ ! [SX3: $i] :
                              ( ! [SX4: $i] :
                                  ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                              | ( p @ ( happ @ SX1 @ SX3 ) ) ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ( p @ ( happ @ SX1 @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3003]) ).

thf(3196,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ( SX1 != SX2 )
                  | ( p @ ( c_24__prop__35353___24a3 @ SX0 @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ ( c_24__prop__35353___24a3 @ SX0 @ SX1 @ SX2 ) )
                  | ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3018]) ).

thf(3197,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
                    | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK14_SY479 @ SX1 @ SX0 ) )
                          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) @ ( sK14_SY479 @ SX1 @ SX0 ) ) ) ) )
                | ( c_24__type__11829___24t @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( c_24__type__11829___24t @ SX0 @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                    | ! [SX3: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3026]) ).

thf(3198,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) )
                  | ( SX2 = SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
                  | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                              ( ( SX2 != SX3 )
                              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
                        | ~ ! [SX2: $i,SX3: $i] :
                              ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) )
                              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2994]) ).

thf(3199,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                  | ( p @ ( happ @ SX3 @ ( happ @ SX2 @ SX4 ) ) ) )
            | ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ SX3 @ ( happ @ SX2 @ SX4 ) ) )
                  | ( chahn_2eHahnSets_2eset__map___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3006]) ).

thf(3200,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ( SX2 != SX3 )
                  | ~ ( p @ ( happ @ SX1 @ SX2 ) )
                  | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( SX2 = SX3 ) )
                  | ~ ! [SX2: $i] :
                        ( ! [SX3: $i] :
                            ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( p @ ( happ @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2998]) ).

thf(3201,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) )
                    | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK4_SY469 @ SX0 ) )
                          | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK5_SY471 @ SX0 ) )
                                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK3_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK4_SY469 @ SX0 ) ) @ ( sK5_SY471 @ SX0 ) ) ) ) ) )
                | ( c_24__type__90___24t @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( c_24__type__90___24t @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( cType___24t @ SX1 )
                    | ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                        | ! [SX3: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX3 )
                            | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3030]) ).

thf(3202,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ~ ( ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SX0 @ SX1 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SX0 @ SX2 ) ) )
                  | ~ ! [SX2: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SX0 @ SX2 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SX0 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3088]) ).

thf(3203,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SX0 ) )
                    | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SX0 ) )
                          | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SX0 ) )
                                | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SX0 ) )
                                      | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK8_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK9_SY473 @ SX0 ) ) @ ( sK10_SY476 @ SX0 ) ) @ ( sK11_SY478 @ SX0 ) ) ) ) ) ) )
                | ( c_24__type__4733___24t @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( c_24__type__4733___24t @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( cType___24t @ SX1 )
                    | ! [SX2: $i] :
                        ( ~ ( cType___24t @ SX2 )
                        | ! [SX3: $i] :
                            ( ~ ( cType___24t @ SX3 )
                            | ! [SX4: $i] :
                                ( ~ ( cType___24t @ SX4 )
                                | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3028]) ).

thf(3204,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                  | ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                  | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 ) )
            | ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) ) )
                  | ~ ! [SX3: $i,SX4: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
                        | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2999]) ).

thf(3205,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX2 ) )
                  | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2991]) ).

thf(3206,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ SX1 )
                  | ~ ( p @ SX2 )
                  | ( p @ ( c_24__prop__35355___24a3 @ SX0 @ SX1 @ SX2 ) ) )
            | ~ ~ ( ~ ! [SX1: $i] :
                        ( ! [SX2: $i] :
                            ~ ( p @ ( c_24__prop__35355___24a3 @ SX0 @ SX1 @ SX2 ) )
                        | ( p @ SX1 ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( p @ ( c_24__prop__35355___24a3 @ SX0 @ SX1 @ SX2 ) )
                        | ( p @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3019]) ).

thf(3207,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                  | ( p @ ( happ @ SX1 @ SX3 ) )
                  | ( p @ ( happ @ SX2 @ SX3 ) ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( p @ ( happ @ SX1 @ SX3 ) )
                        | ( chahn_2eHahnSets_2eset__union___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( p @ ( happ @ SX2 @ SX3 ) )
                        | ( chahn_2eHahnSets_2eset__union___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3008]) ).

thf(3208,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ~ ( ~ ! [SX1: $i] :
                        ( ( p @ SX1 )
                        | ! [SX2: $i] : ( p @ ( c_24__prop__35357___24a3 @ SX0 @ SX1 @ SX2 ) ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( p @ SX2 )
                        | ( p @ ( c_24__prop__35357___24a3 @ SX0 @ SX1 @ SX2 ) ) ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( p @ ( c_24__prop__35357___24a3 @ SX0 @ SX1 @ SX2 ) )
                  | ~ ( p @ SX1 )
                  | ( p @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3021]) ).

thf(3209,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SX0 @ SX1 @ SX2 )
                  | ! [SX3: $i] :
                      ( ~ ( t @ SX3 @ SX0 )
                      | ~ ( ~ ! [SX4: $i] :
                                ( ~ ( t @ SX4 @ SX0 )
                                | ~ ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) )
                                | ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) ) )
                          | ~ ! [SX4: $i] :
                                ( ~ ( t @ SX4 @ SX0 )
                                | ~ ( p @ ( happ @ ( happ @ SX2 @ SX3 ) @ SX4 ) )
                                | ( p @ ( happ @ ( happ @ SX1 @ SX3 ) @ SX4 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3108]) ).

thf(3210,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( happ @ SX1 @ SX3 ) )
                  | ~ ( p @ ( happ @ SX2 @ SX3 ) )
                  | ( chahn_2eHahnSets_2eset__inter___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( p @ ( happ @ SX1 @ SX3 ) ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SX0 @ SX1 @ SX2 @ SX3 )
                        | ( p @ ( happ @ SX2 @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3005]) ).

thf(3211,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( cType___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                  | ~ ( ~ ! [SX3: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX2 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SX0 @ SX2 @ SX3 ) ) ) )
                      | ~ ! [SX3: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ SX3 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SX0 @ SX1 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SX0 @ SX2 @ SX3 ) ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3150]) ).

thf(3212,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ! [SX4: $i,SX5: $i] :
                  ( ~ ( c_24__lam__7800___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
                  | ( p @ ( happ @ ( happ @ SX3 @ ( happ @ SX2 @ SX4 ) ) @ ( happ @ SX2 @ SX5 ) ) ) )
            | ~ ! [SX4: $i,SX5: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX3 @ ( happ @ SX2 @ SX4 ) ) @ ( happ @ SX2 @ SX5 ) ) )
                  | ( c_24__lam__7800___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3016]) ).

thf(3213,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ! [SX4: $i,SX5: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
                  | ( p @ ( happ @ ( happ @ SX3 @ ( happ @ SX2 @ SX4 ) ) @ ( happ @ SX2 @ SX5 ) ) ) )
            | ~ ! [SX4: $i,SX5: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SX3 @ ( happ @ SX2 @ SX4 ) ) @ ( happ @ SX2 @ SX5 ) ) )
                  | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3000]) ).

thf(3214,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( sK15_Vv__CANONICAL__2 @ SX2 @ SX1 @ SX0 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX2 @ ( sK15_Vv__CANONICAL__2 @ SX2 @ SX1 @ SX0 ) ) ) )
                  | ( c_24__type__11787___24t @ SX0 @ SX1 @ SX2 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( c_24__type__11787___24t @ SX0 @ SX1 @ SX2 )
                  | ! [SX3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX2 @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3025]) ).

thf(3215,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ( SX2 != SX3 )
                  | ( p @ ( c_24__prop__35352___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( p @ ( c_24__prop__35352___24a4 @ SX0 @ SX1 @ SX2 @ SX3 ) )
                  | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3017]) ).

thf(3216,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SX0 ) )
                    | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SX0 ) )
                          | ~ ~ ( cType___24t @ ( happ @ ( happ @ SX0 @ ( sK6_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK7_SY472 @ SX0 ) ) ) ) )
                | ( c_24__type__52___24t @ SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( c_24__type__52___24t @ SX0 )
                | ! [SX1: $i] :
                    ( ~ ( cType___24t @ SX1 )
                    | ! [SX2: $i] :
                        ( ~ ( cType___24t @ SX2 )
                        | ( cType___24t @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3029]) ).

thf(3217,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ~ ( ~ ! [SX4: $i,SX5: $i] :
                  ( ( ( happ @ SX2 @ SX4 )
                   != ( happ @ SX2 @ SX5 ) )
                  | ~ ( p @ ( happ @ ( happ @ SX3 @ SX4 ) @ SX5 ) )
                  | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 ) )
            | ~ ~ ( ~ ! [SX4: $i,SX5: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
                        | ( ( happ @ SX2 @ SX4 )
                          = ( happ @ SX2 @ SX5 ) ) )
                  | ~ ! [SX4: $i,SX5: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 @ SX5 )
                        | ( p @ ( happ @ ( happ @ SX3 @ SX4 ) @ SX5 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3002]) ).

thf(3218,plain,
    ! [SV1: $i] :
      ( ( ! [SY481: $i,SY482: $i,SY483: $i,SY484: $i] :
            ( ( c_24__lam__45594___24a5 @ SV1 @ SY481 @ SY482 @ SY483 @ SY484 )
            = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SY481 @ ( happ @ SY483 @ SY484 ) @ SY482 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2975]) ).

thf(3219,plain,
    ! [SV2: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV2 )
        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ SV2 @ SV2 ) @ c_24__lam__35673 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2979]) ).

thf(3220,plain,
    ! [SV3: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV3 )
        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ SV3 ) @ c_24__lam__35673 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2980]) ).

thf(3221,plain,
    ! [SV4: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV4 )
        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ SV4 @ c_24__lam__35673 ) @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2981]) ).

thf(3222,plain,
    ! [SV5: $i] :
      ( ( ~ ( cType___24t @ SV5 )
        | ! [SY485: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY485 )
            | ! [SY486: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY486 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY485 @ SY486 )
                | ! [SY487: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY487 )
                    | ! [SY488: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY488 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY487 @ SY488 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY485 @ SY487 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY486 @ SY488 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2982]) ).

thf(3223,plain,
    ! [SV6: $i] :
      ( ( ~ ( cType___24t @ SV6 )
        | ! [SY489: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV6 @ SY489 )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV6 @ SY489 @ SY489 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2984]) ).

thf(3224,plain,
    ! [SV7: $i] :
      ( ( ! [SY490: $i,SY491: $i] :
            ( ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV7 ) @ SY490 ) @ SY491 )
            = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV7 @ SY490 @ SY491 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2985]) ).

thf(3225,plain,
    ( ( p @ c_24False )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2987]) ).

thf(3226,plain,
    ! [SV8: $i] :
      ( ( ! [SY492: $i,SY493: $i,SY494: $i] :
            ( ( c_24__lam__33077___24a4 @ SV8 @ SY492 @ SY493 @ SY494 )
            = ( happ @ SY493 @ SY494 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3010]) ).

thf(3227,plain,
    ! [SV9: $i] :
      ( ( ! [SY495: $i,SY496: $i,SY497: $i] :
            ( ( c_24__lam__33085___24a4 @ SV9 @ SY495 @ SY496 @ SY497 )
            = ( happ @ SY496 @ SY497 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3011]) ).

thf(3228,plain,
    ! [SV10: $i] :
      ( ( ~ ( cProp___24t @ SV10 )
        | ! [SY498: $i] :
            ( ~ ( cProp___24t @ SY498 )
            | ~ ( p @ SV10 )
            | ~ ( p @ SY498 )
            | ( p @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3080]) ).

thf(3229,plain,
    ! [SV11: $i] :
      ( ( ~ ( cProp___24t @ SV11 )
        | ~ ( p @ SV11 )
        | ( p @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3081]) ).

thf(3230,plain,
    ( ( ( ! [V0__P: $i] :
            ~ ( cProp___24t @ V0__P ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3082]) ).

thf(3231,plain,
    ! [SV12: $i] :
      ( ( ~ ( cProp___24t @ SV12 )
        | ! [SY499: $i] :
            ( ~ ( cProp___24t @ SY499 )
            | ~ ( p @ SV12 )
            | ( p @ SY499 )
            | ( p @ SV12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3085]) ).

thf(3232,plain,
    ! [SV13: $i] :
      ( ( ~ ( cType___24t @ SV13 )
        | ! [SY500: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV13 @ SY500 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SY500 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SY500 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3086]) ).

thf(3233,plain,
    ! [SV14: $i] :
      ( ( ~ ( cType___24t @ SV14 )
        | ! [SY501: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV14 @ SY501 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SY501 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SY501 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3087]) ).

thf(3234,plain,
    ! [SV15: $i] :
      ( ( ~ ( cType___24t @ SV15 )
        | ! [SY502: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY502 )
            | ! [SY503: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY503 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SY502 @ SY503 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY502 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY503 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3089]) ).

thf(3235,plain,
    ! [SV16: $i] :
      ( ( ~ ( cType___24t @ SV16 )
        | ! [SY504: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY504 )
            | ! [SY505: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY505 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SY504 @ SY505 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY504 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY505 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3090]) ).

thf(3236,plain,
    ! [SV17: $i] :
      ( ( ~ ( cType___24t @ SV17 )
        | ! [SY506: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY506 )
            | ! [SY507: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY507 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SY506 @ SY507 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY506 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY507 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3091]) ).

thf(3237,plain,
    ! [SV18: $i] :
      ( ( ~ ( cType___24t @ SV18 )
        | ! [SY508: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY508 )
            | ! [SY509: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY509 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SY508 @ SY509 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY508 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY509 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3092]) ).

thf(3238,plain,
    ! [SV19: $i] :
      ( ( ~ ( cType___24t @ SV19 )
        | ! [SY510: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY510 )
            | ! [SY511: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY511 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SY510 @ SY511 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY510 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY511 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3093]) ).

thf(3239,plain,
    ! [SV20: $i] :
      ( ( ~ ( cType___24t @ SV20 )
        | ! [SY512: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY512 )
            | ! [SY513: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY513 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SY512 @ SY513 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY512 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY513 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3094]) ).

thf(3240,plain,
    ! [SV21: $i] :
      ( ( ~ ( cType___24t @ SV21 )
        | ! [SY514: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY514 )
            | ! [SY515: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY515 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SY514 @ SY515 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY514 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY515 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3095]) ).

thf(3241,plain,
    ! [SV22: $i] :
      ( ( ~ ( cType___24t @ SV22 )
        | ! [SY516: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY516 )
            | ! [SY517: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY517 )
                | ! [SY518: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY518 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY516 @ SY517 ) @ SY518 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY516 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY517 @ SY518 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3097]) ).

thf(3242,plain,
    ! [SV23: $i] :
      ( ( ~ ( cType___24t @ SV23 )
        | ! [SY519: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY519 )
            | ! [SY520: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY520 )
                | ! [SY521: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY521 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY519 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY520 @ SY521 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY520 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY519 @ SY521 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3098]) ).

thf(3243,plain,
    ! [SV24: $i] :
      ( ( ~ ( cType___24t @ SV24 )
        | ! [SY522: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY522 )
            | ! [SY523: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY523 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY522 @ SY523 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY523 @ SY522 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3099]) ).

thf(3244,plain,
    ! [SV25: $i] :
      ( ( ~ ( cType___24t @ SV25 )
        | ! [SY524: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV25 @ SY524 )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV25 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV25 @ SY524 @ SY524 ) @ SY524 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3100]) ).

thf(3245,plain,
    ! [SV26: $i] :
      ( ( ~ ( cType___24t @ SV26 )
        | ! [SY525: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY525 )
            | ! [SY526: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY526 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SY525 @ SY526 ) )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SY526 @ SY525 ) @ SY525 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3101]) ).

thf(3246,plain,
    ! [SV27: $i] :
      ( ( ~ ( cType___24t @ SV27 )
        | ! [SY527: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY527 )
            | ! [SY528: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY528 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SY527 @ SY528 ) )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SY527 @ SY528 ) @ SY527 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3102]) ).

thf(3247,plain,
    ! [SV28: $i] :
      ( ( ~ ( cType___24t @ SV28 )
        | ! [SY529: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY529 )
            | ! [SY530: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY530 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SY529 @ SY530 ) @ SY529 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3103]) ).

thf(3248,plain,
    ! [SV29: $i] :
      ( ( ~ ( cType___24t @ SV29 )
        | ! [SY531: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY531 )
            | ! [SY532: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY532 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY531 @ SY532 )
                | ! [SY533: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY533 )
                    | ! [SY534: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY534 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY533 @ SY534 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY531 @ SY533 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY532 @ SY534 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3104]) ).

thf(3249,plain,
    ! [SV30: $i] :
      ( ( ~ ( cType___24t @ SV30 )
        | ! [SY535: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY535 )
            | ! [SY536: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY536 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY535 @ SY536 ) )
                | ! [SY537: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY537 )
                    | ! [SY538: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY538 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY537 @ SY538 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY535 @ SY537 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY536 @ SY538 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3105]) ).

thf(3250,plain,
    ! [SV31: $i] :
      ( ( ~ ( cType___24t @ SV31 )
        | ! [SY539: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY539 )
            | ! [SY540: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY540 )
                | ! [SY541: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY541 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SY539 @ SY540 ) @ SY541 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY539 @ SY541 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY540 @ SY541 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3107]) ).

thf(3251,plain,
    ! [SV32: $i] :
      ( ( ~ ( cType___24t @ SV32 )
        | ! [SY542: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY542 )
            | ! [SY543: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY543 )
                | ! [SY544: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY544 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY542 @ SY543 ) @ SY544 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY542 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY543 @ SY544 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3109]) ).

thf(3252,plain,
    ! [SV33: $i] :
      ( ( ~ ( cType___24t @ SV33 )
        | ! [SY545: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY545 )
            | ! [SY546: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY546 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY545 @ SY546 )
                | ! [SY547: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY547 )
                    | ! [SY548: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY548 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY547 @ SY548 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY545 @ SY547 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY546 @ SY548 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3110]) ).

thf(3253,plain,
    ! [SV34: $i] :
      ( ( ~ ( cType___24t @ SV34 )
        | ! [SY549: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY549 )
            | ! [SY550: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY550 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY549 @ SY550 ) )
                | ! [SY551: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY551 )
                    | ! [SY552: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY552 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY551 @ SY552 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY549 @ SY551 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY550 @ SY552 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3111]) ).

thf(3254,plain,
    ! [SV35: $i] :
      ( ( ~ ( cType___24t @ SV35 )
        | ! [SY553: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY553 )
            | ! [SY554: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY554 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SY553 @ SY554 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY553 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY554 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3113]) ).

thf(3255,plain,
    ! [SV36: $i] :
      ( ( ~ ( cType___24t @ SV36 )
        | ! [SY555: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY555 )
            | ! [SY556: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY556 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SY555 @ SY556 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY555 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY556 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3114]) ).

thf(3256,plain,
    ! [SV37: $i] :
      ( ( ~ ( cType___24t @ SV37 )
        | ! [SY557: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY557 )
            | ! [SY558: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY558 )
                | ! [SY559: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY559 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY557 @ SY558 ) @ SY559 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY557 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY558 @ SY559 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3115]) ).

thf(3257,plain,
    ! [SV38: $i] :
      ( ( ~ ( cType___24t @ SV38 )
        | ! [SY560: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY560 )
            | ! [SY561: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY561 )
                | ! [SY562: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY562 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY560 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY561 @ SY562 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY561 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY560 @ SY562 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3116]) ).

thf(3258,plain,
    ! [SV39: $i] :
      ( ( ~ ( cType___24t @ SV39 )
        | ! [SY563: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY563 )
            | ! [SY564: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY564 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY563 @ SY564 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY564 @ SY563 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3117]) ).

thf(3259,plain,
    ! [SV40: $i] :
      ( ( ~ ( cType___24t @ SV40 )
        | ! [SY565: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV40 @ SY565 )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV40 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV40 @ SY565 @ SY565 ) @ SY565 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3118]) ).

thf(3260,plain,
    ! [SV41: $i] :
      ( ( ~ ( cType___24t @ SV41 )
        | ! [SY566: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY566 )
            | ! [SY567: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY567 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SY566 @ SY567 ) )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SY566 @ SY567 ) @ SY567 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3119]) ).

thf(3261,plain,
    ! [SV42: $i] :
      ( ( ~ ( cType___24t @ SV42 )
        | ! [SY568: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY568 )
            | ! [SY569: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY569 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SY568 @ SY569 ) )
                | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SY569 @ SY568 ) @ SY569 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3120]) ).

thf(3262,plain,
    ! [SV43: $i] :
      ( ( ~ ( cType___24t @ SV43 )
        | ! [SY570: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY570 )
            | ! [SY571: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY571 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY570 @ SY571 )
                | ! [SY572: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY572 )
                    | ! [SY573: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY573 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY572 @ SY573 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY570 @ SY572 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY571 @ SY573 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3121]) ).

thf(3263,plain,
    ! [SV44: $i] :
      ( ( ~ ( cType___24t @ SV44 )
        | ! [SY574: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY574 )
            | ! [SY575: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY575 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY574 @ SY575 ) )
                | ! [SY576: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY576 )
                    | ! [SY577: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY577 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY576 @ SY577 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY574 @ SY576 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY575 @ SY577 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3122]) ).

thf(3264,plain,
    ! [SV45: $i] :
      ( ( ~ ( cType___24t @ SV45 )
        | ! [SY578: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY578 )
            | ! [SY579: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY579 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SY578 @ SY579 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SY578 @ SY579 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3124]) ).

thf(3265,plain,
    ! [SV46: $i] :
      ( ( ~ ( cType___24t @ SV46 )
        | ! [SY580: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY580 )
            | ! [SY581: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY581 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SY580 @ SY581 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SY581 @ SY580 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3125]) ).

thf(3266,plain,
    ! [SV47: $i] :
      ( ( ~ ( cType___24t @ SV47 )
        | ! [SY582: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY582 )
            | ! [SY583: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY583 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SY582 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SY582 @ SY583 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3126]) ).

thf(3267,plain,
    ! [SV48: $i] :
      ( ( ~ ( cType___24t @ SV48 )
        | ! [SY584: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY584 )
            | ! [SY585: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY585 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SY584 @ SY585 ) )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY585 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY584 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3127]) ).

thf(3268,plain,
    ! [SV49: $i] :
      ( ( ~ ( cType___24t @ SV49 )
        | ! [SY586: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY586 )
            | ! [SY587: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY587 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SY586 @ SY587 ) @ SY586 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3128]) ).

thf(3269,plain,
    ! [SV50: $i] :
      ( ( ~ ( cType___24t @ SV50 )
        | ! [SY588: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY588 )
            | ! [SY589: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY589 )
                | ! [SY590: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY590 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SY588 @ SY590 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SY588 @ SY589 ) @ SY590 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3129]) ).

thf(3270,plain,
    ! [SV51: $i] :
      ( ( ~ ( cType___24t @ SV51 )
        | ! [SY591: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY591 )
            | ! [SY592: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY592 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SY591 @ SY592 ) @ SY592 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3130]) ).

thf(3271,plain,
    ! [SV52: $i] :
      ( ( ~ ( cType___24t @ SV52 )
        | ! [SY593: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY593 )
            | ! [SY594: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY594 )
                | ! [SY595: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY595 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SY594 @ SY595 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SY593 @ SY594 ) @ SY595 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3131]) ).

thf(3272,plain,
    ! [SV53: $i] :
      ( ( ~ ( cType___24t @ SV53 )
        | ! [SY596: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY596 )
            | ! [SY597: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY597 )
                | ! [SY598: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY598 )
                    | ! [SY599: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY599 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY596 @ SY597 ) )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY598 @ SY599 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY596 @ SY598 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY597 @ SY599 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3132]) ).

thf(3273,plain,
    ! [SV54: $i] :
      ( ( ~ ( cType___24t @ SV54 )
        | ! [SY600: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY600 )
            | ! [SY601: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY601 )
                | ! [SY602: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY602 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ SY601 ) )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ SY602 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SY601 @ SY602 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3133]) ).

thf(3274,plain,
    ! [SV55: $i] :
      ( ( ~ ( cType___24t @ SV55 )
        | ! [SY603: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY603 )
            | ! [SY604: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY604 )
                | ! [SY605: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY605 )
                    | ! [SY606: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY606 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY603 @ SY604 ) )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY606 @ SY605 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY603 @ SY605 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY604 @ SY606 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3135]) ).

thf(3275,plain,
    ! [SV56: $i] :
      ( ( ~ ( cType___24t @ SV56 )
        | ! [SY607: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY607 )
            | ! [SY608: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY608 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SY607 @ SY608 ) @ SY607 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3136]) ).

thf(3276,plain,
    ! [SV57: $i] :
      ( ( ~ ( cType___24t @ SV57 )
        | ! [SY609: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY609 )
            | ! [SY610: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY610 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SY609 @ SY610 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY609 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY610 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3137]) ).

thf(3277,plain,
    ! [SV58: $i] :
      ( ( ~ ( cType___24t @ SV58 )
        | ! [SY611: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV58 @ SY611 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV58 @ SY611 @ SY611 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3138]) ).

thf(3278,plain,
    ! [SV59: $i] :
      ( ( ~ ( cType___24t @ SV59 )
        | ! [SY612: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY612 )
            | ! [SY613: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY613 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SY612 @ SY613 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY612 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY613 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3139]) ).

thf(3279,plain,
    ! [SV60: $i] :
      ( ( ~ ( cType___24t @ SV60 )
        | ! [SY614: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY614 )
            | ! [SY615: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY615 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SY614 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY615 ) ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY614 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY615 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3140]) ).

thf(3280,plain,
    ! [SV61: $i] :
      ( ( ~ ( cType___24t @ SV61 )
        | ! [SY616: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY616 )
            | ! [SY617: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY617 )
                | ! [SY618: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY618 )
                    | ! [SY619: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY619 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY616 @ SY617 ) )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY618 @ SY619 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY616 @ SY618 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY617 @ SY619 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3141]) ).

thf(3281,plain,
    ! [SV62: $i] :
      ( ( ~ ( cType___24t @ SV62 )
        | ! [SY620: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY620 )
            | ! [SY621: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY621 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SY620 @ SY621 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SY620 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SY621 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3142]) ).

thf(3282,plain,
    ! [SV63: $i] :
      ( ( ~ ( cType___24t @ SV63 )
        | ! [SY622: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY622 )
            | ! [SY623: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY623 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SY622 @ SY623 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SY622 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SY623 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3143]) ).

thf(3283,plain,
    ! [SV64: $i] :
      ( ( ~ ( cType___24t @ SV64 )
        | ! [SY624: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY624 )
            | ! [SY625: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY625 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SY624 @ SY625 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SY624 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SY625 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3144]) ).

thf(3284,plain,
    ! [SV65: $i] :
      ( ( ~ ( cType___24t @ SV65 )
        | ! [SY626: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY626 )
            | ! [SY627: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY627 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SY626 @ SY627 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY626 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY627 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3145]) ).

thf(3285,plain,
    ! [SV66: $i] :
      ( ( ~ ( cType___24t @ SV66 )
        | ! [SY628: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY628 )
            | ! [SY629: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY629 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SY628 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY629 ) ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY628 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY629 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3146]) ).

thf(3286,plain,
    ! [SV67: $i] :
      ( ( ~ ( cType___24t @ SV67 )
        | ! [SY630: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY630 )
            | ! [SY631: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY631 )
                | ! [SY632: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY632 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY630 @ SY632 ) )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY631 @ SY632 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SY630 @ SY631 ) @ SY632 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3147]) ).

thf(3287,plain,
    ! [SV68: $i] :
      ( ( ~ ( cType___24t @ SV68 )
        | ! [SY633: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY633 )
            | ! [SY634: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY634 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SY633 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SY633 @ SY634 ) @ SY634 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3148]) ).

thf(3288,plain,
    ! [SV69: $i] :
      ( ( ~ ( cType___24t @ SV69 )
        | ! [SY635: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY635 )
            | ! [SY636: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY636 )
                | ! [SY637: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY637 )
                    | ! [SY638: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY638 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY635 @ SY636 ) )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY637 @ SY638 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY635 @ SY637 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY636 @ SY638 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3149]) ).

thf(3289,plain,
    ! [SV70: $i] :
      ( ( ~ ( cType___24t @ SV70 )
        | ! [SY639: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY639 )
            | ! [SY640: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY640 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SY639 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SY639 @ SY640 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3151]) ).

thf(3290,plain,
    ! [SV71: $i] :
      ( ( ~ ( cType___24t @ SV71 )
        | ! [SY641: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY641 )
            | ! [SY642: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY642 )
                | ! [SY643: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY643 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SY641 @ SY642 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SY641 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SY642 @ SY643 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3152]) ).

thf(3291,plain,
    ! [SV72: $i] :
      ( ( ~ ( cType___24t @ SV72 )
        | ! [SY644: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY644 )
            | ! [SY645: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY645 )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SY645 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SY644 @ SY645 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3153]) ).

thf(3292,plain,
    ! [SV73: $i] :
      ( ( ~ ( cType___24t @ SV73 )
        | ! [SY646: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY646 )
            | ! [SY647: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY647 )
                | ! [SY648: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY648 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SY646 @ SY648 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SY646 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SY647 @ SY648 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3154]) ).

thf(3293,plain,
    ! [SV74: $i] :
      ( ( ~ ( cType___24t @ SV74 )
        | ! [SY649: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY649 )
            | ! [SY650: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY650 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SY649 @ SY650 ) )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY650 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY649 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3155]) ).

thf(3294,plain,
    ! [SV75: $i] :
      ( ( ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV75 )
        = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a1 @ SV75 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3156]) ).

thf(3295,plain,
    ! [SV76: $i] :
      ( ( ! [SY651: $i,SY652: $i,SY653: $i,SY654: $i] :
            ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ SV76 ) @ SY651 ) @ SY652 ) @ SY653 ) @ SY654 )
            = ( c_24__lam__45594___24a5 @ SV76 @ SY651 @ SY652 @ SY653 @ SY654 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3159]) ).

thf(3296,plain,
    ! [SV77: $i] :
      ( ( ! [SY655: $i,SY656: $i] :
            ( ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2einclusion @ SV77 ) @ SY655 ) @ SY656 )
            = ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV77 @ SY655 @ SY656 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3161]) ).

thf(3297,plain,
    ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ cr @ cr_27 ) @ c_24__lam__35673 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3162]) ).

thf(3298,plain,
    ! [SV78: $i] :
      ( ( ~ ( cProp___24t @ SV78 )
        | ~ ( ~ ~ ( ~ ! [SY657: $i] :
                        ( ~ ( cProp___24t @ SY657 )
                        | ( p @ SV78 )
                        | ~ ( p @ SV78 )
                        | ( p @ SY657 ) )
                  | ~ ! [SY658: $i] :
                        ( ~ ( cProp___24t @ SY658 )
                        | ( p @ SV78 )
                        | ~ ( p @ SY658 )
                        | ( p @ SY658 ) ) )
            | ~ ~ ( ~ ! [SY659: $i] :
                        ( ~ ( cProp___24t @ SY659 )
                        | ~ ( p @ SY659 )
                        | ~ ( p @ SV78 )
                        | ( p @ SY659 ) )
                  | ~ ! [SX1: $i] :
                        ( ~ ( cProp___24t @ SX1 )
                        | ~ ( p @ SX1 )
                        | ~ ( p @ SX1 )
                        | ( p @ SX1 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3163]) ).

thf(3299,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( sK2_SY468 @ SX0 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ SX0 @ ( sK1_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK2_SY468 @ SX0 ) ) ) ) )
            | ( c_24__type__96___24t @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( c_24__type__96___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3164]) ).

thf(3300,plain,
    ! [SV79: $i] :
      ( ( ~ ( cType___24t @ SV79 )
        | ! [SY661: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY661 )
            | ~ ( ~ ! [SY662: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY662 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SY661 @ SY662 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY661 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY662 ) )
                | ~ ! [SY663: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY663 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SY661 @ SY663 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY663 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY661 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3165]) ).

thf(3301,plain,
    ! [SV80: $i] :
      ( ( ~ ( ~ ! [SY664: $i,SY665: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY664 @ SY665 )
                  | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY664 ) @ SY665 ) ) )
            | ~ ! [SY666: $i,SY667: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY666 ) @ SY667 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY666 @ SY667 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3166]) ).

thf(3302,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c_24__lam__35673___24a2 @ SX0 @ SX1 )
            | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) )
            | ( c_24__lam__35673___24a2 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3167]) ).

thf(3303,plain,
    ! [SV81: $i] :
      ( ( ! [SY668: $i,SY669: $i] :
            ~ ( ~ ! [SY670: $i,SY671: $i] :
                    ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SY668 @ SY669 @ SY670 @ SY671 )
                    | ( p @ ( happ @ ( happ @ SY668 @ SY670 ) @ SY671 ) )
                    | ( p @ ( happ @ ( happ @ SY669 @ SY670 ) @ SY671 ) ) )
              | ~ ~ ( ~ ! [SY672: $i,SY673: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY668 @ SY672 ) @ SY673 ) )
                          | ( c_24__lam__3971___24a5 @ SV81 @ SY668 @ SY669 @ SY672 @ SY673 ) )
                    | ~ ! [SY674: $i,SY675: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY669 @ SY674 ) @ SY675 ) )
                          | ( c_24__lam__3971___24a5 @ SV81 @ SY668 @ SY669 @ SY674 @ SY675 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3168]) ).

thf(3304,plain,
    ! [SV82: $i] :
      ( ( ! [SY676: $i,SY677: $i] :
            ~ ( ~ ! [SY678: $i,SY679: $i] :
                    ( ( ( happ @ SY677 @ SY678 )
                     != ( happ @ SY677 @ SY679 ) )
                    | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SY676 @ SY677 @ SY678 @ SY679 ) )
              | ~ ! [SY680: $i,SY681: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SY676 @ SY677 @ SY680 @ SY681 )
                    | ( ( happ @ SY677 @ SY680 )
                      = ( happ @ SY677 @ SY681 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3169]) ).

thf(3305,plain,
    ! [SV83: $i] :
      ( ( ~ ( cType___24t @ SV83 )
        | ! [SY682: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY682 )
            | ! [SY683: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY683 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY682 @ SY683 )
                | ! [SY684: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY684 )
                    | ~ ( ~ ! [SY685: $i] :
                              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY685 )
                              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY684 @ SY685 )
                              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY682 @ SY684 ) )
                              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY683 @ SY685 ) ) )
                        | ~ ! [SY686: $i] :
                              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY686 )
                              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY684 @ SY686 )
                              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY683 @ SY686 ) )
                              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY682 @ SY684 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3170]) ).

thf(3306,plain,
    ! [SV84: $i] :
      ( ( ! [SY687: $i] :
            ~ ( ~ ! [SY688: $i,SY689: $i] :
                    ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SY687 @ SY688 @ SY689 )
                    | ( p @ ( happ @ ( happ @ SY687 @ SY688 ) @ SY689 ) ) )
              | ~ ! [SY690: $i,SY691: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY687 @ SY690 ) @ SY691 ) )
                    | ( c_24__lam__7591___24a4 @ SV84 @ SY687 @ SY690 @ SY691 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3171]) ).

thf(3307,plain,
    ! [SV85: $i] :
      ( ( ~ ( cType___24t @ SV85 )
        | ! [SY692: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY692 )
            | ~ ( ~ ! [SY693: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY693 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SY692 @ SY693 )
                      | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY692 ) )
                      | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY693 ) ) )
                | ~ ! [SY694: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY694 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SY692 @ SY694 )
                      | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY694 ) )
                      | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY692 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3172]) ).

thf(3308,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( cType___24t @ ( happ @ SX0 @ ( sK12_Vv__CANONICAL__0 @ SX0 ) ) ) )
            | ( c_24__type__28___24t @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( c_24__type__28___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ( cType___24t @ ( happ @ SX0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3173]) ).

thf(3309,plain,
    ! [SV86: $i] :
      ( ( ! [SY695: $i] :
            ~ ( ~ ! [SY696: $i,SY697: $i] :
                    ( ~ ( p @ ( happ @ SY695 @ SY697 ) )
                    | ( p @ ( happ @ SY696 @ SY697 ) )
                    | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SY695 @ SY696 @ SY697 ) )
              | ~ ~ ( ~ ! [SY698: $i,SY699: $i] :
                          ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SY695 @ SY698 @ SY699 )
                          | ( p @ ( happ @ SY695 @ SY699 ) ) )
                    | ~ ! [SY700: $i,SY701: $i] :
                          ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SY695 @ SY700 @ SY701 )
                          | ~ ( p @ ( happ @ SY700 @ SY701 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3174]) ).

thf(3310,plain,
    ! [SV87: $i] :
      ( ( ! [SY702: $i] :
            ~ ( ~ ! [SY703: $i,SY704: $i] :
                    ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SY702 @ SY703 @ SY704 )
                    | ( p @ ( happ @ ( happ @ SY702 @ SY704 ) @ SY703 ) ) )
              | ~ ! [SY705: $i,SY706: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY702 @ SY706 ) @ SY705 ) )
                    | ( c_24__lam__7587___24a4 @ SV87 @ SY702 @ SY705 @ SY706 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3175]) ).

thf(3311,plain,
    ! [SV88: $i] :
      ( ( ~ ( ~ ! [SY707: $i,SY708: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY707 @ SY708 )
                  | ~ ( p @ ( happ @ SY707 @ SY708 ) ) )
            | ~ ! [SY709: $i,SY710: $i] :
                  ( ( p @ ( happ @ SY709 @ SY710 ) )
                  | ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY709 @ SY710 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3176]) ).

thf(3312,plain,
    ! [SV89: $i] :
      ( ( ~ ( cType___24t @ SV89 )
        | ! [SY711: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY711 )
            | ! [SY712: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY712 )
                | ~ ( ~ ! [SY713: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY713 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SY711 @ SY712 ) @ SY713 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SY711 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY712 @ SY713 ) ) ) )
                    | ~ ! [SY714: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY714 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SY711 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY712 @ SY714 ) ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SY711 @ SY712 ) @ SY714 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3177]) ).

thf(3313,plain,
    ! [SV90: $i] :
      ( ( ! [SY715: $i,SY716: $i] :
            ~ ( ~ ! [SY717: $i,SY718: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SY715 @ SY716 @ SY717 @ SY718 )
                    | ( p @ ( happ @ ( happ @ SY715 @ SY717 ) @ SY718 ) )
                    | ( p @ ( happ @ ( happ @ SY716 @ SY717 ) @ SY718 ) ) )
              | ~ ~ ( ~ ! [SY719: $i,SY720: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY715 @ SY719 ) @ SY720 ) )
                          | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SY715 @ SY716 @ SY719 @ SY720 ) )
                    | ~ ! [SY721: $i,SY722: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY716 @ SY721 ) @ SY722 ) )
                          | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SY715 @ SY716 @ SY721 @ SY722 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3178]) ).

thf(3314,plain,
    ! [SV91: $i] :
      ( ( ~ ( cProp___24t @ SV91 )
        | ! [SY723: $i] :
            ( ~ ( cProp___24t @ SY723 )
            | ~ ( ~ ~ ( ~ ! [SY724: $i] :
                            ( ~ ( cProp___24t @ SY724 )
                            | ( p @ SV91 )
                            | ~ ( p @ SV91 )
                            | ( p @ SY723 )
                            | ( p @ SY724 ) )
                      | ~ ! [SY725: $i] :
                            ( ~ ( cProp___24t @ SY725 )
                            | ( p @ SV91 )
                            | ~ ( p @ SY725 )
                            | ( p @ SY723 )
                            | ( p @ SY725 ) ) )
                | ~ ~ ( ~ ! [SY726: $i] :
                            ( ~ ( cProp___24t @ SY726 )
                            | ~ ( p @ SY723 )
                            | ~ ( p @ SV91 )
                            | ( p @ SY723 )
                            | ( p @ SY726 ) )
                      | ~ ! [SX2: $i] :
                            ( ~ ( cProp___24t @ SX2 )
                            | ~ ( p @ SY723 )
                            | ~ ( p @ SX2 )
                            | ( p @ SY723 )
                            | ( p @ SX2 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3179]) ).

thf(3315,plain,
    ! [SV92: $i] :
      ( ( ! [SY728: $i,SY729: $i] :
            ~ ( ~ ! [SY730: $i,SY731: $i] :
                    ( ~ ( p @ ( happ @ SY728 @ SY730 ) )
                    | ~ ( p @ ( happ @ SY729 @ SY731 ) )
                    | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SY728 @ SY729 @ SY730 @ SY731 ) )
              | ~ ~ ( ~ ! [SY732: $i] :
                          ( ! [SY733: $i] :
                              ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SY728 @ SY729 @ SY732 @ SY733 )
                          | ( p @ ( happ @ SY728 @ SY732 ) ) )
                    | ~ ! [SY734: $i,SY735: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SY728 @ SY729 @ SY734 @ SY735 )
                          | ( p @ ( happ @ SY729 @ SY735 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3180]) ).

thf(3316,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) ) )
            | ( c_24__type__11748___24t @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c_24__type__11748___24t @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3181]) ).

thf(3317,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 )
          | $true )
      | ~ ( ~ $true
          | ! [SX0: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3182]) ).

thf(3318,plain,
    ! [SV93: $i] :
      ( ( ! [SY736: $i,SY737: $i] :
            ~ ( ~ ! [SY738: $i,SY739: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SY736 @ SY737 @ SY738 @ SY739 )
                    | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SY736 ) @ SY737 ) @ SY738 ) @ SY739 ) ) )
              | ~ ! [SY740: $i,SY741: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SY736 ) @ SY737 ) @ SY740 ) @ SY741 ) )
                    | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SY736 @ SY737 @ SY740 @ SY741 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3183]) ).

thf(3319,plain,
    ! [SV94: $i] :
      ( ( ~ ( ~ ! [SY742: $i,SY743: $i] :
                  ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY742 @ SY743 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY743 @ SY742 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY742 @ SY743 ) )
            | ~ ~ ( ~ ! [SY744: $i,SY745: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) )
                  | ~ ! [SY746: $i,SY747: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3184]) ).

thf(3320,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) )
            | ~ ( p @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( p @ SX1 )
            | ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3185]) ).

thf(3321,plain,
    ! [SV95: $i] :
      ( ( ! [SY748: $i] :
            ~ ( ~ ! [SY749: $i,SY750: $i] :
                    ( ~ ( p @ ( happ @ SY748 @ SY750 ) )
                    | ~ ( p @ ( happ @ SY749 @ SY750 ) )
                    | ( c_24__lam__40532___24a4 @ SV95 @ SY748 @ SY749 @ SY750 ) )
              | ~ ~ ( ~ ! [SY751: $i,SY752: $i] :
                          ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SY748 @ SY751 @ SY752 )
                          | ( p @ ( happ @ SY748 @ SY752 ) ) )
                    | ~ ! [SY753: $i,SY754: $i] :
                          ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SY748 @ SY753 @ SY754 )
                          | ( p @ ( happ @ SY753 @ SY754 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3186]) ).

thf(3322,plain,
    ! [SV96: $i] :
      ( ( ~ ( cType___24t @ SV96 )
        | ! [SY755: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY755 )
            | ~ ( ~ ! [SY756: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY756 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SY755 @ SY756 )
                      | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY755 ) )
                      | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY756 ) ) )
                | ~ ! [SY757: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY757 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SY755 @ SY757 )
                      | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY757 ) )
                      | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY755 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3187]) ).

thf(3323,plain,
    ! [SV97: $i] :
      ( ( ! [SY758: $i] :
            ~ ( ~ ! [SY759: $i,SY760: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SY758 @ SY759 @ SY760 )
                    | ( SY759 = SY760 )
                    | ( p @ ( happ @ ( happ @ SY758 @ SY759 ) @ SY760 ) ) )
              | ~ ~ ( ~ ! [SY761: $i,SY762: $i] :
                          ( ( SY761 != SY762 )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SY758 @ SY761 @ SY762 ) )
                    | ~ ! [SY763: $i,SY764: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY758 @ SY763 ) @ SY764 ) )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SY758 @ SY763 @ SY764 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3188]) ).

thf(3324,plain,
    ! [SV98: $i] :
      ( ( ~ ( ~ ! [SY765: $i,SY766: $i] :
                  ( ~ ( ~ ( t @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) @ SV98 )
                      | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) @ SV98 )
                            | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SY765 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) )
                                  | ~ ~ ( p @ ( happ @ ( happ @ SY766 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) ) ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY765 @ SY766 ) ) )
            | ~ ! [SY767: $i,SY768: $i] :
                  ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY767 @ SY768 ) )
                  | ! [SY769: $i] :
                      ( ~ ( t @ SY769 @ SV98 )
                      | ! [SY770: $i] :
                          ( ~ ( t @ SY770 @ SV98 )
                          | ~ ( p @ ( happ @ ( happ @ SY767 @ SY769 ) @ SY770 ) )
                          | ( p @ ( happ @ ( happ @ SY768 @ SY769 ) @ SY770 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3189]) ).

thf(3325,plain,
    ! [SV99: $i] :
      ( ( ! [SY771: $i] :
            ~ ( ~ ! [SY772: $i,SY773: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SY771 @ SY772 @ SY773 )
                    | ( p @ ( happ @ ( happ @ SY771 @ SY772 ) @ SY773 ) )
                    | ( p @ ( happ @ ( happ @ SY771 @ SY773 ) @ SY772 ) ) )
              | ~ ~ ( ~ ! [SY774: $i,SY775: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY771 @ SY774 ) @ SY775 ) )
                          | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SY771 @ SY774 @ SY775 ) )
                    | ~ ! [SY776: $i,SY777: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY771 @ SY777 ) @ SY776 ) )
                          | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SY771 @ SY776 @ SY777 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3190]) ).

thf(3326,plain,
    ! [SV100: $i] :
      ( ( ! [SY778: $i,SY779: $i] :
            ~ ( ~ ! [SY780: $i,SY781: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY778 @ SY780 ) @ SY781 ) )
                    | ( p @ ( happ @ ( happ @ SY779 @ SY780 ) @ SY781 ) )
                    | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SY778 @ SY779 @ SY780 @ SY781 ) )
              | ~ ~ ( ~ ! [SY782: $i,SY783: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SY778 @ SY779 @ SY782 @ SY783 )
                          | ( p @ ( happ @ ( happ @ SY778 @ SY782 ) @ SY783 ) ) )
                    | ~ ! [SY784: $i,SY785: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SY778 @ SY779 @ SY784 @ SY785 )
                          | ~ ( p @ ( happ @ ( happ @ SY779 @ SY784 ) @ SY785 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3191]) ).

thf(3327,plain,
    ! [SV101: $i] :
      ( ( ~ ( ~ ! [SY786: $i,SY787: $i] :
                  ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY786 @ ( happ @ SY787 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) ) ) )
                  | ( c_24__type__11699___24t @ SV101 @ SY786 @ SY787 ) )
            | ~ ! [SY788: $i,SY789: $i] :
                  ( ~ ( c_24__type__11699___24t @ SV101 @ SY788 @ SY789 )
                  | ! [SY790: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY790 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY788 @ ( happ @ SY789 @ SY790 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3192]) ).

thf(3328,plain,
    ! [SV102: $i] :
      ( ( ! [SY791: $i,SY792: $i] :
            ~ ( ~ ! [SY793: $i,SY794: $i] :
                    ( ~ ( c_24__lam__16___24a5 @ SV102 @ SY791 @ SY792 @ SY793 @ SY794 )
                    | ( p @ ( happ @ ( happ @ SY792 @ SY793 ) @ SY794 ) ) )
              | ~ ! [SY795: $i,SY796: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY792 @ SY795 ) @ SY796 ) )
                    | ( c_24__lam__16___24a5 @ SV102 @ SY791 @ SY792 @ SY795 @ SY796 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3193]) ).

thf(3329,plain,
    ! [SV103: $i] :
      ( ( ~ ( ~ ! [SY797: $i,SY798: $i] :
                  ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY797 @ SY798 ) )
                  | ( p @ SY797 )
                  | ( p @ SY798 ) )
            | ~ ~ ( ~ ! [SY799: $i] :
                        ( ~ ( p @ SY799 )
                        | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) )
                  | ~ ! [SY801: $i,SY802: $i] :
                        ( ~ ( p @ SY802 )
                        | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3194]) ).

thf(3330,plain,
    ! [SV104: $i] :
      ( ( ! [SY803: $i,SY804: $i] :
            ~ ( ~ ! [SY805: $i,SY806: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY804 @ SY805 ) @ SY806 ) )
                    | ~ ( p @ ( happ @ SY803 @ SY805 ) )
                    | ~ ( p @ ( happ @ SY803 @ SY806 ) )
                    | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SY803 @ SY804 @ SY805 @ SY806 ) )
              | ~ ~ ( ~ ~ ( ~ ! [SY807: $i,SY808: $i] :
                                ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SY803 @ SY804 @ SY807 @ SY808 )
                                | ( p @ ( happ @ ( happ @ SY804 @ SY807 ) @ SY808 ) ) )
                          | ~ ! [SY809: $i] :
                                ( ! [SY810: $i] :
                                    ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SY803 @ SY804 @ SY809 @ SY810 )
                                | ( p @ ( happ @ SY803 @ SY809 ) ) ) )
                    | ~ ! [SY811: $i,SY812: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SY803 @ SY804 @ SY811 @ SY812 )
                          | ( p @ ( happ @ SY803 @ SY812 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3195]) ).

thf(3331,plain,
    ! [SV105: $i] :
      ( ( ~ ( ~ ! [SY813: $i,SY814: $i] :
                  ( ( SY813 != SY814 )
                  | ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY813 @ SY814 ) ) )
            | ~ ! [SY815: $i,SY816: $i] :
                  ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY815 @ SY816 ) )
                  | ( SY815 = SY816 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3196]) ).

thf(3332,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK14_SY479 @ SX1 @ SX0 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) @ ( sK14_SY479 @ SX1 @ SX0 ) ) ) ) )
            | ( c_24__type__11829___24t @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c_24__type__11829___24t @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                | ! [SX3: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3197]) ).

thf(3333,plain,
    ! [SV106: $i] :
      ( ( ! [SY817: $i] :
            ~ ( ~ ! [SY818: $i,SY819: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SY817 @ SY818 @ SY819 )
                    | ( p @ ( happ @ ( happ @ SY817 @ SY819 ) @ SY818 ) )
                    | ( SY818 = SY819 )
                    | ( p @ ( happ @ ( happ @ SY817 @ SY818 ) @ SY819 ) ) )
              | ~ ~ ( ~ ! [SY820: $i,SY821: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY817 @ SY821 ) @ SY820 ) )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SY817 @ SY820 @ SY821 ) )
                    | ~ ~ ( ~ ! [SY822: $i,SY823: $i] :
                                ( ( SY822 != SY823 )
                                | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SY817 @ SY822 @ SY823 ) )
                          | ~ ! [SY824: $i,SY825: $i] :
                                ( ~ ( p @ ( happ @ ( happ @ SY817 @ SY824 ) @ SY825 ) )
                                | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SY817 @ SY824 @ SY825 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3198]) ).

thf(3334,plain,
    ! [SV107: $i] :
      ( ( ! [SY826: $i,SY827: $i] :
            ~ ( ~ ! [SY828: $i,SY829: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SY826 @ SY827 @ SY828 @ SY829 )
                    | ( p @ ( happ @ SY828 @ ( happ @ SY827 @ SY829 ) ) ) )
              | ~ ! [SY830: $i,SY831: $i] :
                    ( ~ ( p @ ( happ @ SY830 @ ( happ @ SY827 @ SY831 ) ) )
                    | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SY826 @ SY827 @ SY830 @ SY831 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3199]) ).

thf(3335,plain,
    ! [SV108: $i] :
      ( ( ! [SY832: $i] :
            ~ ( ~ ! [SY833: $i,SY834: $i] :
                    ( ( SY833 != SY834 )
                    | ~ ( p @ ( happ @ SY832 @ SY833 ) )
                    | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SY832 @ SY833 @ SY834 ) )
              | ~ ~ ( ~ ! [SY835: $i,SY836: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SY832 @ SY835 @ SY836 )
                          | ( SY835 = SY836 ) )
                    | ~ ! [SY837: $i] :
                          ( ! [SY838: $i] :
                              ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SY832 @ SY837 @ SY838 )
                          | ( p @ ( happ @ SY832 @ SY837 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3200]) ).

thf(3336,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK4_SY469 @ SX0 ) )
                      | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK5_SY471 @ SX0 ) )
                            | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK3_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK4_SY469 @ SX0 ) ) @ ( sK5_SY471 @ SX0 ) ) ) ) ) )
            | ( c_24__type__90___24t @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( c_24__type__90___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                    | ! [SX3: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX3 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3201]) ).

thf(3337,plain,
    ! [SV109: $i] :
      ( ( ~ ( cType___24t @ SV109 )
        | ! [SY839: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY839 )
            | ~ ( ~ ! [SY840: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY840 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SY839 @ SY840 )
                      | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY839 ) )
                      | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY840 ) ) )
                | ~ ! [SY841: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY841 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SY839 @ SY841 )
                      | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY841 ) )
                      | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY839 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3202]) ).

thf(3338,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SX0 ) )
                      | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SX0 ) )
                            | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SX0 ) )
                                  | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK8_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK9_SY473 @ SX0 ) ) @ ( sK10_SY476 @ SX0 ) ) @ ( sK11_SY478 @ SX0 ) ) ) ) ) ) )
            | ( c_24__type__4733___24t @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( c_24__type__4733___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cType___24t @ SX2 )
                    | ! [SX3: $i] :
                        ( ~ ( cType___24t @ SX3 )
                        | ! [SX4: $i] :
                            ( ~ ( cType___24t @ SX4 )
                            | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3203]) ).

thf(3339,plain,
    ! [SV110: $i] :
      ( ( ! [SY842: $i,SY843: $i] :
            ~ ( ~ ! [SY844: $i,SY845: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY842 @ SY844 ) @ SY845 ) )
                    | ~ ( p @ ( happ @ ( happ @ SY843 @ SY844 ) @ SY845 ) )
                    | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SY842 @ SY843 @ SY844 @ SY845 ) )
              | ~ ~ ( ~ ! [SY846: $i,SY847: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SY842 @ SY843 @ SY846 @ SY847 )
                          | ( p @ ( happ @ ( happ @ SY842 @ SY846 ) @ SY847 ) ) )
                    | ~ ! [SY848: $i,SY849: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SY842 @ SY843 @ SY848 @ SY849 )
                          | ( p @ ( happ @ ( happ @ SY843 @ SY848 ) @ SY849 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3204]) ).

thf(3340,plain,
    ! [SV111: $i] :
      ( ( ! [SY850: $i] :
            ~ ( ~ ! [SY851: $i,SY852: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SY850 @ SY851 @ SY852 )
                    | ( p @ ( happ @ ( happ @ SY850 @ SY852 ) @ SY851 ) ) )
              | ~ ! [SY853: $i,SY854: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY850 @ SY854 ) @ SY853 ) )
                    | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SY850 @ SY853 @ SY854 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3205]) ).

thf(3341,plain,
    ! [SV112: $i] :
      ( ( ~ ( ~ ! [SY855: $i,SY856: $i] :
                  ( ~ ( p @ SY855 )
                  | ~ ( p @ SY856 )
                  | ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY855 @ SY856 ) ) )
            | ~ ~ ( ~ ! [SY857: $i] :
                        ( ! [SY858: $i] :
                            ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
                        | ( p @ SY857 ) )
                  | ~ ! [SY859: $i,SY860: $i] :
                        ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
                        | ( p @ SY860 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3206]) ).

thf(3342,plain,
    ! [SV113: $i] :
      ( ( ! [SY861: $i] :
            ~ ( ~ ! [SY862: $i,SY863: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SY861 @ SY862 @ SY863 )
                    | ( p @ ( happ @ SY861 @ SY863 ) )
                    | ( p @ ( happ @ SY862 @ SY863 ) ) )
              | ~ ~ ( ~ ! [SY864: $i,SY865: $i] :
                          ( ~ ( p @ ( happ @ SY861 @ SY865 ) )
                          | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SY861 @ SY864 @ SY865 ) )
                    | ~ ! [SY866: $i,SY867: $i] :
                          ( ~ ( p @ ( happ @ SY866 @ SY867 ) )
                          | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SY861 @ SY866 @ SY867 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3207]) ).

thf(3343,plain,
    ! [SV114: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY868: $i] :
                        ( ( p @ SY868 )
                        | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) )
                  | ~ ! [SY870: $i,SY871: $i] :
                        ( ~ ( p @ SY871 )
                        | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) )
            | ~ ! [SY872: $i,SY873: $i] :
                  ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY872 @ SY873 ) )
                  | ~ ( p @ SY872 )
                  | ( p @ SY873 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3208]) ).

thf(3344,plain,
    ! [SV115: $i] :
      ( ( ~ ( cType___24t @ SV115 )
        | ! [SY874: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY874 )
            | ! [SY875: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY875 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SY874 @ SY875 )
                | ! [SY876: $i] :
                    ( ~ ( t @ SY876 @ SV115 )
                    | ~ ( ~ ! [SY877: $i] :
                              ( ~ ( t @ SY877 @ SV115 )
                              | ~ ( p @ ( happ @ ( happ @ SY874 @ SY876 ) @ SY877 ) )
                              | ( p @ ( happ @ ( happ @ SY875 @ SY876 ) @ SY877 ) ) )
                        | ~ ! [SY878: $i] :
                              ( ~ ( t @ SY878 @ SV115 )
                              | ~ ( p @ ( happ @ ( happ @ SY875 @ SY876 ) @ SY878 ) )
                              | ( p @ ( happ @ ( happ @ SY874 @ SY876 ) @ SY878 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3209]) ).

thf(3345,plain,
    ! [SV116: $i] :
      ( ( ! [SY879: $i] :
            ~ ( ~ ! [SY880: $i,SY881: $i] :
                    ( ~ ( p @ ( happ @ SY879 @ SY881 ) )
                    | ~ ( p @ ( happ @ SY880 @ SY881 ) )
                    | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SY879 @ SY880 @ SY881 ) )
              | ~ ~ ( ~ ! [SY882: $i,SY883: $i] :
                          ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SY879 @ SY882 @ SY883 )
                          | ( p @ ( happ @ SY879 @ SY883 ) ) )
                    | ~ ! [SY884: $i,SY885: $i] :
                          ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SY879 @ SY884 @ SY885 )
                          | ( p @ ( happ @ SY884 @ SY885 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3210]) ).

thf(3346,plain,
    ! [SV117: $i] :
      ( ( ~ ( cType___24t @ SV117 )
        | ! [SY886: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY886 )
            | ! [SY887: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY887 )
                | ~ ( ~ ! [SY888: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY888 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ SY887 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY887 @ SY888 ) ) ) )
                    | ~ ! [SY889: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY889 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ SY889 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY887 @ SY889 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3211]) ).

thf(3347,plain,
    ! [SV118: $i] :
      ( ( ! [SY890: $i,SY891: $i,SY892: $i] :
            ~ ( ~ ! [SY893: $i,SY894: $i] :
                    ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SY890 @ SY891 @ SY892 @ SY893 @ SY894 )
                    | ( p @ ( happ @ ( happ @ SY892 @ ( happ @ SY891 @ SY893 ) ) @ ( happ @ SY891 @ SY894 ) ) ) )
              | ~ ! [SY895: $i,SY896: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY892 @ ( happ @ SY891 @ SY895 ) ) @ ( happ @ SY891 @ SY896 ) ) )
                    | ( c_24__lam__7800___24a6 @ SV118 @ SY890 @ SY891 @ SY892 @ SY895 @ SY896 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3212]) ).

thf(3348,plain,
    ! [SV119: $i] :
      ( ( ! [SY897: $i,SY898: $i,SY899: $i] :
            ~ ( ~ ! [SY900: $i,SY901: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SY897 @ SY898 @ SY899 @ SY900 @ SY901 )
                    | ( p @ ( happ @ ( happ @ SY899 @ ( happ @ SY898 @ SY900 ) ) @ ( happ @ SY898 @ SY901 ) ) ) )
              | ~ ! [SY902: $i,SY903: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY899 @ ( happ @ SY898 @ SY902 ) ) @ ( happ @ SY898 @ SY903 ) ) )
                    | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SY897 @ SY898 @ SY899 @ SY902 @ SY903 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3213]) ).

thf(3349,plain,
    ! [SV120: $i] :
      ( ( ~ ( ~ ! [SY904: $i,SY905: $i] :
                  ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY904 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY905 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) ) ) )
                  | ( c_24__type__11787___24t @ SV120 @ SY904 @ SY905 ) )
            | ~ ! [SY906: $i,SY907: $i] :
                  ( ~ ( c_24__type__11787___24t @ SV120 @ SY906 @ SY907 )
                  | ! [SY908: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY906 @ SY908 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY907 @ SY908 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3214]) ).

thf(3350,plain,
    ! [SV121: $i] :
      ( ( ! [SY909: $i] :
            ~ ( ~ ! [SY910: $i,SY911: $i] :
                    ( ( SY910 != SY911 )
                    | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SY909 @ SY910 @ SY911 ) ) )
              | ~ ! [SY912: $i,SY913: $i] :
                    ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SY909 @ SY912 @ SY913 ) )
                    | ( SY912 = SY913 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3215]) ).

thf(3351,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SX0 ) )
                      | ~ ~ ( cType___24t @ ( happ @ ( happ @ SX0 @ ( sK6_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK7_SY472 @ SX0 ) ) ) ) )
            | ( c_24__type__52___24t @ SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( c_24__type__52___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cType___24t @ SX2 )
                    | ( cType___24t @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3216]) ).

thf(3352,plain,
    ! [SV122: $i] :
      ( ( ! [SY914: $i,SY915: $i,SY916: $i] :
            ~ ( ~ ! [SY917: $i,SY918: $i] :
                    ( ( ( happ @ SY915 @ SY917 )
                     != ( happ @ SY915 @ SY918 ) )
                    | ~ ( p @ ( happ @ ( happ @ SY916 @ SY917 ) @ SY918 ) )
                    | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SY914 @ SY915 @ SY916 @ SY917 @ SY918 ) )
              | ~ ~ ( ~ ! [SY919: $i,SY920: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SY914 @ SY915 @ SY916 @ SY919 @ SY920 )
                          | ( ( happ @ SY915 @ SY919 )
                            = ( happ @ SY915 @ SY920 ) ) )
                    | ~ ! [SY921: $i,SY922: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SY914 @ SY915 @ SY916 @ SY921 @ SY922 )
                          | ( p @ ( happ @ ( happ @ SY916 @ SY921 ) @ SY922 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3217]) ).

thf(3353,plain,
    ! [SV123: $i,SV1: $i] :
      ( ( ! [SY923: $i,SY924: $i,SY925: $i] :
            ( ( c_24__lam__45594___24a5 @ SV1 @ SV123 @ SY923 @ SY924 @ SY925 )
            = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV123 @ ( happ @ SY924 @ SY925 ) @ SY923 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3218]) ).

thf(3354,plain,
    ! [SV2: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV2 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ SV2 @ SV2 ) @ c_24__lam__35673 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3219]) ).

thf(3355,plain,
    ! [SV3: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV3 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ SV3 ) @ c_24__lam__35673 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3220]) ).

thf(3356,plain,
    ! [SV4: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV4 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ SV4 @ c_24__lam__35673 ) @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3221]) ).

thf(3357,plain,
    ! [SV5: $i] :
      ( ( ( ~ ( cType___24t @ SV5 ) )
        = $true )
      | ( ( ! [SY485: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY485 )
              | ! [SY486: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY486 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY485 @ SY486 )
                  | ! [SY487: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY487 )
                      | ! [SY488: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY488 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY487 @ SY488 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY485 @ SY487 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY486 @ SY488 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3222]) ).

thf(3358,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( cType___24t @ SV6 ) )
        = $true )
      | ( ( ! [SY489: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV6 @ SY489 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV6 @ SY489 @ SY489 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3223]) ).

thf(3359,plain,
    ! [SV124: $i,SV7: $i] :
      ( ( ! [SY926: $i] :
            ( ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV7 ) @ SV124 ) @ SY926 )
            = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV7 @ SV124 @ SY926 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3224]) ).

thf(3360,plain,
    ! [SV125: $i,SV8: $i] :
      ( ( ! [SY927: $i,SY928: $i] :
            ( ( c_24__lam__33077___24a4 @ SV8 @ SV125 @ SY927 @ SY928 )
            = ( happ @ SY927 @ SY928 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3226]) ).

thf(3361,plain,
    ! [SV126: $i,SV9: $i] :
      ( ( ! [SY929: $i,SY930: $i] :
            ( ( c_24__lam__33085___24a4 @ SV9 @ SV126 @ SY929 @ SY930 )
            = ( happ @ SY929 @ SY930 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3227]) ).

thf(3362,plain,
    ! [SV10: $i] :
      ( ( ( ~ ( cProp___24t @ SV10 ) )
        = $true )
      | ( ( ! [SY498: $i] :
              ( ~ ( cProp___24t @ SY498 )
              | ~ ( p @ SV10 )
              | ~ ( p @ SY498 )
              | ( p @ SV10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3228]) ).

thf(3363,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( cProp___24t @ SV11 ) )
        = $true )
      | ( ( ~ ( p @ SV11 )
          | ( p @ SV11 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3229]) ).

thf(3364,plain,
    ! [SV127: $i] :
      ( ( ( ~ ( cProp___24t @ SV127 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3230]) ).

thf(3365,plain,
    ! [SV12: $i] :
      ( ( ( ~ ( cProp___24t @ SV12 ) )
        = $true )
      | ( ( ! [SY499: $i] :
              ( ~ ( cProp___24t @ SY499 )
              | ~ ( p @ SV12 )
              | ( p @ SY499 )
              | ( p @ SV12 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3231]) ).

thf(3366,plain,
    ! [SV13: $i] :
      ( ( ( ~ ( cType___24t @ SV13 ) )
        = $true )
      | ( ( ! [SY500: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV13 @ SY500 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SY500 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SY500 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3232]) ).

thf(3367,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( cType___24t @ SV14 ) )
        = $true )
      | ( ( ! [SY501: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV14 @ SY501 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SY501 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SY501 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3233]) ).

thf(3368,plain,
    ! [SV15: $i] :
      ( ( ( ~ ( cType___24t @ SV15 ) )
        = $true )
      | ( ( ! [SY502: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY502 )
              | ! [SY503: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY503 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SY502 @ SY503 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY502 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY503 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3234]) ).

thf(3369,plain,
    ! [SV16: $i] :
      ( ( ( ~ ( cType___24t @ SV16 ) )
        = $true )
      | ( ( ! [SY504: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY504 )
              | ! [SY505: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY505 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SY504 @ SY505 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY504 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY505 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3235]) ).

thf(3370,plain,
    ! [SV17: $i] :
      ( ( ( ~ ( cType___24t @ SV17 ) )
        = $true )
      | ( ( ! [SY506: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY506 )
              | ! [SY507: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY507 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SY506 @ SY507 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY506 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY507 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3236]) ).

thf(3371,plain,
    ! [SV18: $i] :
      ( ( ( ~ ( cType___24t @ SV18 ) )
        = $true )
      | ( ( ! [SY508: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY508 )
              | ! [SY509: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY509 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SY508 @ SY509 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY508 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY509 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3237]) ).

thf(3372,plain,
    ! [SV19: $i] :
      ( ( ( ~ ( cType___24t @ SV19 ) )
        = $true )
      | ( ( ! [SY510: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY510 )
              | ! [SY511: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY511 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SY510 @ SY511 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY510 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY511 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3238]) ).

thf(3373,plain,
    ! [SV20: $i] :
      ( ( ( ~ ( cType___24t @ SV20 ) )
        = $true )
      | ( ( ! [SY512: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY512 )
              | ! [SY513: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY513 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SY512 @ SY513 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY512 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY513 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3239]) ).

thf(3374,plain,
    ! [SV21: $i] :
      ( ( ( ~ ( cType___24t @ SV21 ) )
        = $true )
      | ( ( ! [SY514: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY514 )
              | ! [SY515: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY515 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SY514 @ SY515 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY514 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY515 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3240]) ).

thf(3375,plain,
    ! [SV22: $i] :
      ( ( ( ~ ( cType___24t @ SV22 ) )
        = $true )
      | ( ( ! [SY516: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY516 )
              | ! [SY517: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY517 )
                  | ! [SY518: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY518 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY516 @ SY517 ) @ SY518 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY516 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY517 @ SY518 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3241]) ).

thf(3376,plain,
    ! [SV23: $i] :
      ( ( ( ~ ( cType___24t @ SV23 ) )
        = $true )
      | ( ( ! [SY519: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY519 )
              | ! [SY520: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY520 )
                  | ! [SY521: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY521 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY519 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY520 @ SY521 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY520 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY519 @ SY521 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3242]) ).

thf(3377,plain,
    ! [SV24: $i] :
      ( ( ( ~ ( cType___24t @ SV24 ) )
        = $true )
      | ( ( ! [SY522: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY522 )
              | ! [SY523: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY523 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY522 @ SY523 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY523 @ SY522 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3243]) ).

thf(3378,plain,
    ! [SV25: $i] :
      ( ( ( ~ ( cType___24t @ SV25 ) )
        = $true )
      | ( ( ! [SY524: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV25 @ SY524 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV25 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV25 @ SY524 @ SY524 ) @ SY524 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3244]) ).

thf(3379,plain,
    ! [SV26: $i] :
      ( ( ( ~ ( cType___24t @ SV26 ) )
        = $true )
      | ( ( ! [SY525: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY525 )
              | ! [SY526: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY526 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SY525 @ SY526 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SY526 @ SY525 ) @ SY525 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3245]) ).

thf(3380,plain,
    ! [SV27: $i] :
      ( ( ( ~ ( cType___24t @ SV27 ) )
        = $true )
      | ( ( ! [SY527: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY527 )
              | ! [SY528: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY528 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SY527 @ SY528 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SY527 @ SY528 ) @ SY527 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3246]) ).

thf(3381,plain,
    ! [SV28: $i] :
      ( ( ( ~ ( cType___24t @ SV28 ) )
        = $true )
      | ( ( ! [SY529: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY529 )
              | ! [SY530: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY530 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SY529 @ SY530 ) @ SY529 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3247]) ).

thf(3382,plain,
    ! [SV29: $i] :
      ( ( ( ~ ( cType___24t @ SV29 ) )
        = $true )
      | ( ( ! [SY531: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY531 )
              | ! [SY532: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY532 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY531 @ SY532 )
                  | ! [SY533: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY533 )
                      | ! [SY534: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY534 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY533 @ SY534 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY531 @ SY533 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY532 @ SY534 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3248]) ).

thf(3383,plain,
    ! [SV30: $i] :
      ( ( ( ~ ( cType___24t @ SV30 ) )
        = $true )
      | ( ( ! [SY535: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY535 )
              | ! [SY536: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY536 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY535 @ SY536 ) )
                  | ! [SY537: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY537 )
                      | ! [SY538: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY538 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY537 @ SY538 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY535 @ SY537 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY536 @ SY538 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3249]) ).

thf(3384,plain,
    ! [SV31: $i] :
      ( ( ( ~ ( cType___24t @ SV31 ) )
        = $true )
      | ( ( ! [SY539: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY539 )
              | ! [SY540: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY540 )
                  | ! [SY541: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY541 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SY539 @ SY540 ) @ SY541 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY539 @ SY541 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY540 @ SY541 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3250]) ).

thf(3385,plain,
    ! [SV32: $i] :
      ( ( ( ~ ( cType___24t @ SV32 ) )
        = $true )
      | ( ( ! [SY542: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY542 )
              | ! [SY543: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY543 )
                  | ! [SY544: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY544 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY542 @ SY543 ) @ SY544 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY542 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY543 @ SY544 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3251]) ).

thf(3386,plain,
    ! [SV33: $i] :
      ( ( ( ~ ( cType___24t @ SV33 ) )
        = $true )
      | ( ( ! [SY545: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY545 )
              | ! [SY546: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY546 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY545 @ SY546 )
                  | ! [SY547: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY547 )
                      | ! [SY548: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY548 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY547 @ SY548 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY545 @ SY547 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY546 @ SY548 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3252]) ).

thf(3387,plain,
    ! [SV34: $i] :
      ( ( ( ~ ( cType___24t @ SV34 ) )
        = $true )
      | ( ( ! [SY549: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY549 )
              | ! [SY550: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY550 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY549 @ SY550 ) )
                  | ! [SY551: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY551 )
                      | ! [SY552: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY552 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY551 @ SY552 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY549 @ SY551 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY550 @ SY552 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3253]) ).

thf(3388,plain,
    ! [SV35: $i] :
      ( ( ( ~ ( cType___24t @ SV35 ) )
        = $true )
      | ( ( ! [SY553: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY553 )
              | ! [SY554: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY554 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SY553 @ SY554 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY553 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY554 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3254]) ).

thf(3389,plain,
    ! [SV36: $i] :
      ( ( ( ~ ( cType___24t @ SV36 ) )
        = $true )
      | ( ( ! [SY555: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY555 )
              | ! [SY556: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY556 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SY555 @ SY556 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY555 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY556 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3255]) ).

thf(3390,plain,
    ! [SV37: $i] :
      ( ( ( ~ ( cType___24t @ SV37 ) )
        = $true )
      | ( ( ! [SY557: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY557 )
              | ! [SY558: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY558 )
                  | ! [SY559: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY559 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY557 @ SY558 ) @ SY559 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY557 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY558 @ SY559 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3256]) ).

thf(3391,plain,
    ! [SV38: $i] :
      ( ( ( ~ ( cType___24t @ SV38 ) )
        = $true )
      | ( ( ! [SY560: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY560 )
              | ! [SY561: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY561 )
                  | ! [SY562: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY562 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY560 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY561 @ SY562 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY561 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY560 @ SY562 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3257]) ).

thf(3392,plain,
    ! [SV39: $i] :
      ( ( ( ~ ( cType___24t @ SV39 ) )
        = $true )
      | ( ( ! [SY563: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY563 )
              | ! [SY564: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY564 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY563 @ SY564 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY564 @ SY563 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3258]) ).

thf(3393,plain,
    ! [SV40: $i] :
      ( ( ( ~ ( cType___24t @ SV40 ) )
        = $true )
      | ( ( ! [SY565: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV40 @ SY565 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV40 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV40 @ SY565 @ SY565 ) @ SY565 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3259]) ).

thf(3394,plain,
    ! [SV41: $i] :
      ( ( ( ~ ( cType___24t @ SV41 ) )
        = $true )
      | ( ( ! [SY566: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY566 )
              | ! [SY567: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY567 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SY566 @ SY567 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SY566 @ SY567 ) @ SY567 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3260]) ).

thf(3395,plain,
    ! [SV42: $i] :
      ( ( ( ~ ( cType___24t @ SV42 ) )
        = $true )
      | ( ( ! [SY568: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY568 )
              | ! [SY569: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY569 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SY568 @ SY569 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SY569 @ SY568 ) @ SY569 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3261]) ).

thf(3396,plain,
    ! [SV43: $i] :
      ( ( ( ~ ( cType___24t @ SV43 ) )
        = $true )
      | ( ( ! [SY570: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY570 )
              | ! [SY571: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY571 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY570 @ SY571 )
                  | ! [SY572: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY572 )
                      | ! [SY573: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY573 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY572 @ SY573 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY570 @ SY572 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY571 @ SY573 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3262]) ).

thf(3397,plain,
    ! [SV44: $i] :
      ( ( ( ~ ( cType___24t @ SV44 ) )
        = $true )
      | ( ( ! [SY574: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY574 )
              | ! [SY575: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY575 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY574 @ SY575 ) )
                  | ! [SY576: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY576 )
                      | ! [SY577: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY577 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY576 @ SY577 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY574 @ SY576 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY575 @ SY577 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3263]) ).

thf(3398,plain,
    ! [SV45: $i] :
      ( ( ( ~ ( cType___24t @ SV45 ) )
        = $true )
      | ( ( ! [SY578: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY578 )
              | ! [SY579: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY579 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SY578 @ SY579 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SY578 @ SY579 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3264]) ).

thf(3399,plain,
    ! [SV46: $i] :
      ( ( ( ~ ( cType___24t @ SV46 ) )
        = $true )
      | ( ( ! [SY580: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY580 )
              | ! [SY581: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY581 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SY580 @ SY581 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SY581 @ SY580 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3265]) ).

thf(3400,plain,
    ! [SV47: $i] :
      ( ( ( ~ ( cType___24t @ SV47 ) )
        = $true )
      | ( ( ! [SY582: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY582 )
              | ! [SY583: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY583 )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SY582 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SY582 @ SY583 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3266]) ).

thf(3401,plain,
    ! [SV48: $i] :
      ( ( ( ~ ( cType___24t @ SV48 ) )
        = $true )
      | ( ( ! [SY584: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY584 )
              | ! [SY585: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY585 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SY584 @ SY585 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY585 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY584 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3267]) ).

thf(3402,plain,
    ! [SV49: $i] :
      ( ( ( ~ ( cType___24t @ SV49 ) )
        = $true )
      | ( ( ! [SY586: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY586 )
              | ! [SY587: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY587 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SY586 @ SY587 ) @ SY586 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3268]) ).

thf(3403,plain,
    ! [SV50: $i] :
      ( ( ( ~ ( cType___24t @ SV50 ) )
        = $true )
      | ( ( ! [SY588: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY588 )
              | ! [SY589: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY589 )
                  | ! [SY590: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY590 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SY588 @ SY590 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SY588 @ SY589 ) @ SY590 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3269]) ).

thf(3404,plain,
    ! [SV51: $i] :
      ( ( ( ~ ( cType___24t @ SV51 ) )
        = $true )
      | ( ( ! [SY591: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY591 )
              | ! [SY592: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY592 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SY591 @ SY592 ) @ SY592 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3270]) ).

thf(3405,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( cType___24t @ SV52 ) )
        = $true )
      | ( ( ! [SY593: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY593 )
              | ! [SY594: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY594 )
                  | ! [SY595: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY595 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SY594 @ SY595 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SY593 @ SY594 ) @ SY595 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3271]) ).

thf(3406,plain,
    ! [SV53: $i] :
      ( ( ( ~ ( cType___24t @ SV53 ) )
        = $true )
      | ( ( ! [SY596: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY596 )
              | ! [SY597: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY597 )
                  | ! [SY598: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY598 )
                      | ! [SY599: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY599 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY596 @ SY597 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY598 @ SY599 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY596 @ SY598 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY597 @ SY599 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3272]) ).

thf(3407,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( cType___24t @ SV54 ) )
        = $true )
      | ( ( ! [SY600: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY600 )
              | ! [SY601: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY601 )
                  | ! [SY602: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY602 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ SY601 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ SY602 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SY601 @ SY602 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3273]) ).

thf(3408,plain,
    ! [SV55: $i] :
      ( ( ( ~ ( cType___24t @ SV55 ) )
        = $true )
      | ( ( ! [SY603: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY603 )
              | ! [SY604: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY604 )
                  | ! [SY605: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY605 )
                      | ! [SY606: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY606 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY603 @ SY604 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY606 @ SY605 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY603 @ SY605 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY604 @ SY606 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3274]) ).

thf(3409,plain,
    ! [SV56: $i] :
      ( ( ( ~ ( cType___24t @ SV56 ) )
        = $true )
      | ( ( ! [SY607: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY607 )
              | ! [SY608: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY608 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SY607 @ SY608 ) @ SY607 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3275]) ).

thf(3410,plain,
    ! [SV57: $i] :
      ( ( ( ~ ( cType___24t @ SV57 ) )
        = $true )
      | ( ( ! [SY609: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY609 )
              | ! [SY610: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY610 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SY609 @ SY610 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY609 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY610 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3276]) ).

thf(3411,plain,
    ! [SV58: $i] :
      ( ( ( ~ ( cType___24t @ SV58 ) )
        = $true )
      | ( ( ! [SY611: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV58 @ SY611 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV58 @ SY611 @ SY611 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3277]) ).

thf(3412,plain,
    ! [SV59: $i] :
      ( ( ( ~ ( cType___24t @ SV59 ) )
        = $true )
      | ( ( ! [SY612: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY612 )
              | ! [SY613: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY613 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SY612 @ SY613 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY612 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY613 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3278]) ).

thf(3413,plain,
    ! [SV60: $i] :
      ( ( ( ~ ( cType___24t @ SV60 ) )
        = $true )
      | ( ( ! [SY614: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY614 )
              | ! [SY615: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY615 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SY614 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY615 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY614 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY615 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3279]) ).

thf(3414,plain,
    ! [SV61: $i] :
      ( ( ( ~ ( cType___24t @ SV61 ) )
        = $true )
      | ( ( ! [SY616: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY616 )
              | ! [SY617: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY617 )
                  | ! [SY618: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY618 )
                      | ! [SY619: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY619 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY616 @ SY617 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY618 @ SY619 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY616 @ SY618 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY617 @ SY619 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3280]) ).

thf(3415,plain,
    ! [SV62: $i] :
      ( ( ( ~ ( cType___24t @ SV62 ) )
        = $true )
      | ( ( ! [SY620: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY620 )
              | ! [SY621: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY621 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SY620 @ SY621 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SY620 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SY621 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3281]) ).

thf(3416,plain,
    ! [SV63: $i] :
      ( ( ( ~ ( cType___24t @ SV63 ) )
        = $true )
      | ( ( ! [SY622: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY622 )
              | ! [SY623: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY623 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SY622 @ SY623 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SY622 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SY623 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3282]) ).

thf(3417,plain,
    ! [SV64: $i] :
      ( ( ( ~ ( cType___24t @ SV64 ) )
        = $true )
      | ( ( ! [SY624: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY624 )
              | ! [SY625: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY625 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SY624 @ SY625 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SY624 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SY625 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3283]) ).

thf(3418,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( cType___24t @ SV65 ) )
        = $true )
      | ( ( ! [SY626: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY626 )
              | ! [SY627: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY627 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SY626 @ SY627 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY626 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY627 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3284]) ).

thf(3419,plain,
    ! [SV66: $i] :
      ( ( ( ~ ( cType___24t @ SV66 ) )
        = $true )
      | ( ( ! [SY628: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY628 )
              | ! [SY629: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY629 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SY628 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY629 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY628 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY629 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3285]) ).

thf(3420,plain,
    ! [SV67: $i] :
      ( ( ( ~ ( cType___24t @ SV67 ) )
        = $true )
      | ( ( ! [SY630: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY630 )
              | ! [SY631: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY631 )
                  | ! [SY632: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY632 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY630 @ SY632 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY631 @ SY632 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SY630 @ SY631 ) @ SY632 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3286]) ).

thf(3421,plain,
    ! [SV68: $i] :
      ( ( ( ~ ( cType___24t @ SV68 ) )
        = $true )
      | ( ( ! [SY633: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY633 )
              | ! [SY634: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY634 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SY633 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SY633 @ SY634 ) @ SY634 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3287]) ).

thf(3422,plain,
    ! [SV69: $i] :
      ( ( ( ~ ( cType___24t @ SV69 ) )
        = $true )
      | ( ( ! [SY635: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY635 )
              | ! [SY636: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY636 )
                  | ! [SY637: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY637 )
                      | ! [SY638: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY638 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY635 @ SY636 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY637 @ SY638 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY635 @ SY637 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY636 @ SY638 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3288]) ).

thf(3423,plain,
    ! [SV70: $i] :
      ( ( ( ~ ( cType___24t @ SV70 ) )
        = $true )
      | ( ( ! [SY639: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY639 )
              | ! [SY640: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY640 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SY639 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SY639 @ SY640 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3289]) ).

thf(3424,plain,
    ! [SV71: $i] :
      ( ( ( ~ ( cType___24t @ SV71 ) )
        = $true )
      | ( ( ! [SY641: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY641 )
              | ! [SY642: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY642 )
                  | ! [SY643: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY643 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SY641 @ SY642 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SY641 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SY642 @ SY643 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3290]) ).

thf(3425,plain,
    ! [SV72: $i] :
      ( ( ( ~ ( cType___24t @ SV72 ) )
        = $true )
      | ( ( ! [SY644: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY644 )
              | ! [SY645: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY645 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SY645 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SY644 @ SY645 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3291]) ).

thf(3426,plain,
    ! [SV73: $i] :
      ( ( ( ~ ( cType___24t @ SV73 ) )
        = $true )
      | ( ( ! [SY646: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY646 )
              | ! [SY647: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY647 )
                  | ! [SY648: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY648 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SY646 @ SY648 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SY646 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SY647 @ SY648 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3292]) ).

thf(3427,plain,
    ! [SV74: $i] :
      ( ( ( ~ ( cType___24t @ SV74 ) )
        = $true )
      | ( ( ! [SY649: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY649 )
              | ! [SY650: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY650 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SY649 @ SY650 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY650 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY649 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3293]) ).

thf(3428,plain,
    ! [SV128: $i,SV76: $i] :
      ( ( ! [SY931: $i,SY932: $i,SY933: $i] :
            ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ SV76 ) @ SV128 ) @ SY931 ) @ SY932 ) @ SY933 )
            = ( c_24__lam__45594___24a5 @ SV76 @ SV128 @ SY931 @ SY932 @ SY933 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3295]) ).

thf(3429,plain,
    ! [SV129: $i,SV77: $i] :
      ( ( ! [SY934: $i] :
            ( ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2einclusion @ SV77 ) @ SV129 ) @ SY934 )
            = ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV77 @ SV129 @ SY934 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3296]) ).

thf(3430,plain,
    ! [SV78: $i] :
      ( ( ( ~ ( cProp___24t @ SV78 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY657: $i] :
                          ( ~ ( cProp___24t @ SY657 )
                          | ( p @ SV78 )
                          | ~ ( p @ SV78 )
                          | ( p @ SY657 ) )
                    | ~ ! [SY658: $i] :
                          ( ~ ( cProp___24t @ SY658 )
                          | ( p @ SV78 )
                          | ~ ( p @ SY658 )
                          | ( p @ SY658 ) ) )
              | ~ ~ ( ~ ! [SY659: $i] :
                          ( ~ ( cProp___24t @ SY659 )
                          | ~ ( p @ SY659 )
                          | ~ ( p @ SV78 )
                          | ( p @ SY659 ) )
                    | ~ ! [SX1: $i] :
                          ( ~ ( cProp___24t @ SX1 )
                          | ~ ( p @ SX1 )
                          | ~ ( p @ SX1 )
                          | ( p @ SX1 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3298]) ).

thf(3431,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( sK2_SY468 @ SX0 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ SX0 @ ( sK1_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK2_SY468 @ SX0 ) ) ) ) )
            | ( c_24__type__96___24t @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3299]) ).

thf(3432,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( c_24__type__96___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3299]) ).

thf(3433,plain,
    ! [SV79: $i] :
      ( ( ( ~ ( cType___24t @ SV79 ) )
        = $true )
      | ( ( ! [SY661: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY661 )
              | ~ ( ~ ! [SY662: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY662 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SY661 @ SY662 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY661 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY662 ) )
                  | ~ ! [SY663: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY663 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SY661 @ SY663 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY663 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY661 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3300]) ).

thf(3434,plain,
    ! [SV80: $i] :
      ( ( ~ ! [SY664: $i,SY665: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY664 @ SY665 )
              | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY664 ) @ SY665 ) ) )
        | ~ ! [SY666: $i,SY667: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY666 ) @ SY667 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY666 @ SY667 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3301]) ).

thf(3435,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c_24__lam__35673___24a2 @ SX0 @ SX1 )
            | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3302]) ).

thf(3436,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) )
            | ( c_24__lam__35673___24a2 @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3302]) ).

thf(3437,plain,
    ! [SV130: $i,SV81: $i] :
      ( ( ! [SY935: $i] :
            ~ ( ~ ! [SY936: $i,SY937: $i] :
                    ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SY935 @ SY936 @ SY937 )
                    | ( p @ ( happ @ ( happ @ SV130 @ SY936 ) @ SY937 ) )
                    | ( p @ ( happ @ ( happ @ SY935 @ SY936 ) @ SY937 ) ) )
              | ~ ~ ( ~ ! [SY938: $i,SY939: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY938 ) @ SY939 ) )
                          | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SY935 @ SY938 @ SY939 ) )
                    | ~ ! [SY940: $i,SY941: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY935 @ SY940 ) @ SY941 ) )
                          | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SY935 @ SY940 @ SY941 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3303]) ).

thf(3438,plain,
    ! [SV131: $i,SV82: $i] :
      ( ( ! [SY942: $i] :
            ~ ( ~ ! [SY943: $i,SY944: $i] :
                    ( ( ( happ @ SY942 @ SY943 )
                     != ( happ @ SY942 @ SY944 ) )
                    | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SY942 @ SY943 @ SY944 ) )
              | ~ ! [SY945: $i,SY946: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SY942 @ SY945 @ SY946 )
                    | ( ( happ @ SY942 @ SY945 )
                      = ( happ @ SY942 @ SY946 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3304]) ).

thf(3439,plain,
    ! [SV83: $i] :
      ( ( ( ~ ( cType___24t @ SV83 ) )
        = $true )
      | ( ( ! [SY682: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY682 )
              | ! [SY683: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY683 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY682 @ SY683 )
                  | ! [SY684: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY684 )
                      | ~ ( ~ ! [SY685: $i] :
                                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY685 )
                                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY684 @ SY685 )
                                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY682 @ SY684 ) )
                                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY683 @ SY685 ) ) )
                          | ~ ! [SY686: $i] :
                                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY686 )
                                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY684 @ SY686 )
                                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY683 @ SY686 ) )
                                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY682 @ SY684 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3305]) ).

thf(3440,plain,
    ! [SV132: $i,SV84: $i] :
      ( ( ~ ( ~ ! [SY947: $i,SY948: $i] :
                  ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY947 @ SY948 )
                  | ( p @ ( happ @ ( happ @ SV132 @ SY947 ) @ SY948 ) ) )
            | ~ ! [SY949: $i,SY950: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV132 @ SY949 ) @ SY950 ) )
                  | ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY949 @ SY950 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3306]) ).

thf(3441,plain,
    ! [SV85: $i] :
      ( ( ( ~ ( cType___24t @ SV85 ) )
        = $true )
      | ( ( ! [SY692: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY692 )
              | ~ ( ~ ! [SY693: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY693 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SY692 @ SY693 )
                        | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY692 ) )
                        | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY693 ) ) )
                  | ~ ! [SY694: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY694 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SY692 @ SY694 )
                        | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY694 ) )
                        | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY692 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3307]) ).

thf(3442,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( cType___24t @ ( happ @ SX0 @ ( sK12_Vv__CANONICAL__0 @ SX0 ) ) ) )
            | ( c_24__type__28___24t @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3308]) ).

thf(3443,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( c_24__type__28___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ( cType___24t @ ( happ @ SX0 @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3308]) ).

thf(3444,plain,
    ! [SV86: $i,SV133: $i] :
      ( ( ~ ( ~ ! [SY951: $i,SY952: $i] :
                  ( ~ ( p @ ( happ @ SV133 @ SY952 ) )
                  | ( p @ ( happ @ SY951 @ SY952 ) )
                  | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY951 @ SY952 ) )
            | ~ ~ ( ~ ! [SY953: $i,SY954: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
                        | ( p @ ( happ @ SV133 @ SY954 ) ) )
                  | ~ ! [SY955: $i,SY956: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
                        | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3309]) ).

thf(3445,plain,
    ! [SV134: $i,SV87: $i] :
      ( ( ~ ( ~ ! [SY957: $i,SY958: $i] :
                  ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY957 @ SY958 )
                  | ( p @ ( happ @ ( happ @ SV134 @ SY958 ) @ SY957 ) ) )
            | ~ ! [SY959: $i,SY960: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV134 @ SY960 ) @ SY959 ) )
                  | ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY959 @ SY960 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3310]) ).

thf(3446,plain,
    ! [SV88: $i] :
      ( ( ~ ! [SY707: $i,SY708: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY707 @ SY708 )
              | ~ ( p @ ( happ @ SY707 @ SY708 ) ) )
        | ~ ! [SY709: $i,SY710: $i] :
              ( ( p @ ( happ @ SY709 @ SY710 ) )
              | ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY709 @ SY710 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3311]) ).

thf(3447,plain,
    ! [SV89: $i] :
      ( ( ( ~ ( cType___24t @ SV89 ) )
        = $true )
      | ( ( ! [SY711: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY711 )
              | ! [SY712: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY712 )
                  | ~ ( ~ ! [SY713: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY713 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SY711 @ SY712 ) @ SY713 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SY711 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY712 @ SY713 ) ) ) )
                      | ~ ! [SY714: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY714 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SY711 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY712 @ SY714 ) ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SY711 @ SY712 ) @ SY714 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3312]) ).

thf(3448,plain,
    ! [SV135: $i,SV90: $i] :
      ( ( ! [SY961: $i] :
            ~ ( ~ ! [SY962: $i,SY963: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SY961 @ SY962 @ SY963 )
                    | ( p @ ( happ @ ( happ @ SV135 @ SY962 ) @ SY963 ) )
                    | ( p @ ( happ @ ( happ @ SY961 @ SY962 ) @ SY963 ) ) )
              | ~ ~ ( ~ ! [SY964: $i,SY965: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY964 ) @ SY965 ) )
                          | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SY961 @ SY964 @ SY965 ) )
                    | ~ ! [SY966: $i,SY967: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SY961 @ SY966 ) @ SY967 ) )
                          | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SY961 @ SY966 @ SY967 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3313]) ).

thf(3449,plain,
    ! [SV91: $i] :
      ( ( ( ~ ( cProp___24t @ SV91 ) )
        = $true )
      | ( ( ! [SY723: $i] :
              ( ~ ( cProp___24t @ SY723 )
              | ~ ( ~ ~ ( ~ ! [SY724: $i] :
                              ( ~ ( cProp___24t @ SY724 )
                              | ( p @ SV91 )
                              | ~ ( p @ SV91 )
                              | ( p @ SY723 )
                              | ( p @ SY724 ) )
                        | ~ ! [SY725: $i] :
                              ( ~ ( cProp___24t @ SY725 )
                              | ( p @ SV91 )
                              | ~ ( p @ SY725 )
                              | ( p @ SY723 )
                              | ( p @ SY725 ) ) )
                  | ~ ~ ( ~ ! [SY726: $i] :
                              ( ~ ( cProp___24t @ SY726 )
                              | ~ ( p @ SY723 )
                              | ~ ( p @ SV91 )
                              | ( p @ SY723 )
                              | ( p @ SY726 ) )
                        | ~ ! [SX2: $i] :
                              ( ~ ( cProp___24t @ SX2 )
                              | ~ ( p @ SY723 )
                              | ~ ( p @ SX2 )
                              | ( p @ SY723 )
                              | ( p @ SX2 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3314]) ).

thf(3450,plain,
    ! [SV92: $i,SV136: $i] :
      ( ( ! [SY968: $i] :
            ~ ( ~ ! [SY969: $i,SY970: $i] :
                    ( ~ ( p @ ( happ @ SV136 @ SY969 ) )
                    | ~ ( p @ ( happ @ SY968 @ SY970 ) )
                    | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SY968 @ SY969 @ SY970 ) )
              | ~ ~ ( ~ ! [SY971: $i] :
                          ( ! [SY972: $i] :
                              ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SY968 @ SY971 @ SY972 )
                          | ( p @ ( happ @ SV136 @ SY971 ) ) )
                    | ~ ! [SY973: $i,SY974: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SY968 @ SY973 @ SY974 )
                          | ( p @ ( happ @ SY968 @ SY974 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3315]) ).

thf(3451,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) ) )
            | ( c_24__type__11748___24t @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3316]) ).

thf(3452,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c_24__type__11748___24t @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3316]) ).

thf(3453,plain,
    ( ( ~ ( ! [SX0: $i] :
              ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 )
          | $true ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3317]) ).

thf(3454,plain,
    ( ( ~ ( ~ $true
          | ! [SX0: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3317]) ).

thf(3455,plain,
    ! [SV137: $i,SV93: $i] :
      ( ( ! [SY975: $i] :
            ~ ( ~ ! [SY976: $i,SY977: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SY975 @ SY976 @ SY977 )
                    | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SY975 ) @ SY976 ) @ SY977 ) ) )
              | ~ ! [SY978: $i,SY979: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SY975 ) @ SY978 ) @ SY979 ) )
                    | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SY975 @ SY978 @ SY979 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3318]) ).

thf(3456,plain,
    ! [SV94: $i] :
      ( ( ~ ! [SY742: $i,SY743: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY742 @ SY743 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY743 @ SY742 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY742 @ SY743 ) )
        | ~ ~ ( ~ ! [SY744: $i,SY745: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) )
              | ~ ! [SY746: $i,SY747: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3319]) ).

thf(3457,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) )
            | ~ ( p @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3320]) ).

thf(3458,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( p @ SX1 )
            | ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3320]) ).

thf(3459,plain,
    ! [SV95: $i,SV138: $i] :
      ( ( ~ ( ~ ! [SY980: $i,SY981: $i] :
                  ( ~ ( p @ ( happ @ SV138 @ SY981 ) )
                  | ~ ( p @ ( happ @ SY980 @ SY981 ) )
                  | ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY980 @ SY981 ) )
            | ~ ~ ( ~ ! [SY982: $i,SY983: $i] :
                        ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
                        | ( p @ ( happ @ SV138 @ SY983 ) ) )
                  | ~ ! [SY984: $i,SY985: $i] :
                        ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
                        | ( p @ ( happ @ SY984 @ SY985 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3321]) ).

thf(3460,plain,
    ! [SV96: $i] :
      ( ( ( ~ ( cType___24t @ SV96 ) )
        = $true )
      | ( ( ! [SY755: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY755 )
              | ~ ( ~ ! [SY756: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY756 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SY755 @ SY756 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY755 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY756 ) ) )
                  | ~ ! [SY757: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY757 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SY755 @ SY757 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY757 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY755 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3322]) ).

thf(3461,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ( ~ ! [SY986: $i,SY987: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY986 @ SY987 )
                  | ( SY986 = SY987 )
                  | ( p @ ( happ @ ( happ @ SV139 @ SY986 ) @ SY987 ) ) )
            | ~ ~ ( ~ ! [SY988: $i,SY989: $i] :
                        ( ( SY988 != SY989 )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) )
                  | ~ ! [SY990: $i,SY991: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3323]) ).

thf(3462,plain,
    ! [SV98: $i] :
      ( ( ~ ! [SY765: $i,SY766: $i] :
              ( ~ ( ~ ( t @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) @ SV98 )
                  | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) @ SV98 )
                        | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SY765 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) )
                              | ~ ~ ( p @ ( happ @ ( happ @ SY766 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) ) ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY765 @ SY766 ) ) )
        | ~ ! [SY767: $i,SY768: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY767 @ SY768 ) )
              | ! [SY769: $i] :
                  ( ~ ( t @ SY769 @ SV98 )
                  | ! [SY770: $i] :
                      ( ~ ( t @ SY770 @ SV98 )
                      | ~ ( p @ ( happ @ ( happ @ SY767 @ SY769 ) @ SY770 ) )
                      | ( p @ ( happ @ ( happ @ SY768 @ SY769 ) @ SY770 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3324]) ).

thf(3463,plain,
    ! [SV140: $i,SV99: $i] :
      ( ( ~ ( ~ ! [SY992: $i,SY993: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY992 @ SY993 )
                  | ( p @ ( happ @ ( happ @ SV140 @ SY992 ) @ SY993 ) )
                  | ( p @ ( happ @ ( happ @ SV140 @ SY993 ) @ SY992 ) ) )
            | ~ ~ ( ~ ! [SY994: $i,SY995: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) )
                  | ~ ! [SY996: $i,SY997: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3325]) ).

thf(3464,plain,
    ! [SV100: $i,SV141: $i] :
      ( ( ! [SY998: $i] :
            ~ ( ~ ! [SY999: $i,SY1000: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV141 @ SY999 ) @ SY1000 ) )
                    | ( p @ ( happ @ ( happ @ SY998 @ SY999 ) @ SY1000 ) )
                    | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SY998 @ SY999 @ SY1000 ) )
              | ~ ~ ( ~ ! [SY1001: $i,SY1002: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SY998 @ SY1001 @ SY1002 )
                          | ( p @ ( happ @ ( happ @ SV141 @ SY1001 ) @ SY1002 ) ) )
                    | ~ ! [SY1003: $i,SY1004: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SY998 @ SY1003 @ SY1004 )
                          | ~ ( p @ ( happ @ ( happ @ SY998 @ SY1003 ) @ SY1004 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3326]) ).

thf(3465,plain,
    ! [SV101: $i] :
      ( ( ~ ! [SY786: $i,SY787: $i] :
              ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) )
                  | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY786 @ ( happ @ SY787 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) ) ) )
              | ( c_24__type__11699___24t @ SV101 @ SY786 @ SY787 ) )
        | ~ ! [SY788: $i,SY789: $i] :
              ( ~ ( c_24__type__11699___24t @ SV101 @ SY788 @ SY789 )
              | ! [SY790: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY790 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY788 @ ( happ @ SY789 @ SY790 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3327]) ).

thf(3466,plain,
    ! [SV142: $i,SV102: $i] :
      ( ( ! [SY1005: $i] :
            ~ ( ~ ! [SY1006: $i,SY1007: $i] :
                    ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SY1005 @ SY1006 @ SY1007 )
                    | ( p @ ( happ @ ( happ @ SY1005 @ SY1006 ) @ SY1007 ) ) )
              | ~ ! [SY1008: $i,SY1009: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY1005 @ SY1008 ) @ SY1009 ) )
                    | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SY1005 @ SY1008 @ SY1009 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3328]) ).

thf(3467,plain,
    ! [SV103: $i] :
      ( ( ~ ! [SY797: $i,SY798: $i] :
              ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY797 @ SY798 ) )
              | ( p @ SY797 )
              | ( p @ SY798 ) )
        | ~ ~ ( ~ ! [SY799: $i] :
                    ( ~ ( p @ SY799 )
                    | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) )
              | ~ ! [SY801: $i,SY802: $i] :
                    ( ~ ( p @ SY802 )
                    | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3329]) ).

thf(3468,plain,
    ! [SV104: $i,SV143: $i] :
      ( ( ! [SY1010: $i] :
            ~ ( ~ ! [SY1011: $i,SY1012: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY1010 @ SY1011 ) @ SY1012 ) )
                    | ~ ( p @ ( happ @ SV143 @ SY1011 ) )
                    | ~ ( p @ ( happ @ SV143 @ SY1012 ) )
                    | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SY1010 @ SY1011 @ SY1012 ) )
              | ~ ~ ( ~ ~ ( ~ ! [SY1013: $i,SY1014: $i] :
                                ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SY1010 @ SY1013 @ SY1014 )
                                | ( p @ ( happ @ ( happ @ SY1010 @ SY1013 ) @ SY1014 ) ) )
                          | ~ ! [SY1015: $i] :
                                ( ! [SY1016: $i] :
                                    ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SY1010 @ SY1015 @ SY1016 )
                                | ( p @ ( happ @ SV143 @ SY1015 ) ) ) )
                    | ~ ! [SY1017: $i,SY1018: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SY1010 @ SY1017 @ SY1018 )
                          | ( p @ ( happ @ SV143 @ SY1018 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3330]) ).

thf(3469,plain,
    ! [SV105: $i] :
      ( ( ~ ! [SY813: $i,SY814: $i] :
              ( ( SY813 != SY814 )
              | ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY813 @ SY814 ) ) )
        | ~ ! [SY815: $i,SY816: $i] :
              ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY815 @ SY816 ) )
              | ( SY815 = SY816 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3331]) ).

thf(3470,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK14_SY479 @ SX1 @ SX0 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) @ ( sK14_SY479 @ SX1 @ SX0 ) ) ) ) )
            | ( c_24__type__11829___24t @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3332]) ).

thf(3471,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( c_24__type__11829___24t @ SX0 @ SX1 )
            | ! [SX2: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
                | ! [SX3: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3332]) ).

thf(3472,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ( ~ ! [SY1019: $i,SY1020: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1019 @ SY1020 )
                  | ( p @ ( happ @ ( happ @ SV144 @ SY1020 ) @ SY1019 ) )
                  | ( SY1019 = SY1020 )
                  | ( p @ ( happ @ ( happ @ SV144 @ SY1019 ) @ SY1020 ) ) )
            | ~ ~ ( ~ ! [SY1021: $i,SY1022: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) )
                  | ~ ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                              ( ( SY1023 != SY1024 )
                              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
                        | ~ ! [SY1025: $i,SY1026: $i] :
                              ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3333]) ).

thf(3473,plain,
    ! [SV145: $i,SV107: $i] :
      ( ( ! [SY1027: $i] :
            ~ ( ~ ! [SY1028: $i,SY1029: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SY1027 @ SY1028 @ SY1029 )
                    | ( p @ ( happ @ SY1028 @ ( happ @ SY1027 @ SY1029 ) ) ) )
              | ~ ! [SY1030: $i,SY1031: $i] :
                    ( ~ ( p @ ( happ @ SY1030 @ ( happ @ SY1027 @ SY1031 ) ) )
                    | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SY1027 @ SY1030 @ SY1031 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3334]) ).

thf(3474,plain,
    ! [SV108: $i,SV146: $i] :
      ( ( ~ ( ~ ! [SY1032: $i,SY1033: $i] :
                  ( ( SY1032 != SY1033 )
                  | ~ ( p @ ( happ @ SV146 @ SY1032 ) )
                  | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1032 @ SY1033 ) )
            | ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
                        | ( SY1034 = SY1035 ) )
                  | ~ ! [SY1036: $i] :
                        ( ! [SY1037: $i] :
                            ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
                        | ( p @ ( happ @ SV146 @ SY1036 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3335]) ).

thf(3475,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK4_SY469 @ SX0 ) )
                      | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK5_SY471 @ SX0 ) )
                            | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK3_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK4_SY469 @ SX0 ) ) @ ( sK5_SY471 @ SX0 ) ) ) ) ) )
            | ( c_24__type__90___24t @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3336]) ).

thf(3476,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( c_24__type__90___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                    | ! [SX3: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX3 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3336]) ).

thf(3477,plain,
    ! [SV109: $i] :
      ( ( ( ~ ( cType___24t @ SV109 ) )
        = $true )
      | ( ( ! [SY839: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY839 )
              | ~ ( ~ ! [SY840: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY840 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SY839 @ SY840 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY839 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY840 ) ) )
                  | ~ ! [SY841: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY841 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SY839 @ SY841 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY841 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY839 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3337]) ).

thf(3478,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SX0 ) )
                      | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SX0 ) )
                            | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SX0 ) )
                                  | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK8_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK9_SY473 @ SX0 ) ) @ ( sK10_SY476 @ SX0 ) ) @ ( sK11_SY478 @ SX0 ) ) ) ) ) ) )
            | ( c_24__type__4733___24t @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3338]) ).

thf(3479,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( c_24__type__4733___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cType___24t @ SX2 )
                    | ! [SX3: $i] :
                        ( ~ ( cType___24t @ SX3 )
                        | ! [SX4: $i] :
                            ( ~ ( cType___24t @ SX4 )
                            | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3338]) ).

thf(3480,plain,
    ! [SV110: $i,SV147: $i] :
      ( ( ! [SY1038: $i] :
            ~ ( ~ ! [SY1039: $i,SY1040: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV147 @ SY1039 ) @ SY1040 ) )
                    | ~ ( p @ ( happ @ ( happ @ SY1038 @ SY1039 ) @ SY1040 ) )
                    | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SY1038 @ SY1039 @ SY1040 ) )
              | ~ ~ ( ~ ! [SY1041: $i,SY1042: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SY1038 @ SY1041 @ SY1042 )
                          | ( p @ ( happ @ ( happ @ SV147 @ SY1041 ) @ SY1042 ) ) )
                    | ~ ! [SY1043: $i,SY1044: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SY1038 @ SY1043 @ SY1044 )
                          | ( p @ ( happ @ ( happ @ SY1038 @ SY1043 ) @ SY1044 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3339]) ).

thf(3481,plain,
    ! [SV148: $i,SV111: $i] :
      ( ( ~ ( ~ ! [SY1045: $i,SY1046: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1045 @ SY1046 )
                  | ( p @ ( happ @ ( happ @ SV148 @ SY1046 ) @ SY1045 ) ) )
            | ~ ! [SY1047: $i,SY1048: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV148 @ SY1048 ) @ SY1047 ) )
                  | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1047 @ SY1048 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3340]) ).

thf(3482,plain,
    ! [SV112: $i] :
      ( ( ~ ! [SY855: $i,SY856: $i] :
              ( ~ ( p @ SY855 )
              | ~ ( p @ SY856 )
              | ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY855 @ SY856 ) ) )
        | ~ ~ ( ~ ! [SY857: $i] :
                    ( ! [SY858: $i] :
                        ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
                    | ( p @ SY857 ) )
              | ~ ! [SY859: $i,SY860: $i] :
                    ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
                    | ( p @ SY860 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3341]) ).

thf(3483,plain,
    ! [SV149: $i,SV113: $i] :
      ( ( ~ ( ~ ! [SY1049: $i,SY1050: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1049 @ SY1050 )
                  | ( p @ ( happ @ SV149 @ SY1050 ) )
                  | ( p @ ( happ @ SY1049 @ SY1050 ) ) )
            | ~ ~ ( ~ ! [SY1051: $i,SY1052: $i] :
                        ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
                        | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) )
                  | ~ ! [SY1053: $i,SY1054: $i] :
                        ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
                        | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3342]) ).

thf(3484,plain,
    ! [SV114: $i] :
      ( ( ~ ~ ( ~ ! [SY868: $i] :
                    ( ( p @ SY868 )
                    | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) )
              | ~ ! [SY870: $i,SY871: $i] :
                    ( ~ ( p @ SY871 )
                    | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) )
        | ~ ! [SY872: $i,SY873: $i] :
              ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY872 @ SY873 ) )
              | ~ ( p @ SY872 )
              | ( p @ SY873 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3343]) ).

thf(3485,plain,
    ! [SV115: $i] :
      ( ( ( ~ ( cType___24t @ SV115 ) )
        = $true )
      | ( ( ! [SY874: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY874 )
              | ! [SY875: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY875 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SY874 @ SY875 )
                  | ! [SY876: $i] :
                      ( ~ ( t @ SY876 @ SV115 )
                      | ~ ( ~ ! [SY877: $i] :
                                ( ~ ( t @ SY877 @ SV115 )
                                | ~ ( p @ ( happ @ ( happ @ SY874 @ SY876 ) @ SY877 ) )
                                | ( p @ ( happ @ ( happ @ SY875 @ SY876 ) @ SY877 ) ) )
                          | ~ ! [SY878: $i] :
                                ( ~ ( t @ SY878 @ SV115 )
                                | ~ ( p @ ( happ @ ( happ @ SY875 @ SY876 ) @ SY878 ) )
                                | ( p @ ( happ @ ( happ @ SY874 @ SY876 ) @ SY878 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3344]) ).

thf(3486,plain,
    ! [SV116: $i,SV150: $i] :
      ( ( ~ ( ~ ! [SY1055: $i,SY1056: $i] :
                  ( ~ ( p @ ( happ @ SV150 @ SY1056 ) )
                  | ~ ( p @ ( happ @ SY1055 @ SY1056 ) )
                  | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1055 @ SY1056 ) )
            | ~ ~ ( ~ ! [SY1057: $i,SY1058: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
                        | ( p @ ( happ @ SV150 @ SY1058 ) ) )
                  | ~ ! [SY1059: $i,SY1060: $i] :
                        ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
                        | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3345]) ).

thf(3487,plain,
    ! [SV117: $i] :
      ( ( ( ~ ( cType___24t @ SV117 ) )
        = $true )
      | ( ( ! [SY886: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY886 )
              | ! [SY887: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY887 )
                  | ~ ( ~ ! [SY888: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY888 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ SY887 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY887 @ SY888 ) ) ) )
                      | ~ ! [SY889: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY889 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ SY889 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY887 @ SY889 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3346]) ).

thf(3488,plain,
    ! [SV151: $i,SV118: $i] :
      ( ( ! [SY1061: $i,SY1062: $i] :
            ~ ( ~ ! [SY1063: $i,SY1064: $i] :
                    ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SY1061 @ SY1062 @ SY1063 @ SY1064 )
                    | ( p @ ( happ @ ( happ @ SY1062 @ ( happ @ SY1061 @ SY1063 ) ) @ ( happ @ SY1061 @ SY1064 ) ) ) )
              | ~ ! [SY1065: $i,SY1066: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY1062 @ ( happ @ SY1061 @ SY1065 ) ) @ ( happ @ SY1061 @ SY1066 ) ) )
                    | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SY1061 @ SY1062 @ SY1065 @ SY1066 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3347]) ).

thf(3489,plain,
    ! [SV152: $i,SV119: $i] :
      ( ( ! [SY1067: $i,SY1068: $i] :
            ~ ( ~ ! [SY1069: $i,SY1070: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SY1067 @ SY1068 @ SY1069 @ SY1070 )
                    | ( p @ ( happ @ ( happ @ SY1068 @ ( happ @ SY1067 @ SY1069 ) ) @ ( happ @ SY1067 @ SY1070 ) ) ) )
              | ~ ! [SY1071: $i,SY1072: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY1068 @ ( happ @ SY1067 @ SY1071 ) ) @ ( happ @ SY1067 @ SY1072 ) ) )
                    | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SY1067 @ SY1068 @ SY1071 @ SY1072 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3348]) ).

thf(3490,plain,
    ! [SV120: $i] :
      ( ( ~ ! [SY904: $i,SY905: $i] :
              ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY904 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) )
                  | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY905 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) ) ) )
              | ( c_24__type__11787___24t @ SV120 @ SY904 @ SY905 ) )
        | ~ ! [SY906: $i,SY907: $i] :
              ( ~ ( c_24__type__11787___24t @ SV120 @ SY906 @ SY907 )
              | ! [SY908: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY906 @ SY908 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY907 @ SY908 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3349]) ).

thf(3491,plain,
    ! [SV153: $i,SV121: $i] :
      ( ( ~ ( ~ ! [SY1073: $i,SY1074: $i] :
                  ( ( SY1073 != SY1074 )
                  | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1073 @ SY1074 ) ) )
            | ~ ! [SY1075: $i,SY1076: $i] :
                  ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1075 @ SY1076 ) )
                  | ( SY1075 = SY1076 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3350]) ).

thf(3492,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SX0 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SX0 ) )
                      | ~ ~ ( cType___24t @ ( happ @ ( happ @ SX0 @ ( sK6_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK7_SY472 @ SX0 ) ) ) ) )
            | ( c_24__type__52___24t @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3351]) ).

thf(3493,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( c_24__type__52___24t @ SX0 )
            | ! [SX1: $i] :
                ( ~ ( cType___24t @ SX1 )
                | ! [SX2: $i] :
                    ( ~ ( cType___24t @ SX2 )
                    | ( cType___24t @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3351]) ).

thf(3494,plain,
    ! [SV154: $i,SV122: $i] :
      ( ( ! [SY1077: $i,SY1078: $i] :
            ~ ( ~ ! [SY1079: $i,SY1080: $i] :
                    ( ( ( happ @ SY1077 @ SY1079 )
                     != ( happ @ SY1077 @ SY1080 ) )
                    | ~ ( p @ ( happ @ ( happ @ SY1078 @ SY1079 ) @ SY1080 ) )
                    | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SY1077 @ SY1078 @ SY1079 @ SY1080 ) )
              | ~ ~ ( ~ ! [SY1081: $i,SY1082: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SY1077 @ SY1078 @ SY1081 @ SY1082 )
                          | ( ( happ @ SY1077 @ SY1081 )
                            = ( happ @ SY1077 @ SY1082 ) ) )
                    | ~ ! [SY1083: $i,SY1084: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SY1077 @ SY1078 @ SY1083 @ SY1084 )
                          | ( p @ ( happ @ ( happ @ SY1078 @ SY1083 ) @ SY1084 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3352]) ).

thf(3495,plain,
    ! [SV155: $i,SV123: $i,SV1: $i] :
      ( ( ! [SY1085: $i,SY1086: $i] :
            ( ( c_24__lam__45594___24a5 @ SV1 @ SV123 @ SV155 @ SY1085 @ SY1086 )
            = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV123 @ ( happ @ SY1085 @ SY1086 ) @ SV155 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3353]) ).

thf(3496,plain,
    ! [SV2: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV2 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ SV2 @ SV2 ) @ c_24__lam__35673 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3354]) ).

thf(3497,plain,
    ! [SV3: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV3 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ c_24__lam__35673 @ SV3 ) @ c_24__lam__35673 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3355]) ).

thf(3498,plain,
    ! [SV4: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ cA @ SV4 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ cA @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ cA @ SV4 @ c_24__lam__35673 ) @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3356]) ).

thf(3499,plain,
    ! [SV5: $i] :
      ( ( ( cType___24t @ SV5 )
        = $false )
      | ( ( ! [SY485: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY485 )
              | ! [SY486: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY486 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY485 @ SY486 )
                  | ! [SY487: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY487 )
                      | ! [SY488: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY488 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY487 @ SY488 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY485 @ SY487 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY486 @ SY488 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3357]) ).

thf(3500,plain,
    ! [SV6: $i] :
      ( ( ( cType___24t @ SV6 )
        = $false )
      | ( ( ! [SY489: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV6 @ SY489 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV6 @ SY489 @ SY489 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3358]) ).

thf(3501,plain,
    ! [SV156: $i,SV124: $i,SV7: $i] :
      ( ( ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV7 ) @ SV124 ) @ SV156 )
        = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV7 @ SV124 @ SV156 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3359]) ).

thf(3502,plain,
    ! [SV157: $i,SV125: $i,SV8: $i] :
      ( ( ! [SY1087: $i] :
            ( ( c_24__lam__33077___24a4 @ SV8 @ SV125 @ SV157 @ SY1087 )
            = ( happ @ SV157 @ SY1087 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3360]) ).

thf(3503,plain,
    ! [SV158: $i,SV126: $i,SV9: $i] :
      ( ( ! [SY1088: $i] :
            ( ( c_24__lam__33085___24a4 @ SV9 @ SV126 @ SV158 @ SY1088 )
            = ( happ @ SV158 @ SY1088 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3361]) ).

thf(3504,plain,
    ! [SV10: $i] :
      ( ( ( cProp___24t @ SV10 )
        = $false )
      | ( ( ! [SY498: $i] :
              ( ~ ( cProp___24t @ SY498 )
              | ~ ( p @ SV10 )
              | ~ ( p @ SY498 )
              | ( p @ SV10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3362]) ).

thf(3505,plain,
    ! [SV11: $i] :
      ( ( ( cProp___24t @ SV11 )
        = $false )
      | ( ( ~ ( p @ SV11 )
          | ( p @ SV11 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3363]) ).

thf(3506,plain,
    ! [SV127: $i] :
      ( ( ( cProp___24t @ SV127 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3364]) ).

thf(3507,plain,
    ! [SV12: $i] :
      ( ( ( cProp___24t @ SV12 )
        = $false )
      | ( ( ! [SY499: $i] :
              ( ~ ( cProp___24t @ SY499 )
              | ~ ( p @ SV12 )
              | ( p @ SY499 )
              | ( p @ SV12 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3365]) ).

thf(3508,plain,
    ! [SV13: $i] :
      ( ( ( cType___24t @ SV13 )
        = $false )
      | ( ( ! [SY500: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV13 @ SY500 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SY500 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SY500 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3366]) ).

thf(3509,plain,
    ! [SV14: $i] :
      ( ( ( cType___24t @ SV14 )
        = $false )
      | ( ( ! [SY501: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV14 @ SY501 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SY501 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SY501 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3367]) ).

thf(3510,plain,
    ! [SV15: $i] :
      ( ( ( cType___24t @ SV15 )
        = $false )
      | ( ( ! [SY502: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY502 )
              | ! [SY503: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY503 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SY502 @ SY503 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY502 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY503 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3368]) ).

thf(3511,plain,
    ! [SV16: $i] :
      ( ( ( cType___24t @ SV16 )
        = $false )
      | ( ( ! [SY504: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY504 )
              | ! [SY505: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY505 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SY504 @ SY505 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY504 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY505 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3369]) ).

thf(3512,plain,
    ! [SV17: $i] :
      ( ( ( cType___24t @ SV17 )
        = $false )
      | ( ( ! [SY506: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY506 )
              | ! [SY507: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY507 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SY506 @ SY507 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY506 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY507 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3370]) ).

thf(3513,plain,
    ! [SV18: $i] :
      ( ( ( cType___24t @ SV18 )
        = $false )
      | ( ( ! [SY508: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY508 )
              | ! [SY509: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY509 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SY508 @ SY509 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY508 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY509 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3371]) ).

thf(3514,plain,
    ! [SV19: $i] :
      ( ( ( cType___24t @ SV19 )
        = $false )
      | ( ( ! [SY510: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY510 )
              | ! [SY511: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY511 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SY510 @ SY511 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY510 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY511 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3372]) ).

thf(3515,plain,
    ! [SV20: $i] :
      ( ( ( cType___24t @ SV20 )
        = $false )
      | ( ( ! [SY512: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY512 )
              | ! [SY513: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY513 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SY512 @ SY513 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY512 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY513 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3373]) ).

thf(3516,plain,
    ! [SV21: $i] :
      ( ( ( cType___24t @ SV21 )
        = $false )
      | ( ( ! [SY514: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY514 )
              | ! [SY515: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY515 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SY514 @ SY515 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY514 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY515 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3374]) ).

thf(3517,plain,
    ! [SV22: $i] :
      ( ( ( cType___24t @ SV22 )
        = $false )
      | ( ( ! [SY516: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY516 )
              | ! [SY517: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY517 )
                  | ! [SY518: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY518 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY516 @ SY517 ) @ SY518 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY516 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY517 @ SY518 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3375]) ).

thf(3518,plain,
    ! [SV23: $i] :
      ( ( ( cType___24t @ SV23 )
        = $false )
      | ( ( ! [SY519: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY519 )
              | ! [SY520: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY520 )
                  | ! [SY521: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY521 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY519 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY520 @ SY521 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY520 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY519 @ SY521 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3376]) ).

thf(3519,plain,
    ! [SV24: $i] :
      ( ( ( cType___24t @ SV24 )
        = $false )
      | ( ( ! [SY522: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY522 )
              | ! [SY523: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY523 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY522 @ SY523 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY523 @ SY522 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3377]) ).

thf(3520,plain,
    ! [SV25: $i] :
      ( ( ( cType___24t @ SV25 )
        = $false )
      | ( ( ! [SY524: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV25 @ SY524 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV25 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV25 @ SY524 @ SY524 ) @ SY524 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3378]) ).

thf(3521,plain,
    ! [SV26: $i] :
      ( ( ( cType___24t @ SV26 )
        = $false )
      | ( ( ! [SY525: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY525 )
              | ! [SY526: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY526 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SY525 @ SY526 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SY526 @ SY525 ) @ SY525 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3379]) ).

thf(3522,plain,
    ! [SV27: $i] :
      ( ( ( cType___24t @ SV27 )
        = $false )
      | ( ( ! [SY527: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY527 )
              | ! [SY528: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY528 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SY527 @ SY528 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SY527 @ SY528 ) @ SY527 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3380]) ).

thf(3523,plain,
    ! [SV28: $i] :
      ( ( ( cType___24t @ SV28 )
        = $false )
      | ( ( ! [SY529: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY529 )
              | ! [SY530: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY530 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SY529 @ SY530 ) @ SY529 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3381]) ).

thf(3524,plain,
    ! [SV29: $i] :
      ( ( ( cType___24t @ SV29 )
        = $false )
      | ( ( ! [SY531: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY531 )
              | ! [SY532: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY532 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY531 @ SY532 )
                  | ! [SY533: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY533 )
                      | ! [SY534: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY534 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY533 @ SY534 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY531 @ SY533 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY532 @ SY534 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3382]) ).

thf(3525,plain,
    ! [SV30: $i] :
      ( ( ( cType___24t @ SV30 )
        = $false )
      | ( ( ! [SY535: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY535 )
              | ! [SY536: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY536 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY535 @ SY536 ) )
                  | ! [SY537: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY537 )
                      | ! [SY538: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY538 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY537 @ SY538 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY535 @ SY537 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY536 @ SY538 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3383]) ).

thf(3526,plain,
    ! [SV31: $i] :
      ( ( ( cType___24t @ SV31 )
        = $false )
      | ( ( ! [SY539: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY539 )
              | ! [SY540: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY540 )
                  | ! [SY541: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY541 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SY539 @ SY540 ) @ SY541 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY539 @ SY541 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY540 @ SY541 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3384]) ).

thf(3527,plain,
    ! [SV32: $i] :
      ( ( ( cType___24t @ SV32 )
        = $false )
      | ( ( ! [SY542: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY542 )
              | ! [SY543: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY543 )
                  | ! [SY544: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY544 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY542 @ SY543 ) @ SY544 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY542 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY543 @ SY544 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3385]) ).

thf(3528,plain,
    ! [SV33: $i] :
      ( ( ( cType___24t @ SV33 )
        = $false )
      | ( ( ! [SY545: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY545 )
              | ! [SY546: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY546 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY545 @ SY546 )
                  | ! [SY547: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY547 )
                      | ! [SY548: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY548 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY547 @ SY548 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY545 @ SY547 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY546 @ SY548 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3386]) ).

thf(3529,plain,
    ! [SV34: $i] :
      ( ( ( cType___24t @ SV34 )
        = $false )
      | ( ( ! [SY549: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY549 )
              | ! [SY550: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY550 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY549 @ SY550 ) )
                  | ! [SY551: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY551 )
                      | ! [SY552: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY552 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY551 @ SY552 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY549 @ SY551 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY550 @ SY552 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3387]) ).

thf(3530,plain,
    ! [SV35: $i] :
      ( ( ( cType___24t @ SV35 )
        = $false )
      | ( ( ! [SY553: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY553 )
              | ! [SY554: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY554 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SY553 @ SY554 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY553 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY554 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3388]) ).

thf(3531,plain,
    ! [SV36: $i] :
      ( ( ( cType___24t @ SV36 )
        = $false )
      | ( ( ! [SY555: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY555 )
              | ! [SY556: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY556 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SY555 @ SY556 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY555 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY556 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3389]) ).

thf(3532,plain,
    ! [SV37: $i] :
      ( ( ( cType___24t @ SV37 )
        = $false )
      | ( ( ! [SY557: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY557 )
              | ! [SY558: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY558 )
                  | ! [SY559: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY559 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY557 @ SY558 ) @ SY559 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY557 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY558 @ SY559 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3390]) ).

thf(3533,plain,
    ! [SV38: $i] :
      ( ( ( cType___24t @ SV38 )
        = $false )
      | ( ( ! [SY560: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY560 )
              | ! [SY561: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY561 )
                  | ! [SY562: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY562 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY560 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY561 @ SY562 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY561 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY560 @ SY562 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3391]) ).

thf(3534,plain,
    ! [SV39: $i] :
      ( ( ( cType___24t @ SV39 )
        = $false )
      | ( ( ! [SY563: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY563 )
              | ! [SY564: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY564 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY563 @ SY564 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY564 @ SY563 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3392]) ).

thf(3535,plain,
    ! [SV40: $i] :
      ( ( ( cType___24t @ SV40 )
        = $false )
      | ( ( ! [SY565: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV40 @ SY565 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV40 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV40 @ SY565 @ SY565 ) @ SY565 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3393]) ).

thf(3536,plain,
    ! [SV41: $i] :
      ( ( ( cType___24t @ SV41 )
        = $false )
      | ( ( ! [SY566: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY566 )
              | ! [SY567: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY567 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SY566 @ SY567 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SY566 @ SY567 ) @ SY567 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3394]) ).

thf(3537,plain,
    ! [SV42: $i] :
      ( ( ( cType___24t @ SV42 )
        = $false )
      | ( ( ! [SY568: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY568 )
              | ! [SY569: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY569 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SY568 @ SY569 ) )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SY569 @ SY568 ) @ SY569 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3395]) ).

thf(3538,plain,
    ! [SV43: $i] :
      ( ( ( cType___24t @ SV43 )
        = $false )
      | ( ( ! [SY570: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY570 )
              | ! [SY571: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY571 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY570 @ SY571 )
                  | ! [SY572: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY572 )
                      | ! [SY573: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY573 )
                          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY572 @ SY573 )
                          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY570 @ SY572 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY571 @ SY573 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3396]) ).

thf(3539,plain,
    ! [SV44: $i] :
      ( ( ( cType___24t @ SV44 )
        = $false )
      | ( ( ! [SY574: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY574 )
              | ! [SY575: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY575 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY574 @ SY575 ) )
                  | ! [SY576: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY576 )
                      | ! [SY577: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY577 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY576 @ SY577 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY574 @ SY576 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY575 @ SY577 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3397]) ).

thf(3540,plain,
    ! [SV45: $i] :
      ( ( ( cType___24t @ SV45 )
        = $false )
      | ( ( ! [SY578: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY578 )
              | ! [SY579: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY579 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SY578 @ SY579 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SY578 @ SY579 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3398]) ).

thf(3541,plain,
    ! [SV46: $i] :
      ( ( ( cType___24t @ SV46 )
        = $false )
      | ( ( ! [SY580: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY580 )
              | ! [SY581: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY581 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SY580 @ SY581 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SY581 @ SY580 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3399]) ).

thf(3542,plain,
    ! [SV47: $i] :
      ( ( ( cType___24t @ SV47 )
        = $false )
      | ( ( ! [SY582: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY582 )
              | ! [SY583: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY583 )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SY582 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SY582 @ SY583 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3400]) ).

thf(3543,plain,
    ! [SV48: $i] :
      ( ( ( cType___24t @ SV48 )
        = $false )
      | ( ( ! [SY584: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY584 )
              | ! [SY585: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY585 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SY584 @ SY585 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY585 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY584 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3401]) ).

thf(3544,plain,
    ! [SV49: $i] :
      ( ( ( cType___24t @ SV49 )
        = $false )
      | ( ( ! [SY586: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY586 )
              | ! [SY587: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY587 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SY586 @ SY587 ) @ SY586 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3402]) ).

thf(3545,plain,
    ! [SV50: $i] :
      ( ( ( cType___24t @ SV50 )
        = $false )
      | ( ( ! [SY588: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY588 )
              | ! [SY589: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY589 )
                  | ! [SY590: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY590 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SY588 @ SY590 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SY588 @ SY589 ) @ SY590 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3403]) ).

thf(3546,plain,
    ! [SV51: $i] :
      ( ( ( cType___24t @ SV51 )
        = $false )
      | ( ( ! [SY591: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY591 )
              | ! [SY592: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY592 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SY591 @ SY592 ) @ SY592 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3404]) ).

thf(3547,plain,
    ! [SV52: $i] :
      ( ( ( cType___24t @ SV52 )
        = $false )
      | ( ( ! [SY593: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY593 )
              | ! [SY594: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY594 )
                  | ! [SY595: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY595 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SY594 @ SY595 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SY593 @ SY594 ) @ SY595 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3405]) ).

thf(3548,plain,
    ! [SV53: $i] :
      ( ( ( cType___24t @ SV53 )
        = $false )
      | ( ( ! [SY596: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY596 )
              | ! [SY597: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY597 )
                  | ! [SY598: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY598 )
                      | ! [SY599: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY599 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY596 @ SY597 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY598 @ SY599 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY596 @ SY598 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY597 @ SY599 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3406]) ).

thf(3549,plain,
    ! [SV54: $i] :
      ( ( ( cType___24t @ SV54 )
        = $false )
      | ( ( ! [SY600: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY600 )
              | ! [SY601: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY601 )
                  | ! [SY602: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY602 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ SY601 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ SY602 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SY600 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SY601 @ SY602 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3407]) ).

thf(3550,plain,
    ! [SV55: $i] :
      ( ( ( cType___24t @ SV55 )
        = $false )
      | ( ( ! [SY603: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY603 )
              | ! [SY604: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY604 )
                  | ! [SY605: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY605 )
                      | ! [SY606: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY606 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY603 @ SY604 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY606 @ SY605 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY603 @ SY605 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY604 @ SY606 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3408]) ).

thf(3551,plain,
    ! [SV56: $i] :
      ( ( ( cType___24t @ SV56 )
        = $false )
      | ( ( ! [SY607: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY607 )
              | ! [SY608: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY608 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SY607 @ SY608 ) @ SY607 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3409]) ).

thf(3552,plain,
    ! [SV57: $i] :
      ( ( ( cType___24t @ SV57 )
        = $false )
      | ( ( ! [SY609: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY609 )
              | ! [SY610: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY610 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SY609 @ SY610 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY609 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY610 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3410]) ).

thf(3553,plain,
    ! [SV58: $i] :
      ( ( ( cType___24t @ SV58 )
        = $false )
      | ( ( ! [SY611: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV58 @ SY611 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV58 @ SY611 @ SY611 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3411]) ).

thf(3554,plain,
    ! [SV59: $i] :
      ( ( ( cType___24t @ SV59 )
        = $false )
      | ( ( ! [SY612: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY612 )
              | ! [SY613: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY613 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SY612 @ SY613 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY612 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY613 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3412]) ).

thf(3555,plain,
    ! [SV60: $i] :
      ( ( ( cType___24t @ SV60 )
        = $false )
      | ( ( ! [SY614: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY614 )
              | ! [SY615: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY615 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SY614 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY615 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY614 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY615 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3413]) ).

thf(3556,plain,
    ! [SV61: $i] :
      ( ( ( cType___24t @ SV61 )
        = $false )
      | ( ( ! [SY616: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY616 )
              | ! [SY617: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY617 )
                  | ! [SY618: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY618 )
                      | ! [SY619: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY619 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY616 @ SY617 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY618 @ SY619 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY616 @ SY618 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY617 @ SY619 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3414]) ).

thf(3557,plain,
    ! [SV62: $i] :
      ( ( ( cType___24t @ SV62 )
        = $false )
      | ( ( ! [SY620: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY620 )
              | ! [SY621: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY621 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SY620 @ SY621 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SY620 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SY621 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3415]) ).

thf(3558,plain,
    ! [SV63: $i] :
      ( ( ( cType___24t @ SV63 )
        = $false )
      | ( ( ! [SY622: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY622 )
              | ! [SY623: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY623 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SY622 @ SY623 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SY622 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SY623 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3416]) ).

thf(3559,plain,
    ! [SV64: $i] :
      ( ( ( cType___24t @ SV64 )
        = $false )
      | ( ( ! [SY624: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY624 )
              | ! [SY625: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY625 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SY624 @ SY625 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SY624 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SY625 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3417]) ).

thf(3560,plain,
    ! [SV65: $i] :
      ( ( ( cType___24t @ SV65 )
        = $false )
      | ( ( ! [SY626: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY626 )
              | ! [SY627: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY627 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SY626 @ SY627 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY626 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY627 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3418]) ).

thf(3561,plain,
    ! [SV66: $i] :
      ( ( ( cType___24t @ SV66 )
        = $false )
      | ( ( ! [SY628: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY628 )
              | ! [SY629: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY629 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SY628 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY629 ) ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY628 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY629 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3419]) ).

thf(3562,plain,
    ! [SV67: $i] :
      ( ( ( cType___24t @ SV67 )
        = $false )
      | ( ( ! [SY630: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY630 )
              | ! [SY631: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY631 )
                  | ! [SY632: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY632 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY630 @ SY632 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY631 @ SY632 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SY630 @ SY631 ) @ SY632 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3420]) ).

thf(3563,plain,
    ! [SV68: $i] :
      ( ( ( cType___24t @ SV68 )
        = $false )
      | ( ( ! [SY633: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY633 )
              | ! [SY634: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY634 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SY633 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SY633 @ SY634 ) @ SY634 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3421]) ).

thf(3564,plain,
    ! [SV69: $i] :
      ( ( ( cType___24t @ SV69 )
        = $false )
      | ( ( ! [SY635: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY635 )
              | ! [SY636: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY636 )
                  | ! [SY637: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY637 )
                      | ! [SY638: $i] :
                          ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY638 )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY635 @ SY636 ) )
                          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY637 @ SY638 ) )
                          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY635 @ SY637 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY636 @ SY638 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3422]) ).

thf(3565,plain,
    ! [SV70: $i] :
      ( ( ( cType___24t @ SV70 )
        = $false )
      | ( ( ! [SY639: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY639 )
              | ! [SY640: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY640 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SY639 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SY639 @ SY640 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3423]) ).

thf(3566,plain,
    ! [SV71: $i] :
      ( ( ( cType___24t @ SV71 )
        = $false )
      | ( ( ! [SY641: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY641 )
              | ! [SY642: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY642 )
                  | ! [SY643: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY643 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SY641 @ SY642 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SY641 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SY642 @ SY643 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3424]) ).

thf(3567,plain,
    ! [SV72: $i] :
      ( ( ( cType___24t @ SV72 )
        = $false )
      | ( ( ! [SY644: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY644 )
              | ! [SY645: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY645 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SY645 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SY644 @ SY645 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3425]) ).

thf(3568,plain,
    ! [SV73: $i] :
      ( ( ( cType___24t @ SV73 )
        = $false )
      | ( ( ! [SY646: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY646 )
              | ! [SY647: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY647 )
                  | ! [SY648: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY648 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SY646 @ SY648 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SY646 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SY647 @ SY648 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3426]) ).

thf(3569,plain,
    ! [SV74: $i] :
      ( ( ( cType___24t @ SV74 )
        = $false )
      | ( ( ! [SY649: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY649 )
              | ! [SY650: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY650 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SY649 @ SY650 ) )
                  | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY650 ) )
                  | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY649 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3427]) ).

thf(3570,plain,
    ! [SV159: $i,SV128: $i,SV76: $i] :
      ( ( ! [SY1089: $i,SY1090: $i] :
            ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ SV76 ) @ SV128 ) @ SV159 ) @ SY1089 ) @ SY1090 )
            = ( c_24__lam__45594___24a5 @ SV76 @ SV128 @ SV159 @ SY1089 @ SY1090 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3428]) ).

thf(3571,plain,
    ! [SV160: $i,SV129: $i,SV77: $i] :
      ( ( ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2einclusion @ SV77 ) @ SV129 ) @ SV160 )
        = ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV77 @ SV129 @ SV160 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3429]) ).

thf(3572,plain,
    ! [SV78: $i] :
      ( ( ( cProp___24t @ SV78 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ! [SY657: $i] :
                          ( ~ ( cProp___24t @ SY657 )
                          | ( p @ SV78 )
                          | ~ ( p @ SV78 )
                          | ( p @ SY657 ) )
                    | ~ ! [SY658: $i] :
                          ( ~ ( cProp___24t @ SY658 )
                          | ( p @ SV78 )
                          | ~ ( p @ SY658 )
                          | ( p @ SY658 ) ) )
              | ~ ~ ( ~ ! [SY659: $i] :
                          ( ~ ( cProp___24t @ SY659 )
                          | ~ ( p @ SY659 )
                          | ~ ( p @ SV78 )
                          | ( p @ SY659 ) )
                    | ~ ! [SX1: $i] :
                          ( ~ ( cProp___24t @ SX1 )
                          | ~ ( p @ SX1 )
                          | ~ ( p @ SX1 )
                          | ( p @ SX1 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3430]) ).

thf(3573,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( sK2_SY468 @ SX0 ) )
                    | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ SX0 @ ( sK1_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK2_SY468 @ SX0 ) ) ) ) )
          | ( c_24__type__96___24t @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3431]) ).

thf(3574,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( c_24__type__96___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cType___24t @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3432]) ).

thf(3575,plain,
    ! [SV79: $i] :
      ( ( ( cType___24t @ SV79 )
        = $false )
      | ( ( ! [SY661: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY661 )
              | ~ ( ~ ! [SY662: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY662 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SY661 @ SY662 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY661 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY662 ) )
                  | ~ ! [SY663: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY663 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SY661 @ SY663 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY663 )
                        | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY661 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3433]) ).

thf(3576,plain,
    ! [SV80: $i] :
      ( ( ~ ! [SY664: $i,SY665: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY664 @ SY665 )
              | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY664 ) @ SY665 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3434]) ).

thf(3577,plain,
    ! [SV80: $i] :
      ( ( ~ ! [SY666: $i,SY667: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY666 ) @ SY667 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY666 @ SY667 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3434]) ).

thf(3578,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( c_24__lam__35673___24a2 @ SX0 @ SX1 )
          | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3435]) ).

thf(3579,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SX0 ) @ SX1 ) )
          | ( c_24__lam__35673___24a2 @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3436]) ).

thf(3580,plain,
    ! [SV161: $i,SV130: $i,SV81: $i] :
      ( ( ~ ( ~ ! [SY1091: $i,SY1092: $i] :
                  ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1091 @ SY1092 )
                  | ( p @ ( happ @ ( happ @ SV130 @ SY1091 ) @ SY1092 ) )
                  | ( p @ ( happ @ ( happ @ SV161 @ SY1091 ) @ SY1092 ) ) )
            | ~ ~ ( ~ ! [SY1093: $i,SY1094: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
                        | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) )
                  | ~ ! [SY1095: $i,SY1096: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
                        | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3437]) ).

thf(3581,plain,
    ! [SV131: $i,SV82: $i,SV162: $i] :
      ( ( ~ ( ~ ! [SY1097: $i,SY1098: $i] :
                  ( ( ( happ @ SV162 @ SY1097 )
                   != ( happ @ SV162 @ SY1098 ) )
                  | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1097 @ SY1098 ) )
            | ~ ! [SY1099: $i,SY1100: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1099 @ SY1100 )
                  | ( ( happ @ SV162 @ SY1099 )
                    = ( happ @ SV162 @ SY1100 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3438]) ).

thf(3582,plain,
    ! [SV83: $i] :
      ( ( ( cType___24t @ SV83 )
        = $false )
      | ( ( ! [SY682: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY682 )
              | ! [SY683: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY683 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY682 @ SY683 )
                  | ! [SY684: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY684 )
                      | ~ ( ~ ! [SY685: $i] :
                                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY685 )
                                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY684 @ SY685 )
                                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY682 @ SY684 ) )
                                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY683 @ SY685 ) ) )
                          | ~ ! [SY686: $i] :
                                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY686 )
                                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY684 @ SY686 )
                                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY683 @ SY686 ) )
                                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY682 @ SY684 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3439]) ).

thf(3583,plain,
    ! [SV132: $i,SV84: $i] :
      ( ( ~ ! [SY947: $i,SY948: $i] :
              ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY947 @ SY948 )
              | ( p @ ( happ @ ( happ @ SV132 @ SY947 ) @ SY948 ) ) )
        | ~ ! [SY949: $i,SY950: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV132 @ SY949 ) @ SY950 ) )
              | ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY949 @ SY950 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3440]) ).

thf(3584,plain,
    ! [SV85: $i] :
      ( ( ( cType___24t @ SV85 )
        = $false )
      | ( ( ! [SY692: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY692 )
              | ~ ( ~ ! [SY693: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY693 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SY692 @ SY693 )
                        | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY692 ) )
                        | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY693 ) ) )
                  | ~ ! [SY694: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY694 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SY692 @ SY694 )
                        | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY694 ) )
                        | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY692 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3441]) ).

thf(3585,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SX0 ) )
              | ~ ~ ( cType___24t @ ( happ @ SX0 @ ( sK12_Vv__CANONICAL__0 @ SX0 ) ) ) )
          | ( c_24__type__28___24t @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3442]) ).

thf(3586,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( c_24__type__28___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cType___24t @ SX1 )
              | ( cType___24t @ ( happ @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3443]) ).

thf(3587,plain,
    ! [SV86: $i,SV133: $i] :
      ( ( ~ ! [SY951: $i,SY952: $i] :
              ( ~ ( p @ ( happ @ SV133 @ SY952 ) )
              | ( p @ ( happ @ SY951 @ SY952 ) )
              | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY951 @ SY952 ) )
        | ~ ~ ( ~ ! [SY953: $i,SY954: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
                    | ( p @ ( happ @ SV133 @ SY954 ) ) )
              | ~ ! [SY955: $i,SY956: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
                    | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3444]) ).

thf(3588,plain,
    ! [SV134: $i,SV87: $i] :
      ( ( ~ ! [SY957: $i,SY958: $i] :
              ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY957 @ SY958 )
              | ( p @ ( happ @ ( happ @ SV134 @ SY958 ) @ SY957 ) ) )
        | ~ ! [SY959: $i,SY960: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV134 @ SY960 ) @ SY959 ) )
              | ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY959 @ SY960 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3445]) ).

thf(3589,plain,
    ! [SV88: $i] :
      ( ( ~ ! [SY707: $i,SY708: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY707 @ SY708 )
              | ~ ( p @ ( happ @ SY707 @ SY708 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3446]) ).

thf(3590,plain,
    ! [SV88: $i] :
      ( ( ~ ! [SY709: $i,SY710: $i] :
              ( ( p @ ( happ @ SY709 @ SY710 ) )
              | ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY709 @ SY710 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3446]) ).

thf(3591,plain,
    ! [SV89: $i] :
      ( ( ( cType___24t @ SV89 )
        = $false )
      | ( ( ! [SY711: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY711 )
              | ! [SY712: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY712 )
                  | ~ ( ~ ! [SY713: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY713 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SY711 @ SY712 ) @ SY713 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SY711 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY712 @ SY713 ) ) ) )
                      | ~ ! [SY714: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY714 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SY711 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY712 @ SY714 ) ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SY711 @ SY712 ) @ SY714 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3447]) ).

thf(3592,plain,
    ! [SV163: $i,SV135: $i,SV90: $i] :
      ( ( ~ ( ~ ! [SY1101: $i,SY1102: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1101 @ SY1102 )
                  | ( p @ ( happ @ ( happ @ SV135 @ SY1101 ) @ SY1102 ) )
                  | ( p @ ( happ @ ( happ @ SV163 @ SY1101 ) @ SY1102 ) ) )
            | ~ ~ ( ~ ! [SY1103: $i,SY1104: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
                        | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) )
                  | ~ ! [SY1105: $i,SY1106: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
                        | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3448]) ).

thf(3593,plain,
    ! [SV91: $i] :
      ( ( ( cProp___24t @ SV91 )
        = $false )
      | ( ( ! [SY723: $i] :
              ( ~ ( cProp___24t @ SY723 )
              | ~ ( ~ ~ ( ~ ! [SY724: $i] :
                              ( ~ ( cProp___24t @ SY724 )
                              | ( p @ SV91 )
                              | ~ ( p @ SV91 )
                              | ( p @ SY723 )
                              | ( p @ SY724 ) )
                        | ~ ! [SY725: $i] :
                              ( ~ ( cProp___24t @ SY725 )
                              | ( p @ SV91 )
                              | ~ ( p @ SY725 )
                              | ( p @ SY723 )
                              | ( p @ SY725 ) ) )
                  | ~ ~ ( ~ ! [SY726: $i] :
                              ( ~ ( cProp___24t @ SY726 )
                              | ~ ( p @ SY723 )
                              | ~ ( p @ SV91 )
                              | ( p @ SY723 )
                              | ( p @ SY726 ) )
                        | ~ ! [SX2: $i] :
                              ( ~ ( cProp___24t @ SX2 )
                              | ~ ( p @ SY723 )
                              | ~ ( p @ SX2 )
                              | ( p @ SY723 )
                              | ( p @ SX2 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3449]) ).

thf(3594,plain,
    ! [SV92: $i,SV164: $i,SV136: $i] :
      ( ( ~ ( ~ ! [SY1107: $i,SY1108: $i] :
                  ( ~ ( p @ ( happ @ SV136 @ SY1107 ) )
                  | ~ ( p @ ( happ @ SV164 @ SY1108 ) )
                  | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1107 @ SY1108 ) )
            | ~ ~ ( ~ ! [SY1109: $i] :
                        ( ! [SY1110: $i] :
                            ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
                        | ( p @ ( happ @ SV136 @ SY1109 ) ) )
                  | ~ ! [SY1111: $i,SY1112: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
                        | ( p @ ( happ @ SV164 @ SY1112 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3450]) ).

thf(3595,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ ( sK16_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) ) )
          | ( c_24__type__11748___24t @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3451]) ).

thf(3596,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( c_24__type__11748___24t @ SX0 @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3452]) ).

thf(3597,plain,
    ( ( ! [SX0: $i] :
          ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 )
      | $true )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3453]) ).

thf(3598,plain,
    ( ( ~ $true
      | ! [SX0: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3454]) ).

thf(3599,plain,
    ! [SV165: $i,SV137: $i,SV93: $i] :
      ( ( ~ ( ~ ! [SY1113: $i,SY1114: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1113 @ SY1114 )
                  | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1113 ) @ SY1114 ) ) )
            | ~ ! [SY1115: $i,SY1116: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1115 ) @ SY1116 ) )
                  | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1115 @ SY1116 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3455]) ).

thf(3600,plain,
    ! [SV94: $i] :
      ( ( ~ ! [SY742: $i,SY743: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY742 @ SY743 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY743 @ SY742 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY742 @ SY743 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3456]) ).

thf(3601,plain,
    ! [SV94: $i] :
      ( ( ~ ~ ( ~ ! [SY744: $i,SY745: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) )
              | ~ ! [SY746: $i,SY747: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3456]) ).

thf(3602,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) )
          | ~ ( p @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3457]) ).

thf(3603,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( p @ SX1 )
          | ( p @ ( c_24__prop__35358___24a2 @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3458]) ).

thf(3604,plain,
    ! [SV95: $i,SV138: $i] :
      ( ( ~ ! [SY980: $i,SY981: $i] :
              ( ~ ( p @ ( happ @ SV138 @ SY981 ) )
              | ~ ( p @ ( happ @ SY980 @ SY981 ) )
              | ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY980 @ SY981 ) )
        | ~ ~ ( ~ ! [SY982: $i,SY983: $i] :
                    ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
                    | ( p @ ( happ @ SV138 @ SY983 ) ) )
              | ~ ! [SY984: $i,SY985: $i] :
                    ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
                    | ( p @ ( happ @ SY984 @ SY985 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3459]) ).

thf(3605,plain,
    ! [SV96: $i] :
      ( ( ( cType___24t @ SV96 )
        = $false )
      | ( ( ! [SY755: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY755 )
              | ~ ( ~ ! [SY756: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY756 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SY755 @ SY756 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY755 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY756 ) ) )
                  | ~ ! [SY757: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY757 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SY755 @ SY757 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY757 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY755 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3460]) ).

thf(3606,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ! [SY986: $i,SY987: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY986 @ SY987 )
              | ( SY986 = SY987 )
              | ( p @ ( happ @ ( happ @ SV139 @ SY986 ) @ SY987 ) ) )
        | ~ ~ ( ~ ! [SY988: $i,SY989: $i] :
                    ( ( SY988 != SY989 )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) )
              | ~ ! [SY990: $i,SY991: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3461]) ).

thf(3607,plain,
    ! [SV98: $i] :
      ( ( ~ ! [SY765: $i,SY766: $i] :
              ( ~ ( ~ ( t @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) @ SV98 )
                  | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) @ SV98 )
                        | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SY765 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) )
                              | ~ ~ ( p @ ( happ @ ( happ @ SY766 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) ) ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY765 @ SY766 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3462]) ).

thf(3608,plain,
    ! [SV98: $i] :
      ( ( ~ ! [SY767: $i,SY768: $i] :
              ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY767 @ SY768 ) )
              | ! [SY769: $i] :
                  ( ~ ( t @ SY769 @ SV98 )
                  | ! [SY770: $i] :
                      ( ~ ( t @ SY770 @ SV98 )
                      | ~ ( p @ ( happ @ ( happ @ SY767 @ SY769 ) @ SY770 ) )
                      | ( p @ ( happ @ ( happ @ SY768 @ SY769 ) @ SY770 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3462]) ).

thf(3609,plain,
    ! [SV140: $i,SV99: $i] :
      ( ( ~ ! [SY992: $i,SY993: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY992 @ SY993 )
              | ( p @ ( happ @ ( happ @ SV140 @ SY992 ) @ SY993 ) )
              | ( p @ ( happ @ ( happ @ SV140 @ SY993 ) @ SY992 ) ) )
        | ~ ~ ( ~ ! [SY994: $i,SY995: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) )
              | ~ ! [SY996: $i,SY997: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3463]) ).

thf(3610,plain,
    ! [SV100: $i,SV166: $i,SV141: $i] :
      ( ( ~ ( ~ ! [SY1117: $i,SY1118: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV141 @ SY1117 ) @ SY1118 ) )
                  | ( p @ ( happ @ ( happ @ SV166 @ SY1117 ) @ SY1118 ) )
                  | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1117 @ SY1118 ) )
            | ~ ~ ( ~ ! [SY1119: $i,SY1120: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
                        | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) )
                  | ~ ! [SY1121: $i,SY1122: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
                        | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3464]) ).

thf(3611,plain,
    ! [SV101: $i] :
      ( ( ~ ! [SY786: $i,SY787: $i] :
              ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) )
                  | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY786 @ ( happ @ SY787 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) ) ) )
              | ( c_24__type__11699___24t @ SV101 @ SY786 @ SY787 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3465]) ).

thf(3612,plain,
    ! [SV101: $i] :
      ( ( ~ ! [SY788: $i,SY789: $i] :
              ( ~ ( c_24__type__11699___24t @ SV101 @ SY788 @ SY789 )
              | ! [SY790: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY790 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY788 @ ( happ @ SY789 @ SY790 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3465]) ).

thf(3613,plain,
    ! [SV167: $i,SV142: $i,SV102: $i] :
      ( ( ~ ( ~ ! [SY1123: $i,SY1124: $i] :
                  ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1123 @ SY1124 )
                  | ( p @ ( happ @ ( happ @ SV167 @ SY1123 ) @ SY1124 ) ) )
            | ~ ! [SY1125: $i,SY1126: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV167 @ SY1125 ) @ SY1126 ) )
                  | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1125 @ SY1126 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3466]) ).

thf(3614,plain,
    ! [SV103: $i] :
      ( ( ~ ! [SY797: $i,SY798: $i] :
              ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY797 @ SY798 ) )
              | ( p @ SY797 )
              | ( p @ SY798 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3467]) ).

thf(3615,plain,
    ! [SV103: $i] :
      ( ( ~ ~ ( ~ ! [SY799: $i] :
                    ( ~ ( p @ SY799 )
                    | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) )
              | ~ ! [SY801: $i,SY802: $i] :
                    ( ~ ( p @ SY802 )
                    | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3467]) ).

thf(3616,plain,
    ! [SV104: $i,SV143: $i,SV168: $i] :
      ( ( ~ ( ~ ! [SY1127: $i,SY1128: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV168 @ SY1127 ) @ SY1128 ) )
                  | ~ ( p @ ( happ @ SV143 @ SY1127 ) )
                  | ~ ( p @ ( happ @ SV143 @ SY1128 ) )
                  | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1127 @ SY1128 ) )
            | ~ ~ ( ~ ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                              | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
                        | ~ ! [SY1131: $i] :
                              ( ! [SY1132: $i] :
                                  ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                              | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
                  | ~ ! [SY1133: $i,SY1134: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
                        | ( p @ ( happ @ SV143 @ SY1134 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3468]) ).

thf(3617,plain,
    ! [SV105: $i] :
      ( ( ~ ! [SY813: $i,SY814: $i] :
              ( ( SY813 != SY814 )
              | ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY813 @ SY814 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3469]) ).

thf(3618,plain,
    ! [SV105: $i] :
      ( ( ~ ! [SY815: $i,SY816: $i] :
              ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY815 @ SY816 ) )
              | ( SY815 = SY816 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3469]) ).

thf(3619,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( sK14_SY479 @ SX1 @ SX0 ) )
                    | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ ( sK13_Vv__CANONICAL__1 @ SX1 @ SX0 ) ) @ ( sK14_SY479 @ SX1 @ SX0 ) ) ) ) )
          | ( c_24__type__11829___24t @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3470]) ).

thf(3620,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( c_24__type__11829___24t @ SX0 @ SX1 )
          | ! [SX2: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX2 )
              | ! [SX3: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ SX3 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX0 @ ( happ @ ( happ @ SX1 @ SX2 ) @ SX3 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3471]) ).

thf(3621,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ! [SY1019: $i,SY1020: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1019 @ SY1020 )
              | ( p @ ( happ @ ( happ @ SV144 @ SY1020 ) @ SY1019 ) )
              | ( SY1019 = SY1020 )
              | ( p @ ( happ @ ( happ @ SV144 @ SY1019 ) @ SY1020 ) ) )
        | ~ ~ ( ~ ! [SY1021: $i,SY1022: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) )
              | ~ ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                          ( ( SY1023 != SY1024 )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
                    | ~ ! [SY1025: $i,SY1026: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3472]) ).

thf(3622,plain,
    ! [SV169: $i,SV145: $i,SV107: $i] :
      ( ( ~ ( ~ ! [SY1135: $i,SY1136: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1135 @ SY1136 )
                  | ( p @ ( happ @ SY1135 @ ( happ @ SV169 @ SY1136 ) ) ) )
            | ~ ! [SY1137: $i,SY1138: $i] :
                  ( ~ ( p @ ( happ @ SY1137 @ ( happ @ SV169 @ SY1138 ) ) )
                  | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1137 @ SY1138 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3473]) ).

thf(3623,plain,
    ! [SV108: $i,SV146: $i] :
      ( ( ~ ! [SY1032: $i,SY1033: $i] :
              ( ( SY1032 != SY1033 )
              | ~ ( p @ ( happ @ SV146 @ SY1032 ) )
              | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1032 @ SY1033 ) )
        | ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
                    | ( SY1034 = SY1035 ) )
              | ~ ! [SY1036: $i] :
                    ( ! [SY1037: $i] :
                        ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
                    | ( p @ ( happ @ SV146 @ SY1036 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3474]) ).

thf(3624,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK4_SY469 @ SX0 ) )
                    | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( sK5_SY471 @ SX0 ) )
                          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SX0 ) @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK3_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK4_SY469 @ SX0 ) ) @ ( sK5_SY471 @ SX0 ) ) ) ) ) )
          | ( c_24__type__90___24t @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3475]) ).

thf(3625,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( c_24__type__90___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cType___24t @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX2 )
                  | ! [SX3: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ SX3 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SX1 @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3476]) ).

thf(3626,plain,
    ! [SV109: $i] :
      ( ( ( cType___24t @ SV109 )
        = $false )
      | ( ( ! [SY839: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY839 )
              | ~ ( ~ ! [SY840: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY840 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SY839 @ SY840 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY839 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY840 ) ) )
                  | ~ ! [SY841: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY841 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SY839 @ SY841 )
                        | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY841 ) )
                        | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY839 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3477]) ).

thf(3627,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SX0 ) )
              | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SX0 ) )
                    | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SX0 ) )
                          | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SX0 ) )
                                | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ ( sK8_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK9_SY473 @ SX0 ) ) @ ( sK10_SY476 @ SX0 ) ) @ ( sK11_SY478 @ SX0 ) ) ) ) ) ) )
          | ( c_24__type__4733___24t @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3478]) ).

thf(3628,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( c_24__type__4733___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cType___24t @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cType___24t @ SX2 )
                  | ! [SX3: $i] :
                      ( ~ ( cType___24t @ SX3 )
                      | ! [SX4: $i] :
                          ( ~ ( cType___24t @ SX4 )
                          | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) @ SX3 ) @ SX4 ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3479]) ).

thf(3629,plain,
    ! [SV110: $i,SV170: $i,SV147: $i] :
      ( ( ~ ( ~ ! [SY1139: $i,SY1140: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV147 @ SY1139 ) @ SY1140 ) )
                  | ~ ( p @ ( happ @ ( happ @ SV170 @ SY1139 ) @ SY1140 ) )
                  | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1139 @ SY1140 ) )
            | ~ ~ ( ~ ! [SY1141: $i,SY1142: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
                        | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) )
                  | ~ ! [SY1143: $i,SY1144: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
                        | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3480]) ).

thf(3630,plain,
    ! [SV148: $i,SV111: $i] :
      ( ( ~ ! [SY1045: $i,SY1046: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1045 @ SY1046 )
              | ( p @ ( happ @ ( happ @ SV148 @ SY1046 ) @ SY1045 ) ) )
        | ~ ! [SY1047: $i,SY1048: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV148 @ SY1048 ) @ SY1047 ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1047 @ SY1048 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3481]) ).

thf(3631,plain,
    ! [SV112: $i] :
      ( ( ~ ! [SY855: $i,SY856: $i] :
              ( ~ ( p @ SY855 )
              | ~ ( p @ SY856 )
              | ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY855 @ SY856 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3482]) ).

thf(3632,plain,
    ! [SV112: $i] :
      ( ( ~ ~ ( ~ ! [SY857: $i] :
                    ( ! [SY858: $i] :
                        ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
                    | ( p @ SY857 ) )
              | ~ ! [SY859: $i,SY860: $i] :
                    ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
                    | ( p @ SY860 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3482]) ).

thf(3633,plain,
    ! [SV149: $i,SV113: $i] :
      ( ( ~ ! [SY1049: $i,SY1050: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1049 @ SY1050 )
              | ( p @ ( happ @ SV149 @ SY1050 ) )
              | ( p @ ( happ @ SY1049 @ SY1050 ) ) )
        | ~ ~ ( ~ ! [SY1051: $i,SY1052: $i] :
                    ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
                    | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) )
              | ~ ! [SY1053: $i,SY1054: $i] :
                    ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
                    | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3483]) ).

thf(3634,plain,
    ! [SV114: $i] :
      ( ( ~ ~ ( ~ ! [SY868: $i] :
                    ( ( p @ SY868 )
                    | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) )
              | ~ ! [SY870: $i,SY871: $i] :
                    ( ~ ( p @ SY871 )
                    | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3484]) ).

thf(3635,plain,
    ! [SV114: $i] :
      ( ( ~ ! [SY872: $i,SY873: $i] :
              ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY872 @ SY873 ) )
              | ~ ( p @ SY872 )
              | ( p @ SY873 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3484]) ).

thf(3636,plain,
    ! [SV115: $i] :
      ( ( ( cType___24t @ SV115 )
        = $false )
      | ( ( ! [SY874: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY874 )
              | ! [SY875: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY875 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SY874 @ SY875 )
                  | ! [SY876: $i] :
                      ( ~ ( t @ SY876 @ SV115 )
                      | ~ ( ~ ! [SY877: $i] :
                                ( ~ ( t @ SY877 @ SV115 )
                                | ~ ( p @ ( happ @ ( happ @ SY874 @ SY876 ) @ SY877 ) )
                                | ( p @ ( happ @ ( happ @ SY875 @ SY876 ) @ SY877 ) ) )
                          | ~ ! [SY878: $i] :
                                ( ~ ( t @ SY878 @ SV115 )
                                | ~ ( p @ ( happ @ ( happ @ SY875 @ SY876 ) @ SY878 ) )
                                | ( p @ ( happ @ ( happ @ SY874 @ SY876 ) @ SY878 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3485]) ).

thf(3637,plain,
    ! [SV116: $i,SV150: $i] :
      ( ( ~ ! [SY1055: $i,SY1056: $i] :
              ( ~ ( p @ ( happ @ SV150 @ SY1056 ) )
              | ~ ( p @ ( happ @ SY1055 @ SY1056 ) )
              | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1055 @ SY1056 ) )
        | ~ ~ ( ~ ! [SY1057: $i,SY1058: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
                    | ( p @ ( happ @ SV150 @ SY1058 ) ) )
              | ~ ! [SY1059: $i,SY1060: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
                    | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3486]) ).

thf(3638,plain,
    ! [SV117: $i] :
      ( ( ( cType___24t @ SV117 )
        = $false )
      | ( ( ! [SY886: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY886 )
              | ! [SY887: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY887 )
                  | ~ ( ~ ! [SY888: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY888 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ SY887 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY887 @ SY888 ) ) ) )
                      | ~ ! [SY889: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY889 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ SY889 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SY886 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY887 @ SY889 ) ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3487]) ).

thf(3639,plain,
    ! [SV171: $i,SV151: $i,SV118: $i] :
      ( ( ! [SY1145: $i] :
            ~ ( ~ ! [SY1146: $i,SY1147: $i] :
                    ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SY1145 @ SY1146 @ SY1147 )
                    | ( p @ ( happ @ ( happ @ SY1145 @ ( happ @ SV171 @ SY1146 ) ) @ ( happ @ SV171 @ SY1147 ) ) ) )
              | ~ ! [SY1148: $i,SY1149: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY1145 @ ( happ @ SV171 @ SY1148 ) ) @ ( happ @ SV171 @ SY1149 ) ) )
                    | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SY1145 @ SY1148 @ SY1149 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3488]) ).

thf(3640,plain,
    ! [SV172: $i,SV152: $i,SV119: $i] :
      ( ( ! [SY1150: $i] :
            ~ ( ~ ! [SY1151: $i,SY1152: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SY1150 @ SY1151 @ SY1152 )
                    | ( p @ ( happ @ ( happ @ SY1150 @ ( happ @ SV172 @ SY1151 ) ) @ ( happ @ SV172 @ SY1152 ) ) ) )
              | ~ ! [SY1153: $i,SY1154: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SY1150 @ ( happ @ SV172 @ SY1153 ) ) @ ( happ @ SV172 @ SY1154 ) ) )
                    | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SY1150 @ SY1153 @ SY1154 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3489]) ).

thf(3641,plain,
    ! [SV120: $i] :
      ( ( ~ ! [SY904: $i,SY905: $i] :
              ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY904 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) )
                  | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY905 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) ) ) )
              | ( c_24__type__11787___24t @ SV120 @ SY904 @ SY905 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3490]) ).

thf(3642,plain,
    ! [SV120: $i] :
      ( ( ~ ! [SY906: $i,SY907: $i] :
              ( ~ ( c_24__type__11787___24t @ SV120 @ SY906 @ SY907 )
              | ! [SY908: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY906 @ SY908 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY907 @ SY908 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3490]) ).

thf(3643,plain,
    ! [SV153: $i,SV121: $i] :
      ( ( ~ ! [SY1073: $i,SY1074: $i] :
              ( ( SY1073 != SY1074 )
              | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1073 @ SY1074 ) ) )
        | ~ ! [SY1075: $i,SY1076: $i] :
              ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1075 @ SY1076 ) )
              | ( SY1075 = SY1076 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3491]) ).

thf(3644,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SX0 ) )
              | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SX0 ) )
                    | ~ ~ ( cType___24t @ ( happ @ ( happ @ SX0 @ ( sK6_Vv__CANONICAL__0 @ SX0 ) ) @ ( sK7_SY472 @ SX0 ) ) ) ) )
          | ( c_24__type__52___24t @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3492]) ).

thf(3645,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( c_24__type__52___24t @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( cType___24t @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( cType___24t @ SX2 )
                  | ( cType___24t @ ( happ @ ( happ @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3493]) ).

thf(3646,plain,
    ! [SV154: $i,SV122: $i,SV173: $i] :
      ( ( ! [SY1155: $i] :
            ~ ( ~ ! [SY1156: $i,SY1157: $i] :
                    ( ( ( happ @ SV173 @ SY1156 )
                     != ( happ @ SV173 @ SY1157 ) )
                    | ~ ( p @ ( happ @ ( happ @ SY1155 @ SY1156 ) @ SY1157 ) )
                    | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SY1155 @ SY1156 @ SY1157 ) )
              | ~ ~ ( ~ ! [SY1158: $i,SY1159: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SY1155 @ SY1158 @ SY1159 )
                          | ( ( happ @ SV173 @ SY1158 )
                            = ( happ @ SV173 @ SY1159 ) ) )
                    | ~ ! [SY1160: $i,SY1161: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SY1155 @ SY1160 @ SY1161 )
                          | ( p @ ( happ @ ( happ @ SY1155 @ SY1160 ) @ SY1161 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3494]) ).

thf(3647,plain,
    ! [SV174: $i,SV155: $i,SV123: $i,SV1: $i] :
      ( ( ! [SY1162: $i] :
            ( ( c_24__lam__45594___24a5 @ SV1 @ SV123 @ SV155 @ SV174 @ SY1162 )
            = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV123 @ ( happ @ SV174 @ SY1162 ) @ SV155 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3495]) ).

thf(3648,plain,
    ! [SV175: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
          | ! [SY1163: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1163 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SY1163 )
              | ! [SY1164: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1164 )
                  | ! [SY1165: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1165 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1164 @ SY1165 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1164 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY1163 @ SY1165 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3499]) ).

thf(3649,plain,
    ! [SV176: $i,SV6: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV6 @ SV176 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV6 @ SV176 @ SV176 ) )
        = $true )
      | ( ( cType___24t @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3500]) ).

thf(3650,plain,
    ! [SV177: $i,SV157: $i,SV125: $i,SV8: $i] :
      ( ( ( c_24__lam__33077___24a4 @ SV8 @ SV125 @ SV157 @ SV177 )
        = ( happ @ SV157 @ SV177 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3502]) ).

thf(3651,plain,
    ! [SV178: $i,SV158: $i,SV126: $i,SV9: $i] :
      ( ( ( c_24__lam__33085___24a4 @ SV9 @ SV126 @ SV158 @ SV178 )
        = ( happ @ SV158 @ SV178 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3503]) ).

thf(3652,plain,
    ! [SV10: $i,SV179: $i] :
      ( ( ( ~ ( cProp___24t @ SV179 )
          | ~ ( p @ SV10 )
          | ~ ( p @ SV179 )
          | ( p @ SV10 ) )
        = $true )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3504]) ).

thf(3653,plain,
    ! [SV11: $i] :
      ( ( ( ~ ( p @ SV11 ) )
        = $true )
      | ( ( p @ SV11 )
        = $true )
      | ( ( cProp___24t @ SV11 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3505]) ).

thf(3654,plain,
    ! [SV12: $i,SV180: $i] :
      ( ( ( ~ ( cProp___24t @ SV180 )
          | ~ ( p @ SV12 )
          | ( p @ SV180 )
          | ( p @ SV12 ) )
        = $true )
      | ( ( cProp___24t @ SV12 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3507]) ).

thf(3655,plain,
    ! [SV181: $i,SV13: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV13 @ SV181 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SV181 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SV181 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV13 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3508]) ).

thf(3656,plain,
    ! [SV182: $i,SV14: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV14 @ SV182 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SV182 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SV182 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV14 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3509]) ).

thf(3657,plain,
    ! [SV183: $i,SV15: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
          | ! [SY1166: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY1166 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SY1166 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY1166 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3510]) ).

thf(3658,plain,
    ! [SV184: $i,SV16: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
          | ! [SY1167: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY1167 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SY1167 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY1167 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3511]) ).

thf(3659,plain,
    ! [SV185: $i,SV17: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
          | ! [SY1168: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY1168 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SY1168 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY1168 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3512]) ).

thf(3660,plain,
    ! [SV186: $i,SV18: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
          | ! [SY1169: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY1169 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SY1169 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY1169 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3513]) ).

thf(3661,plain,
    ! [SV187: $i,SV19: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
          | ! [SY1170: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY1170 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SY1170 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY1170 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3514]) ).

thf(3662,plain,
    ! [SV188: $i,SV20: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
          | ! [SY1171: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY1171 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SY1171 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY1171 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3515]) ).

thf(3663,plain,
    ! [SV189: $i,SV21: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
          | ! [SY1172: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY1172 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SY1172 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY1172 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3516]) ).

thf(3664,plain,
    ! [SV190: $i,SV22: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
          | ! [SY1173: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1173 )
              | ! [SY1174: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1174 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SY1173 ) @ SY1174 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY1173 @ SY1174 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3517]) ).

thf(3665,plain,
    ! [SV191: $i,SV23: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
          | ! [SY1175: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1175 )
              | ! [SY1176: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1176 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY1175 @ SY1176 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY1175 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SY1176 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3518]) ).

thf(3666,plain,
    ! [SV192: $i,SV24: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV192 )
          | ! [SY1177: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY1177 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV192 @ SY1177 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY1177 @ SV192 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3519]) ).

thf(3667,plain,
    ! [SV193: $i,SV25: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV25 @ SV193 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV25 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV25 @ SV193 @ SV193 ) @ SV193 ) )
        = $true )
      | ( ( cType___24t @ SV25 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3520]) ).

thf(3668,plain,
    ! [SV194: $i,SV26: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
          | ! [SY1178: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY1178 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SY1178 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SY1178 @ SV194 ) @ SV194 ) ) )
        = $true )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3521]) ).

thf(3669,plain,
    ! [SV195: $i,SV27: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
          | ! [SY1179: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY1179 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SY1179 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SY1179 ) @ SV195 ) ) )
        = $true )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3522]) ).

thf(3670,plain,
    ! [SV196: $i,SV28: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV196 )
          | ! [SY1180: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY1180 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SV196 @ SY1180 ) @ SV196 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV28 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3523]) ).

thf(3671,plain,
    ! [SV197: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
          | ! [SY1181: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1181 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SY1181 )
              | ! [SY1182: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1182 )
                  | ! [SY1183: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1183 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1182 @ SY1183 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1182 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY1181 @ SY1183 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3524]) ).

thf(3672,plain,
    ! [SV198: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
          | ! [SY1184: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1184 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SY1184 ) )
              | ! [SY1185: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1185 )
                  | ! [SY1186: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1186 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1185 @ SY1186 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1185 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY1184 @ SY1186 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3525]) ).

thf(3673,plain,
    ! [SV199: $i,SV31: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
          | ! [SY1187: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1187 )
              | ! [SY1188: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1188 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SY1187 ) @ SY1188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SY1188 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY1187 @ SY1188 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3526]) ).

thf(3674,plain,
    ! [SV200: $i,SV32: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
          | ! [SY1189: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1189 )
              | ! [SY1190: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1190 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SY1189 ) @ SY1190 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY1189 @ SY1190 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3527]) ).

thf(3675,plain,
    ! [SV201: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
          | ! [SY1191: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1191 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SY1191 )
              | ! [SY1192: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1192 )
                  | ! [SY1193: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1193 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1192 @ SY1193 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1192 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY1191 @ SY1193 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3528]) ).

thf(3676,plain,
    ! [SV202: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
          | ! [SY1194: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1194 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SY1194 ) )
              | ! [SY1195: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1195 )
                  | ! [SY1196: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1196 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1195 @ SY1196 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1195 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY1194 @ SY1196 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3529]) ).

thf(3677,plain,
    ! [SV203: $i,SV35: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
          | ! [SY1197: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY1197 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SY1197 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY1197 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3530]) ).

thf(3678,plain,
    ! [SV204: $i,SV36: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
          | ! [SY1198: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY1198 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SY1198 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY1198 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3531]) ).

thf(3679,plain,
    ! [SV205: $i,SV37: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
          | ! [SY1199: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1199 )
              | ! [SY1200: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1200 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SY1199 ) @ SY1200 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY1199 @ SY1200 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3532]) ).

thf(3680,plain,
    ! [SV206: $i,SV38: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
          | ! [SY1201: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1201 )
              | ! [SY1202: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1202 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY1201 @ SY1202 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY1201 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SY1202 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3533]) ).

thf(3681,plain,
    ! [SV207: $i,SV39: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV207 )
          | ! [SY1203: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY1203 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV207 @ SY1203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY1203 @ SV207 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3534]) ).

thf(3682,plain,
    ! [SV208: $i,SV40: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV40 @ SV208 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV40 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV40 @ SV208 @ SV208 ) @ SV208 ) )
        = $true )
      | ( ( cType___24t @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3535]) ).

thf(3683,plain,
    ! [SV209: $i,SV41: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
          | ! [SY1204: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY1204 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SY1204 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SY1204 ) @ SY1204 ) ) )
        = $true )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3536]) ).

thf(3684,plain,
    ! [SV210: $i,SV42: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
          | ! [SY1205: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY1205 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SY1205 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SY1205 @ SV210 ) @ SY1205 ) ) )
        = $true )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3537]) ).

thf(3685,plain,
    ! [SV211: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
          | ! [SY1206: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1206 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SY1206 )
              | ! [SY1207: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1207 )
                  | ! [SY1208: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1208 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1207 @ SY1208 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1207 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY1206 @ SY1208 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3538]) ).

thf(3686,plain,
    ! [SV212: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
          | ! [SY1209: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1209 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SY1209 ) )
              | ! [SY1210: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1210 )
                  | ! [SY1211: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1211 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1210 @ SY1211 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1210 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY1209 @ SY1211 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3539]) ).

thf(3687,plain,
    ! [SV213: $i,SV45: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
          | ! [SY1212: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY1212 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SY1212 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SY1212 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3540]) ).

thf(3688,plain,
    ! [SV214: $i,SV46: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
          | ! [SY1213: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY1213 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SY1213 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SY1213 @ SV214 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3541]) ).

thf(3689,plain,
    ! [SV215: $i,SV47: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
          | ! [SY1214: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY1214 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SY1214 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3542]) ).

thf(3690,plain,
    ! [SV216: $i,SV48: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
          | ! [SY1215: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY1215 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SY1215 ) )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY1215 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3543]) ).

thf(3691,plain,
    ! [SV217: $i,SV49: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV217 )
          | ! [SY1216: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY1216 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SV217 @ SY1216 ) @ SV217 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV49 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3544]) ).

thf(3692,plain,
    ! [SV218: $i,SV50: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
          | ! [SY1217: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1217 )
              | ! [SY1218: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1218 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SY1218 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SY1217 ) @ SY1218 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3545]) ).

thf(3693,plain,
    ! [SV219: $i,SV51: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV219 )
          | ! [SY1219: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY1219 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SV219 @ SY1219 ) @ SY1219 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV51 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3546]) ).

thf(3694,plain,
    ! [SV220: $i,SV52: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
          | ! [SY1220: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1220 )
              | ! [SY1221: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1221 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SY1220 @ SY1221 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SY1220 ) @ SY1221 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3547]) ).

thf(3695,plain,
    ! [SV221: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
          | ! [SY1222: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1222 )
              | ! [SY1223: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1223 )
                  | ! [SY1224: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1224 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SY1222 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY1223 @ SY1224 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SY1223 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY1222 @ SY1224 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3548]) ).

thf(3696,plain,
    ! [SV222: $i,SV54: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
          | ! [SY1225: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1225 )
              | ! [SY1226: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1226 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1225 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1226 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SY1225 @ SY1226 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3549]) ).

thf(3697,plain,
    ! [SV223: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
          | ! [SY1227: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1227 )
              | ! [SY1228: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1228 )
                  | ! [SY1229: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1229 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SY1227 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1229 @ SY1228 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SY1228 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY1227 @ SY1229 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3550]) ).

thf(3698,plain,
    ! [SV224: $i,SV56: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV224 )
          | ! [SY1230: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY1230 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SV224 @ SY1230 ) @ SV224 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV56 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3551]) ).

thf(3699,plain,
    ! [SV225: $i,SV57: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
          | ! [SY1231: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY1231 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SY1231 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY1231 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3552]) ).

thf(3700,plain,
    ! [SV226: $i,SV58: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV58 @ SV226 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV58 @ SV226 @ SV226 ) ) )
        = $true )
      | ( ( cType___24t @ SV58 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3553]) ).

thf(3701,plain,
    ! [SV227: $i,SV59: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
          | ! [SY1232: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY1232 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SY1232 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY1232 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3554]) ).

thf(3702,plain,
    ! [SV228: $i,SV60: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
          | ! [SY1233: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY1233 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY1233 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY1233 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3555]) ).

thf(3703,plain,
    ! [SV229: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
          | ! [SY1234: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1234 )
              | ! [SY1235: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1235 )
                  | ! [SY1236: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1236 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SY1234 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY1235 @ SY1236 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SY1235 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY1234 @ SY1236 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3556]) ).

thf(3704,plain,
    ! [SV230: $i,SV62: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
          | ! [SY1237: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY1237 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SY1237 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SY1237 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3557]) ).

thf(3705,plain,
    ! [SV231: $i,SV63: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
          | ! [SY1238: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY1238 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SY1238 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SY1238 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3558]) ).

thf(3706,plain,
    ! [SV232: $i,SV64: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
          | ! [SY1239: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY1239 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SY1239 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SY1239 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3559]) ).

thf(3707,plain,
    ! [SV233: $i,SV65: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
          | ! [SY1240: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY1240 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SY1240 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY1240 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3560]) ).

thf(3708,plain,
    ! [SV234: $i,SV66: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
          | ! [SY1241: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY1241 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY1241 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY1241 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3561]) ).

thf(3709,plain,
    ! [SV235: $i,SV67: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
          | ! [SY1242: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1242 )
              | ! [SY1243: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1243 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SY1243 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY1242 @ SY1243 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SY1242 ) @ SY1243 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3562]) ).

thf(3710,plain,
    ! [SV236: $i,SV68: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV236 )
          | ! [SY1244: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY1244 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SV236 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SV236 @ SY1244 ) @ SY1244 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV68 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3563]) ).

thf(3711,plain,
    ! [SV237: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
          | ! [SY1245: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1245 )
              | ! [SY1246: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1246 )
                  | ! [SY1247: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1247 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SY1245 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY1246 @ SY1247 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SY1246 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY1245 @ SY1247 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3564]) ).

thf(3712,plain,
    ! [SV238: $i,SV70: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV238 )
          | ! [SY1248: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY1248 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SV238 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SV238 @ SY1248 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV70 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3565]) ).

thf(3713,plain,
    ! [SV239: $i,SV71: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
          | ! [SY1249: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1249 )
              | ! [SY1250: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1250 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SY1249 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SY1249 @ SY1250 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3566]) ).

thf(3714,plain,
    ! [SV240: $i,SV72: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV240 )
          | ! [SY1251: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY1251 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SY1251 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SV240 @ SY1251 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV72 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3567]) ).

thf(3715,plain,
    ! [SV241: $i,SV73: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
          | ! [SY1252: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1252 )
              | ! [SY1253: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1253 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SY1253 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SY1252 @ SY1253 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3568]) ).

thf(3716,plain,
    ! [SV242: $i,SV74: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
          | ! [SY1254: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY1254 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SY1254 ) )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY1254 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3569]) ).

thf(3717,plain,
    ! [SV243: $i,SV159: $i,SV128: $i,SV76: $i] :
      ( ( ! [SY1255: $i] :
            ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ SV76 ) @ SV128 ) @ SV159 ) @ SV243 ) @ SY1255 )
            = ( c_24__lam__45594___24a5 @ SV76 @ SV128 @ SV159 @ SV243 @ SY1255 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3570]) ).

thf(3718,plain,
    ! [SV78: $i] :
      ( ( ( ~ ~ ( ~ ! [SY657: $i] :
                      ( ~ ( cProp___24t @ SY657 )
                      | ( p @ SV78 )
                      | ~ ( p @ SV78 )
                      | ( p @ SY657 ) )
                | ~ ! [SY658: $i] :
                      ( ~ ( cProp___24t @ SY658 )
                      | ( p @ SV78 )
                      | ~ ( p @ SY658 )
                      | ( p @ SY658 ) ) )
          | ~ ~ ( ~ ! [SY659: $i] :
                      ( ~ ( cProp___24t @ SY659 )
                      | ~ ( p @ SY659 )
                      | ~ ( p @ SV78 )
                      | ( p @ SY659 ) )
                | ~ ! [SX1: $i] :
                      ( ~ ( cProp___24t @ SX1 )
                      | ~ ( p @ SX1 )
                      | ~ ( p @ SX1 )
                      | ( p @ SX1 ) ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3572]) ).

thf(3719,plain,
    ! [SV244: $i] :
      ( ( ~ ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) )
            | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
                  | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) ) )
        | ( c_24__type__96___24t @ SV244 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3573]) ).

thf(3720,plain,
    ! [SV245: $i] :
      ( ( ~ ( c_24__type__96___24t @ SV245 )
        | ! [SY1256: $i] :
            ( ~ ( cType___24t @ SY1256 )
            | ! [SY1257: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1256 @ SY1257 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1256 @ ( happ @ ( happ @ SV245 @ SY1256 ) @ SY1257 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3574]) ).

thf(3721,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
          | ~ ( ~ ! [SY1258: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1258 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1258 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1258 ) )
              | ~ ! [SY1259: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1259 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1259 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1259 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3575]) ).

thf(3722,plain,
    ! [SV80: $i] :
      ( ( ! [SY664: $i,SY665: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY664 @ SY665 )
            | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY664 ) @ SY665 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3576]) ).

thf(3723,plain,
    ! [SV80: $i] :
      ( ( ! [SY666: $i,SY667: $i] :
            ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SY666 ) @ SY667 ) )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SY666 @ SY667 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3577]) ).

thf(3724,plain,
    ! [SV247: $i] :
      ( ( ! [SY1260: $i] :
            ( ~ ( c_24__lam__35673___24a2 @ SV247 @ SY1260 )
            | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV247 ) @ SY1260 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3578]) ).

thf(3725,plain,
    ! [SV248: $i] :
      ( ( ! [SY1261: $i] :
            ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV248 ) @ SY1261 ) )
            | ( c_24__lam__35673___24a2 @ SV248 @ SY1261 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3579]) ).

thf(3726,plain,
    ! [SV161: $i,SV130: $i,SV81: $i] :
      ( ( ~ ! [SY1091: $i,SY1092: $i] :
              ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1091 @ SY1092 )
              | ( p @ ( happ @ ( happ @ SV130 @ SY1091 ) @ SY1092 ) )
              | ( p @ ( happ @ ( happ @ SV161 @ SY1091 ) @ SY1092 ) ) )
        | ~ ~ ( ~ ! [SY1093: $i,SY1094: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
                    | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) )
              | ~ ! [SY1095: $i,SY1096: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
                    | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3580]) ).

thf(3727,plain,
    ! [SV131: $i,SV82: $i,SV162: $i] :
      ( ( ~ ! [SY1097: $i,SY1098: $i] :
              ( ( ( happ @ SV162 @ SY1097 )
               != ( happ @ SV162 @ SY1098 ) )
              | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1097 @ SY1098 ) )
        | ~ ! [SY1099: $i,SY1100: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1099 @ SY1100 )
              | ( ( happ @ SV162 @ SY1099 )
                = ( happ @ SV162 @ SY1100 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3581]) ).

thf(3728,plain,
    ! [SV249: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
          | ! [SY1262: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1262 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SY1262 )
              | ! [SY1263: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1263 )
                  | ~ ( ~ ! [SY1264: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1264 )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1263 @ SY1264 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1263 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY1262 @ SY1264 ) ) )
                      | ~ ! [SY1265: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1265 )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1263 @ SY1265 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY1262 @ SY1265 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1263 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3582]) ).

thf(3729,plain,
    ! [SV132: $i,SV84: $i] :
      ( ( ~ ! [SY947: $i,SY948: $i] :
              ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY947 @ SY948 )
              | ( p @ ( happ @ ( happ @ SV132 @ SY947 ) @ SY948 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3583]) ).

thf(3730,plain,
    ! [SV84: $i,SV132: $i] :
      ( ( ~ ! [SY949: $i,SY950: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV132 @ SY949 ) @ SY950 ) )
              | ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY949 @ SY950 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3583]) ).

thf(3731,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
          | ~ ( ~ ! [SY1266: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1266 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1266 )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1266 ) ) )
              | ~ ! [SY1267: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1267 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1267 )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1267 ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3584]) ).

thf(3732,plain,
    ! [SV251: $i] :
      ( ( ~ ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SV251 ) )
            | ~ ~ ( cType___24t @ ( happ @ SV251 @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) ) )
        | ( c_24__type__28___24t @ SV251 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3585]) ).

thf(3733,plain,
    ! [SV252: $i] :
      ( ( ~ ( c_24__type__28___24t @ SV252 )
        | ! [SY1268: $i] :
            ( ~ ( cType___24t @ SY1268 )
            | ( cType___24t @ ( happ @ SV252 @ SY1268 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3586]) ).

thf(3734,plain,
    ! [SV86: $i,SV133: $i] :
      ( ( ~ ! [SY951: $i,SY952: $i] :
              ( ~ ( p @ ( happ @ SV133 @ SY952 ) )
              | ( p @ ( happ @ SY951 @ SY952 ) )
              | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY951 @ SY952 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3587]) ).

thf(3735,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ~ ~ ( ~ ! [SY953: $i,SY954: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
                    | ( p @ ( happ @ SV133 @ SY954 ) ) )
              | ~ ! [SY955: $i,SY956: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
                    | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3587]) ).

thf(3736,plain,
    ! [SV134: $i,SV87: $i] :
      ( ( ~ ! [SY957: $i,SY958: $i] :
              ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY957 @ SY958 )
              | ( p @ ( happ @ ( happ @ SV134 @ SY958 ) @ SY957 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3588]) ).

thf(3737,plain,
    ! [SV87: $i,SV134: $i] :
      ( ( ~ ! [SY959: $i,SY960: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV134 @ SY960 ) @ SY959 ) )
              | ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY959 @ SY960 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3588]) ).

thf(3738,plain,
    ! [SV88: $i] :
      ( ( ! [SY707: $i,SY708: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY707 @ SY708 )
            | ~ ( p @ ( happ @ SY707 @ SY708 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3589]) ).

thf(3739,plain,
    ! [SV88: $i] :
      ( ( ! [SY709: $i,SY710: $i] :
            ( ( p @ ( happ @ SY709 @ SY710 ) )
            | ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SY709 @ SY710 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3590]) ).

thf(3740,plain,
    ! [SV253: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
          | ! [SY1269: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1269 )
              | ~ ( ~ ! [SY1270: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1270 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SY1269 ) @ SY1270 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY1269 @ SY1270 ) ) ) )
                  | ~ ! [SY1271: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1271 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY1269 @ SY1271 ) ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SY1269 ) @ SY1271 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3591]) ).

thf(3741,plain,
    ! [SV163: $i,SV135: $i,SV90: $i] :
      ( ( ~ ! [SY1101: $i,SY1102: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1101 @ SY1102 )
              | ( p @ ( happ @ ( happ @ SV135 @ SY1101 ) @ SY1102 ) )
              | ( p @ ( happ @ ( happ @ SV163 @ SY1101 ) @ SY1102 ) ) )
        | ~ ~ ( ~ ! [SY1103: $i,SY1104: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
                    | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) )
              | ~ ! [SY1105: $i,SY1106: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
                    | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3592]) ).

thf(3742,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ( cProp___24t @ SV254 )
          | ~ ( ~ ~ ( ~ ! [SY1272: $i] :
                          ( ~ ( cProp___24t @ SY1272 )
                          | ( p @ SV91 )
                          | ~ ( p @ SV91 )
                          | ( p @ SV254 )
                          | ( p @ SY1272 ) )
                    | ~ ! [SY1273: $i] :
                          ( ~ ( cProp___24t @ SY1273 )
                          | ( p @ SV91 )
                          | ~ ( p @ SY1273 )
                          | ( p @ SV254 )
                          | ( p @ SY1273 ) ) )
              | ~ ~ ( ~ ! [SY1274: $i] :
                          ( ~ ( cProp___24t @ SY1274 )
                          | ~ ( p @ SV254 )
                          | ~ ( p @ SV91 )
                          | ( p @ SV254 )
                          | ( p @ SY1274 ) )
                    | ~ ! [SY1275: $i] :
                          ( ~ ( cProp___24t @ SY1275 )
                          | ~ ( p @ SV254 )
                          | ~ ( p @ SY1275 )
                          | ( p @ SV254 )
                          | ( p @ SY1275 ) ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3593]) ).

thf(3743,plain,
    ! [SV92: $i,SV164: $i,SV136: $i] :
      ( ( ~ ! [SY1107: $i,SY1108: $i] :
              ( ~ ( p @ ( happ @ SV136 @ SY1107 ) )
              | ~ ( p @ ( happ @ SV164 @ SY1108 ) )
              | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1107 @ SY1108 ) )
        | ~ ~ ( ~ ! [SY1109: $i] :
                    ( ! [SY1110: $i] :
                        ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
                    | ( p @ ( happ @ SV136 @ SY1109 ) ) )
              | ~ ! [SY1111: $i,SY1112: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
                    | ( p @ ( happ @ SV164 @ SY1112 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3594]) ).

thf(3744,plain,
    ! [SV255: $i] :
      ( ( ! [SY1276: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( sK16_Vv__CANONICAL__1 @ SY1276 @ SV255 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SY1276 @ ( sK16_Vv__CANONICAL__1 @ SY1276 @ SV255 ) ) ) )
            | ( c_24__type__11748___24t @ SV255 @ SY1276 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3595]) ).

thf(3745,plain,
    ! [SV256: $i] :
      ( ( ! [SY1277: $i] :
            ( ~ ( c_24__type__11748___24t @ SV256 @ SY1277 )
            | ! [SY1278: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SY1278 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SY1277 @ SY1278 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3596]) ).

thf(3746,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3597]) ).

thf(3747,plain,
    ( ( ( ~ $true ) = $true )
    | ( ( ! [SX0: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3598]) ).

thf(3748,plain,
    ! [SV165: $i,SV137: $i,SV93: $i] :
      ( ( ~ ! [SY1113: $i,SY1114: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1113 @ SY1114 )
              | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1113 ) @ SY1114 ) ) )
        | ~ ! [SY1115: $i,SY1116: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1115 ) @ SY1116 ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1115 @ SY1116 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3599]) ).

thf(3749,plain,
    ! [SV94: $i] :
      ( ( ! [SY742: $i,SY743: $i] :
            ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY742 @ SY743 ) )
            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY743 @ SY742 ) )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY742 @ SY743 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3600]) ).

thf(3750,plain,
    ! [SV94: $i] :
      ( ( ~ ( ~ ! [SY744: $i,SY745: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) )
            | ~ ! [SY746: $i,SY747: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3601]) ).

thf(3751,plain,
    ! [SV257: $i] :
      ( ( ! [SY1279: $i] :
            ( ~ ( p @ ( c_24__prop__35358___24a2 @ SV257 @ SY1279 ) )
            | ~ ( p @ SY1279 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3602]) ).

thf(3752,plain,
    ! [SV258: $i] :
      ( ( ! [SY1280: $i] :
            ( ( p @ SY1280 )
            | ( p @ ( c_24__prop__35358___24a2 @ SV258 @ SY1280 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3603]) ).

thf(3753,plain,
    ! [SV95: $i,SV138: $i] :
      ( ( ~ ! [SY980: $i,SY981: $i] :
              ( ~ ( p @ ( happ @ SV138 @ SY981 ) )
              | ~ ( p @ ( happ @ SY980 @ SY981 ) )
              | ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY980 @ SY981 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3604]) ).

thf(3754,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ~ ~ ( ~ ! [SY982: $i,SY983: $i] :
                    ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
                    | ( p @ ( happ @ SV138 @ SY983 ) ) )
              | ~ ! [SY984: $i,SY985: $i] :
                    ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
                    | ( p @ ( happ @ SY984 @ SY985 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3604]) ).

thf(3755,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
          | ~ ( ~ ! [SY1281: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1281 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1281 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1281 ) ) )
              | ~ ! [SY1282: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1282 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1282 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1282 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3605]) ).

thf(3756,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ! [SY986: $i,SY987: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY986 @ SY987 )
              | ( SY986 = SY987 )
              | ( p @ ( happ @ ( happ @ SV139 @ SY986 ) @ SY987 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3606]) ).

thf(3757,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ~ ( ~ ! [SY988: $i,SY989: $i] :
                    ( ( SY988 != SY989 )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) )
              | ~ ! [SY990: $i,SY991: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3606]) ).

thf(3758,plain,
    ! [SV98: $i] :
      ( ( ! [SY765: $i,SY766: $i] :
            ( ~ ( ~ ( t @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) @ SV98 )
                | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) @ SV98 )
                      | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SY765 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) )
                            | ~ ~ ( p @ ( happ @ ( happ @ SY766 @ ( sK18_V3__x @ SY766 @ SY765 @ SV98 ) ) @ ( sK19_SY480 @ SY766 @ SY765 @ SV98 ) ) ) ) ) )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY765 @ SY766 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3607]) ).

thf(3759,plain,
    ! [SV98: $i] :
      ( ( ! [SY767: $i,SY768: $i] :
            ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SY767 @ SY768 ) )
            | ! [SY769: $i] :
                ( ~ ( t @ SY769 @ SV98 )
                | ! [SY770: $i] :
                    ( ~ ( t @ SY770 @ SV98 )
                    | ~ ( p @ ( happ @ ( happ @ SY767 @ SY769 ) @ SY770 ) )
                    | ( p @ ( happ @ ( happ @ SY768 @ SY769 ) @ SY770 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3608]) ).

thf(3760,plain,
    ! [SV140: $i,SV99: $i] :
      ( ( ~ ! [SY992: $i,SY993: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY992 @ SY993 )
              | ( p @ ( happ @ ( happ @ SV140 @ SY992 ) @ SY993 ) )
              | ( p @ ( happ @ ( happ @ SV140 @ SY993 ) @ SY992 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3609]) ).

thf(3761,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ~ ~ ( ~ ! [SY994: $i,SY995: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) )
              | ~ ! [SY996: $i,SY997: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3609]) ).

thf(3762,plain,
    ! [SV100: $i,SV166: $i,SV141: $i] :
      ( ( ~ ! [SY1117: $i,SY1118: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV141 @ SY1117 ) @ SY1118 ) )
              | ( p @ ( happ @ ( happ @ SV166 @ SY1117 ) @ SY1118 ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1117 @ SY1118 ) )
        | ~ ~ ( ~ ! [SY1119: $i,SY1120: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
                    | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) )
              | ~ ! [SY1121: $i,SY1122: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
                    | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3610]) ).

thf(3763,plain,
    ! [SV101: $i] :
      ( ( ! [SY786: $i,SY787: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY786 @ ( happ @ SY787 @ ( sK17_Vv__CANONICAL__2 @ SY787 @ SY786 @ SV101 ) ) ) )
            | ( c_24__type__11699___24t @ SV101 @ SY786 @ SY787 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3611]) ).

thf(3764,plain,
    ! [SV101: $i] :
      ( ( ! [SY788: $i,SY789: $i] :
            ( ~ ( c_24__type__11699___24t @ SV101 @ SY788 @ SY789 )
            | ! [SY790: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY790 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY788 @ ( happ @ SY789 @ SY790 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3612]) ).

thf(3765,plain,
    ! [SV167: $i,SV142: $i,SV102: $i] :
      ( ( ~ ! [SY1123: $i,SY1124: $i] :
              ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1123 @ SY1124 )
              | ( p @ ( happ @ ( happ @ SV167 @ SY1123 ) @ SY1124 ) ) )
        | ~ ! [SY1125: $i,SY1126: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV167 @ SY1125 ) @ SY1126 ) )
              | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1125 @ SY1126 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3613]) ).

thf(3766,plain,
    ! [SV103: $i] :
      ( ( ! [SY797: $i,SY798: $i] :
            ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY797 @ SY798 ) )
            | ( p @ SY797 )
            | ( p @ SY798 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3614]) ).

thf(3767,plain,
    ! [SV103: $i] :
      ( ( ~ ( ~ ! [SY799: $i] :
                  ( ~ ( p @ SY799 )
                  | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) )
            | ~ ! [SY801: $i,SY802: $i] :
                  ( ~ ( p @ SY802 )
                  | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3615]) ).

thf(3768,plain,
    ! [SV104: $i,SV143: $i,SV168: $i] :
      ( ( ~ ! [SY1127: $i,SY1128: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV168 @ SY1127 ) @ SY1128 ) )
              | ~ ( p @ ( happ @ SV143 @ SY1127 ) )
              | ~ ( p @ ( happ @ SV143 @ SY1128 ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1127 @ SY1128 ) )
        | ~ ~ ( ~ ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                          | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
                    | ~ ! [SY1131: $i] :
                          ( ! [SY1132: $i] :
                              ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                          | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
              | ~ ! [SY1133: $i,SY1134: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
                    | ( p @ ( happ @ SV143 @ SY1134 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3616]) ).

thf(3769,plain,
    ! [SV105: $i] :
      ( ( ! [SY813: $i,SY814: $i] :
            ( ( SY813 != SY814 )
            | ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY813 @ SY814 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3617]) ).

thf(3770,plain,
    ! [SV105: $i] :
      ( ( ! [SY815: $i,SY816: $i] :
            ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SY815 @ SY816 ) )
            | ( SY815 = SY816 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3618]) ).

thf(3771,plain,
    ! [SV260: $i] :
      ( ( ! [SY1283: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK13_Vv__CANONICAL__1 @ SY1283 @ SV260 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SY1283 @ SV260 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SY1283 @ ( sK13_Vv__CANONICAL__1 @ SY1283 @ SV260 ) ) @ ( sK14_SY479 @ SY1283 @ SV260 ) ) ) ) )
            | ( c_24__type__11829___24t @ SV260 @ SY1283 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3619]) ).

thf(3772,plain,
    ! [SV261: $i] :
      ( ( ! [SY1284: $i] :
            ( ~ ( c_24__type__11829___24t @ SV261 @ SY1284 )
            | ! [SY1285: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1285 )
                | ! [SY1286: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1286 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SY1284 @ SY1285 ) @ SY1286 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3620]) ).

thf(3773,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ! [SY1019: $i,SY1020: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1019 @ SY1020 )
              | ( p @ ( happ @ ( happ @ SV144 @ SY1020 ) @ SY1019 ) )
              | ( SY1019 = SY1020 )
              | ( p @ ( happ @ ( happ @ SV144 @ SY1019 ) @ SY1020 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3621]) ).

thf(3774,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ~ ~ ( ~ ! [SY1021: $i,SY1022: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) )
              | ~ ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                          ( ( SY1023 != SY1024 )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
                    | ~ ! [SY1025: $i,SY1026: $i] :
                          ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                          | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3621]) ).

thf(3775,plain,
    ! [SV169: $i,SV145: $i,SV107: $i] :
      ( ( ~ ! [SY1135: $i,SY1136: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1135 @ SY1136 )
              | ( p @ ( happ @ SY1135 @ ( happ @ SV169 @ SY1136 ) ) ) )
        | ~ ! [SY1137: $i,SY1138: $i] :
              ( ~ ( p @ ( happ @ SY1137 @ ( happ @ SV169 @ SY1138 ) ) )
              | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1137 @ SY1138 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3622]) ).

thf(3776,plain,
    ! [SV108: $i,SV146: $i] :
      ( ( ~ ! [SY1032: $i,SY1033: $i] :
              ( ( SY1032 != SY1033 )
              | ~ ( p @ ( happ @ SV146 @ SY1032 ) )
              | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1032 @ SY1033 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3623]) ).

thf(3777,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ~ ~ ( ~ ! [SY1034: $i,SY1035: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
                    | ( SY1034 = SY1035 ) )
              | ~ ! [SY1036: $i] :
                    ( ! [SY1037: $i] :
                        ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
                    | ( p @ ( happ @ SV146 @ SY1036 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3623]) ).

thf(3778,plain,
    ! [SV262: $i] :
      ( ( ~ ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) )
            | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
                  | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                        | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) ) )
        | ( c_24__type__90___24t @ SV262 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3624]) ).

thf(3779,plain,
    ! [SV263: $i] :
      ( ( ~ ( c_24__type__90___24t @ SV263 )
        | ! [SY1287: $i] :
            ( ~ ( cType___24t @ SY1287 )
            | ! [SY1288: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ SY1288 )
                | ! [SY1289: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ SY1289 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ ( happ @ ( happ @ ( happ @ SV263 @ SY1287 ) @ SY1288 ) @ SY1289 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3625]) ).

thf(3780,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
          | ~ ( ~ ! [SY1290: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1290 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1290 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1290 ) ) )
              | ~ ! [SY1291: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1291 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1291 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1291 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3626]) ).

thf(3781,plain,
    ! [SV265: $i] :
      ( ( ~ ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SV265 ) )
            | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) )
                  | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                        | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                              | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) ) )
        | ( c_24__type__4733___24t @ SV265 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3627]) ).

thf(3782,plain,
    ! [SV266: $i] :
      ( ( ~ ( c_24__type__4733___24t @ SV266 )
        | ! [SY1292: $i] :
            ( ~ ( cType___24t @ SY1292 )
            | ! [SY1293: $i] :
                ( ~ ( cType___24t @ SY1293 )
                | ! [SY1294: $i] :
                    ( ~ ( cType___24t @ SY1294 )
                    | ! [SY1295: $i] :
                        ( ~ ( cType___24t @ SY1295 )
                        | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SY1292 ) @ SY1293 ) @ SY1294 ) @ SY1295 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3628]) ).

thf(3783,plain,
    ! [SV110: $i,SV170: $i,SV147: $i] :
      ( ( ~ ! [SY1139: $i,SY1140: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV147 @ SY1139 ) @ SY1140 ) )
              | ~ ( p @ ( happ @ ( happ @ SV170 @ SY1139 ) @ SY1140 ) )
              | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1139 @ SY1140 ) )
        | ~ ~ ( ~ ! [SY1141: $i,SY1142: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
                    | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) )
              | ~ ! [SY1143: $i,SY1144: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
                    | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3629]) ).

thf(3784,plain,
    ! [SV148: $i,SV111: $i] :
      ( ( ~ ! [SY1045: $i,SY1046: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1045 @ SY1046 )
              | ( p @ ( happ @ ( happ @ SV148 @ SY1046 ) @ SY1045 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3630]) ).

thf(3785,plain,
    ! [SV111: $i,SV148: $i] :
      ( ( ~ ! [SY1047: $i,SY1048: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV148 @ SY1048 ) @ SY1047 ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1047 @ SY1048 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3630]) ).

thf(3786,plain,
    ! [SV112: $i] :
      ( ( ! [SY855: $i,SY856: $i] :
            ( ~ ( p @ SY855 )
            | ~ ( p @ SY856 )
            | ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY855 @ SY856 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3631]) ).

thf(3787,plain,
    ! [SV112: $i] :
      ( ( ~ ( ~ ! [SY857: $i] :
                  ( ! [SY858: $i] :
                      ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
                  | ( p @ SY857 ) )
            | ~ ! [SY859: $i,SY860: $i] :
                  ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
                  | ( p @ SY860 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3632]) ).

thf(3788,plain,
    ! [SV149: $i,SV113: $i] :
      ( ( ~ ! [SY1049: $i,SY1050: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1049 @ SY1050 )
              | ( p @ ( happ @ SV149 @ SY1050 ) )
              | ( p @ ( happ @ SY1049 @ SY1050 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3633]) ).

thf(3789,plain,
    ! [SV113: $i,SV149: $i] :
      ( ( ~ ~ ( ~ ! [SY1051: $i,SY1052: $i] :
                    ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
                    | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) )
              | ~ ! [SY1053: $i,SY1054: $i] :
                    ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
                    | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3633]) ).

thf(3790,plain,
    ! [SV114: $i] :
      ( ( ~ ( ~ ! [SY868: $i] :
                  ( ( p @ SY868 )
                  | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) )
            | ~ ! [SY870: $i,SY871: $i] :
                  ( ~ ( p @ SY871 )
                  | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3634]) ).

thf(3791,plain,
    ! [SV114: $i] :
      ( ( ! [SY872: $i,SY873: $i] :
            ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY872 @ SY873 ) )
            | ~ ( p @ SY872 )
            | ( p @ SY873 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3635]) ).

thf(3792,plain,
    ! [SV267: $i,SV115: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
          | ! [SY1296: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY1296 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SY1296 )
              | ! [SY1297: $i] :
                  ( ~ ( t @ SY1297 @ SV115 )
                  | ~ ( ~ ! [SY1298: $i] :
                            ( ~ ( t @ SY1298 @ SV115 )
                            | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1297 ) @ SY1298 ) )
                            | ( p @ ( happ @ ( happ @ SY1296 @ SY1297 ) @ SY1298 ) ) )
                      | ~ ! [SY1299: $i] :
                            ( ~ ( t @ SY1299 @ SV115 )
                            | ~ ( p @ ( happ @ ( happ @ SY1296 @ SY1297 ) @ SY1299 ) )
                            | ( p @ ( happ @ ( happ @ SV267 @ SY1297 ) @ SY1299 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3636]) ).

thf(3793,plain,
    ! [SV116: $i,SV150: $i] :
      ( ( ~ ! [SY1055: $i,SY1056: $i] :
              ( ~ ( p @ ( happ @ SV150 @ SY1056 ) )
              | ~ ( p @ ( happ @ SY1055 @ SY1056 ) )
              | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1055 @ SY1056 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3637]) ).

thf(3794,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ~ ~ ( ~ ! [SY1057: $i,SY1058: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
                    | ( p @ ( happ @ SV150 @ SY1058 ) ) )
              | ~ ! [SY1059: $i,SY1060: $i] :
                    ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
                    | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3637]) ).

thf(3795,plain,
    ! [SV268: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
          | ! [SY1300: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1300 )
              | ~ ( ~ ! [SY1301: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1301 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1300 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY1300 @ SY1301 ) ) ) )
                  | ~ ! [SY1302: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1302 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1302 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY1300 @ SY1302 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3638]) ).

thf(3796,plain,
    ! [SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ~ ( ~ ! [SY1303: $i,SY1304: $i] :
                  ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1303 @ SY1304 )
                  | ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1303 ) ) @ ( happ @ SV171 @ SY1304 ) ) ) )
            | ~ ! [SY1305: $i,SY1306: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1305 ) ) @ ( happ @ SV171 @ SY1306 ) ) )
                  | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1305 @ SY1306 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3639]) ).

thf(3797,plain,
    ! [SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ~ ( ~ ! [SY1307: $i,SY1308: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1307 @ SY1308 )
                  | ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1307 ) ) @ ( happ @ SV172 @ SY1308 ) ) ) )
            | ~ ! [SY1309: $i,SY1310: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1309 ) ) @ ( happ @ SV172 @ SY1310 ) ) )
                  | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1309 @ SY1310 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3640]) ).

thf(3798,plain,
    ! [SV120: $i] :
      ( ( ! [SY904: $i,SY905: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY904 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY905 @ ( sK15_Vv__CANONICAL__2 @ SY905 @ SY904 @ SV120 ) ) ) )
            | ( c_24__type__11787___24t @ SV120 @ SY904 @ SY905 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3641]) ).

thf(3799,plain,
    ! [SV120: $i] :
      ( ( ! [SY906: $i,SY907: $i] :
            ( ~ ( c_24__type__11787___24t @ SV120 @ SY906 @ SY907 )
            | ! [SY908: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY906 @ SY908 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY907 @ SY908 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3642]) ).

thf(3800,plain,
    ! [SV153: $i,SV121: $i] :
      ( ( ~ ! [SY1073: $i,SY1074: $i] :
              ( ( SY1073 != SY1074 )
              | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1073 @ SY1074 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3643]) ).

thf(3801,plain,
    ! [SV153: $i,SV121: $i] :
      ( ( ~ ! [SY1075: $i,SY1076: $i] :
              ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1075 @ SY1076 ) )
              | ( SY1075 = SY1076 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3643]) ).

thf(3802,plain,
    ! [SV271: $i] :
      ( ( ~ ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SV271 ) )
            | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) )
                  | ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) ) )
        | ( c_24__type__52___24t @ SV271 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3644]) ).

thf(3803,plain,
    ! [SV272: $i] :
      ( ( ~ ( c_24__type__52___24t @ SV272 )
        | ! [SY1311: $i] :
            ( ~ ( cType___24t @ SY1311 )
            | ! [SY1312: $i] :
                ( ~ ( cType___24t @ SY1312 )
                | ( cType___24t @ ( happ @ ( happ @ SV272 @ SY1311 ) @ SY1312 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3645]) ).

thf(3804,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV173: $i] :
      ( ( ~ ( ~ ! [SY1313: $i,SY1314: $i] :
                  ( ( ( happ @ SV173 @ SY1313 )
                   != ( happ @ SV173 @ SY1314 ) )
                  | ~ ( p @ ( happ @ ( happ @ SV273 @ SY1313 ) @ SY1314 ) )
                  | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1313 @ SY1314 ) )
            | ~ ~ ( ~ ! [SY1315: $i,SY1316: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
                        | ( ( happ @ SV173 @ SY1315 )
                          = ( happ @ SV173 @ SY1316 ) ) )
                  | ~ ! [SY1317: $i,SY1318: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
                        | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3646]) ).

thf(3805,plain,
    ! [SV274: $i,SV174: $i,SV155: $i,SV123: $i,SV1: $i] :
      ( ( ( c_24__lam__45594___24a5 @ SV1 @ SV123 @ SV155 @ SV174 @ SV274 )
        = ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV123 @ ( happ @ SV174 @ SV274 ) @ SV155 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3647]) ).

thf(3806,plain,
    ! [SV175: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 ) )
        = $true )
      | ( ( ! [SY1163: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1163 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SY1163 )
              | ! [SY1164: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1164 )
                  | ! [SY1165: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1165 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1164 @ SY1165 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1164 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY1163 @ SY1165 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3648]) ).

thf(3807,plain,
    ! [SV176: $i,SV6: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV6 @ SV176 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV6 @ SV176 @ SV176 )
        = $true )
      | ( ( cType___24t @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3649]) ).

thf(3808,plain,
    ! [SV10: $i,SV179: $i] :
      ( ( ( ~ ( cProp___24t @ SV179 ) )
        = $true )
      | ( ( ~ ( p @ SV10 )
          | ~ ( p @ SV179 )
          | ( p @ SV10 ) )
        = $true )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3652]) ).

thf(3809,plain,
    ! [SV11: $i] :
      ( ( ( p @ SV11 )
        = $false )
      | ( ( p @ SV11 )
        = $true )
      | ( ( cProp___24t @ SV11 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3653]) ).

thf(3810,plain,
    ! [SV12: $i,SV180: $i] :
      ( ( ( ~ ( cProp___24t @ SV180 ) )
        = $true )
      | ( ( ~ ( p @ SV12 )
          | ( p @ SV180 )
          | ( p @ SV12 ) )
        = $true )
      | ( ( cProp___24t @ SV12 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3654]) ).

thf(3811,plain,
    ! [SV181: $i,SV13: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV13 @ SV181 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SV181 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SV181 ) ) )
        = $true )
      | ( ( cType___24t @ SV13 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3655]) ).

thf(3812,plain,
    ! [SV182: $i,SV14: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV14 @ SV182 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SV182 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SV182 ) ) )
        = $true )
      | ( ( cType___24t @ SV14 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3656]) ).

thf(3813,plain,
    ! [SV183: $i,SV15: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 ) )
        = $true )
      | ( ( ! [SY1166: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY1166 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SY1166 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY1166 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3657]) ).

thf(3814,plain,
    ! [SV184: $i,SV16: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 ) )
        = $true )
      | ( ( ! [SY1167: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY1167 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SY1167 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY1167 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3658]) ).

thf(3815,plain,
    ! [SV185: $i,SV17: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 ) )
        = $true )
      | ( ( ! [SY1168: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY1168 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SY1168 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY1168 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3659]) ).

thf(3816,plain,
    ! [SV186: $i,SV18: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 ) )
        = $true )
      | ( ( ! [SY1169: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY1169 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SY1169 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY1169 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3660]) ).

thf(3817,plain,
    ! [SV187: $i,SV19: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 ) )
        = $true )
      | ( ( ! [SY1170: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY1170 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SY1170 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY1170 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3661]) ).

thf(3818,plain,
    ! [SV188: $i,SV20: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 ) )
        = $true )
      | ( ( ! [SY1171: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY1171 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SY1171 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY1171 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3662]) ).

thf(3819,plain,
    ! [SV189: $i,SV21: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 ) )
        = $true )
      | ( ( ! [SY1172: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY1172 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SY1172 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY1172 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3663]) ).

thf(3820,plain,
    ! [SV190: $i,SV22: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 ) )
        = $true )
      | ( ( ! [SY1173: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1173 )
              | ! [SY1174: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1174 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SY1173 ) @ SY1174 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY1173 @ SY1174 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3664]) ).

thf(3821,plain,
    ! [SV191: $i,SV23: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 ) )
        = $true )
      | ( ( ! [SY1175: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1175 )
              | ! [SY1176: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1176 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY1175 @ SY1176 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY1175 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SY1176 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3665]) ).

thf(3822,plain,
    ! [SV192: $i,SV24: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV192 ) )
        = $true )
      | ( ( ! [SY1177: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY1177 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV192 @ SY1177 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY1177 @ SV192 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3666]) ).

thf(3823,plain,
    ! [SV193: $i,SV25: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV25 @ SV193 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV25 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV25 @ SV193 @ SV193 ) @ SV193 )
        = $true )
      | ( ( cType___24t @ SV25 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3667]) ).

thf(3824,plain,
    ! [SV194: $i,SV26: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 ) )
        = $true )
      | ( ( ! [SY1178: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY1178 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SY1178 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SY1178 @ SV194 ) @ SV194 ) ) )
        = $true )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3668]) ).

thf(3825,plain,
    ! [SV195: $i,SV27: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 ) )
        = $true )
      | ( ( ! [SY1179: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY1179 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SY1179 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SY1179 ) @ SV195 ) ) )
        = $true )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3669]) ).

thf(3826,plain,
    ! [SV196: $i,SV28: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV196 ) )
        = $true )
      | ( ( ! [SY1180: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY1180 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SV196 @ SY1180 ) @ SV196 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV28 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3670]) ).

thf(3827,plain,
    ! [SV197: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 ) )
        = $true )
      | ( ( ! [SY1181: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1181 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SY1181 )
              | ! [SY1182: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1182 )
                  | ! [SY1183: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1183 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1182 @ SY1183 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1182 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY1181 @ SY1183 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3671]) ).

thf(3828,plain,
    ! [SV198: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 ) )
        = $true )
      | ( ( ! [SY1184: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1184 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SY1184 ) )
              | ! [SY1185: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1185 )
                  | ! [SY1186: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1186 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1185 @ SY1186 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1185 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY1184 @ SY1186 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3672]) ).

thf(3829,plain,
    ! [SV199: $i,SV31: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 ) )
        = $true )
      | ( ( ! [SY1187: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1187 )
              | ! [SY1188: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1188 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SY1187 ) @ SY1188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SY1188 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY1187 @ SY1188 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3673]) ).

thf(3830,plain,
    ! [SV200: $i,SV32: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 ) )
        = $true )
      | ( ( ! [SY1189: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1189 )
              | ! [SY1190: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1190 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SY1189 ) @ SY1190 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY1189 @ SY1190 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3674]) ).

thf(3831,plain,
    ! [SV201: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 ) )
        = $true )
      | ( ( ! [SY1191: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1191 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SY1191 )
              | ! [SY1192: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1192 )
                  | ! [SY1193: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1193 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1192 @ SY1193 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1192 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY1191 @ SY1193 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3675]) ).

thf(3832,plain,
    ! [SV202: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 ) )
        = $true )
      | ( ( ! [SY1194: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1194 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SY1194 ) )
              | ! [SY1195: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1195 )
                  | ! [SY1196: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1196 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1195 @ SY1196 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1195 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY1194 @ SY1196 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3676]) ).

thf(3833,plain,
    ! [SV203: $i,SV35: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 ) )
        = $true )
      | ( ( ! [SY1197: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY1197 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SY1197 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY1197 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3677]) ).

thf(3834,plain,
    ! [SV204: $i,SV36: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 ) )
        = $true )
      | ( ( ! [SY1198: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY1198 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SY1198 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY1198 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3678]) ).

thf(3835,plain,
    ! [SV205: $i,SV37: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 ) )
        = $true )
      | ( ( ! [SY1199: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1199 )
              | ! [SY1200: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1200 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SY1199 ) @ SY1200 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY1199 @ SY1200 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3679]) ).

thf(3836,plain,
    ! [SV206: $i,SV38: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 ) )
        = $true )
      | ( ( ! [SY1201: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1201 )
              | ! [SY1202: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1202 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY1201 @ SY1202 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY1201 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SY1202 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3680]) ).

thf(3837,plain,
    ! [SV207: $i,SV39: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV207 ) )
        = $true )
      | ( ( ! [SY1203: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY1203 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV207 @ SY1203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY1203 @ SV207 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3681]) ).

thf(3838,plain,
    ! [SV208: $i,SV40: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV40 @ SV208 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV40 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV40 @ SV208 @ SV208 ) @ SV208 )
        = $true )
      | ( ( cType___24t @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3682]) ).

thf(3839,plain,
    ! [SV209: $i,SV41: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 ) )
        = $true )
      | ( ( ! [SY1204: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY1204 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SY1204 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SY1204 ) @ SY1204 ) ) )
        = $true )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3683]) ).

thf(3840,plain,
    ! [SV210: $i,SV42: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 ) )
        = $true )
      | ( ( ! [SY1205: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY1205 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SY1205 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SY1205 @ SV210 ) @ SY1205 ) ) )
        = $true )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3684]) ).

thf(3841,plain,
    ! [SV211: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 ) )
        = $true )
      | ( ( ! [SY1206: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1206 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SY1206 )
              | ! [SY1207: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1207 )
                  | ! [SY1208: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1208 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1207 @ SY1208 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1207 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY1206 @ SY1208 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3685]) ).

thf(3842,plain,
    ! [SV212: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 ) )
        = $true )
      | ( ( ! [SY1209: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1209 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SY1209 ) )
              | ! [SY1210: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1210 )
                  | ! [SY1211: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1211 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1210 @ SY1211 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1210 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY1209 @ SY1211 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3686]) ).

thf(3843,plain,
    ! [SV213: $i,SV45: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 ) )
        = $true )
      | ( ( ! [SY1212: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY1212 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SY1212 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SY1212 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3687]) ).

thf(3844,plain,
    ! [SV214: $i,SV46: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 ) )
        = $true )
      | ( ( ! [SY1213: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY1213 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SY1213 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SY1213 @ SV214 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3688]) ).

thf(3845,plain,
    ! [SV215: $i,SV47: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 ) )
        = $true )
      | ( ( ! [SY1214: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY1214 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SY1214 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3689]) ).

thf(3846,plain,
    ! [SV216: $i,SV48: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 ) )
        = $true )
      | ( ( ! [SY1215: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY1215 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SY1215 ) )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY1215 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3690]) ).

thf(3847,plain,
    ! [SV217: $i,SV49: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV217 ) )
        = $true )
      | ( ( ! [SY1216: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY1216 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SV217 @ SY1216 ) @ SV217 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV49 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3691]) ).

thf(3848,plain,
    ! [SV218: $i,SV50: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 ) )
        = $true )
      | ( ( ! [SY1217: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1217 )
              | ! [SY1218: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1218 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SY1218 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SY1217 ) @ SY1218 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3692]) ).

thf(3849,plain,
    ! [SV219: $i,SV51: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV219 ) )
        = $true )
      | ( ( ! [SY1219: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY1219 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SV219 @ SY1219 ) @ SY1219 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV51 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3693]) ).

thf(3850,plain,
    ! [SV220: $i,SV52: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 ) )
        = $true )
      | ( ( ! [SY1220: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1220 )
              | ! [SY1221: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1221 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SY1220 @ SY1221 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SY1220 ) @ SY1221 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3694]) ).

thf(3851,plain,
    ! [SV221: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 ) )
        = $true )
      | ( ( ! [SY1222: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1222 )
              | ! [SY1223: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1223 )
                  | ! [SY1224: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1224 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SY1222 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY1223 @ SY1224 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SY1223 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY1222 @ SY1224 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3695]) ).

thf(3852,plain,
    ! [SV222: $i,SV54: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 ) )
        = $true )
      | ( ( ! [SY1225: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1225 )
              | ! [SY1226: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1226 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1225 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1226 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SY1225 @ SY1226 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3696]) ).

thf(3853,plain,
    ! [SV223: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 ) )
        = $true )
      | ( ( ! [SY1227: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1227 )
              | ! [SY1228: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1228 )
                  | ! [SY1229: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1229 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SY1227 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1229 @ SY1228 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SY1228 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY1227 @ SY1229 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3697]) ).

thf(3854,plain,
    ! [SV224: $i,SV56: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV224 ) )
        = $true )
      | ( ( ! [SY1230: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY1230 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SV224 @ SY1230 ) @ SV224 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV56 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3698]) ).

thf(3855,plain,
    ! [SV225: $i,SV57: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 ) )
        = $true )
      | ( ( ! [SY1231: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY1231 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SY1231 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY1231 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3699]) ).

thf(3856,plain,
    ! [SV226: $i,SV58: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV58 @ SV226 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV58 @ SV226 @ SV226 ) )
        = $true )
      | ( ( cType___24t @ SV58 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3700]) ).

thf(3857,plain,
    ! [SV227: $i,SV59: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 ) )
        = $true )
      | ( ( ! [SY1232: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY1232 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SY1232 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY1232 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3701]) ).

thf(3858,plain,
    ! [SV228: $i,SV60: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 ) )
        = $true )
      | ( ( ! [SY1233: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY1233 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY1233 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY1233 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3702]) ).

thf(3859,plain,
    ! [SV229: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 ) )
        = $true )
      | ( ( ! [SY1234: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1234 )
              | ! [SY1235: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1235 )
                  | ! [SY1236: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1236 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SY1234 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY1235 @ SY1236 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SY1235 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY1234 @ SY1236 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3703]) ).

thf(3860,plain,
    ! [SV230: $i,SV62: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 ) )
        = $true )
      | ( ( ! [SY1237: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY1237 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SY1237 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SY1237 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3704]) ).

thf(3861,plain,
    ! [SV231: $i,SV63: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 ) )
        = $true )
      | ( ( ! [SY1238: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY1238 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SY1238 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SY1238 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3705]) ).

thf(3862,plain,
    ! [SV232: $i,SV64: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 ) )
        = $true )
      | ( ( ! [SY1239: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY1239 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SY1239 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SY1239 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3706]) ).

thf(3863,plain,
    ! [SV233: $i,SV65: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 ) )
        = $true )
      | ( ( ! [SY1240: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY1240 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SY1240 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY1240 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3707]) ).

thf(3864,plain,
    ! [SV234: $i,SV66: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 ) )
        = $true )
      | ( ( ! [SY1241: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY1241 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY1241 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY1241 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3708]) ).

thf(3865,plain,
    ! [SV235: $i,SV67: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 ) )
        = $true )
      | ( ( ! [SY1242: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1242 )
              | ! [SY1243: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1243 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SY1243 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY1242 @ SY1243 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SY1242 ) @ SY1243 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3709]) ).

thf(3866,plain,
    ! [SV236: $i,SV68: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV236 ) )
        = $true )
      | ( ( ! [SY1244: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY1244 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SV236 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SV236 @ SY1244 ) @ SY1244 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV68 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3710]) ).

thf(3867,plain,
    ! [SV237: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 ) )
        = $true )
      | ( ( ! [SY1245: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1245 )
              | ! [SY1246: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1246 )
                  | ! [SY1247: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1247 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SY1245 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY1246 @ SY1247 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SY1246 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY1245 @ SY1247 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3711]) ).

thf(3868,plain,
    ! [SV238: $i,SV70: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV238 ) )
        = $true )
      | ( ( ! [SY1248: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY1248 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SV238 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SV238 @ SY1248 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV70 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3712]) ).

thf(3869,plain,
    ! [SV239: $i,SV71: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 ) )
        = $true )
      | ( ( ! [SY1249: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1249 )
              | ! [SY1250: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1250 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SY1249 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SY1249 @ SY1250 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3713]) ).

thf(3870,plain,
    ! [SV240: $i,SV72: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV240 ) )
        = $true )
      | ( ( ! [SY1251: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY1251 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SY1251 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SV240 @ SY1251 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV72 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3714]) ).

thf(3871,plain,
    ! [SV241: $i,SV73: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 ) )
        = $true )
      | ( ( ! [SY1252: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1252 )
              | ! [SY1253: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1253 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SY1253 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SY1252 @ SY1253 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3715]) ).

thf(3872,plain,
    ! [SV242: $i,SV74: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 ) )
        = $true )
      | ( ( ! [SY1254: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY1254 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SY1254 ) )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY1254 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3716]) ).

thf(3873,plain,
    ! [SV275: $i,SV243: $i,SV159: $i,SV128: $i,SV76: $i] :
      ( ( ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ c_24__lam__45594 @ SV76 ) @ SV128 ) @ SV159 ) @ SV243 ) @ SV275 )
        = ( c_24__lam__45594___24a5 @ SV76 @ SV128 @ SV159 @ SV243 @ SV275 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3717]) ).

thf(3874,plain,
    ! [SV78: $i] :
      ( ( ( ~ ~ ( ~ ! [SY657: $i] :
                      ( ~ ( cProp___24t @ SY657 )
                      | ( p @ SV78 )
                      | ~ ( p @ SV78 )
                      | ( p @ SY657 ) )
                | ~ ! [SY658: $i] :
                      ( ~ ( cProp___24t @ SY658 )
                      | ( p @ SV78 )
                      | ~ ( p @ SY658 )
                      | ( p @ SY658 ) ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3718]) ).

thf(3875,plain,
    ! [SV78: $i] :
      ( ( ( ~ ~ ( ~ ! [SY659: $i] :
                      ( ~ ( cProp___24t @ SY659 )
                      | ~ ( p @ SY659 )
                      | ~ ( p @ SV78 )
                      | ( p @ SY659 ) )
                | ~ ! [SX1: $i] :
                      ( ~ ( cProp___24t @ SX1 )
                      | ~ ( p @ SX1 )
                      | ~ ( p @ SX1 )
                      | ( p @ SX1 ) ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3718]) ).

thf(3876,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
                    | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3719]) ).

thf(3877,plain,
    ! [SV245: $i] :
      ( ( ( ~ ( c_24__type__96___24t @ SV245 ) )
        = $true )
      | ( ( ! [SY1256: $i] :
              ( ~ ( cType___24t @ SY1256 )
              | ! [SY1257: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1256 @ SY1257 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1256 @ ( happ @ ( happ @ SV245 @ SY1256 ) @ SY1257 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3720]) ).

thf(3878,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1258: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1258 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1258 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1258 ) )
              | ~ ! [SY1259: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1259 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1259 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1259 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3721]) ).

thf(3879,plain,
    ! [SV276: $i,SV80: $i] :
      ( ( ! [SY1319: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV276 @ SY1319 )
            | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV276 ) @ SY1319 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3722]) ).

thf(3880,plain,
    ! [SV277: $i,SV80: $i] :
      ( ( ! [SY1320: $i] :
            ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV277 ) @ SY1320 ) )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV277 @ SY1320 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3723]) ).

thf(3881,plain,
    ! [SV278: $i,SV247: $i] :
      ( ( ~ ( c_24__lam__35673___24a2 @ SV247 @ SV278 )
        | ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV247 ) @ SV278 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3724]) ).

thf(3882,plain,
    ! [SV279: $i,SV248: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV248 ) @ SV279 ) )
        | ( c_24__lam__35673___24a2 @ SV248 @ SV279 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3725]) ).

thf(3883,plain,
    ! [SV161: $i,SV130: $i,SV81: $i] :
      ( ( ~ ! [SY1091: $i,SY1092: $i] :
              ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1091 @ SY1092 )
              | ( p @ ( happ @ ( happ @ SV130 @ SY1091 ) @ SY1092 ) )
              | ( p @ ( happ @ ( happ @ SV161 @ SY1091 ) @ SY1092 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3726]) ).

thf(3884,plain,
    ! [SV161: $i,SV81: $i,SV130: $i] :
      ( ( ~ ~ ( ~ ! [SY1093: $i,SY1094: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
                    | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) )
              | ~ ! [SY1095: $i,SY1096: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
                    | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3726]) ).

thf(3885,plain,
    ! [SV131: $i,SV82: $i,SV162: $i] :
      ( ( ~ ! [SY1097: $i,SY1098: $i] :
              ( ( ( happ @ SV162 @ SY1097 )
               != ( happ @ SV162 @ SY1098 ) )
              | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1097 @ SY1098 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3727]) ).

thf(3886,plain,
    ! [SV162: $i,SV131: $i,SV82: $i] :
      ( ( ~ ! [SY1099: $i,SY1100: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1099 @ SY1100 )
              | ( ( happ @ SV162 @ SY1099 )
                = ( happ @ SV162 @ SY1100 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3727]) ).

thf(3887,plain,
    ! [SV249: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 ) )
        = $true )
      | ( ( ! [SY1262: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1262 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SY1262 )
              | ! [SY1263: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1263 )
                  | ~ ( ~ ! [SY1264: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1264 )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1263 @ SY1264 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1263 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY1262 @ SY1264 ) ) )
                      | ~ ! [SY1265: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1265 )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1263 @ SY1265 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY1262 @ SY1265 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1263 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3728]) ).

thf(3888,plain,
    ! [SV132: $i,SV84: $i] :
      ( ( ! [SY947: $i,SY948: $i] :
            ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY947 @ SY948 )
            | ( p @ ( happ @ ( happ @ SV132 @ SY947 ) @ SY948 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3729]) ).

thf(3889,plain,
    ! [SV84: $i,SV132: $i] :
      ( ( ! [SY949: $i,SY950: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV132 @ SY949 ) @ SY950 ) )
            | ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SY949 @ SY950 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3730]) ).

thf(3890,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1266: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1266 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1266 )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1266 ) ) )
              | ~ ! [SY1267: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1267 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1267 )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1267 ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3731]) ).

thf(3891,plain,
    ! [SV251: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SV251 ) )
              | ~ ~ ( cType___24t @ ( happ @ SV251 @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) ) ) )
        = $true )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3732]) ).

thf(3892,plain,
    ! [SV252: $i] :
      ( ( ( ~ ( c_24__type__28___24t @ SV252 ) )
        = $true )
      | ( ( ! [SY1268: $i] :
              ( ~ ( cType___24t @ SY1268 )
              | ( cType___24t @ ( happ @ SV252 @ SY1268 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3733]) ).

thf(3893,plain,
    ! [SV86: $i,SV133: $i] :
      ( ( ! [SY951: $i,SY952: $i] :
            ( ~ ( p @ ( happ @ SV133 @ SY952 ) )
            | ( p @ ( happ @ SY951 @ SY952 ) )
            | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY951 @ SY952 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3734]) ).

thf(3894,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ~ ( ~ ! [SY953: $i,SY954: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
                  | ( p @ ( happ @ SV133 @ SY954 ) ) )
            | ~ ! [SY955: $i,SY956: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
                  | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3735]) ).

thf(3895,plain,
    ! [SV134: $i,SV87: $i] :
      ( ( ! [SY957: $i,SY958: $i] :
            ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY957 @ SY958 )
            | ( p @ ( happ @ ( happ @ SV134 @ SY958 ) @ SY957 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3736]) ).

thf(3896,plain,
    ! [SV87: $i,SV134: $i] :
      ( ( ! [SY959: $i,SY960: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV134 @ SY960 ) @ SY959 ) )
            | ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SY959 @ SY960 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3737]) ).

thf(3897,plain,
    ! [SV280: $i,SV88: $i] :
      ( ( ! [SY1321: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV280 @ SY1321 )
            | ~ ( p @ ( happ @ SV280 @ SY1321 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3738]) ).

thf(3898,plain,
    ! [SV88: $i,SV281: $i] :
      ( ( ! [SY1322: $i] :
            ( ( p @ ( happ @ SV281 @ SY1322 ) )
            | ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV281 @ SY1322 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3739]) ).

thf(3899,plain,
    ! [SV253: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 ) )
        = $true )
      | ( ( ! [SY1269: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1269 )
              | ~ ( ~ ! [SY1270: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1270 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SY1269 ) @ SY1270 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY1269 @ SY1270 ) ) ) )
                  | ~ ! [SY1271: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1271 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY1269 @ SY1271 ) ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SY1269 ) @ SY1271 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3740]) ).

thf(3900,plain,
    ! [SV163: $i,SV135: $i,SV90: $i] :
      ( ( ~ ! [SY1101: $i,SY1102: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1101 @ SY1102 )
              | ( p @ ( happ @ ( happ @ SV135 @ SY1101 ) @ SY1102 ) )
              | ( p @ ( happ @ ( happ @ SV163 @ SY1101 ) @ SY1102 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3741]) ).

thf(3901,plain,
    ! [SV163: $i,SV90: $i,SV135: $i] :
      ( ( ~ ~ ( ~ ! [SY1103: $i,SY1104: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
                    | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) )
              | ~ ! [SY1105: $i,SY1106: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
                    | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3741]) ).

thf(3902,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ( cProp___24t @ SV254 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ! [SY1272: $i] :
                          ( ~ ( cProp___24t @ SY1272 )
                          | ( p @ SV91 )
                          | ~ ( p @ SV91 )
                          | ( p @ SV254 )
                          | ( p @ SY1272 ) )
                    | ~ ! [SY1273: $i] :
                          ( ~ ( cProp___24t @ SY1273 )
                          | ( p @ SV91 )
                          | ~ ( p @ SY1273 )
                          | ( p @ SV254 )
                          | ( p @ SY1273 ) ) )
              | ~ ~ ( ~ ! [SY1274: $i] :
                          ( ~ ( cProp___24t @ SY1274 )
                          | ~ ( p @ SV254 )
                          | ~ ( p @ SV91 )
                          | ( p @ SV254 )
                          | ( p @ SY1274 ) )
                    | ~ ! [SY1275: $i] :
                          ( ~ ( cProp___24t @ SY1275 )
                          | ~ ( p @ SV254 )
                          | ~ ( p @ SY1275 )
                          | ( p @ SV254 )
                          | ( p @ SY1275 ) ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3742]) ).

thf(3903,plain,
    ! [SV92: $i,SV164: $i,SV136: $i] :
      ( ( ~ ! [SY1107: $i,SY1108: $i] :
              ( ~ ( p @ ( happ @ SV136 @ SY1107 ) )
              | ~ ( p @ ( happ @ SV164 @ SY1108 ) )
              | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1107 @ SY1108 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3743]) ).

thf(3904,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ~ ~ ( ~ ! [SY1109: $i] :
                    ( ! [SY1110: $i] :
                        ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
                    | ( p @ ( happ @ SV136 @ SY1109 ) ) )
              | ~ ! [SY1111: $i,SY1112: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
                    | ( p @ ( happ @ SV164 @ SY1112 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3743]) ).

thf(3905,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) )
            | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SV282 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) ) )
        | ( c_24__type__11748___24t @ SV255 @ SV282 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3744]) ).

thf(3906,plain,
    ! [SV283: $i,SV256: $i] :
      ( ( ~ ( c_24__type__11748___24t @ SV256 @ SV283 )
        | ! [SY1323: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SY1323 )
            | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SV283 @ SY1323 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3745]) ).

thf(3907,plain,
    ! [SV284: $i] :
      ( ( ( ~ ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SV284 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3746]) ).

thf(3908,plain,
    ( ( $true = $false )
    | ( ( ! [SX0: $i] : ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SX0 ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3747]) ).

thf(3909,plain,
    ! [SV165: $i,SV137: $i,SV93: $i] :
      ( ( ~ ! [SY1113: $i,SY1114: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1113 @ SY1114 )
              | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1113 ) @ SY1114 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3748]) ).

thf(3910,plain,
    ! [SV165: $i,SV137: $i,SV93: $i] :
      ( ( ~ ! [SY1115: $i,SY1116: $i] :
              ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1115 ) @ SY1116 ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1115 @ SY1116 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3748]) ).

thf(3911,plain,
    ! [SV285: $i,SV94: $i] :
      ( ( ! [SY1324: $i] :
            ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV285 @ SY1324 ) )
            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY1324 @ SV285 ) )
            | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV285 @ SY1324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3749]) ).

thf(3912,plain,
    ! [SV94: $i] :
      ( ( ~ ! [SY744: $i,SY745: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) )
        | ~ ! [SY746: $i,SY747: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3750]) ).

thf(3913,plain,
    ! [SV286: $i,SV257: $i] :
      ( ( ~ ( p @ ( c_24__prop__35358___24a2 @ SV257 @ SV286 ) )
        | ~ ( p @ SV286 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3751]) ).

thf(3914,plain,
    ! [SV258: $i,SV287: $i] :
      ( ( ( p @ SV287 )
        | ( p @ ( c_24__prop__35358___24a2 @ SV258 @ SV287 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3752]) ).

thf(3915,plain,
    ! [SV95: $i,SV138: $i] :
      ( ( ! [SY980: $i,SY981: $i] :
            ( ~ ( p @ ( happ @ SV138 @ SY981 ) )
            | ~ ( p @ ( happ @ SY980 @ SY981 ) )
            | ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY980 @ SY981 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3753]) ).

thf(3916,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ~ ( ~ ! [SY982: $i,SY983: $i] :
                  ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
                  | ( p @ ( happ @ SV138 @ SY983 ) ) )
            | ~ ! [SY984: $i,SY985: $i] :
                  ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
                  | ( p @ ( happ @ SY984 @ SY985 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3754]) ).

thf(3917,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1281: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1281 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1281 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1281 ) ) )
              | ~ ! [SY1282: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1282 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1282 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1282 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3755]) ).

thf(3918,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ! [SY986: $i,SY987: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY986 @ SY987 )
            | ( SY986 = SY987 )
            | ( p @ ( happ @ ( happ @ SV139 @ SY986 ) @ SY987 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3756]) ).

thf(3919,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ( ~ ! [SY988: $i,SY989: $i] :
                  ( ( SY988 != SY989 )
                  | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) )
            | ~ ! [SY990: $i,SY991: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
                  | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3757]) ).

thf(3920,plain,
    ! [SV98: $i,SV288: $i] :
      ( ( ! [SY1325: $i] :
            ( ~ ( ~ ( t @ ( sK18_V3__x @ SY1325 @ SV288 @ SV98 ) @ SV98 )
                | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SY1325 @ SV288 @ SV98 ) @ SV98 )
                      | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SY1325 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SY1325 @ SV288 @ SV98 ) ) )
                            | ~ ~ ( p @ ( happ @ ( happ @ SY1325 @ ( sK18_V3__x @ SY1325 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SY1325 @ SV288 @ SV98 ) ) ) ) ) )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SY1325 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3758]) ).

thf(3921,plain,
    ! [SV289: $i,SV98: $i] :
      ( ( ! [SY1326: $i] :
            ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SY1326 ) )
            | ! [SY1327: $i] :
                ( ~ ( t @ SY1327 @ SV98 )
                | ! [SY1328: $i] :
                    ( ~ ( t @ SY1328 @ SV98 )
                    | ~ ( p @ ( happ @ ( happ @ SV289 @ SY1327 ) @ SY1328 ) )
                    | ( p @ ( happ @ ( happ @ SY1326 @ SY1327 ) @ SY1328 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3759]) ).

thf(3922,plain,
    ! [SV140: $i,SV99: $i] :
      ( ( ! [SY992: $i,SY993: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY992 @ SY993 )
            | ( p @ ( happ @ ( happ @ SV140 @ SY992 ) @ SY993 ) )
            | ( p @ ( happ @ ( happ @ SV140 @ SY993 ) @ SY992 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3760]) ).

thf(3923,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ~ ( ~ ! [SY994: $i,SY995: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
                  | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) )
            | ~ ! [SY996: $i,SY997: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
                  | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3761]) ).

thf(3924,plain,
    ! [SV100: $i,SV166: $i,SV141: $i] :
      ( ( ~ ! [SY1117: $i,SY1118: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV141 @ SY1117 ) @ SY1118 ) )
              | ( p @ ( happ @ ( happ @ SV166 @ SY1117 ) @ SY1118 ) )
              | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1117 @ SY1118 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3762]) ).

thf(3925,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ~ ( ~ ! [SY1119: $i,SY1120: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
                    | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) )
              | ~ ! [SY1121: $i,SY1122: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
                    | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3762]) ).

thf(3926,plain,
    ! [SV290: $i,SV101: $i] :
      ( ( ! [SY1329: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SY1329 @ SV290 @ SV101 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SY1329 @ ( sK17_Vv__CANONICAL__2 @ SY1329 @ SV290 @ SV101 ) ) ) )
            | ( c_24__type__11699___24t @ SV101 @ SV290 @ SY1329 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3763]) ).

thf(3927,plain,
    ! [SV291: $i,SV101: $i] :
      ( ( ! [SY1330: $i] :
            ( ~ ( c_24__type__11699___24t @ SV101 @ SV291 @ SY1330 )
            | ! [SY1331: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY1331 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SY1330 @ SY1331 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3764]) ).

thf(3928,plain,
    ! [SV167: $i,SV142: $i,SV102: $i] :
      ( ( ~ ! [SY1123: $i,SY1124: $i] :
              ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1123 @ SY1124 )
              | ( p @ ( happ @ ( happ @ SV167 @ SY1123 ) @ SY1124 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3765]) ).

thf(3929,plain,
    ! [SV142: $i,SV102: $i,SV167: $i] :
      ( ( ~ ! [SY1125: $i,SY1126: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV167 @ SY1125 ) @ SY1126 ) )
              | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1125 @ SY1126 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3765]) ).

thf(3930,plain,
    ! [SV292: $i,SV103: $i] :
      ( ( ! [SY1332: $i] :
            ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV292 @ SY1332 ) )
            | ( p @ SV292 )
            | ( p @ SY1332 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3766]) ).

thf(3931,plain,
    ! [SV103: $i] :
      ( ( ~ ! [SY799: $i] :
              ( ~ ( p @ SY799 )
              | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) )
        | ~ ! [SY801: $i,SY802: $i] :
              ( ~ ( p @ SY802 )
              | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3767]) ).

thf(3932,plain,
    ! [SV104: $i,SV143: $i,SV168: $i] :
      ( ( ~ ! [SY1127: $i,SY1128: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV168 @ SY1127 ) @ SY1128 ) )
              | ~ ( p @ ( happ @ SV143 @ SY1127 ) )
              | ~ ( p @ ( happ @ SV143 @ SY1128 ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1127 @ SY1128 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3768]) ).

thf(3933,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                          ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                          | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
                    | ~ ! [SY1131: $i] :
                          ( ! [SY1132: $i] :
                              ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                          | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
              | ~ ! [SY1133: $i,SY1134: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
                    | ( p @ ( happ @ SV143 @ SY1134 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3768]) ).

thf(3934,plain,
    ! [SV105: $i,SV293: $i] :
      ( ( ! [SY1333: $i] :
            ( ( SV293 != SY1333 )
            | ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV293 @ SY1333 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3769]) ).

thf(3935,plain,
    ! [SV294: $i,SV105: $i] :
      ( ( ! [SY1334: $i] :
            ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV294 @ SY1334 ) )
            | ( SV294 = SY1334 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3770]) ).

thf(3936,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) )
            | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
                  | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) ) )
        | ( c_24__type__11829___24t @ SV260 @ SV295 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3771]) ).

thf(3937,plain,
    ! [SV296: $i,SV261: $i] :
      ( ( ~ ( c_24__type__11829___24t @ SV261 @ SV296 )
        | ! [SY1335: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1335 )
            | ! [SY1336: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1336 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SY1335 ) @ SY1336 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3772]) ).

thf(3938,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ! [SY1019: $i,SY1020: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1019 @ SY1020 )
            | ( p @ ( happ @ ( happ @ SV144 @ SY1020 ) @ SY1019 ) )
            | ( SY1019 = SY1020 )
            | ( p @ ( happ @ ( happ @ SV144 @ SY1019 ) @ SY1020 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3773]) ).

thf(3939,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ~ ( ~ ! [SY1021: $i,SY1022: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
                  | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) )
            | ~ ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                        ( ( SY1023 != SY1024 )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
                  | ~ ! [SY1025: $i,SY1026: $i] :
                        ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3774]) ).

thf(3940,plain,
    ! [SV169: $i,SV145: $i,SV107: $i] :
      ( ( ~ ! [SY1135: $i,SY1136: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1135 @ SY1136 )
              | ( p @ ( happ @ SY1135 @ ( happ @ SV169 @ SY1136 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3775]) ).

thf(3941,plain,
    ! [SV145: $i,SV107: $i,SV169: $i] :
      ( ( ~ ! [SY1137: $i,SY1138: $i] :
              ( ~ ( p @ ( happ @ SY1137 @ ( happ @ SV169 @ SY1138 ) ) )
              | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1137 @ SY1138 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3775]) ).

thf(3942,plain,
    ! [SV108: $i,SV146: $i] :
      ( ( ! [SY1032: $i,SY1033: $i] :
            ( ( SY1032 != SY1033 )
            | ~ ( p @ ( happ @ SV146 @ SY1032 ) )
            | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1032 @ SY1033 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3776]) ).

thf(3943,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ~ ( ~ ! [SY1034: $i,SY1035: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
                  | ( SY1034 = SY1035 ) )
            | ~ ! [SY1036: $i] :
                  ( ! [SY1037: $i] :
                      ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
                  | ( p @ ( happ @ SV146 @ SY1036 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3777]) ).

thf(3944,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
                    | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3778]) ).

thf(3945,plain,
    ! [SV263: $i] :
      ( ( ( ~ ( c_24__type__90___24t @ SV263 ) )
        = $true )
      | ( ( ! [SY1287: $i] :
              ( ~ ( cType___24t @ SY1287 )
              | ! [SY1288: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ SY1288 )
                  | ! [SY1289: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ SY1289 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ ( happ @ ( happ @ ( happ @ SV263 @ SY1287 ) @ SY1288 ) @ SY1289 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3779]) ).

thf(3946,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1290: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1290 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1290 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1290 ) ) )
              | ~ ! [SY1291: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1291 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1291 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1291 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3780]) ).

thf(3947,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SV265 ) )
              | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) )
                    | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                          | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                                | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3781]) ).

thf(3948,plain,
    ! [SV266: $i] :
      ( ( ( ~ ( c_24__type__4733___24t @ SV266 ) )
        = $true )
      | ( ( ! [SY1292: $i] :
              ( ~ ( cType___24t @ SY1292 )
              | ! [SY1293: $i] :
                  ( ~ ( cType___24t @ SY1293 )
                  | ! [SY1294: $i] :
                      ( ~ ( cType___24t @ SY1294 )
                      | ! [SY1295: $i] :
                          ( ~ ( cType___24t @ SY1295 )
                          | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SY1292 ) @ SY1293 ) @ SY1294 ) @ SY1295 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3782]) ).

thf(3949,plain,
    ! [SV110: $i,SV170: $i,SV147: $i] :
      ( ( ~ ! [SY1139: $i,SY1140: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV147 @ SY1139 ) @ SY1140 ) )
              | ~ ( p @ ( happ @ ( happ @ SV170 @ SY1139 ) @ SY1140 ) )
              | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1139 @ SY1140 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3783]) ).

thf(3950,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ~ ( ~ ! [SY1141: $i,SY1142: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
                    | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) )
              | ~ ! [SY1143: $i,SY1144: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
                    | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3783]) ).

thf(3951,plain,
    ! [SV148: $i,SV111: $i] :
      ( ( ! [SY1045: $i,SY1046: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1045 @ SY1046 )
            | ( p @ ( happ @ ( happ @ SV148 @ SY1046 ) @ SY1045 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3784]) ).

thf(3952,plain,
    ! [SV111: $i,SV148: $i] :
      ( ( ! [SY1047: $i,SY1048: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV148 @ SY1048 ) @ SY1047 ) )
            | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SY1047 @ SY1048 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3785]) ).

thf(3953,plain,
    ! [SV112: $i,SV297: $i] :
      ( ( ! [SY1337: $i] :
            ( ~ ( p @ SV297 )
            | ~ ( p @ SY1337 )
            | ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV297 @ SY1337 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3786]) ).

thf(3954,plain,
    ! [SV112: $i] :
      ( ( ~ ! [SY857: $i] :
              ( ! [SY858: $i] :
                  ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
              | ( p @ SY857 ) )
        | ~ ! [SY859: $i,SY860: $i] :
              ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
              | ( p @ SY860 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3787]) ).

thf(3955,plain,
    ! [SV149: $i,SV113: $i] :
      ( ( ! [SY1049: $i,SY1050: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1049 @ SY1050 )
            | ( p @ ( happ @ SV149 @ SY1050 ) )
            | ( p @ ( happ @ SY1049 @ SY1050 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3788]) ).

thf(3956,plain,
    ! [SV113: $i,SV149: $i] :
      ( ( ~ ( ~ ! [SY1051: $i,SY1052: $i] :
                  ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
                  | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) )
            | ~ ! [SY1053: $i,SY1054: $i] :
                  ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
                  | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3789]) ).

thf(3957,plain,
    ! [SV114: $i] :
      ( ( ~ ! [SY868: $i] :
              ( ( p @ SY868 )
              | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) )
        | ~ ! [SY870: $i,SY871: $i] :
              ( ~ ( p @ SY871 )
              | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3790]) ).

thf(3958,plain,
    ! [SV298: $i,SV114: $i] :
      ( ( ! [SY1338: $i] :
            ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV298 @ SY1338 ) )
            | ~ ( p @ SV298 )
            | ( p @ SY1338 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3791]) ).

thf(3959,plain,
    ! [SV267: $i,SV115: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 ) )
        = $true )
      | ( ( ! [SY1296: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY1296 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SY1296 )
              | ! [SY1297: $i] :
                  ( ~ ( t @ SY1297 @ SV115 )
                  | ~ ( ~ ! [SY1298: $i] :
                            ( ~ ( t @ SY1298 @ SV115 )
                            | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1297 ) @ SY1298 ) )
                            | ( p @ ( happ @ ( happ @ SY1296 @ SY1297 ) @ SY1298 ) ) )
                      | ~ ! [SY1299: $i] :
                            ( ~ ( t @ SY1299 @ SV115 )
                            | ~ ( p @ ( happ @ ( happ @ SY1296 @ SY1297 ) @ SY1299 ) )
                            | ( p @ ( happ @ ( happ @ SV267 @ SY1297 ) @ SY1299 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3792]) ).

thf(3960,plain,
    ! [SV116: $i,SV150: $i] :
      ( ( ! [SY1055: $i,SY1056: $i] :
            ( ~ ( p @ ( happ @ SV150 @ SY1056 ) )
            | ~ ( p @ ( happ @ SY1055 @ SY1056 ) )
            | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1055 @ SY1056 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3793]) ).

thf(3961,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ~ ( ~ ! [SY1057: $i,SY1058: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
                  | ( p @ ( happ @ SV150 @ SY1058 ) ) )
            | ~ ! [SY1059: $i,SY1060: $i] :
                  ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
                  | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3794]) ).

thf(3962,plain,
    ! [SV268: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 ) )
        = $true )
      | ( ( ! [SY1300: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1300 )
              | ~ ( ~ ! [SY1301: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1301 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1300 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY1300 @ SY1301 ) ) ) )
                  | ~ ! [SY1302: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1302 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1302 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY1300 @ SY1302 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3795]) ).

thf(3963,plain,
    ! [SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ~ ! [SY1303: $i,SY1304: $i] :
              ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1303 @ SY1304 )
              | ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1303 ) ) @ ( happ @ SV171 @ SY1304 ) ) ) )
        | ~ ! [SY1305: $i,SY1306: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1305 ) ) @ ( happ @ SV171 @ SY1306 ) ) )
              | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1305 @ SY1306 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3796]) ).

thf(3964,plain,
    ! [SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ~ ! [SY1307: $i,SY1308: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1307 @ SY1308 )
              | ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1307 ) ) @ ( happ @ SV172 @ SY1308 ) ) ) )
        | ~ ! [SY1309: $i,SY1310: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1309 ) ) @ ( happ @ SV172 @ SY1310 ) ) )
              | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1309 @ SY1310 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3797]) ).

thf(3965,plain,
    ! [SV120: $i,SV299: $i] :
      ( ( ! [SY1339: $i] :
            ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV299 @ ( sK15_Vv__CANONICAL__2 @ SY1339 @ SV299 @ SV120 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY1339 @ ( sK15_Vv__CANONICAL__2 @ SY1339 @ SV299 @ SV120 ) ) ) )
            | ( c_24__type__11787___24t @ SV120 @ SV299 @ SY1339 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3798]) ).

thf(3966,plain,
    ! [SV300: $i,SV120: $i] :
      ( ( ! [SY1340: $i] :
            ( ~ ( c_24__type__11787___24t @ SV120 @ SV300 @ SY1340 )
            | ! [SY1341: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SY1341 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SY1340 @ SY1341 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3799]) ).

thf(3967,plain,
    ! [SV153: $i,SV121: $i] :
      ( ( ! [SY1073: $i,SY1074: $i] :
            ( ( SY1073 != SY1074 )
            | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1073 @ SY1074 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3800]) ).

thf(3968,plain,
    ! [SV153: $i,SV121: $i] :
      ( ( ! [SY1075: $i,SY1076: $i] :
            ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SY1075 @ SY1076 ) )
            | ( SY1075 = SY1076 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3801]) ).

thf(3969,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SV271 ) )
              | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) )
                    | ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3802]) ).

thf(3970,plain,
    ! [SV272: $i] :
      ( ( ( ~ ( c_24__type__52___24t @ SV272 ) )
        = $true )
      | ( ( ! [SY1311: $i] :
              ( ~ ( cType___24t @ SY1311 )
              | ! [SY1312: $i] :
                  ( ~ ( cType___24t @ SY1312 )
                  | ( cType___24t @ ( happ @ ( happ @ SV272 @ SY1311 ) @ SY1312 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3803]) ).

thf(3971,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV173: $i] :
      ( ( ~ ! [SY1313: $i,SY1314: $i] :
              ( ( ( happ @ SV173 @ SY1313 )
               != ( happ @ SV173 @ SY1314 ) )
              | ~ ( p @ ( happ @ ( happ @ SV273 @ SY1313 ) @ SY1314 ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1313 @ SY1314 ) )
        | ~ ~ ( ~ ! [SY1315: $i,SY1316: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
                    | ( ( happ @ SV173 @ SY1315 )
                      = ( happ @ SV173 @ SY1316 ) ) )
              | ~ ! [SY1317: $i,SY1318: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
                    | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3804]) ).

thf(3972,plain,
    ! [SV175: $i,SV5: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( ! [SY1163: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1163 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SY1163 )
              | ! [SY1164: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1164 )
                  | ! [SY1165: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1165 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1164 @ SY1165 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1164 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SY1163 @ SY1165 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3806]) ).

thf(3973,plain,
    ! [SV176: $i,SV6: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV6 @ SV176 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV6 @ SV176 @ SV176 )
        = $true )
      | ( ( cType___24t @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3807]) ).

thf(3974,plain,
    ! [SV10: $i,SV179: $i] :
      ( ( ( cProp___24t @ SV179 )
        = $false )
      | ( ( ~ ( p @ SV10 )
          | ~ ( p @ SV179 )
          | ( p @ SV10 ) )
        = $true )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3808]) ).

thf(3975,plain,
    ! [SV12: $i,SV180: $i] :
      ( ( ( cProp___24t @ SV180 )
        = $false )
      | ( ( ~ ( p @ SV12 )
          | ( p @ SV180 )
          | ( p @ SV12 ) )
        = $true )
      | ( ( cProp___24t @ SV12 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3810]) ).

thf(3976,plain,
    ! [SV181: $i,SV13: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV13 @ SV181 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SV181 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans___24a2 @ SV13 @ SV181 ) ) )
        = $true )
      | ( ( cType___24t @ SV13 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3811]) ).

thf(3977,plain,
    ! [SV182: $i,SV14: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV14 @ SV182 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SV182 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV14 @ SV182 ) ) )
        = $true )
      | ( ( cType___24t @ SV14 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3812]) ).

thf(3978,plain,
    ! [SV183: $i,SV15: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
        = $false )
      | ( ( ! [SY1166: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SY1166 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SY1166 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SY1166 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3813]) ).

thf(3979,plain,
    ! [SV184: $i,SV16: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
        = $false )
      | ( ( ! [SY1167: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SY1167 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SY1167 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SY1167 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3814]) ).

thf(3980,plain,
    ! [SV185: $i,SV17: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
        = $false )
      | ( ( ! [SY1168: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SY1168 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SY1168 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SY1168 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3815]) ).

thf(3981,plain,
    ! [SV186: $i,SV18: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
        = $false )
      | ( ( ! [SY1169: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SY1169 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SY1169 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SY1169 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3816]) ).

thf(3982,plain,
    ! [SV187: $i,SV19: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
        = $false )
      | ( ( ! [SY1170: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SY1170 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SY1170 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SY1170 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3817]) ).

thf(3983,plain,
    ! [SV188: $i,SV20: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
        = $false )
      | ( ( ! [SY1171: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SY1171 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SY1171 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SY1171 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3818]) ).

thf(3984,plain,
    ! [SV189: $i,SV21: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
        = $false )
      | ( ( ! [SY1172: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SY1172 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SY1172 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SY1172 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3819]) ).

thf(3985,plain,
    ! [SV190: $i,SV22: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( ! [SY1173: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1173 )
              | ! [SY1174: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1174 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SY1173 ) @ SY1174 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SY1173 @ SY1174 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3820]) ).

thf(3986,plain,
    ! [SV191: $i,SV23: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( ! [SY1175: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1175 )
              | ! [SY1176: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1176 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY1175 @ SY1176 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SY1175 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SY1176 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3821]) ).

thf(3987,plain,
    ! [SV192: $i,SV24: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV192 )
        = $false )
      | ( ( ! [SY1177: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SY1177 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV192 @ SY1177 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SY1177 @ SV192 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3822]) ).

thf(3988,plain,
    ! [SV193: $i,SV25: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV25 @ SV193 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV25 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV25 @ SV193 @ SV193 ) @ SV193 )
        = $true )
      | ( ( cType___24t @ SV25 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3823]) ).

thf(3989,plain,
    ! [SV194: $i,SV26: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
        = $false )
      | ( ( ! [SY1178: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SY1178 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SY1178 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SY1178 @ SV194 ) @ SV194 ) ) )
        = $true )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3824]) ).

thf(3990,plain,
    ! [SV195: $i,SV27: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
        = $false )
      | ( ( ! [SY1179: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SY1179 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SY1179 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SY1179 ) @ SV195 ) ) )
        = $true )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3825]) ).

thf(3991,plain,
    ! [SV196: $i,SV28: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV196 )
        = $false )
      | ( ( ! [SY1180: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SY1180 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SV196 @ SY1180 ) @ SV196 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3826]) ).

thf(3992,plain,
    ! [SV197: $i,SV29: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( ! [SY1181: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1181 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SY1181 )
              | ! [SY1182: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1182 )
                  | ! [SY1183: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1183 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1182 @ SY1183 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1182 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SY1181 @ SY1183 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3827]) ).

thf(3993,plain,
    ! [SV198: $i,SV30: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( ! [SY1184: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1184 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SY1184 ) )
              | ! [SY1185: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1185 )
                  | ! [SY1186: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1186 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1185 @ SY1186 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1185 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SY1184 @ SY1186 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3828]) ).

thf(3994,plain,
    ! [SV199: $i,SV31: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( ! [SY1187: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1187 )
              | ! [SY1188: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1188 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SY1187 ) @ SY1188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SY1188 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SY1187 @ SY1188 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3829]) ).

thf(3995,plain,
    ! [SV200: $i,SV32: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( ! [SY1189: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1189 )
              | ! [SY1190: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1190 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SY1189 ) @ SY1190 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SY1189 @ SY1190 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3830]) ).

thf(3996,plain,
    ! [SV201: $i,SV33: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( ! [SY1191: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1191 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SY1191 )
              | ! [SY1192: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1192 )
                  | ! [SY1193: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1193 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1192 @ SY1193 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1192 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SY1191 @ SY1193 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3831]) ).

thf(3997,plain,
    ! [SV202: $i,SV34: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( ! [SY1194: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1194 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SY1194 ) )
              | ! [SY1195: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1195 )
                  | ! [SY1196: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1196 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1195 @ SY1196 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1195 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SY1194 @ SY1196 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3832]) ).

thf(3998,plain,
    ! [SV203: $i,SV35: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
        = $false )
      | ( ( ! [SY1197: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SY1197 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SY1197 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SY1197 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3833]) ).

thf(3999,plain,
    ! [SV204: $i,SV36: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
        = $false )
      | ( ( ! [SY1198: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SY1198 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SY1198 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SY1198 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3834]) ).

thf(4000,plain,
    ! [SV205: $i,SV37: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( ! [SY1199: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1199 )
              | ! [SY1200: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1200 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SY1199 ) @ SY1200 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SY1199 @ SY1200 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3835]) ).

thf(4001,plain,
    ! [SV206: $i,SV38: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( ! [SY1201: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1201 )
              | ! [SY1202: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1202 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY1201 @ SY1202 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SY1201 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SY1202 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3836]) ).

thf(4002,plain,
    ! [SV207: $i,SV39: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV207 )
        = $false )
      | ( ( ! [SY1203: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SY1203 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV207 @ SY1203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SY1203 @ SV207 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3837]) ).

thf(4003,plain,
    ! [SV208: $i,SV40: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV40 @ SV208 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV40 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV40 @ SV208 @ SV208 ) @ SV208 )
        = $true )
      | ( ( cType___24t @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3838]) ).

thf(4004,plain,
    ! [SV209: $i,SV41: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
        = $false )
      | ( ( ! [SY1204: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SY1204 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SY1204 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SY1204 ) @ SY1204 ) ) )
        = $true )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3839]) ).

thf(4005,plain,
    ! [SV210: $i,SV42: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
        = $false )
      | ( ( ! [SY1205: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SY1205 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SY1205 ) )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SY1205 @ SV210 ) @ SY1205 ) ) )
        = $true )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3840]) ).

thf(4006,plain,
    ! [SV211: $i,SV43: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( ! [SY1206: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1206 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SY1206 )
              | ! [SY1207: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1207 )
                  | ! [SY1208: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1208 )
                      | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1207 @ SY1208 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1207 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SY1206 @ SY1208 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3841]) ).

thf(4007,plain,
    ! [SV212: $i,SV44: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( ! [SY1209: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1209 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SY1209 ) )
              | ! [SY1210: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1210 )
                  | ! [SY1211: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1211 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1210 @ SY1211 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1210 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SY1209 @ SY1211 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3842]) ).

thf(4008,plain,
    ! [SV213: $i,SV45: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
        = $false )
      | ( ( ! [SY1212: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SY1212 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SY1212 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SY1212 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3843]) ).

thf(4009,plain,
    ! [SV214: $i,SV46: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
        = $false )
      | ( ( ! [SY1213: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SY1213 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SY1213 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SY1213 @ SV214 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3844]) ).

thf(4010,plain,
    ! [SV215: $i,SV47: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
        = $false )
      | ( ( ! [SY1214: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SY1214 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SY1214 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3845]) ).

thf(4011,plain,
    ! [SV216: $i,SV48: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( ! [SY1215: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SY1215 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SY1215 ) )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SY1215 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3846]) ).

thf(4012,plain,
    ! [SV217: $i,SV49: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV217 )
        = $false )
      | ( ( ! [SY1216: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SY1216 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SV217 @ SY1216 ) @ SV217 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV49 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3847]) ).

thf(4013,plain,
    ! [SV218: $i,SV50: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( ! [SY1217: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1217 )
              | ! [SY1218: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1218 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SY1218 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SY1217 ) @ SY1218 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3848]) ).

thf(4014,plain,
    ! [SV219: $i,SV51: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV219 )
        = $false )
      | ( ( ! [SY1219: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SY1219 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SV219 @ SY1219 ) @ SY1219 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV51 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3849]) ).

thf(4015,plain,
    ! [SV220: $i,SV52: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( ! [SY1220: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1220 )
              | ! [SY1221: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1221 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SY1220 @ SY1221 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SY1220 ) @ SY1221 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3850]) ).

thf(4016,plain,
    ! [SV221: $i,SV53: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( ! [SY1222: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1222 )
              | ! [SY1223: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1223 )
                  | ! [SY1224: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1224 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SY1222 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY1223 @ SY1224 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SY1223 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SY1222 @ SY1224 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3851]) ).

thf(4017,plain,
    ! [SV222: $i,SV54: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( ! [SY1225: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1225 )
              | ! [SY1226: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1226 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1225 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1226 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SY1225 @ SY1226 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3852]) ).

thf(4018,plain,
    ! [SV223: $i,SV55: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( ! [SY1227: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1227 )
              | ! [SY1228: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1228 )
                  | ! [SY1229: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1229 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SY1227 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1229 @ SY1228 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SY1228 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SY1227 @ SY1229 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3853]) ).

thf(4019,plain,
    ! [SV224: $i,SV56: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV224 )
        = $false )
      | ( ( ! [SY1230: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SY1230 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SV224 @ SY1230 ) @ SV224 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV56 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3854]) ).

thf(4020,plain,
    ! [SV225: $i,SV57: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
        = $false )
      | ( ( ! [SY1231: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SY1231 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SY1231 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SY1231 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3855]) ).

thf(4021,plain,
    ! [SV226: $i,SV58: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV58 @ SV226 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV58 @ SV226 @ SV226 ) )
        = $true )
      | ( ( cType___24t @ SV58 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3856]) ).

thf(4022,plain,
    ! [SV227: $i,SV59: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
        = $false )
      | ( ( ! [SY1232: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SY1232 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SY1232 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SY1232 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3857]) ).

thf(4023,plain,
    ! [SV228: $i,SV60: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
        = $false )
      | ( ( ! [SY1233: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SY1233 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY1233 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SY1233 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3858]) ).

thf(4024,plain,
    ! [SV229: $i,SV61: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( ! [SY1234: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1234 )
              | ! [SY1235: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1235 )
                  | ! [SY1236: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1236 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SY1234 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY1235 @ SY1236 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SY1235 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SY1234 @ SY1236 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3859]) ).

thf(4025,plain,
    ! [SV230: $i,SV62: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
        = $false )
      | ( ( ! [SY1237: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SY1237 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SY1237 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SY1237 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3860]) ).

thf(4026,plain,
    ! [SV231: $i,SV63: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
        = $false )
      | ( ( ! [SY1238: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SY1238 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SY1238 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SY1238 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3861]) ).

thf(4027,plain,
    ! [SV232: $i,SV64: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
        = $false )
      | ( ( ! [SY1239: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SY1239 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SY1239 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SY1239 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3862]) ).

thf(4028,plain,
    ! [SV233: $i,SV65: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
        = $false )
      | ( ( ! [SY1240: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SY1240 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SY1240 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SY1240 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3863]) ).

thf(4029,plain,
    ! [SV234: $i,SV66: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
        = $false )
      | ( ( ! [SY1241: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SY1241 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY1241 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SY1241 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3864]) ).

thf(4030,plain,
    ! [SV235: $i,SV67: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( ! [SY1242: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1242 )
              | ! [SY1243: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1243 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SY1243 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SY1242 @ SY1243 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SY1242 ) @ SY1243 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3865]) ).

thf(4031,plain,
    ! [SV236: $i,SV68: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV236 )
        = $false )
      | ( ( ! [SY1244: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SY1244 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SV236 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SV236 @ SY1244 ) @ SY1244 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV68 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3866]) ).

thf(4032,plain,
    ! [SV237: $i,SV69: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( ! [SY1245: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1245 )
              | ! [SY1246: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1246 )
                  | ! [SY1247: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1247 )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SY1245 ) )
                      | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY1246 @ SY1247 ) )
                      | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SY1246 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SY1245 @ SY1247 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3867]) ).

thf(4033,plain,
    ! [SV238: $i,SV70: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV238 )
        = $false )
      | ( ( ! [SY1248: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SY1248 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SV238 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SV238 @ SY1248 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV70 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3868]) ).

thf(4034,plain,
    ! [SV239: $i,SV71: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( ! [SY1249: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1249 )
              | ! [SY1250: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1250 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SY1249 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SY1249 @ SY1250 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3869]) ).

thf(4035,plain,
    ! [SV240: $i,SV72: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV240 )
        = $false )
      | ( ( ! [SY1251: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SY1251 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SY1251 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SV240 @ SY1251 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV72 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3870]) ).

thf(4036,plain,
    ! [SV241: $i,SV73: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( ! [SY1252: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1252 )
              | ! [SY1253: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1253 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SY1253 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SY1252 @ SY1253 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3871]) ).

thf(4037,plain,
    ! [SV242: $i,SV74: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( ! [SY1254: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SY1254 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SY1254 ) )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SY1254 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3872]) ).

thf(4038,plain,
    ! [SV78: $i] :
      ( ( ( ~ ( ~ ! [SY657: $i] :
                    ( ~ ( cProp___24t @ SY657 )
                    | ( p @ SV78 )
                    | ~ ( p @ SV78 )
                    | ( p @ SY657 ) )
              | ~ ! [SY658: $i] :
                    ( ~ ( cProp___24t @ SY658 )
                    | ( p @ SV78 )
                    | ~ ( p @ SY658 )
                    | ( p @ SY658 ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3874]) ).

thf(4039,plain,
    ! [SV78: $i] :
      ( ( ( ~ ( ~ ! [SY659: $i] :
                    ( ~ ( cProp___24t @ SY659 )
                    | ~ ( p @ SY659 )
                    | ~ ( p @ SV78 )
                    | ( p @ SY659 ) )
              | ~ ! [SX1: $i] :
                    ( ~ ( cProp___24t @ SX1 )
                    | ~ ( p @ SX1 )
                    | ~ ( p @ SX1 )
                    | ( p @ SX1 ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3875]) ).

thf(4040,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) )
          | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3876]) ).

thf(4041,plain,
    ! [SV245: $i] :
      ( ( ( c_24__type__96___24t @ SV245 )
        = $false )
      | ( ( ! [SY1256: $i] :
              ( ~ ( cType___24t @ SY1256 )
              | ! [SY1257: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1256 @ SY1257 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1256 @ ( happ @ ( happ @ SV245 @ SY1256 ) @ SY1257 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3877]) ).

thf(4042,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( ~ ( ~ ! [SY1258: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1258 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1258 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1258 ) )
              | ~ ! [SY1259: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1259 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1259 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1259 )
                    | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3878]) ).

thf(4043,plain,
    ! [SV301: $i,SV276: $i,SV80: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV276 @ SV301 )
        | ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV276 ) @ SV301 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3879]) ).

thf(4044,plain,
    ! [SV302: $i,SV277: $i,SV80: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV277 ) @ SV302 ) )
        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV277 @ SV302 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3880]) ).

thf(4045,plain,
    ! [SV278: $i,SV247: $i] :
      ( ( ( ~ ( c_24__lam__35673___24a2 @ SV247 @ SV278 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV247 ) @ SV278 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3881]) ).

thf(4046,plain,
    ! [SV279: $i,SV248: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV248 ) @ SV279 ) ) )
        = $true )
      | ( ( c_24__lam__35673___24a2 @ SV248 @ SV279 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3882]) ).

thf(4047,plain,
    ! [SV161: $i,SV130: $i,SV81: $i] :
      ( ( ! [SY1091: $i,SY1092: $i] :
            ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1091 @ SY1092 )
            | ( p @ ( happ @ ( happ @ SV130 @ SY1091 ) @ SY1092 ) )
            | ( p @ ( happ @ ( happ @ SV161 @ SY1091 ) @ SY1092 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3883]) ).

thf(4048,plain,
    ! [SV161: $i,SV81: $i,SV130: $i] :
      ( ( ~ ( ~ ! [SY1093: $i,SY1094: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
                  | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) )
            | ~ ! [SY1095: $i,SY1096: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
                  | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3884]) ).

thf(4049,plain,
    ! [SV131: $i,SV82: $i,SV162: $i] :
      ( ( ! [SY1097: $i,SY1098: $i] :
            ( ( ( happ @ SV162 @ SY1097 )
             != ( happ @ SV162 @ SY1098 ) )
            | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1097 @ SY1098 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3885]) ).

thf(4050,plain,
    ! [SV162: $i,SV131: $i,SV82: $i] :
      ( ( ! [SY1099: $i,SY1100: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SY1099 @ SY1100 )
            | ( ( happ @ SV162 @ SY1099 )
              = ( happ @ SV162 @ SY1100 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3886]) ).

thf(4051,plain,
    ! [SV249: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( ! [SY1262: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1262 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SY1262 )
              | ! [SY1263: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1263 )
                  | ~ ( ~ ! [SY1264: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1264 )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1263 @ SY1264 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1263 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY1262 @ SY1264 ) ) )
                      | ~ ! [SY1265: $i] :
                            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1265 )
                            | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1263 @ SY1265 )
                            | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SY1262 @ SY1265 ) )
                            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1263 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3887]) ).

thf(4052,plain,
    ! [SV303: $i,SV132: $i,SV84: $i] :
      ( ( ! [SY1342: $i] :
            ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV303 @ SY1342 )
            | ( p @ ( happ @ ( happ @ SV132 @ SV303 ) @ SY1342 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3888]) ).

thf(4053,plain,
    ! [SV84: $i,SV304: $i,SV132: $i] :
      ( ( ! [SY1343: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV132 @ SV304 ) @ SY1343 ) )
            | ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV304 @ SY1343 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3889]) ).

thf(4054,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( ~ ( ~ ! [SY1266: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1266 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1266 )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1266 ) ) )
              | ~ ! [SY1267: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1267 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1267 )
                    | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1267 ) )
                    | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3890]) ).

thf(4055,plain,
    ! [SV251: $i] :
      ( ( ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SV251 ) )
          | ~ ~ ( cType___24t @ ( happ @ SV251 @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) ) )
        = $false )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3891]) ).

thf(4056,plain,
    ! [SV252: $i] :
      ( ( ( c_24__type__28___24t @ SV252 )
        = $false )
      | ( ( ! [SY1268: $i] :
              ( ~ ( cType___24t @ SY1268 )
              | ( cType___24t @ ( happ @ SV252 @ SY1268 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3892]) ).

thf(4057,plain,
    ! [SV86: $i,SV305: $i,SV133: $i] :
      ( ( ! [SY1344: $i] :
            ( ~ ( p @ ( happ @ SV133 @ SY1344 ) )
            | ( p @ ( happ @ SV305 @ SY1344 ) )
            | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV305 @ SY1344 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3893]) ).

thf(4058,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ~ ! [SY953: $i,SY954: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
              | ( p @ ( happ @ SV133 @ SY954 ) ) )
        | ~ ! [SY955: $i,SY956: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
              | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3894]) ).

thf(4059,plain,
    ! [SV306: $i,SV134: $i,SV87: $i] :
      ( ( ! [SY1345: $i] :
            ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV306 @ SY1345 )
            | ( p @ ( happ @ ( happ @ SV134 @ SY1345 ) @ SV306 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3895]) ).

thf(4060,plain,
    ! [SV87: $i,SV307: $i,SV134: $i] :
      ( ( ! [SY1346: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV134 @ SY1346 ) @ SV307 ) )
            | ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV307 @ SY1346 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3896]) ).

thf(4061,plain,
    ! [SV308: $i,SV280: $i,SV88: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV280 @ SV308 )
        | ~ ( p @ ( happ @ SV280 @ SV308 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3897]) ).

thf(4062,plain,
    ! [SV88: $i,SV309: $i,SV281: $i] :
      ( ( ( p @ ( happ @ SV281 @ SV309 ) )
        | ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV281 @ SV309 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3898]) ).

thf(4063,plain,
    ! [SV253: $i,SV89: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( ! [SY1269: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1269 )
              | ~ ( ~ ! [SY1270: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1270 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SY1269 ) @ SY1270 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY1269 @ SY1270 ) ) ) )
                  | ~ ! [SY1271: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1271 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SY1269 @ SY1271 ) ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SY1269 ) @ SY1271 ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3899]) ).

thf(4064,plain,
    ! [SV163: $i,SV135: $i,SV90: $i] :
      ( ( ! [SY1101: $i,SY1102: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1101 @ SY1102 )
            | ( p @ ( happ @ ( happ @ SV135 @ SY1101 ) @ SY1102 ) )
            | ( p @ ( happ @ ( happ @ SV163 @ SY1101 ) @ SY1102 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3900]) ).

thf(4065,plain,
    ! [SV163: $i,SV90: $i,SV135: $i] :
      ( ( ~ ( ~ ! [SY1103: $i,SY1104: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
                  | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) )
            | ~ ! [SY1105: $i,SY1106: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
                  | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3901]) ).

thf(4066,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ! [SY1272: $i] :
                          ( ~ ( cProp___24t @ SY1272 )
                          | ( p @ SV91 )
                          | ~ ( p @ SV91 )
                          | ( p @ SV254 )
                          | ( p @ SY1272 ) )
                    | ~ ! [SY1273: $i] :
                          ( ~ ( cProp___24t @ SY1273 )
                          | ( p @ SV91 )
                          | ~ ( p @ SY1273 )
                          | ( p @ SV254 )
                          | ( p @ SY1273 ) ) )
              | ~ ~ ( ~ ! [SY1274: $i] :
                          ( ~ ( cProp___24t @ SY1274 )
                          | ~ ( p @ SV254 )
                          | ~ ( p @ SV91 )
                          | ( p @ SV254 )
                          | ( p @ SY1274 ) )
                    | ~ ! [SY1275: $i] :
                          ( ~ ( cProp___24t @ SY1275 )
                          | ~ ( p @ SV254 )
                          | ~ ( p @ SY1275 )
                          | ( p @ SV254 )
                          | ( p @ SY1275 ) ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3902]) ).

thf(4067,plain,
    ! [SV92: $i,SV164: $i,SV136: $i] :
      ( ( ! [SY1107: $i,SY1108: $i] :
            ( ~ ( p @ ( happ @ SV136 @ SY1107 ) )
            | ~ ( p @ ( happ @ SV164 @ SY1108 ) )
            | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1107 @ SY1108 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3903]) ).

thf(4068,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ~ ( ~ ! [SY1109: $i] :
                  ( ! [SY1110: $i] :
                      ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
                  | ( p @ ( happ @ SV136 @ SY1109 ) ) )
            | ~ ! [SY1111: $i,SY1112: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
                  | ( p @ ( happ @ SV164 @ SY1112 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3904]) ).

thf(4069,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SV282 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) ) ) )
        = $true )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3905]) ).

thf(4070,plain,
    ! [SV283: $i,SV256: $i] :
      ( ( ( ~ ( c_24__type__11748___24t @ SV256 @ SV283 ) )
        = $true )
      | ( ( ! [SY1323: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SY1323 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SV283 @ SY1323 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3906]) ).

thf(4071,plain,
    ! [SV284: $i] :
      ( ( ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SV284 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3907]) ).

thf(4072,plain,
    ! [SV310: $i] :
      ( ( ( cCoq_2eLogic_2eDecidable_2edecidable___24a1 @ SV310 )
        = $true )
      | ( $true = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3908]) ).

thf(4073,plain,
    ! [SV165: $i,SV137: $i,SV93: $i] :
      ( ( ! [SY1113: $i,SY1114: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1113 @ SY1114 )
            | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1113 ) @ SY1114 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3909]) ).

thf(4074,plain,
    ! [SV165: $i,SV137: $i,SV93: $i] :
      ( ( ! [SY1115: $i,SY1116: $i] :
            ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SY1115 ) @ SY1116 ) )
            | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SY1115 @ SY1116 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3910]) ).

thf(4075,plain,
    ! [SV311: $i,SV285: $i,SV94: $i] :
      ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV285 @ SV311 ) )
        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV311 @ SV285 ) )
        | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV285 @ SV311 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3911]) ).

thf(4076,plain,
    ! [SV94: $i] :
      ( ( ~ ! [SY744: $i,SY745: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3912]) ).

thf(4077,plain,
    ! [SV94: $i] :
      ( ( ~ ! [SY746: $i,SY747: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3912]) ).

thf(4078,plain,
    ! [SV286: $i,SV257: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35358___24a2 @ SV257 @ SV286 ) ) )
        = $true )
      | ( ( ~ ( p @ SV286 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3913]) ).

thf(4079,plain,
    ! [SV258: $i,SV287: $i] :
      ( ( ( p @ SV287 )
        = $true )
      | ( ( p @ ( c_24__prop__35358___24a2 @ SV258 @ SV287 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3914]) ).

thf(4080,plain,
    ! [SV95: $i,SV312: $i,SV138: $i] :
      ( ( ! [SY1347: $i] :
            ( ~ ( p @ ( happ @ SV138 @ SY1347 ) )
            | ~ ( p @ ( happ @ SV312 @ SY1347 ) )
            | ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV312 @ SY1347 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3915]) ).

thf(4081,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ~ ! [SY982: $i,SY983: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
              | ( p @ ( happ @ SV138 @ SY983 ) ) )
        | ~ ! [SY984: $i,SY985: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
              | ( p @ ( happ @ SY984 @ SY985 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3916]) ).

thf(4082,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( ~ ( ~ ! [SY1281: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1281 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1281 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1281 ) ) )
              | ~ ! [SY1282: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1282 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1282 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1282 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3917]) ).

thf(4083,plain,
    ! [SV313: $i,SV139: $i,SV97: $i] :
      ( ( ! [SY1348: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV313 @ SY1348 )
            | ( SV313 = SY1348 )
            | ( p @ ( happ @ ( happ @ SV139 @ SV313 ) @ SY1348 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3918]) ).

thf(4084,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ! [SY988: $i,SY989: $i] :
              ( ( SY988 != SY989 )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) )
        | ~ ! [SY990: $i,SY991: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3919]) ).

thf(4085,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ~ ( ~ ( t @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) @ SV98 )
            | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
                  | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                        | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) ) )
        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3920]) ).

thf(4086,plain,
    ! [SV315: $i,SV289: $i,SV98: $i] :
      ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        | ! [SY1349: $i] :
            ( ~ ( t @ SY1349 @ SV98 )
            | ! [SY1350: $i] :
                ( ~ ( t @ SY1350 @ SV98 )
                | ~ ( p @ ( happ @ ( happ @ SV289 @ SY1349 ) @ SY1350 ) )
                | ( p @ ( happ @ ( happ @ SV315 @ SY1349 ) @ SY1350 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3921]) ).

thf(4087,plain,
    ! [SV316: $i,SV140: $i,SV99: $i] :
      ( ( ! [SY1351: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV316 @ SY1351 )
            | ( p @ ( happ @ ( happ @ SV140 @ SV316 ) @ SY1351 ) )
            | ( p @ ( happ @ ( happ @ SV140 @ SY1351 ) @ SV316 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3922]) ).

thf(4088,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ~ ! [SY994: $i,SY995: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) )
        | ~ ! [SY996: $i,SY997: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3923]) ).

thf(4089,plain,
    ! [SV100: $i,SV166: $i,SV141: $i] :
      ( ( ! [SY1117: $i,SY1118: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV141 @ SY1117 ) @ SY1118 ) )
            | ( p @ ( happ @ ( happ @ SV166 @ SY1117 ) @ SY1118 ) )
            | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1117 @ SY1118 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3924]) ).

thf(4090,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ( ~ ! [SY1119: $i,SY1120: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
                  | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) )
            | ~ ! [SY1121: $i,SY1122: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
                  | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3925]) ).

thf(4091,plain,
    ! [SV290: $i,SV317: $i,SV101: $i] :
      ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) )
            | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SV317 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) ) )
        | ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3926]) ).

thf(4092,plain,
    ! [SV318: $i,SV291: $i,SV101: $i] :
      ( ( ~ ( c_24__type__11699___24t @ SV101 @ SV291 @ SV318 )
        | ! [SY1352: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY1352 )
            | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SV318 @ SY1352 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3927]) ).

thf(4093,plain,
    ! [SV167: $i,SV142: $i,SV102: $i] :
      ( ( ! [SY1123: $i,SY1124: $i] :
            ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1123 @ SY1124 )
            | ( p @ ( happ @ ( happ @ SV167 @ SY1123 ) @ SY1124 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3928]) ).

thf(4094,plain,
    ! [SV142: $i,SV102: $i,SV167: $i] :
      ( ( ! [SY1125: $i,SY1126: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV167 @ SY1125 ) @ SY1126 ) )
            | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SY1125 @ SY1126 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3929]) ).

thf(4095,plain,
    ! [SV319: $i,SV292: $i,SV103: $i] :
      ( ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV292 @ SV319 ) )
        | ( p @ SV292 )
        | ( p @ SV319 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3930]) ).

thf(4096,plain,
    ! [SV103: $i] :
      ( ( ~ ! [SY799: $i] :
              ( ~ ( p @ SY799 )
              | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3931]) ).

thf(4097,plain,
    ! [SV103: $i] :
      ( ( ~ ! [SY801: $i,SY802: $i] :
              ( ~ ( p @ SY802 )
              | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3931]) ).

thf(4098,plain,
    ! [SV104: $i,SV143: $i,SV168: $i] :
      ( ( ! [SY1127: $i,SY1128: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV168 @ SY1127 ) @ SY1128 ) )
            | ~ ( p @ ( happ @ SV143 @ SY1127 ) )
            | ~ ( p @ ( happ @ SV143 @ SY1128 ) )
            | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1127 @ SY1128 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3932]) ).

thf(4099,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                        ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                        | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
                  | ~ ! [SY1131: $i] :
                        ( ! [SY1132: $i] :
                            ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                        | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
            | ~ ! [SY1133: $i,SY1134: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
                  | ( p @ ( happ @ SV143 @ SY1134 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3933]) ).

thf(4100,plain,
    ! [SV105: $i,SV320: $i,SV293: $i] :
      ( ( ( SV293 != SV320 )
        | ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV293 @ SV320 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3934]) ).

thf(4101,plain,
    ! [SV321: $i,SV294: $i,SV105: $i] :
      ( ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV294 @ SV321 ) )
        | ( SV294 = SV321 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3935]) ).

thf(4102,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
                    | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3936]) ).

thf(4103,plain,
    ! [SV296: $i,SV261: $i] :
      ( ( ( ~ ( c_24__type__11829___24t @ SV261 @ SV296 ) )
        = $true )
      | ( ( ! [SY1335: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1335 )
              | ! [SY1336: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1336 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SY1335 ) @ SY1336 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3937]) ).

thf(4104,plain,
    ! [SV322: $i,SV144: $i,SV106: $i] :
      ( ( ! [SY1353: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV322 @ SY1353 )
            | ( p @ ( happ @ ( happ @ SV144 @ SY1353 ) @ SV322 ) )
            | ( SV322 = SY1353 )
            | ( p @ ( happ @ ( happ @ SV144 @ SV322 ) @ SY1353 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3938]) ).

thf(4105,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ~ ! [SY1021: $i,SY1022: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) )
        | ~ ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                    ( ( SY1023 != SY1024 )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
              | ~ ! [SY1025: $i,SY1026: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3939]) ).

thf(4106,plain,
    ! [SV169: $i,SV145: $i,SV107: $i] :
      ( ( ! [SY1135: $i,SY1136: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1135 @ SY1136 )
            | ( p @ ( happ @ SY1135 @ ( happ @ SV169 @ SY1136 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3940]) ).

thf(4107,plain,
    ! [SV145: $i,SV107: $i,SV169: $i] :
      ( ( ! [SY1137: $i,SY1138: $i] :
            ( ~ ( p @ ( happ @ SY1137 @ ( happ @ SV169 @ SY1138 ) ) )
            | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SY1137 @ SY1138 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3941]) ).

thf(4108,plain,
    ! [SV108: $i,SV146: $i,SV323: $i] :
      ( ( ! [SY1354: $i] :
            ( ( SV323 != SY1354 )
            | ~ ( p @ ( happ @ SV146 @ SV323 ) )
            | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV323 @ SY1354 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3942]) ).

thf(4109,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ~ ! [SY1034: $i,SY1035: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
              | ( SY1034 = SY1035 ) )
        | ~ ! [SY1036: $i] :
              ( ! [SY1037: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
              | ( p @ ( happ @ SV146 @ SY1036 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3943]) ).

thf(4110,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) )
          | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3944]) ).

thf(4111,plain,
    ! [SV263: $i] :
      ( ( ( c_24__type__90___24t @ SV263 )
        = $false )
      | ( ( ! [SY1287: $i] :
              ( ~ ( cType___24t @ SY1287 )
              | ! [SY1288: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ SY1288 )
                  | ! [SY1289: $i] :
                      ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ SY1289 )
                      | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SY1287 @ ( happ @ ( happ @ ( happ @ SV263 @ SY1287 ) @ SY1288 ) @ SY1289 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3945]) ).

thf(4112,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( ~ ( ~ ! [SY1290: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1290 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1290 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1290 ) ) )
              | ~ ! [SY1291: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1291 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1291 )
                    | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1291 ) )
                    | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3946]) ).

thf(4113,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SV265 ) )
          | ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                      | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                            | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3947]) ).

thf(4114,plain,
    ! [SV266: $i] :
      ( ( ( c_24__type__4733___24t @ SV266 )
        = $false )
      | ( ( ! [SY1292: $i] :
              ( ~ ( cType___24t @ SY1292 )
              | ! [SY1293: $i] :
                  ( ~ ( cType___24t @ SY1293 )
                  | ! [SY1294: $i] :
                      ( ~ ( cType___24t @ SY1294 )
                      | ! [SY1295: $i] :
                          ( ~ ( cType___24t @ SY1295 )
                          | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SY1292 ) @ SY1293 ) @ SY1294 ) @ SY1295 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3948]) ).

thf(4115,plain,
    ! [SV110: $i,SV170: $i,SV147: $i] :
      ( ( ! [SY1139: $i,SY1140: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV147 @ SY1139 ) @ SY1140 ) )
            | ~ ( p @ ( happ @ ( happ @ SV170 @ SY1139 ) @ SY1140 ) )
            | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1139 @ SY1140 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3949]) ).

thf(4116,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ( ~ ! [SY1141: $i,SY1142: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
                  | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) )
            | ~ ! [SY1143: $i,SY1144: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
                  | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3950]) ).

thf(4117,plain,
    ! [SV324: $i,SV148: $i,SV111: $i] :
      ( ( ! [SY1355: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV324 @ SY1355 )
            | ( p @ ( happ @ ( happ @ SV148 @ SY1355 ) @ SV324 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3951]) ).

thf(4118,plain,
    ! [SV111: $i,SV325: $i,SV148: $i] :
      ( ( ! [SY1356: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV148 @ SY1356 ) @ SV325 ) )
            | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV325 @ SY1356 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3952]) ).

thf(4119,plain,
    ! [SV112: $i,SV326: $i,SV297: $i] :
      ( ( ~ ( p @ SV297 )
        | ~ ( p @ SV326 )
        | ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV297 @ SV326 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3953]) ).

thf(4120,plain,
    ! [SV112: $i] :
      ( ( ~ ! [SY857: $i] :
              ( ! [SY858: $i] :
                  ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
              | ( p @ SY857 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3954]) ).

thf(4121,plain,
    ! [SV112: $i] :
      ( ( ~ ! [SY859: $i,SY860: $i] :
              ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
              | ( p @ SY860 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3954]) ).

thf(4122,plain,
    ! [SV327: $i,SV149: $i,SV113: $i] :
      ( ( ! [SY1357: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV327 @ SY1357 )
            | ( p @ ( happ @ SV149 @ SY1357 ) )
            | ( p @ ( happ @ SV327 @ SY1357 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3955]) ).

thf(4123,plain,
    ! [SV113: $i,SV149: $i] :
      ( ( ~ ! [SY1051: $i,SY1052: $i] :
              ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) )
        | ~ ! [SY1053: $i,SY1054: $i] :
              ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3956]) ).

thf(4124,plain,
    ! [SV114: $i] :
      ( ( ~ ! [SY868: $i] :
              ( ( p @ SY868 )
              | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3957]) ).

thf(4125,plain,
    ! [SV114: $i] :
      ( ( ~ ! [SY870: $i,SY871: $i] :
              ( ~ ( p @ SY871 )
              | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3957]) ).

thf(4126,plain,
    ! [SV328: $i,SV298: $i,SV114: $i] :
      ( ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV298 @ SV328 ) )
        | ~ ( p @ SV298 )
        | ( p @ SV328 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3958]) ).

thf(4127,plain,
    ! [SV267: $i,SV115: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( ! [SY1296: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SY1296 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SY1296 )
              | ! [SY1297: $i] :
                  ( ~ ( t @ SY1297 @ SV115 )
                  | ~ ( ~ ! [SY1298: $i] :
                            ( ~ ( t @ SY1298 @ SV115 )
                            | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1297 ) @ SY1298 ) )
                            | ( p @ ( happ @ ( happ @ SY1296 @ SY1297 ) @ SY1298 ) ) )
                      | ~ ! [SY1299: $i] :
                            ( ~ ( t @ SY1299 @ SV115 )
                            | ~ ( p @ ( happ @ ( happ @ SY1296 @ SY1297 ) @ SY1299 ) )
                            | ( p @ ( happ @ ( happ @ SV267 @ SY1297 ) @ SY1299 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3959]) ).

thf(4128,plain,
    ! [SV116: $i,SV329: $i,SV150: $i] :
      ( ( ! [SY1358: $i] :
            ( ~ ( p @ ( happ @ SV150 @ SY1358 ) )
            | ~ ( p @ ( happ @ SV329 @ SY1358 ) )
            | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV329 @ SY1358 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3960]) ).

thf(4129,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ~ ! [SY1057: $i,SY1058: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
              | ( p @ ( happ @ SV150 @ SY1058 ) ) )
        | ~ ! [SY1059: $i,SY1060: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
              | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[3961]) ).

thf(4130,plain,
    ! [SV268: $i,SV117: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( ! [SY1300: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1300 )
              | ~ ( ~ ! [SY1301: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1301 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1300 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY1300 @ SY1301 ) ) ) )
                  | ~ ! [SY1302: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1302 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1302 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SY1300 @ SY1302 ) ) ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3962]) ).

thf(4131,plain,
    ! [SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ~ ! [SY1303: $i,SY1304: $i] :
              ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1303 @ SY1304 )
              | ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1303 ) ) @ ( happ @ SV171 @ SY1304 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3963]) ).

thf(4132,plain,
    ! [SV151: $i,SV118: $i,SV171: $i,SV269: $i] :
      ( ( ~ ! [SY1305: $i,SY1306: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1305 ) ) @ ( happ @ SV171 @ SY1306 ) ) )
              | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1305 @ SY1306 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3963]) ).

thf(4133,plain,
    ! [SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ~ ! [SY1307: $i,SY1308: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1307 @ SY1308 )
              | ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1307 ) ) @ ( happ @ SV172 @ SY1308 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3964]) ).

thf(4134,plain,
    ! [SV152: $i,SV119: $i,SV172: $i,SV270: $i] :
      ( ( ~ ! [SY1309: $i,SY1310: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1309 ) ) @ ( happ @ SV172 @ SY1310 ) ) )
              | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1309 @ SY1310 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3964]) ).

thf(4135,plain,
    ! [SV120: $i,SV330: $i,SV299: $i] :
      ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV299 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) )
            | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV330 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) ) )
        | ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3965]) ).

thf(4136,plain,
    ! [SV331: $i,SV300: $i,SV120: $i] :
      ( ( ~ ( c_24__type__11787___24t @ SV120 @ SV300 @ SV331 )
        | ! [SY1359: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SY1359 )
            | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV331 @ SY1359 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3966]) ).

thf(4137,plain,
    ! [SV153: $i,SV121: $i,SV332: $i] :
      ( ( ! [SY1360: $i] :
            ( ( SV332 != SY1360 )
            | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV332 @ SY1360 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3967]) ).

thf(4138,plain,
    ! [SV333: $i,SV153: $i,SV121: $i] :
      ( ( ! [SY1361: $i] :
            ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV333 @ SY1361 ) )
            | ( SV333 = SY1361 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3968]) ).

thf(4139,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SV271 ) )
          | ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) )
                | ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3969]) ).

thf(4140,plain,
    ! [SV272: $i] :
      ( ( ( c_24__type__52___24t @ SV272 )
        = $false )
      | ( ( ! [SY1311: $i] :
              ( ~ ( cType___24t @ SY1311 )
              | ! [SY1312: $i] :
                  ( ~ ( cType___24t @ SY1312 )
                  | ( cType___24t @ ( happ @ ( happ @ SV272 @ SY1311 ) @ SY1312 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3970]) ).

thf(4141,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV173: $i] :
      ( ( ~ ! [SY1313: $i,SY1314: $i] :
              ( ( ( happ @ SV173 @ SY1313 )
               != ( happ @ SV173 @ SY1314 ) )
              | ~ ( p @ ( happ @ ( happ @ SV273 @ SY1313 ) @ SY1314 ) )
              | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1313 @ SY1314 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3971]) ).

thf(4142,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ~ ( ~ ! [SY1315: $i,SY1316: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
                    | ( ( happ @ SV173 @ SY1315 )
                      = ( happ @ SV173 @ SY1316 ) ) )
              | ~ ! [SY1317: $i,SY1318: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
                    | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[3971]) ).

thf(4143,plain,
    ! [SV175: $i,SV334: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
          | ! [SY1362: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1362 )
              | ! [SY1363: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1363 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1362 @ SY1363 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1362 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1363 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3972]) ).

thf(4144,plain,
    ! [SV179: $i,SV10: $i] :
      ( ( ( ~ ( p @ SV10 )
          | ~ ( p @ SV179 ) )
        = $true )
      | ( ( p @ SV10 )
        = $true )
      | ( ( cProp___24t @ SV179 )
        = $false )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3974]) ).

thf(4145,plain,
    ! [SV180: $i,SV12: $i] :
      ( ( ( ~ ( p @ SV12 )
          | ( p @ SV180 ) )
        = $true )
      | ( ( p @ SV12 )
        = $true )
      | ( ( cProp___24t @ SV180 )
        = $false )
      | ( ( cProp___24t @ SV12 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3975]) ).

thf(4146,plain,
    ! [SV183: $i,SV335: $i,SV15: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV335 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SV335 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV335 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
        = $false )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3978]) ).

thf(4147,plain,
    ! [SV184: $i,SV336: $i,SV16: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV336 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SV336 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV336 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
        = $false )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3979]) ).

thf(4148,plain,
    ! [SV185: $i,SV337: $i,SV17: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV337 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SV337 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV337 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
        = $false )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3980]) ).

thf(4149,plain,
    ! [SV186: $i,SV338: $i,SV18: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV338 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SV338 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV338 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
        = $false )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3981]) ).

thf(4150,plain,
    ! [SV187: $i,SV339: $i,SV19: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV339 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SV339 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV339 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
        = $false )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3982]) ).

thf(4151,plain,
    ! [SV188: $i,SV340: $i,SV20: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV340 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SV340 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV340 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
        = $false )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3983]) ).

thf(4152,plain,
    ! [SV189: $i,SV341: $i,SV21: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV341 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SV341 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV341 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
        = $false )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3984]) ).

thf(4153,plain,
    ! [SV190: $i,SV342: $i,SV22: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV342 )
          | ! [SY1364: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1364 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SV342 ) @ SY1364 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV342 @ SY1364 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3985]) ).

thf(4154,plain,
    ! [SV191: $i,SV343: $i,SV23: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV343 )
          | ! [SY1365: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1365 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ SY1365 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SY1365 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3986]) ).

thf(4155,plain,
    ! [SV192: $i,SV344: $i,SV24: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV344 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV192 @ SV344 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV344 @ SV192 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV192 )
        = $false )
      | ( ( cType___24t @ SV24 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3987]) ).

thf(4156,plain,
    ! [SV194: $i,SV345: $i,SV26: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV345 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SV345 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SV345 @ SV194 ) @ SV194 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
        = $false )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3989]) ).

thf(4157,plain,
    ! [SV195: $i,SV346: $i,SV27: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV346 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SV346 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SV346 ) @ SV195 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
        = $false )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3990]) ).

thf(4158,plain,
    ! [SV196: $i,SV347: $i,SV28: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV347 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SV196 @ SV347 ) @ SV196 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV196 )
        = $false )
      | ( ( cType___24t @ SV28 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3991]) ).

thf(4159,plain,
    ! [SV197: $i,SV348: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
          | ! [SY1366: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1366 )
              | ! [SY1367: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1367 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1366 @ SY1367 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1366 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1367 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3992]) ).

thf(4160,plain,
    ! [SV198: $i,SV349: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
          | ! [SY1368: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1368 )
              | ! [SY1369: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1369 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1368 @ SY1369 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1368 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1369 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3993]) ).

thf(4161,plain,
    ! [SV199: $i,SV350: $i,SV31: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV350 )
          | ! [SY1370: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1370 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SV350 ) @ SY1370 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SY1370 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV350 @ SY1370 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3994]) ).

thf(4162,plain,
    ! [SV200: $i,SV351: $i,SV32: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV351 )
          | ! [SY1371: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1371 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SV351 ) @ SY1371 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV351 @ SY1371 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3995]) ).

thf(4163,plain,
    ! [SV201: $i,SV352: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
          | ! [SY1372: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1372 )
              | ! [SY1373: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1373 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1372 @ SY1373 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1372 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1373 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3996]) ).

thf(4164,plain,
    ! [SV202: $i,SV353: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
          | ! [SY1374: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1374 )
              | ! [SY1375: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1375 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1374 @ SY1375 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1374 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1375 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3997]) ).

thf(4165,plain,
    ! [SV203: $i,SV354: $i,SV35: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV354 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SV354 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV354 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
        = $false )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3998]) ).

thf(4166,plain,
    ! [SV204: $i,SV355: $i,SV36: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV355 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SV355 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV355 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
        = $false )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3999]) ).

thf(4167,plain,
    ! [SV205: $i,SV356: $i,SV37: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV356 )
          | ! [SY1376: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1376 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SV356 ) @ SY1376 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV356 @ SY1376 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4000]) ).

thf(4168,plain,
    ! [SV206: $i,SV357: $i,SV38: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV357 )
          | ! [SY1377: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1377 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ SY1377 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SY1377 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4001]) ).

thf(4169,plain,
    ! [SV207: $i,SV358: $i,SV39: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV358 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV207 @ SV358 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV358 @ SV207 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV207 )
        = $false )
      | ( ( cType___24t @ SV39 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4002]) ).

thf(4170,plain,
    ! [SV209: $i,SV359: $i,SV41: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV359 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SV359 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SV359 ) @ SV359 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
        = $false )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4004]) ).

thf(4171,plain,
    ! [SV210: $i,SV360: $i,SV42: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV360 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SV360 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SV360 @ SV210 ) @ SV360 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
        = $false )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4005]) ).

thf(4172,plain,
    ! [SV211: $i,SV361: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
          | ! [SY1378: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1378 )
              | ! [SY1379: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1379 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1378 @ SY1379 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1378 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1379 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4006]) ).

thf(4173,plain,
    ! [SV212: $i,SV362: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
          | ! [SY1380: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1380 )
              | ! [SY1381: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1381 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1380 @ SY1381 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1380 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1381 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4007]) ).

thf(4174,plain,
    ! [SV213: $i,SV363: $i,SV45: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV363 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SV363 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SV363 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
        = $false )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4008]) ).

thf(4175,plain,
    ! [SV214: $i,SV364: $i,SV46: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV364 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SV364 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SV364 @ SV214 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
        = $false )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4009]) ).

thf(4176,plain,
    ! [SV215: $i,SV365: $i,SV47: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV365 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SV365 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
        = $false )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4010]) ).

thf(4177,plain,
    ! [SV216: $i,SV366: $i,SV48: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4011]) ).

thf(4178,plain,
    ! [SV217: $i,SV367: $i,SV49: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV367 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SV217 @ SV367 ) @ SV217 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV217 )
        = $false )
      | ( ( cType___24t @ SV49 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4012]) ).

thf(4179,plain,
    ! [SV218: $i,SV368: $i,SV50: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
          | ! [SY1382: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1382 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SY1382 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SY1382 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4013]) ).

thf(4180,plain,
    ! [SV219: $i,SV369: $i,SV51: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV369 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SV219 @ SV369 ) @ SV369 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV219 )
        = $false )
      | ( ( cType___24t @ SV51 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4014]) ).

thf(4181,plain,
    ! [SV220: $i,SV370: $i,SV52: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
          | ! [SY1383: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1383 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SY1383 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SY1383 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4015]) ).

thf(4182,plain,
    ! [SV221: $i,SV371: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
          | ! [SY1384: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1384 )
              | ! [SY1385: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1385 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY1384 @ SY1385 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SY1384 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SY1385 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4016]) ).

thf(4183,plain,
    ! [SV222: $i,SV372: $i,SV54: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
          | ! [SY1386: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1386 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1386 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SY1386 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4017]) ).

thf(4184,plain,
    ! [SV223: $i,SV373: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
          | ! [SY1387: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1387 )
              | ! [SY1388: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1388 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1388 @ SY1387 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SY1387 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SY1388 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4018]) ).

thf(4185,plain,
    ! [SV224: $i,SV374: $i,SV56: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV374 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SV224 @ SV374 ) @ SV224 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV224 )
        = $false )
      | ( ( cType___24t @ SV56 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4019]) ).

thf(4186,plain,
    ! [SV225: $i,SV375: $i,SV57: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV375 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SV375 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV375 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
        = $false )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4020]) ).

thf(4187,plain,
    ! [SV227: $i,SV376: $i,SV59: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV376 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SV376 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV376 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
        = $false )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4022]) ).

thf(4188,plain,
    ! [SV228: $i,SV377: $i,SV60: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV377 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
        = $false )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4023]) ).

thf(4189,plain,
    ! [SV229: $i,SV378: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
          | ! [SY1389: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1389 )
              | ! [SY1390: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1390 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY1389 @ SY1390 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SY1389 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SY1390 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4024]) ).

thf(4190,plain,
    ! [SV230: $i,SV379: $i,SV62: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV379 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SV379 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SV379 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
        = $false )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4025]) ).

thf(4191,plain,
    ! [SV231: $i,SV380: $i,SV63: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV380 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SV380 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SV380 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
        = $false )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4026]) ).

thf(4192,plain,
    ! [SV232: $i,SV381: $i,SV64: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV381 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SV381 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SV381 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
        = $false )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4027]) ).

thf(4193,plain,
    ! [SV233: $i,SV382: $i,SV65: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV382 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SV382 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV382 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
        = $false )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4028]) ).

thf(4194,plain,
    ! [SV234: $i,SV383: $i,SV66: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV383 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
        = $false )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4029]) ).

thf(4195,plain,
    ! [SV235: $i,SV384: $i,SV67: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
          | ! [SY1391: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1391 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SY1391 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SY1391 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SY1391 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4030]) ).

thf(4196,plain,
    ! [SV236: $i,SV385: $i,SV68: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV385 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SV236 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SV236 @ SV385 ) @ SV385 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV236 )
        = $false )
      | ( ( cType___24t @ SV68 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4031]) ).

thf(4197,plain,
    ! [SV237: $i,SV386: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
          | ! [SY1392: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1392 )
              | ! [SY1393: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1393 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY1392 @ SY1393 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SY1392 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SY1393 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4032]) ).

thf(4198,plain,
    ! [SV238: $i,SV387: $i,SV70: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV387 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SV238 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SV238 @ SV387 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV238 )
        = $false )
      | ( ( cType___24t @ SV70 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4033]) ).

thf(4199,plain,
    ! [SV239: $i,SV388: $i,SV71: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
          | ! [SY1394: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1394 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SY1394 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4034]) ).

thf(4200,plain,
    ! [SV240: $i,SV389: $i,SV72: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV389 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SV389 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SV240 @ SV389 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV240 )
        = $false )
      | ( ( cType___24t @ SV72 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4035]) ).

thf(4201,plain,
    ! [SV241: $i,SV390: $i,SV73: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
          | ! [SY1395: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1395 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SY1395 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SY1395 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4036]) ).

thf(4202,plain,
    ! [SV242: $i,SV391: $i,SV74: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4037]) ).

thf(4203,plain,
    ! [SV78: $i] :
      ( ( ( ~ ! [SY657: $i] :
                ( ~ ( cProp___24t @ SY657 )
                | ( p @ SV78 )
                | ~ ( p @ SV78 )
                | ( p @ SY657 ) )
          | ~ ! [SY658: $i] :
                ( ~ ( cProp___24t @ SY658 )
                | ( p @ SV78 )
                | ~ ( p @ SY658 )
                | ( p @ SY658 ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4038]) ).

thf(4204,plain,
    ! [SV78: $i] :
      ( ( ( ~ ! [SY659: $i] :
                ( ~ ( cProp___24t @ SY659 )
                | ~ ( p @ SY659 )
                | ~ ( p @ SV78 )
                | ( p @ SY659 ) )
          | ~ ! [SX1: $i] :
                ( ~ ( cProp___24t @ SX1 )
                | ~ ( p @ SX1 )
                | ~ ( p @ SX1 )
                | ( p @ SX1 ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4039]) ).

thf(4205,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4040]) ).

thf(4206,plain,
    ! [SV244: $i] :
      ( ( ( ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4040]) ).

thf(4207,plain,
    ! [SV245: $i,SV392: $i] :
      ( ( ( ~ ( cType___24t @ SV392 )
          | ! [SY1396: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ SY1396 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ ( happ @ ( happ @ SV245 @ SV392 ) @ SY1396 ) ) ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV245 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4041]) ).

thf(4208,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ~ ! [SY1258: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1258 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1258 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1258 ) )
          | ~ ! [SY1259: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1259 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1259 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1259 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4042]) ).

thf(4209,plain,
    ! [SV301: $i,SV276: $i,SV80: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV276 @ SV301 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV276 ) @ SV301 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4043]) ).

thf(4210,plain,
    ! [SV302: $i,SV277: $i,SV80: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV277 ) @ SV302 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV277 @ SV302 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4044]) ).

thf(4211,plain,
    ! [SV278: $i,SV247: $i] :
      ( ( ( c_24__lam__35673___24a2 @ SV247 @ SV278 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV247 ) @ SV278 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4045]) ).

thf(4212,plain,
    ! [SV279: $i,SV248: $i] :
      ( ( ( p @ ( happ @ ( happ @ c_24__lam__35673 @ SV248 ) @ SV279 ) )
        = $false )
      | ( ( c_24__lam__35673___24a2 @ SV248 @ SV279 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4046]) ).

thf(4213,plain,
    ! [SV393: $i,SV161: $i,SV130: $i,SV81: $i] :
      ( ( ! [SY1397: $i] :
            ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV393 @ SY1397 )
            | ( p @ ( happ @ ( happ @ SV130 @ SV393 ) @ SY1397 ) )
            | ( p @ ( happ @ ( happ @ SV161 @ SV393 ) @ SY1397 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4047]) ).

thf(4214,plain,
    ! [SV161: $i,SV81: $i,SV130: $i] :
      ( ( ~ ! [SY1093: $i,SY1094: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
              | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) )
        | ~ ! [SY1095: $i,SY1096: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
              | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4048]) ).

thf(4215,plain,
    ! [SV131: $i,SV82: $i,SV394: $i,SV162: $i] :
      ( ( ! [SY1398: $i] :
            ( ( ( happ @ SV162 @ SV394 )
             != ( happ @ SV162 @ SY1398 ) )
            | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV394 @ SY1398 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4049]) ).

thf(4216,plain,
    ! [SV395: $i,SV162: $i,SV131: $i,SV82: $i] :
      ( ( ! [SY1399: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV395 @ SY1399 )
            | ( ( happ @ SV162 @ SV395 )
              = ( happ @ SV162 @ SY1399 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4050]) ).

thf(4217,plain,
    ! [SV249: $i,SV396: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
          | ! [SY1400: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1400 )
              | ~ ( ~ ! [SY1401: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1401 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1401 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1401 ) ) )
                  | ~ ! [SY1402: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1402 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1402 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1402 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4051]) ).

thf(4218,plain,
    ! [SV397: $i,SV303: $i,SV132: $i,SV84: $i] :
      ( ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV303 @ SV397 )
        | ( p @ ( happ @ ( happ @ SV132 @ SV303 ) @ SV397 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4052]) ).

thf(4219,plain,
    ! [SV84: $i,SV398: $i,SV304: $i,SV132: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV132 @ SV304 ) @ SV398 ) )
        | ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV304 @ SV398 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4053]) ).

thf(4220,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ~ ! [SY1266: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1266 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1266 )
                | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
                | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1266 ) ) )
          | ~ ! [SY1267: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1267 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1267 )
                | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1267 ) )
                | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4054]) ).

thf(4221,plain,
    ! [SV251: $i] :
      ( ( ( ~ ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) )
        = $false )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4055]) ).

thf(4222,plain,
    ! [SV251: $i] :
      ( ( ( ~ ~ ( cType___24t @ ( happ @ SV251 @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) ) )
        = $false )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4055]) ).

thf(4223,plain,
    ! [SV252: $i,SV399: $i] :
      ( ( ( ~ ( cType___24t @ SV399 )
          | ( cType___24t @ ( happ @ SV252 @ SV399 ) ) )
        = $true )
      | ( ( c_24__type__28___24t @ SV252 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4056]) ).

thf(4224,plain,
    ! [SV86: $i,SV305: $i,SV400: $i,SV133: $i] :
      ( ( ~ ( p @ ( happ @ SV133 @ SV400 ) )
        | ( p @ ( happ @ SV305 @ SV400 ) )
        | ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV305 @ SV400 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4057]) ).

thf(4225,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ~ ! [SY953: $i,SY954: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
              | ( p @ ( happ @ SV133 @ SY954 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4058]) ).

thf(4226,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ~ ! [SY955: $i,SY956: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
              | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4058]) ).

thf(4227,plain,
    ! [SV401: $i,SV306: $i,SV134: $i,SV87: $i] :
      ( ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV306 @ SV401 )
        | ( p @ ( happ @ ( happ @ SV134 @ SV401 ) @ SV306 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4059]) ).

thf(4228,plain,
    ! [SV87: $i,SV307: $i,SV402: $i,SV134: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV134 @ SV402 ) @ SV307 ) )
        | ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV307 @ SV402 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4060]) ).

thf(4229,plain,
    ! [SV308: $i,SV280: $i,SV88: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV280 @ SV308 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV280 @ SV308 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4061]) ).

thf(4230,plain,
    ! [SV88: $i,SV309: $i,SV281: $i] :
      ( ( ( p @ ( happ @ SV281 @ SV309 ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV281 @ SV309 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4062]) ).

thf(4231,plain,
    ! [SV253: $i,SV403: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
          | ~ ( ~ ! [SY1403: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1403 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1403 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1403 ) ) ) )
              | ~ ! [SY1404: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1404 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1404 ) ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1404 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4063]) ).

thf(4232,plain,
    ! [SV404: $i,SV163: $i,SV135: $i,SV90: $i] :
      ( ( ! [SY1405: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV404 @ SY1405 )
            | ( p @ ( happ @ ( happ @ SV135 @ SV404 ) @ SY1405 ) )
            | ( p @ ( happ @ ( happ @ SV163 @ SV404 ) @ SY1405 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4064]) ).

thf(4233,plain,
    ! [SV163: $i,SV90: $i,SV135: $i] :
      ( ( ~ ! [SY1103: $i,SY1104: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) )
        | ~ ! [SY1105: $i,SY1106: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4065]) ).

thf(4234,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ~ ~ ( ~ ! [SY1272: $i] :
                      ( ~ ( cProp___24t @ SY1272 )
                      | ( p @ SV91 )
                      | ~ ( p @ SV91 )
                      | ( p @ SV254 )
                      | ( p @ SY1272 ) )
                | ~ ! [SY1273: $i] :
                      ( ~ ( cProp___24t @ SY1273 )
                      | ( p @ SV91 )
                      | ~ ( p @ SY1273 )
                      | ( p @ SV254 )
                      | ( p @ SY1273 ) ) )
          | ~ ~ ( ~ ! [SY1274: $i] :
                      ( ~ ( cProp___24t @ SY1274 )
                      | ~ ( p @ SV254 )
                      | ~ ( p @ SV91 )
                      | ( p @ SV254 )
                      | ( p @ SY1274 ) )
                | ~ ! [SY1275: $i] :
                      ( ~ ( cProp___24t @ SY1275 )
                      | ~ ( p @ SV254 )
                      | ~ ( p @ SY1275 )
                      | ( p @ SV254 )
                      | ( p @ SY1275 ) ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4066]) ).

thf(4235,plain,
    ! [SV92: $i,SV164: $i,SV405: $i,SV136: $i] :
      ( ( ! [SY1406: $i] :
            ( ~ ( p @ ( happ @ SV136 @ SV405 ) )
            | ~ ( p @ ( happ @ SV164 @ SY1406 ) )
            | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV405 @ SY1406 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4067]) ).

thf(4236,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ~ ! [SY1109: $i] :
              ( ! [SY1110: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
              | ( p @ ( happ @ SV136 @ SY1109 ) ) )
        | ~ ! [SY1111: $i,SY1112: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
              | ( p @ ( happ @ SV164 @ SY1112 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4068]) ).

thf(4237,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) )
          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SV282 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) ) )
        = $false )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4069]) ).

thf(4238,plain,
    ! [SV283: $i,SV256: $i] :
      ( ( ( c_24__type__11748___24t @ SV256 @ SV283 )
        = $false )
      | ( ( ! [SY1323: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SY1323 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SV283 @ SY1323 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4070]) ).

thf(4239,plain,
    ! [SV406: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ! [SY1407: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV406 @ SY1407 )
            | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV406 ) @ SY1407 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4073]) ).

thf(4240,plain,
    ! [SV407: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ! [SY1408: $i] :
            ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV407 ) @ SY1408 ) )
            | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV407 @ SY1408 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4074]) ).

thf(4241,plain,
    ! [SV311: $i,SV285: $i,SV94: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV285 @ SV311 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV311 @ SV285 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV285 @ SV311 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4075]) ).

thf(4242,plain,
    ! [SV94: $i] :
      ( ( ! [SY744: $i,SY745: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY744 @ SY745 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY744 @ SY745 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4076]) ).

thf(4243,plain,
    ! [SV94: $i] :
      ( ( ! [SY746: $i,SY747: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SY746 @ SY747 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY747 @ SY746 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4077]) ).

thf(4244,plain,
    ! [SV286: $i,SV257: $i] :
      ( ( ( p @ ( c_24__prop__35358___24a2 @ SV257 @ SV286 ) )
        = $false )
      | ( ( ~ ( p @ SV286 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4078]) ).

thf(4245,plain,
    ! [SV95: $i,SV312: $i,SV408: $i,SV138: $i] :
      ( ( ~ ( p @ ( happ @ SV138 @ SV408 ) )
        | ~ ( p @ ( happ @ SV312 @ SV408 ) )
        | ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV312 @ SV408 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4080]) ).

thf(4246,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ~ ! [SY982: $i,SY983: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
              | ( p @ ( happ @ SV138 @ SY983 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4081]) ).

thf(4247,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ~ ! [SY984: $i,SY985: $i] :
              ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
              | ( p @ ( happ @ SY984 @ SY985 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4081]) ).

thf(4248,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ~ ! [SY1281: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1281 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1281 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1281 ) ) )
          | ~ ! [SY1282: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1282 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1282 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1282 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4082]) ).

thf(4249,plain,
    ! [SV409: $i,SV313: $i,SV139: $i,SV97: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV313 @ SV409 )
        | ( SV313 = SV409 )
        | ( p @ ( happ @ ( happ @ SV139 @ SV313 ) @ SV409 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4083]) ).

thf(4250,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ~ ! [SY988: $i,SY989: $i] :
              ( ( SY988 != SY989 )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4084]) ).

thf(4251,plain,
    ! [SV97: $i,SV139: $i] :
      ( ( ~ ! [SY990: $i,SY991: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4084]) ).

thf(4252,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( ~ ( t @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) @ SV98 )
              | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
                    | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                          | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4085]) ).

thf(4253,plain,
    ! [SV315: $i,SV289: $i,SV98: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) ) )
        = $true )
      | ( ( ! [SY1349: $i] :
              ( ~ ( t @ SY1349 @ SV98 )
              | ! [SY1350: $i] :
                  ( ~ ( t @ SY1350 @ SV98 )
                  | ~ ( p @ ( happ @ ( happ @ SV289 @ SY1349 ) @ SY1350 ) )
                  | ( p @ ( happ @ ( happ @ SV315 @ SY1349 ) @ SY1350 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4086]) ).

thf(4254,plain,
    ! [SV410: $i,SV316: $i,SV140: $i,SV99: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV316 @ SV410 )
        | ( p @ ( happ @ ( happ @ SV140 @ SV316 ) @ SV410 ) )
        | ( p @ ( happ @ ( happ @ SV140 @ SV410 ) @ SV316 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4087]) ).

thf(4255,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ~ ! [SY994: $i,SY995: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4088]) ).

thf(4256,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ~ ! [SY996: $i,SY997: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4088]) ).

thf(4257,plain,
    ! [SV100: $i,SV166: $i,SV411: $i,SV141: $i] :
      ( ( ! [SY1409: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV141 @ SV411 ) @ SY1409 ) )
            | ( p @ ( happ @ ( happ @ SV166 @ SV411 ) @ SY1409 ) )
            | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV411 @ SY1409 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4089]) ).

thf(4258,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ! [SY1119: $i,SY1120: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
              | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) )
        | ~ ! [SY1121: $i,SY1122: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
              | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4090]) ).

thf(4259,plain,
    ! [SV290: $i,SV317: $i,SV101: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SV317 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) ) ) )
        = $true )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4091]) ).

thf(4260,plain,
    ! [SV318: $i,SV291: $i,SV101: $i] :
      ( ( ( ~ ( c_24__type__11699___24t @ SV101 @ SV291 @ SV318 ) )
        = $true )
      | ( ( ! [SY1352: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY1352 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SV318 @ SY1352 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4092]) ).

thf(4261,plain,
    ! [SV412: $i,SV167: $i,SV142: $i,SV102: $i] :
      ( ( ! [SY1410: $i] :
            ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV412 @ SY1410 )
            | ( p @ ( happ @ ( happ @ SV167 @ SV412 ) @ SY1410 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4093]) ).

thf(4262,plain,
    ! [SV142: $i,SV102: $i,SV413: $i,SV167: $i] :
      ( ( ! [SY1411: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV167 @ SV413 ) @ SY1411 ) )
            | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV413 @ SY1411 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4094]) ).

thf(4263,plain,
    ! [SV319: $i,SV292: $i,SV103: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV292 @ SV319 ) ) )
        = $true )
      | ( ( ( p @ SV292 )
          | ( p @ SV319 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4095]) ).

thf(4264,plain,
    ! [SV103: $i] :
      ( ( ! [SY799: $i] :
            ( ~ ( p @ SY799 )
            | ! [SY800: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY799 @ SY800 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4096]) ).

thf(4265,plain,
    ! [SV103: $i] :
      ( ( ! [SY801: $i,SY802: $i] :
            ( ~ ( p @ SY802 )
            | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SY801 @ SY802 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4097]) ).

thf(4266,plain,
    ! [SV104: $i,SV143: $i,SV414: $i,SV168: $i] :
      ( ( ! [SY1412: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SY1412 ) )
            | ~ ( p @ ( happ @ SV143 @ SV414 ) )
            | ~ ( p @ ( happ @ SV143 @ SY1412 ) )
            | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SY1412 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4098]) ).

thf(4267,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                    | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
              | ~ ! [SY1131: $i] :
                    ( ! [SY1132: $i] :
                        ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                    | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
        | ~ ! [SY1133: $i,SY1134: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
              | ( p @ ( happ @ SV143 @ SY1134 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4099]) ).

thf(4268,plain,
    ! [SV105: $i,SV320: $i,SV293: $i] :
      ( ( ( SV293 != SV320 )
        = $true )
      | ( ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV293 @ SV320 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4100]) ).

thf(4269,plain,
    ! [SV321: $i,SV294: $i,SV105: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV294 @ SV321 ) ) )
        = $true )
      | ( ( SV294 = SV321 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4101]) ).

thf(4270,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) )
          | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4102]) ).

thf(4271,plain,
    ! [SV296: $i,SV261: $i] :
      ( ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false )
      | ( ( ! [SY1335: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1335 )
              | ! [SY1336: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1336 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SY1335 ) @ SY1336 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4103]) ).

thf(4272,plain,
    ! [SV415: $i,SV322: $i,SV144: $i,SV106: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV322 @ SV415 )
        | ( p @ ( happ @ ( happ @ SV144 @ SV415 ) @ SV322 ) )
        | ( SV322 = SV415 )
        | ( p @ ( happ @ ( happ @ SV144 @ SV322 ) @ SV415 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4104]) ).

thf(4273,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ~ ! [SY1021: $i,SY1022: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4105]) ).

thf(4274,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                    ( ( SY1023 != SY1024 )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
              | ~ ! [SY1025: $i,SY1026: $i] :
                    ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                    | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4105]) ).

thf(4275,plain,
    ! [SV416: $i,SV169: $i,SV145: $i,SV107: $i] :
      ( ( ! [SY1413: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV416 @ SY1413 )
            | ( p @ ( happ @ SV416 @ ( happ @ SV169 @ SY1413 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4106]) ).

thf(4276,plain,
    ! [SV145: $i,SV107: $i,SV169: $i,SV417: $i] :
      ( ( ! [SY1414: $i] :
            ( ~ ( p @ ( happ @ SV417 @ ( happ @ SV169 @ SY1414 ) ) )
            | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV417 @ SY1414 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4107]) ).

thf(4277,plain,
    ! [SV108: $i,SV146: $i,SV418: $i,SV323: $i] :
      ( ( ( SV323 != SV418 )
        | ~ ( p @ ( happ @ SV146 @ SV323 ) )
        | ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV323 @ SV418 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4108]) ).

thf(4278,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ~ ! [SY1034: $i,SY1035: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
              | ( SY1034 = SY1035 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4109]) ).

thf(4279,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ~ ! [SY1036: $i] :
              ( ! [SY1037: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
              | ( p @ ( happ @ SV146 @ SY1036 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4109]) ).

thf(4280,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4110]) ).

thf(4281,plain,
    ! [SV262: $i] :
      ( ( ( ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
                | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                      | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4110]) ).

thf(4282,plain,
    ! [SV263: $i,SV419: $i] :
      ( ( ( ~ ( cType___24t @ SV419 )
          | ! [SY1415: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1415 )
              | ! [SY1416: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1416 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SY1415 ) @ SY1416 ) ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4111]) ).

thf(4283,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ~ ! [SY1290: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1290 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1290 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1290 ) ) )
          | ~ ! [SY1291: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1291 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1291 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1291 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4112]) ).

thf(4284,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4113]) ).

thf(4285,plain,
    ! [SV265: $i] :
      ( ( ( ~ ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                      | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                            | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4113]) ).

thf(4286,plain,
    ! [SV266: $i,SV420: $i] :
      ( ( ( ~ ( cType___24t @ SV420 )
          | ! [SY1417: $i] :
              ( ~ ( cType___24t @ SY1417 )
              | ! [SY1418: $i] :
                  ( ~ ( cType___24t @ SY1418 )
                  | ! [SY1419: $i] :
                      ( ~ ( cType___24t @ SY1419 )
                      | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SY1417 ) @ SY1418 ) @ SY1419 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4114]) ).

thf(4287,plain,
    ! [SV110: $i,SV170: $i,SV421: $i,SV147: $i] :
      ( ( ! [SY1420: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV147 @ SV421 ) @ SY1420 ) )
            | ~ ( p @ ( happ @ ( happ @ SV170 @ SV421 ) @ SY1420 ) )
            | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV421 @ SY1420 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4115]) ).

thf(4288,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ! [SY1141: $i,SY1142: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
              | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) )
        | ~ ! [SY1143: $i,SY1144: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
              | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4116]) ).

thf(4289,plain,
    ! [SV422: $i,SV324: $i,SV148: $i,SV111: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV324 @ SV422 )
        | ( p @ ( happ @ ( happ @ SV148 @ SV422 ) @ SV324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4117]) ).

thf(4290,plain,
    ! [SV111: $i,SV325: $i,SV423: $i,SV148: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV148 @ SV423 ) @ SV325 ) )
        | ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV325 @ SV423 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4118]) ).

thf(4291,plain,
    ! [SV112: $i,SV326: $i,SV297: $i] :
      ( ( ( ~ ( p @ SV297 )
          | ~ ( p @ SV326 ) )
        = $true )
      | ( ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV297 @ SV326 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4119]) ).

thf(4292,plain,
    ! [SV112: $i] :
      ( ( ! [SY857: $i] :
            ( ! [SY858: $i] :
                ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY857 @ SY858 ) )
            | ( p @ SY857 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4120]) ).

thf(4293,plain,
    ! [SV112: $i] :
      ( ( ! [SY859: $i,SY860: $i] :
            ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SY859 @ SY860 ) )
            | ( p @ SY860 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4121]) ).

thf(4294,plain,
    ! [SV424: $i,SV327: $i,SV149: $i,SV113: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV327 @ SV424 )
        | ( p @ ( happ @ SV149 @ SV424 ) )
        | ( p @ ( happ @ SV327 @ SV424 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4122]) ).

thf(4295,plain,
    ! [SV113: $i,SV149: $i] :
      ( ( ~ ! [SY1051: $i,SY1052: $i] :
              ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4123]) ).

thf(4296,plain,
    ! [SV149: $i,SV113: $i] :
      ( ( ~ ! [SY1053: $i,SY1054: $i] :
              ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
              | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4123]) ).

thf(4297,plain,
    ! [SV114: $i] :
      ( ( ! [SY868: $i] :
            ( ( p @ SY868 )
            | ! [SY869: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY868 @ SY869 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4124]) ).

thf(4298,plain,
    ! [SV114: $i] :
      ( ( ! [SY870: $i,SY871: $i] :
            ( ~ ( p @ SY871 )
            | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SY870 @ SY871 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4125]) ).

thf(4299,plain,
    ! [SV328: $i,SV298: $i,SV114: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV298 @ SV328 ) ) )
        = $true )
      | ( ( ~ ( p @ SV298 )
          | ( p @ SV328 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4126]) ).

thf(4300,plain,
    ! [SV267: $i,SV425: $i,SV115: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
          | ! [SY1421: $i] :
              ( ~ ( t @ SY1421 @ SV115 )
              | ~ ( ~ ! [SY1422: $i] :
                        ( ~ ( t @ SY1422 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1422 ) )
                        | ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1422 ) ) )
                  | ~ ! [SY1423: $i] :
                        ( ~ ( t @ SY1423 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1423 ) )
                        | ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1423 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4127]) ).

thf(4301,plain,
    ! [SV116: $i,SV329: $i,SV426: $i,SV150: $i] :
      ( ( ~ ( p @ ( happ @ SV150 @ SV426 ) )
        | ~ ( p @ ( happ @ SV329 @ SV426 ) )
        | ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV329 @ SV426 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4128]) ).

thf(4302,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ~ ! [SY1057: $i,SY1058: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
              | ( p @ ( happ @ SV150 @ SY1058 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4129]) ).

thf(4303,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ~ ! [SY1059: $i,SY1060: $i] :
              ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
              | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4129]) ).

thf(4304,plain,
    ! [SV268: $i,SV427: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
          | ~ ( ~ ! [SY1424: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1424 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1424 ) ) ) )
              | ~ ! [SY1425: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1425 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1425 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1425 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4130]) ).

thf(4305,plain,
    ! [SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ! [SY1303: $i,SY1304: $i] :
            ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1303 @ SY1304 )
            | ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1303 ) ) @ ( happ @ SV171 @ SY1304 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4131]) ).

thf(4306,plain,
    ! [SV151: $i,SV118: $i,SV171: $i,SV269: $i] :
      ( ( ! [SY1305: $i,SY1306: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SY1305 ) ) @ ( happ @ SV171 @ SY1306 ) ) )
            | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SY1305 @ SY1306 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4132]) ).

thf(4307,plain,
    ! [SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ! [SY1307: $i,SY1308: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1307 @ SY1308 )
            | ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1307 ) ) @ ( happ @ SV172 @ SY1308 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4133]) ).

thf(4308,plain,
    ! [SV152: $i,SV119: $i,SV172: $i,SV270: $i] :
      ( ( ! [SY1309: $i,SY1310: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SY1309 ) ) @ ( happ @ SV172 @ SY1310 ) ) )
            | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SY1309 @ SY1310 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4134]) ).

thf(4309,plain,
    ! [SV120: $i,SV330: $i,SV299: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV299 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV330 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) ) ) )
        = $true )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4135]) ).

thf(4310,plain,
    ! [SV331: $i,SV300: $i,SV120: $i] :
      ( ( ( ~ ( c_24__type__11787___24t @ SV120 @ SV300 @ SV331 ) )
        = $true )
      | ( ( ! [SY1359: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SY1359 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV331 @ SY1359 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4136]) ).

thf(4311,plain,
    ! [SV153: $i,SV121: $i,SV428: $i,SV332: $i] :
      ( ( ( SV332 != SV428 )
        | ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV332 @ SV428 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4137]) ).

thf(4312,plain,
    ! [SV429: $i,SV333: $i,SV153: $i,SV121: $i] :
      ( ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV333 @ SV429 ) )
        | ( SV333 = SV429 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4138]) ).

thf(4313,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4139]) ).

thf(4314,plain,
    ! [SV271: $i] :
      ( ( ( ~ ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) )
                | ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4139]) ).

thf(4315,plain,
    ! [SV272: $i,SV430: $i] :
      ( ( ( ~ ( cType___24t @ SV430 )
          | ! [SY1426: $i] :
              ( ~ ( cType___24t @ SY1426 )
              | ( cType___24t @ ( happ @ ( happ @ SV272 @ SV430 ) @ SY1426 ) ) ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV272 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4140]) ).

thf(4316,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV173: $i] :
      ( ( ! [SY1313: $i,SY1314: $i] :
            ( ( ( happ @ SV173 @ SY1313 )
             != ( happ @ SV173 @ SY1314 ) )
            | ~ ( p @ ( happ @ ( happ @ SV273 @ SY1313 ) @ SY1314 ) )
            | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1313 @ SY1314 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4141]) ).

thf(4317,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ( ~ ! [SY1315: $i,SY1316: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
                  | ( ( happ @ SV173 @ SY1315 )
                    = ( happ @ SV173 @ SY1316 ) ) )
            | ~ ! [SY1317: $i,SY1318: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
                  | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4142]) ).

thf(4318,plain,
    ! [SV175: $i,SV334: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
          | ! [SY1362: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1362 )
              | ! [SY1363: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1363 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1362 @ SY1363 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1362 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1363 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4143]) ).

thf(4319,plain,
    ! [SV179: $i,SV10: $i] :
      ( ( ( ~ ( p @ SV10 ) )
        = $true )
      | ( ( ~ ( p @ SV179 ) )
        = $true )
      | ( ( p @ SV10 )
        = $true )
      | ( ( cProp___24t @ SV179 )
        = $false )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4144]) ).

thf(4320,plain,
    ! [SV180: $i,SV12: $i] :
      ( ( ( ~ ( p @ SV12 ) )
        = $true )
      | ( ( p @ SV180 )
        = $true )
      | ( ( p @ SV12 )
        = $true )
      | ( ( cProp___24t @ SV180 )
        = $false )
      | ( ( cProp___24t @ SV12 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4145]) ).

thf(4321,plain,
    ! [SV183: $i,SV335: $i,SV15: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV335 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SV335 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV335 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
        = $false )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4146]) ).

thf(4322,plain,
    ! [SV184: $i,SV336: $i,SV16: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV336 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SV336 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV336 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
        = $false )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4147]) ).

thf(4323,plain,
    ! [SV185: $i,SV337: $i,SV17: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV337 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SV337 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV337 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
        = $false )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4148]) ).

thf(4324,plain,
    ! [SV186: $i,SV338: $i,SV18: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV338 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SV338 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV338 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
        = $false )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4149]) ).

thf(4325,plain,
    ! [SV187: $i,SV339: $i,SV19: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV339 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SV339 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV339 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
        = $false )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4150]) ).

thf(4326,plain,
    ! [SV188: $i,SV340: $i,SV20: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV340 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SV340 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV340 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
        = $false )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4151]) ).

thf(4327,plain,
    ! [SV189: $i,SV341: $i,SV21: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV341 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SV341 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV341 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
        = $false )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4152]) ).

thf(4328,plain,
    ! [SV190: $i,SV342: $i,SV22: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV342 ) )
        = $true )
      | ( ( ! [SY1364: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1364 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SV342 ) @ SY1364 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV342 @ SY1364 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4153]) ).

thf(4329,plain,
    ! [SV191: $i,SV343: $i,SV23: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV343 ) )
        = $true )
      | ( ( ! [SY1365: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1365 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ SY1365 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SY1365 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4154]) ).

thf(4330,plain,
    ! [SV192: $i,SV344: $i,SV24: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV344 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV192 @ SV344 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV344 @ SV192 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV192 )
        = $false )
      | ( ( cType___24t @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4155]) ).

thf(4331,plain,
    ! [SV194: $i,SV345: $i,SV26: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV345 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SV345 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SV345 @ SV194 ) @ SV194 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
        = $false )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4156]) ).

thf(4332,plain,
    ! [SV195: $i,SV346: $i,SV27: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV346 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SV346 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SV346 ) @ SV195 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
        = $false )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4157]) ).

thf(4333,plain,
    ! [SV196: $i,SV347: $i,SV28: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV347 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SV196 @ SV347 ) @ SV196 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV196 )
        = $false )
      | ( ( cType___24t @ SV28 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4158]) ).

thf(4334,plain,
    ! [SV197: $i,SV348: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
          | ! [SY1366: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1366 )
              | ! [SY1367: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1367 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1366 @ SY1367 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1366 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1367 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4159]) ).

thf(4335,plain,
    ! [SV198: $i,SV349: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
          | ! [SY1368: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1368 )
              | ! [SY1369: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1369 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1368 @ SY1369 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1368 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1369 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4160]) ).

thf(4336,plain,
    ! [SV199: $i,SV350: $i,SV31: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV350 ) )
        = $true )
      | ( ( ! [SY1370: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1370 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SV350 ) @ SY1370 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SY1370 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV350 @ SY1370 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4161]) ).

thf(4337,plain,
    ! [SV200: $i,SV351: $i,SV32: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV351 ) )
        = $true )
      | ( ( ! [SY1371: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1371 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SV351 ) @ SY1371 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV351 @ SY1371 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4162]) ).

thf(4338,plain,
    ! [SV201: $i,SV352: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
          | ! [SY1372: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1372 )
              | ! [SY1373: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1373 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1372 @ SY1373 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1372 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1373 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4163]) ).

thf(4339,plain,
    ! [SV202: $i,SV353: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
          | ! [SY1374: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1374 )
              | ! [SY1375: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1375 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1374 @ SY1375 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1374 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1375 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4164]) ).

thf(4340,plain,
    ! [SV203: $i,SV354: $i,SV35: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV354 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SV354 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV354 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
        = $false )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4165]) ).

thf(4341,plain,
    ! [SV204: $i,SV355: $i,SV36: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV355 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SV355 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV355 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
        = $false )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4166]) ).

thf(4342,plain,
    ! [SV205: $i,SV356: $i,SV37: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV356 ) )
        = $true )
      | ( ( ! [SY1376: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1376 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SV356 ) @ SY1376 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV356 @ SY1376 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4167]) ).

thf(4343,plain,
    ! [SV206: $i,SV357: $i,SV38: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV357 ) )
        = $true )
      | ( ( ! [SY1377: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1377 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ SY1377 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SY1377 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4168]) ).

thf(4344,plain,
    ! [SV207: $i,SV358: $i,SV39: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV358 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV207 @ SV358 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV358 @ SV207 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV207 )
        = $false )
      | ( ( cType___24t @ SV39 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4169]) ).

thf(4345,plain,
    ! [SV209: $i,SV359: $i,SV41: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV359 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SV359 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SV359 ) @ SV359 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
        = $false )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4170]) ).

thf(4346,plain,
    ! [SV210: $i,SV360: $i,SV42: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV360 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SV360 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SV360 @ SV210 ) @ SV360 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
        = $false )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4171]) ).

thf(4347,plain,
    ! [SV211: $i,SV361: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
          | ! [SY1378: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1378 )
              | ! [SY1379: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1379 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1378 @ SY1379 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1378 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1379 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4172]) ).

thf(4348,plain,
    ! [SV212: $i,SV362: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
          | ! [SY1380: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1380 )
              | ! [SY1381: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1381 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1380 @ SY1381 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1380 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1381 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4173]) ).

thf(4349,plain,
    ! [SV213: $i,SV363: $i,SV45: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV363 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SV363 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SV363 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
        = $false )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4174]) ).

thf(4350,plain,
    ! [SV214: $i,SV364: $i,SV46: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV364 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SV364 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SV364 @ SV214 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
        = $false )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4175]) ).

thf(4351,plain,
    ! [SV215: $i,SV365: $i,SV47: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV365 ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SV365 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
        = $false )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4176]) ).

thf(4352,plain,
    ! [SV216: $i,SV366: $i,SV48: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4177]) ).

thf(4353,plain,
    ! [SV217: $i,SV367: $i,SV49: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV367 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SV217 @ SV367 ) @ SV217 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV217 )
        = $false )
      | ( ( cType___24t @ SV49 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4178]) ).

thf(4354,plain,
    ! [SV218: $i,SV368: $i,SV50: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 ) )
        = $true )
      | ( ( ! [SY1382: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1382 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SY1382 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SY1382 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4179]) ).

thf(4355,plain,
    ! [SV219: $i,SV369: $i,SV51: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV369 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SV219 @ SV369 ) @ SV369 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV219 )
        = $false )
      | ( ( cType___24t @ SV51 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4180]) ).

thf(4356,plain,
    ! [SV220: $i,SV370: $i,SV52: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 ) )
        = $true )
      | ( ( ! [SY1383: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1383 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SY1383 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SY1383 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4181]) ).

thf(4357,plain,
    ! [SV221: $i,SV371: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 ) )
        = $true )
      | ( ( ! [SY1384: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1384 )
              | ! [SY1385: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1385 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY1384 @ SY1385 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SY1384 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SY1385 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4182]) ).

thf(4358,plain,
    ! [SV222: $i,SV372: $i,SV54: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 ) )
        = $true )
      | ( ( ! [SY1386: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1386 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1386 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SY1386 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4183]) ).

thf(4359,plain,
    ! [SV223: $i,SV373: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 ) )
        = $true )
      | ( ( ! [SY1387: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1387 )
              | ! [SY1388: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1388 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1388 @ SY1387 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SY1387 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SY1388 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4184]) ).

thf(4360,plain,
    ! [SV224: $i,SV374: $i,SV56: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV374 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SV224 @ SV374 ) @ SV224 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV224 )
        = $false )
      | ( ( cType___24t @ SV56 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4185]) ).

thf(4361,plain,
    ! [SV225: $i,SV375: $i,SV57: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV375 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SV375 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV375 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
        = $false )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4186]) ).

thf(4362,plain,
    ! [SV227: $i,SV376: $i,SV59: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV376 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SV376 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV376 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
        = $false )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4187]) ).

thf(4363,plain,
    ! [SV228: $i,SV377: $i,SV60: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV377 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
        = $false )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4188]) ).

thf(4364,plain,
    ! [SV229: $i,SV378: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 ) )
        = $true )
      | ( ( ! [SY1389: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1389 )
              | ! [SY1390: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1390 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY1389 @ SY1390 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SY1389 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SY1390 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4189]) ).

thf(4365,plain,
    ! [SV230: $i,SV379: $i,SV62: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV379 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SV379 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SV379 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
        = $false )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4190]) ).

thf(4366,plain,
    ! [SV231: $i,SV380: $i,SV63: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV380 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SV380 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SV380 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
        = $false )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4191]) ).

thf(4367,plain,
    ! [SV232: $i,SV381: $i,SV64: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV381 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SV381 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SV381 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
        = $false )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4192]) ).

thf(4368,plain,
    ! [SV233: $i,SV382: $i,SV65: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV382 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SV382 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV382 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
        = $false )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4193]) ).

thf(4369,plain,
    ! [SV234: $i,SV383: $i,SV66: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV383 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
        = $false )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4194]) ).

thf(4370,plain,
    ! [SV235: $i,SV384: $i,SV67: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 ) )
        = $true )
      | ( ( ! [SY1391: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1391 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SY1391 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SY1391 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SY1391 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4195]) ).

thf(4371,plain,
    ! [SV236: $i,SV385: $i,SV68: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV385 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SV236 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SV236 @ SV385 ) @ SV385 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV236 )
        = $false )
      | ( ( cType___24t @ SV68 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4196]) ).

thf(4372,plain,
    ! [SV237: $i,SV386: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 ) )
        = $true )
      | ( ( ! [SY1392: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1392 )
              | ! [SY1393: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1393 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY1392 @ SY1393 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SY1392 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SY1393 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4197]) ).

thf(4373,plain,
    ! [SV238: $i,SV387: $i,SV70: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV387 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SV238 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SV238 @ SV387 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV238 )
        = $false )
      | ( ( cType___24t @ SV70 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4198]) ).

thf(4374,plain,
    ! [SV239: $i,SV388: $i,SV71: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 ) )
        = $true )
      | ( ( ! [SY1394: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1394 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SY1394 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4199]) ).

thf(4375,plain,
    ! [SV240: $i,SV389: $i,SV72: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV389 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SV389 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SV240 @ SV389 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV240 )
        = $false )
      | ( ( cType___24t @ SV72 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4200]) ).

thf(4376,plain,
    ! [SV241: $i,SV390: $i,SV73: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 ) )
        = $true )
      | ( ( ! [SY1395: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1395 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SY1395 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SY1395 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4201]) ).

thf(4377,plain,
    ! [SV242: $i,SV391: $i,SV74: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4202]) ).

thf(4378,plain,
    ! [SV78: $i] :
      ( ( ( ~ ! [SY657: $i] :
                ( ~ ( cProp___24t @ SY657 )
                | ( p @ SV78 )
                | ~ ( p @ SV78 )
                | ( p @ SY657 ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4203]) ).

thf(4379,plain,
    ! [SV78: $i] :
      ( ( ( ~ ! [SY658: $i] :
                ( ~ ( cProp___24t @ SY658 )
                | ( p @ SV78 )
                | ~ ( p @ SY658 )
                | ( p @ SY658 ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4203]) ).

thf(4380,plain,
    ! [SV78: $i] :
      ( ( ( ~ ! [SY659: $i] :
                ( ~ ( cProp___24t @ SY659 )
                | ~ ( p @ SY659 )
                | ~ ( p @ SV78 )
                | ( p @ SY659 ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4204]) ).

thf(4381,plain,
    ! [SV78: $i] :
      ( ( ( ~ ! [SX1: $i] :
                ( ~ ( cProp___24t @ SX1 )
                | ~ ( p @ SX1 )
                | ~ ( p @ SX1 )
                | ( p @ SX1 ) ) )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4204]) ).

thf(4382,plain,
    ! [SV244: $i] :
      ( ( ( cType___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4205]) ).

thf(4383,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4206]) ).

thf(4384,plain,
    ! [SV245: $i,SV392: $i] :
      ( ( ( ~ ( cType___24t @ SV392 ) )
        = $true )
      | ( ( ! [SY1396: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ SY1396 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ ( happ @ ( happ @ SV245 @ SV392 ) @ SY1396 ) ) ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV245 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4207]) ).

thf(4385,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ~ ! [SY1258: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1258 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1258 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1258 ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4208]) ).

thf(4386,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ~ ! [SY1259: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1259 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1259 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1259 )
                | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4208]) ).

thf(4387,plain,
    ! [SV301: $i,SV276: $i,SV80: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV276 @ SV301 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV276 ) @ SV301 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4209]) ).

thf(4388,plain,
    ! [SV302: $i,SV277: $i,SV80: $i] :
      ( ( ( p @ ( happ @ ( happ @ ( happ @ cCoq_2eRelations_2eRelation__Definitions_2esame__relation @ SV80 ) @ SV277 ) @ SV302 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV80 @ SV277 @ SV302 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4210]) ).

thf(4389,plain,
    ! [SV431: $i,SV393: $i,SV161: $i,SV130: $i,SV81: $i] :
      ( ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV393 @ SV431 )
        | ( p @ ( happ @ ( happ @ SV130 @ SV393 ) @ SV431 ) )
        | ( p @ ( happ @ ( happ @ SV161 @ SV393 ) @ SV431 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4213]) ).

thf(4390,plain,
    ! [SV161: $i,SV81: $i,SV130: $i] :
      ( ( ~ ! [SY1093: $i,SY1094: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
              | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4214]) ).

thf(4391,plain,
    ! [SV130: $i,SV81: $i,SV161: $i] :
      ( ( ~ ! [SY1095: $i,SY1096: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
              | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4214]) ).

thf(4392,plain,
    ! [SV131: $i,SV82: $i,SV432: $i,SV394: $i,SV162: $i] :
      ( ( ( ( happ @ SV162 @ SV394 )
         != ( happ @ SV162 @ SV432 ) )
        | ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV394 @ SV432 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4215]) ).

thf(4393,plain,
    ! [SV433: $i,SV395: $i,SV162: $i,SV131: $i,SV82: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV395 @ SV433 )
        | ( ( happ @ SV162 @ SV395 )
          = ( happ @ SV162 @ SV433 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4216]) ).

thf(4394,plain,
    ! [SV249: $i,SV396: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
          | ! [SY1400: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1400 )
              | ~ ( ~ ! [SY1401: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1401 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1401 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1401 ) ) )
                  | ~ ! [SY1402: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1402 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1402 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1402 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4217]) ).

thf(4395,plain,
    ! [SV397: $i,SV303: $i,SV132: $i,SV84: $i] :
      ( ( ( ~ ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV303 @ SV397 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV132 @ SV303 ) @ SV397 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4218]) ).

thf(4396,plain,
    ! [SV84: $i,SV398: $i,SV304: $i,SV132: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV132 @ SV304 ) @ SV398 ) ) )
        = $true )
      | ( ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV304 @ SV398 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4219]) ).

thf(4397,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ~ ! [SY1266: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1266 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1266 )
                | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
                | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1266 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4220]) ).

thf(4398,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ~ ! [SY1267: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1267 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1267 )
                | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1267 ) )
                | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4220]) ).

thf(4399,plain,
    ! [SV251: $i] :
      ( ( ( cType___24t @ ( sK12_Vv__CANONICAL__0 @ SV251 ) )
        = $true )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4221]) ).

thf(4400,plain,
    ! [SV251: $i] :
      ( ( ( ~ ( cType___24t @ ( happ @ SV251 @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) ) )
        = $true )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4222]) ).

thf(4401,plain,
    ! [SV252: $i,SV399: $i] :
      ( ( ( ~ ( cType___24t @ SV399 ) )
        = $true )
      | ( ( cType___24t @ ( happ @ SV252 @ SV399 ) )
        = $true )
      | ( ( c_24__type__28___24t @ SV252 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4223]) ).

thf(4402,plain,
    ! [SV86: $i,SV305: $i,SV400: $i,SV133: $i] :
      ( ( ( ~ ( p @ ( happ @ SV133 @ SV400 ) )
          | ( p @ ( happ @ SV305 @ SV400 ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV305 @ SV400 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4224]) ).

thf(4403,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ! [SY953: $i,SY954: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY953 @ SY954 )
            | ( p @ ( happ @ SV133 @ SY954 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4225]) ).

thf(4404,plain,
    ! [SV133: $i,SV86: $i] :
      ( ( ! [SY955: $i,SY956: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SY955 @ SY956 )
            | ~ ( p @ ( happ @ SY955 @ SY956 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4226]) ).

thf(4405,plain,
    ! [SV401: $i,SV306: $i,SV134: $i,SV87: $i] :
      ( ( ( ~ ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV306 @ SV401 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV134 @ SV401 ) @ SV306 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4227]) ).

thf(4406,plain,
    ! [SV87: $i,SV307: $i,SV402: $i,SV134: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV134 @ SV402 ) @ SV307 ) ) )
        = $true )
      | ( ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV307 @ SV402 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4228]) ).

thf(4407,plain,
    ! [SV308: $i,SV280: $i,SV88: $i] :
      ( ( ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV280 @ SV308 )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV280 @ SV308 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4229]) ).

thf(4408,plain,
    ! [SV253: $i,SV403: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1403: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1403 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1403 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1403 ) ) ) )
              | ~ ! [SY1404: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1404 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1404 ) ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1404 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4231]) ).

thf(4409,plain,
    ! [SV434: $i,SV404: $i,SV163: $i,SV135: $i,SV90: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV404 @ SV434 )
        | ( p @ ( happ @ ( happ @ SV135 @ SV404 ) @ SV434 ) )
        | ( p @ ( happ @ ( happ @ SV163 @ SV404 ) @ SV434 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4232]) ).

thf(4410,plain,
    ! [SV163: $i,SV90: $i,SV135: $i] :
      ( ( ~ ! [SY1103: $i,SY1104: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4233]) ).

thf(4411,plain,
    ! [SV135: $i,SV90: $i,SV163: $i] :
      ( ( ~ ! [SY1105: $i,SY1106: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
              | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4233]) ).

thf(4412,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ~ ~ ( ~ ! [SY1272: $i] :
                      ( ~ ( cProp___24t @ SY1272 )
                      | ( p @ SV91 )
                      | ~ ( p @ SV91 )
                      | ( p @ SV254 )
                      | ( p @ SY1272 ) )
                | ~ ! [SY1273: $i] :
                      ( ~ ( cProp___24t @ SY1273 )
                      | ( p @ SV91 )
                      | ~ ( p @ SY1273 )
                      | ( p @ SV254 )
                      | ( p @ SY1273 ) ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4234]) ).

thf(4413,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ~ ( ~ ! [SY1274: $i] :
                      ( ~ ( cProp___24t @ SY1274 )
                      | ~ ( p @ SV254 )
                      | ~ ( p @ SV91 )
                      | ( p @ SV254 )
                      | ( p @ SY1274 ) )
                | ~ ! [SY1275: $i] :
                      ( ~ ( cProp___24t @ SY1275 )
                      | ~ ( p @ SV254 )
                      | ~ ( p @ SY1275 )
                      | ( p @ SV254 )
                      | ( p @ SY1275 ) ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4234]) ).

thf(4414,plain,
    ! [SV92: $i,SV435: $i,SV164: $i,SV405: $i,SV136: $i] :
      ( ( ~ ( p @ ( happ @ SV136 @ SV405 ) )
        | ~ ( p @ ( happ @ SV164 @ SV435 ) )
        | ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV405 @ SV435 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4235]) ).

thf(4415,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ~ ! [SY1109: $i] :
              ( ! [SY1110: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
              | ( p @ ( happ @ SV136 @ SY1109 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4236]) ).

thf(4416,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ~ ! [SY1111: $i,SY1112: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
              | ( p @ ( happ @ SV164 @ SY1112 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4236]) ).

thf(4417,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) )
        = $false )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4237]) ).

thf(4418,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SV282 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) ) )
        = $false )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4237]) ).

thf(4419,plain,
    ! [SV283: $i,SV436: $i,SV256: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SV436 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SV283 @ SV436 ) ) )
        = $true )
      | ( ( c_24__type__11748___24t @ SV256 @ SV283 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4238]) ).

thf(4420,plain,
    ! [SV437: $i,SV406: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV406 @ SV437 )
        | ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV406 ) @ SV437 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4239]) ).

thf(4421,plain,
    ! [SV438: $i,SV407: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV407 ) @ SV438 ) )
        | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV407 @ SV438 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4240]) ).

thf(4422,plain,
    ! [SV311: $i,SV285: $i,SV94: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV285 @ SV311 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV311 @ SV285 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV285 @ SV311 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4241]) ).

thf(4423,plain,
    ! [SV439: $i,SV94: $i] :
      ( ( ! [SY1427: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV439 @ SY1427 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV439 @ SY1427 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4242]) ).

thf(4424,plain,
    ! [SV440: $i,SV94: $i] :
      ( ( ! [SY1428: $i] :
            ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV440 @ SY1428 )
            | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SY1428 @ SV440 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4243]) ).

thf(4425,plain,
    ! [SV257: $i,SV286: $i] :
      ( ( ( p @ SV286 )
        = $false )
      | ( ( p @ ( c_24__prop__35358___24a2 @ SV257 @ SV286 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4244]) ).

thf(4426,plain,
    ! [SV95: $i,SV312: $i,SV408: $i,SV138: $i] :
      ( ( ( ~ ( p @ ( happ @ SV138 @ SV408 ) )
          | ~ ( p @ ( happ @ SV312 @ SV408 ) ) )
        = $true )
      | ( ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV312 @ SV408 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4245]) ).

thf(4427,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ! [SY982: $i,SY983: $i] :
            ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY982 @ SY983 )
            | ( p @ ( happ @ SV138 @ SY983 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4246]) ).

thf(4428,plain,
    ! [SV138: $i,SV95: $i] :
      ( ( ! [SY984: $i,SY985: $i] :
            ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SY984 @ SY985 )
            | ( p @ ( happ @ SY984 @ SY985 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4247]) ).

thf(4429,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ~ ! [SY1281: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1281 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1281 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1281 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4248]) ).

thf(4430,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ~ ! [SY1282: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1282 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1282 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1282 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4248]) ).

thf(4431,plain,
    ! [SV409: $i,SV313: $i,SV139: $i,SV97: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV313 @ SV409 ) )
        = $true )
      | ( ( ( SV313 = SV409 )
          | ( p @ ( happ @ ( happ @ SV139 @ SV313 ) @ SV409 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4249]) ).

thf(4432,plain,
    ! [SV139: $i,SV97: $i] :
      ( ( ! [SY988: $i,SY989: $i] :
            ( ( SY988 != SY989 )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY988 @ SY989 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4250]) ).

thf(4433,plain,
    ! [SV97: $i,SV139: $i] :
      ( ( ! [SY990: $i,SY991: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV139 @ SY990 ) @ SY991 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SY990 @ SY991 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4251]) ).

thf(4434,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( t @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) @ SV98 )
          | ~ ~ ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
                | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                      | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4252]) ).

thf(4435,plain,
    ! [SV315: $i,SV289: $i,SV98: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false )
      | ( ( ! [SY1349: $i] :
              ( ~ ( t @ SY1349 @ SV98 )
              | ! [SY1350: $i] :
                  ( ~ ( t @ SY1350 @ SV98 )
                  | ~ ( p @ ( happ @ ( happ @ SV289 @ SY1349 ) @ SY1350 ) )
                  | ( p @ ( happ @ ( happ @ SV315 @ SY1349 ) @ SY1350 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4253]) ).

thf(4436,plain,
    ! [SV410: $i,SV316: $i,SV140: $i,SV99: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV316 @ SV410 ) )
        = $true )
      | ( ( ( p @ ( happ @ ( happ @ SV140 @ SV316 ) @ SV410 ) )
          | ( p @ ( happ @ ( happ @ SV140 @ SV410 ) @ SV316 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4254]) ).

thf(4437,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ! [SY994: $i,SY995: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY994 ) @ SY995 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY994 @ SY995 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4255]) ).

thf(4438,plain,
    ! [SV99: $i,SV140: $i] :
      ( ( ! [SY996: $i,SY997: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY997 ) @ SY996 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SY996 @ SY997 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4256]) ).

thf(4439,plain,
    ! [SV100: $i,SV166: $i,SV441: $i,SV411: $i,SV141: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV141 @ SV411 ) @ SV441 ) )
        | ( p @ ( happ @ ( happ @ SV166 @ SV411 ) @ SV441 ) )
        | ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV411 @ SV441 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4257]) ).

thf(4440,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ! [SY1119: $i,SY1120: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
              | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4258]) ).

thf(4441,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ! [SY1121: $i,SY1122: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
              | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4258]) ).

thf(4442,plain,
    ! [SV290: $i,SV317: $i,SV101: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) )
          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SV317 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) ) )
        = $false )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4259]) ).

thf(4443,plain,
    ! [SV318: $i,SV291: $i,SV101: $i] :
      ( ( ( c_24__type__11699___24t @ SV101 @ SV291 @ SV318 )
        = $false )
      | ( ( ! [SY1352: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SY1352 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SV318 @ SY1352 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4260]) ).

thf(4444,plain,
    ! [SV442: $i,SV412: $i,SV167: $i,SV142: $i,SV102: $i] :
      ( ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV412 @ SV442 )
        | ( p @ ( happ @ ( happ @ SV167 @ SV412 ) @ SV442 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4261]) ).

thf(4445,plain,
    ! [SV142: $i,SV102: $i,SV443: $i,SV413: $i,SV167: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV167 @ SV413 ) @ SV443 ) )
        | ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV413 @ SV443 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4262]) ).

thf(4446,plain,
    ! [SV319: $i,SV292: $i,SV103: $i] :
      ( ( ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV292 @ SV319 ) )
        = $false )
      | ( ( ( p @ SV292 )
          | ( p @ SV319 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4263]) ).

thf(4447,plain,
    ! [SV103: $i,SV444: $i] :
      ( ( ~ ( p @ SV444 )
        | ! [SY1429: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV444 @ SY1429 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4264]) ).

thf(4448,plain,
    ! [SV445: $i,SV103: $i] :
      ( ( ! [SY1430: $i] :
            ( ~ ( p @ SY1430 )
            | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV445 @ SY1430 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4265]) ).

thf(4449,plain,
    ! [SV104: $i,SV143: $i,SV446: $i,SV414: $i,SV168: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) )
        | ~ ( p @ ( happ @ SV143 @ SV414 ) )
        | ~ ( p @ ( happ @ SV143 @ SV446 ) )
        | ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4266]) ).

thf(4450,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                    ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                    | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
              | ~ ! [SY1131: $i] :
                    ( ! [SY1132: $i] :
                        ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                    | ( p @ ( happ @ SV143 @ SY1131 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4267]) ).

thf(4451,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ! [SY1133: $i,SY1134: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
              | ( p @ ( happ @ SV143 @ SY1134 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4267]) ).

thf(4452,plain,
    ! [SV105: $i,SV320: $i,SV293: $i] :
      ( ( ( SV293 = SV320 )
        = $false )
      | ( ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV293 @ SV320 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4268]) ).

thf(4453,plain,
    ! [SV321: $i,SV294: $i,SV105: $i] :
      ( ( ( p @ ( c_24__prop__35353___24a3 @ SV105 @ SV294 @ SV321 ) )
        = $false )
      | ( ( SV294 = SV321 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4269]) ).

thf(4454,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4270]) ).

thf(4455,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4270]) ).

thf(4456,plain,
    ! [SV296: $i,SV447: $i,SV261: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV447 )
          | ! [SY1431: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1431 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SV447 ) @ SY1431 ) ) ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4271]) ).

thf(4457,plain,
    ! [SV415: $i,SV322: $i,SV144: $i,SV106: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV322 @ SV415 ) )
        = $true )
      | ( ( ( p @ ( happ @ ( happ @ SV144 @ SV415 ) @ SV322 ) )
          | ( SV322 = SV415 )
          | ( p @ ( happ @ ( happ @ SV144 @ SV322 ) @ SV415 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4272]) ).

thf(4458,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ! [SY1021: $i,SY1022: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1022 ) @ SY1021 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1021 @ SY1022 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4273]) ).

thf(4459,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ( ~ ! [SY1023: $i,SY1024: $i] :
                  ( ( SY1023 != SY1024 )
                  | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
            | ~ ! [SY1025: $i,SY1026: $i] :
                  ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
                  | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4274]) ).

thf(4460,plain,
    ! [SV448: $i,SV416: $i,SV169: $i,SV145: $i,SV107: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV416 @ SV448 )
        | ( p @ ( happ @ SV416 @ ( happ @ SV169 @ SV448 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4275]) ).

thf(4461,plain,
    ! [SV145: $i,SV107: $i,SV449: $i,SV169: $i,SV417: $i] :
      ( ( ~ ( p @ ( happ @ SV417 @ ( happ @ SV169 @ SV449 ) ) )
        | ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV417 @ SV449 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4276]) ).

thf(4462,plain,
    ! [SV108: $i,SV146: $i,SV418: $i,SV323: $i] :
      ( ( ( ( SV323 != SV418 )
          | ~ ( p @ ( happ @ SV146 @ SV323 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV323 @ SV418 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4277]) ).

thf(4463,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ! [SY1034: $i,SY1035: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1034 @ SY1035 )
            | ( SY1034 = SY1035 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4278]) ).

thf(4464,plain,
    ! [SV146: $i,SV108: $i] :
      ( ( ! [SY1036: $i] :
            ( ! [SY1037: $i] :
                ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SY1036 @ SY1037 )
            | ( p @ ( happ @ SV146 @ SY1036 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4279]) ).

thf(4465,plain,
    ! [SV262: $i] :
      ( ( ( cType___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4280]) ).

thf(4466,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
              | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                    | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4281]) ).

thf(4467,plain,
    ! [SV263: $i,SV419: $i] :
      ( ( ( ~ ( cType___24t @ SV419 ) )
        = $true )
      | ( ( ! [SY1415: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1415 )
              | ! [SY1416: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1416 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SY1415 ) @ SY1416 ) ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4282]) ).

thf(4468,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ~ ! [SY1290: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1290 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1290 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1290 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4283]) ).

thf(4469,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ~ ! [SY1291: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1291 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1291 )
                | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1291 ) )
                | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4283]) ).

thf(4470,plain,
    ! [SV265: $i] :
      ( ( ( cType___24t @ ( sK8_Vv__CANONICAL__0 @ SV265 ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4284]) ).

thf(4471,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) )
              | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                    | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                          | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4285]) ).

thf(4472,plain,
    ! [SV266: $i,SV420: $i] :
      ( ( ( ~ ( cType___24t @ SV420 ) )
        = $true )
      | ( ( ! [SY1417: $i] :
              ( ~ ( cType___24t @ SY1417 )
              | ! [SY1418: $i] :
                  ( ~ ( cType___24t @ SY1418 )
                  | ! [SY1419: $i] :
                      ( ~ ( cType___24t @ SY1419 )
                      | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SY1417 ) @ SY1418 ) @ SY1419 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4286]) ).

thf(4473,plain,
    ! [SV110: $i,SV170: $i,SV450: $i,SV421: $i,SV147: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV147 @ SV421 ) @ SV450 ) )
        | ~ ( p @ ( happ @ ( happ @ SV170 @ SV421 ) @ SV450 ) )
        | ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV421 @ SV450 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4287]) ).

thf(4474,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ! [SY1141: $i,SY1142: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
              | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4288]) ).

thf(4475,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ! [SY1143: $i,SY1144: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
              | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4288]) ).

thf(4476,plain,
    ! [SV422: $i,SV324: $i,SV148: $i,SV111: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV324 @ SV422 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV148 @ SV422 ) @ SV324 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4289]) ).

thf(4477,plain,
    ! [SV111: $i,SV325: $i,SV423: $i,SV148: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV148 @ SV423 ) @ SV325 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV325 @ SV423 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4290]) ).

thf(4478,plain,
    ! [SV112: $i,SV326: $i,SV297: $i] :
      ( ( ( ~ ( p @ SV297 ) )
        = $true )
      | ( ( ~ ( p @ SV326 ) )
        = $true )
      | ( ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV297 @ SV326 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4291]) ).

thf(4479,plain,
    ! [SV451: $i,SV112: $i] :
      ( ( ! [SY1432: $i] :
            ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV451 @ SY1432 ) )
        | ( p @ SV451 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4292]) ).

thf(4480,plain,
    ! [SV452: $i,SV112: $i] :
      ( ( ! [SY1433: $i] :
            ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV452 @ SY1433 ) )
            | ( p @ SY1433 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4293]) ).

thf(4481,plain,
    ! [SV424: $i,SV327: $i,SV149: $i,SV113: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV327 @ SV424 ) )
        = $true )
      | ( ( ( p @ ( happ @ SV149 @ SV424 ) )
          | ( p @ ( happ @ SV327 @ SV424 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4294]) ).

thf(4482,plain,
    ! [SV113: $i,SV149: $i] :
      ( ( ! [SY1051: $i,SY1052: $i] :
            ( ~ ( p @ ( happ @ SV149 @ SY1052 ) )
            | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1051 @ SY1052 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4295]) ).

thf(4483,plain,
    ! [SV149: $i,SV113: $i] :
      ( ( ! [SY1053: $i,SY1054: $i] :
            ( ~ ( p @ ( happ @ SY1053 @ SY1054 ) )
            | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SY1053 @ SY1054 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4296]) ).

thf(4484,plain,
    ! [SV114: $i,SV453: $i] :
      ( ( ( p @ SV453 )
        | ! [SY1434: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV453 @ SY1434 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4297]) ).

thf(4485,plain,
    ! [SV454: $i,SV114: $i] :
      ( ( ! [SY1435: $i] :
            ( ~ ( p @ SY1435 )
            | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV454 @ SY1435 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4298]) ).

thf(4486,plain,
    ! [SV328: $i,SV298: $i,SV114: $i] :
      ( ( ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV298 @ SV328 ) )
        = $false )
      | ( ( ~ ( p @ SV298 )
          | ( p @ SV328 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4299]) ).

thf(4487,plain,
    ! [SV267: $i,SV425: $i,SV115: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
          | ! [SY1421: $i] :
              ( ~ ( t @ SY1421 @ SV115 )
              | ~ ( ~ ! [SY1422: $i] :
                        ( ~ ( t @ SY1422 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1422 ) )
                        | ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1422 ) ) )
                  | ~ ! [SY1423: $i] :
                        ( ~ ( t @ SY1423 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1423 ) )
                        | ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1423 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4300]) ).

thf(4488,plain,
    ! [SV116: $i,SV329: $i,SV426: $i,SV150: $i] :
      ( ( ( ~ ( p @ ( happ @ SV150 @ SV426 ) )
          | ~ ( p @ ( happ @ SV329 @ SV426 ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV329 @ SV426 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4301]) ).

thf(4489,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ! [SY1057: $i,SY1058: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1057 @ SY1058 )
            | ( p @ ( happ @ SV150 @ SY1058 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4302]) ).

thf(4490,plain,
    ! [SV150: $i,SV116: $i] :
      ( ( ! [SY1059: $i,SY1060: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SY1059 @ SY1060 )
            | ( p @ ( happ @ SY1059 @ SY1060 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4303]) ).

thf(4491,plain,
    ! [SV268: $i,SV427: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1424: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1424 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1424 ) ) ) )
              | ~ ! [SY1425: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1425 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1425 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1425 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4304]) ).

thf(4492,plain,
    ! [SV455: $i,SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ! [SY1436: $i] :
            ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV455 @ SY1436 )
            | ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV455 ) ) @ ( happ @ SV171 @ SY1436 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4305]) ).

thf(4493,plain,
    ! [SV151: $i,SV118: $i,SV456: $i,SV171: $i,SV269: $i] :
      ( ( ! [SY1437: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV456 ) ) @ ( happ @ SV171 @ SY1437 ) ) )
            | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV456 @ SY1437 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4306]) ).

thf(4494,plain,
    ! [SV457: $i,SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ! [SY1438: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV457 @ SY1438 )
            | ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV457 ) ) @ ( happ @ SV172 @ SY1438 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4307]) ).

thf(4495,plain,
    ! [SV152: $i,SV119: $i,SV458: $i,SV172: $i,SV270: $i] :
      ( ( ! [SY1439: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV458 ) ) @ ( happ @ SV172 @ SY1439 ) ) )
            | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV458 @ SY1439 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4308]) ).

thf(4496,plain,
    ! [SV120: $i,SV330: $i,SV299: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV299 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) )
          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV330 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) ) )
        = $false )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4309]) ).

thf(4497,plain,
    ! [SV331: $i,SV300: $i,SV120: $i] :
      ( ( ( c_24__type__11787___24t @ SV120 @ SV300 @ SV331 )
        = $false )
      | ( ( ! [SY1359: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SY1359 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV331 @ SY1359 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4310]) ).

thf(4498,plain,
    ! [SV153: $i,SV121: $i,SV428: $i,SV332: $i] :
      ( ( ( SV332 != SV428 )
        = $true )
      | ( ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV332 @ SV428 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4311]) ).

thf(4499,plain,
    ! [SV429: $i,SV333: $i,SV153: $i,SV121: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV333 @ SV429 ) ) )
        = $true )
      | ( ( SV333 = SV429 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4312]) ).

thf(4500,plain,
    ! [SV271: $i] :
      ( ( ( cType___24t @ ( sK6_Vv__CANONICAL__0 @ SV271 ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4313]) ).

thf(4501,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) )
              | ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4314]) ).

thf(4502,plain,
    ! [SV272: $i,SV430: $i] :
      ( ( ( ~ ( cType___24t @ SV430 ) )
        = $true )
      | ( ( ! [SY1426: $i] :
              ( ~ ( cType___24t @ SY1426 )
              | ( cType___24t @ ( happ @ ( happ @ SV272 @ SV430 ) @ SY1426 ) ) ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV272 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4315]) ).

thf(4503,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV459: $i,SV173: $i] :
      ( ( ! [SY1440: $i] :
            ( ( ( happ @ SV173 @ SV459 )
             != ( happ @ SV173 @ SY1440 ) )
            | ~ ( p @ ( happ @ ( happ @ SV273 @ SV459 ) @ SY1440 ) )
            | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV459 @ SY1440 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4316]) ).

thf(4504,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ! [SY1315: $i,SY1316: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
              | ( ( happ @ SV173 @ SY1315 )
                = ( happ @ SV173 @ SY1316 ) ) )
        | ~ ! [SY1317: $i,SY1318: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
              | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4317]) ).

thf(4505,plain,
    ! [SV175: $i,SV334: $i,SV5: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
          | ! [SY1362: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1362 )
              | ! [SY1363: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1363 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1362 @ SY1363 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1362 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1363 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4318]) ).

thf(4506,plain,
    ! [SV179: $i,SV10: $i] :
      ( ( ( p @ SV10 )
        = $false )
      | ( ( ~ ( p @ SV179 ) )
        = $true )
      | ( ( p @ SV10 )
        = $true )
      | ( ( cProp___24t @ SV179 )
        = $false )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4319]) ).

thf(4507,plain,
    ! [SV180: $i,SV12: $i] :
      ( ( ( p @ SV12 )
        = $false )
      | ( ( p @ SV180 )
        = $true )
      | ( ( p @ SV12 )
        = $true )
      | ( ( cProp___24t @ SV180 )
        = $false )
      | ( ( cProp___24t @ SV12 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4320]) ).

thf(4508,plain,
    ! [SV183: $i,SV335: $i,SV15: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV335 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SV335 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV335 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
        = $false )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4321]) ).

thf(4509,plain,
    ! [SV184: $i,SV336: $i,SV16: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV336 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SV336 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV336 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
        = $false )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4322]) ).

thf(4510,plain,
    ! [SV185: $i,SV337: $i,SV17: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV337 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SV337 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV337 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
        = $false )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4323]) ).

thf(4511,plain,
    ! [SV186: $i,SV338: $i,SV18: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV338 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SV338 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV338 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
        = $false )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4324]) ).

thf(4512,plain,
    ! [SV187: $i,SV339: $i,SV19: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV339 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SV339 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV339 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
        = $false )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4325]) ).

thf(4513,plain,
    ! [SV188: $i,SV340: $i,SV20: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV340 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SV340 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV340 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
        = $false )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4326]) ).

thf(4514,plain,
    ! [SV189: $i,SV341: $i,SV21: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV341 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SV341 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV341 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
        = $false )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4327]) ).

thf(4515,plain,
    ! [SV190: $i,SV342: $i,SV22: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV342 )
        = $false )
      | ( ( ! [SY1364: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SY1364 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SV342 ) @ SY1364 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV342 @ SY1364 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4328]) ).

thf(4516,plain,
    ! [SV191: $i,SV343: $i,SV23: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV343 )
        = $false )
      | ( ( ! [SY1365: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SY1365 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ SY1365 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SY1365 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4329]) ).

thf(4517,plain,
    ! [SV192: $i,SV344: $i,SV24: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV344 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV24 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV192 @ SV344 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV24 @ SV344 @ SV192 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV24 @ SV192 )
        = $false )
      | ( ( cType___24t @ SV24 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4330]) ).

thf(4518,plain,
    ! [SV194: $i,SV345: $i,SV26: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV345 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SV345 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SV345 @ SV194 ) @ SV194 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
        = $false )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4331]) ).

thf(4519,plain,
    ! [SV195: $i,SV346: $i,SV27: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV346 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SV346 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SV346 ) @ SV195 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
        = $false )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4332]) ).

thf(4520,plain,
    ! [SV196: $i,SV347: $i,SV28: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV347 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV28 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV28 @ SV196 @ SV347 ) @ SV196 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV28 @ SV196 )
        = $false )
      | ( ( cType___24t @ SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4333]) ).

thf(4521,plain,
    ! [SV197: $i,SV348: $i,SV29: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
          | ! [SY1366: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1366 )
              | ! [SY1367: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1367 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1366 @ SY1367 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1366 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1367 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4334]) ).

thf(4522,plain,
    ! [SV198: $i,SV349: $i,SV30: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
          | ! [SY1368: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1368 )
              | ! [SY1369: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1369 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1368 @ SY1369 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1368 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1369 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4335]) ).

thf(4523,plain,
    ! [SV199: $i,SV350: $i,SV31: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV350 )
        = $false )
      | ( ( ! [SY1370: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SY1370 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SV350 ) @ SY1370 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SY1370 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV350 @ SY1370 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4336]) ).

thf(4524,plain,
    ! [SV200: $i,SV351: $i,SV32: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV351 )
        = $false )
      | ( ( ! [SY1371: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SY1371 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SV351 ) @ SY1371 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV351 @ SY1371 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4337]) ).

thf(4525,plain,
    ! [SV201: $i,SV352: $i,SV33: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
          | ! [SY1372: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1372 )
              | ! [SY1373: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1373 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1372 @ SY1373 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1372 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1373 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4338]) ).

thf(4526,plain,
    ! [SV202: $i,SV353: $i,SV34: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
          | ! [SY1374: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1374 )
              | ! [SY1375: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1375 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1374 @ SY1375 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1374 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1375 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4339]) ).

thf(4527,plain,
    ! [SV203: $i,SV354: $i,SV35: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV354 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SV354 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV354 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
        = $false )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4340]) ).

thf(4528,plain,
    ! [SV204: $i,SV355: $i,SV36: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV355 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SV355 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV355 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
        = $false )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4341]) ).

thf(4529,plain,
    ! [SV205: $i,SV356: $i,SV37: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV356 )
        = $false )
      | ( ( ! [SY1376: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SY1376 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SV356 ) @ SY1376 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV356 @ SY1376 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4342]) ).

thf(4530,plain,
    ! [SV206: $i,SV357: $i,SV38: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV357 )
        = $false )
      | ( ( ! [SY1377: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SY1377 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ SY1377 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SY1377 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4343]) ).

thf(4531,plain,
    ! [SV207: $i,SV358: $i,SV39: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV358 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV39 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV207 @ SV358 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV39 @ SV358 @ SV207 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV39 @ SV207 )
        = $false )
      | ( ( cType___24t @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4344]) ).

thf(4532,plain,
    ! [SV209: $i,SV359: $i,SV41: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV359 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SV359 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SV359 ) @ SV359 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
        = $false )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4345]) ).

thf(4533,plain,
    ! [SV210: $i,SV360: $i,SV42: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV360 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SV360 ) )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SV360 @ SV210 ) @ SV360 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
        = $false )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4346]) ).

thf(4534,plain,
    ! [SV211: $i,SV361: $i,SV43: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
          | ! [SY1378: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1378 )
              | ! [SY1379: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1379 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1378 @ SY1379 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1378 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1379 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4347]) ).

thf(4535,plain,
    ! [SV212: $i,SV362: $i,SV44: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
          | ! [SY1380: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1380 )
              | ! [SY1381: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1381 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1380 @ SY1381 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1380 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1381 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4348]) ).

thf(4536,plain,
    ! [SV213: $i,SV363: $i,SV45: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV363 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SV363 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SV363 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
        = $false )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4349]) ).

thf(4537,plain,
    ! [SV214: $i,SV364: $i,SV46: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV364 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SV364 )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SV364 @ SV214 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
        = $false )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4350]) ).

thf(4538,plain,
    ! [SV215: $i,SV365: $i,SV47: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV365 )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SV365 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
        = $false )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4351]) ).

thf(4539,plain,
    ! [SV216: $i,SV366: $i,SV48: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4352]) ).

thf(4540,plain,
    ! [SV217: $i,SV367: $i,SV49: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV367 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV49 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV49 @ SV217 @ SV367 ) @ SV217 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV49 @ SV217 )
        = $false )
      | ( ( cType___24t @ SV49 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4353]) ).

thf(4541,plain,
    ! [SV218: $i,SV368: $i,SV50: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
        = $false )
      | ( ( ! [SY1382: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SY1382 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SY1382 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SY1382 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4354]) ).

thf(4542,plain,
    ! [SV219: $i,SV369: $i,SV51: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV369 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV51 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV51 @ SV219 @ SV369 ) @ SV369 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV51 @ SV219 )
        = $false )
      | ( ( cType___24t @ SV51 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4355]) ).

thf(4543,plain,
    ! [SV220: $i,SV370: $i,SV52: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
        = $false )
      | ( ( ! [SY1383: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SY1383 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SY1383 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SY1383 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4356]) ).

thf(4544,plain,
    ! [SV221: $i,SV371: $i,SV53: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( ! [SY1384: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1384 )
              | ! [SY1385: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1385 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SY1384 @ SY1385 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SY1384 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SY1385 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4357]) ).

thf(4545,plain,
    ! [SV222: $i,SV372: $i,SV54: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( ! [SY1386: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SY1386 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SY1386 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SY1386 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4358]) ).

thf(4546,plain,
    ! [SV223: $i,SV373: $i,SV55: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( ! [SY1387: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1387 )
              | ! [SY1388: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1388 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1388 @ SY1387 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SY1387 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SY1388 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4359]) ).

thf(4547,plain,
    ! [SV224: $i,SV374: $i,SV56: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV374 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV56 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV56 @ SV224 @ SV374 ) @ SV224 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV56 @ SV224 )
        = $false )
      | ( ( cType___24t @ SV56 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4360]) ).

thf(4548,plain,
    ! [SV225: $i,SV375: $i,SV57: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV375 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SV375 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV375 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
        = $false )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4361]) ).

thf(4549,plain,
    ! [SV227: $i,SV376: $i,SV59: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV376 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SV376 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV376 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
        = $false )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4362]) ).

thf(4550,plain,
    ! [SV228: $i,SV377: $i,SV60: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV377 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
        = $false )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4363]) ).

thf(4551,plain,
    ! [SV229: $i,SV378: $i,SV61: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( ! [SY1389: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1389 )
              | ! [SY1390: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1390 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SY1389 @ SY1390 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SY1389 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SY1390 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4364]) ).

thf(4552,plain,
    ! [SV230: $i,SV379: $i,SV62: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV379 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SV379 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SV379 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
        = $false )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4365]) ).

thf(4553,plain,
    ! [SV231: $i,SV380: $i,SV63: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV380 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SV380 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SV380 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
        = $false )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4366]) ).

thf(4554,plain,
    ! [SV232: $i,SV381: $i,SV64: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV381 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SV381 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SV381 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
        = $false )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4367]) ).

thf(4555,plain,
    ! [SV233: $i,SV382: $i,SV65: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV382 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SV382 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV382 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
        = $false )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4368]) ).

thf(4556,plain,
    ! [SV234: $i,SV383: $i,SV66: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV383 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
        = $false )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4369]) ).

thf(4557,plain,
    ! [SV235: $i,SV384: $i,SV67: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( ! [SY1391: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SY1391 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SY1391 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SY1391 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SY1391 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4370]) ).

thf(4558,plain,
    ! [SV236: $i,SV385: $i,SV68: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV385 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV68 @ SV236 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV68 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV68 @ SV236 @ SV385 ) @ SV385 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV68 @ SV236 )
        = $false )
      | ( ( cType___24t @ SV68 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4371]) ).

thf(4559,plain,
    ! [SV237: $i,SV386: $i,SV69: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( ! [SY1392: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1392 )
              | ! [SY1393: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1393 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SY1392 @ SY1393 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SY1392 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SY1393 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4372]) ).

thf(4560,plain,
    ! [SV238: $i,SV387: $i,SV70: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV387 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV70 @ SV238 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV70 @ SV238 @ SV387 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV70 @ SV238 )
        = $false )
      | ( ( cType___24t @ SV70 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4373]) ).

thf(4561,plain,
    ! [SV239: $i,SV388: $i,SV71: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
        = $false )
      | ( ( ! [SY1394: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SY1394 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SY1394 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4374]) ).

thf(4562,plain,
    ! [SV240: $i,SV389: $i,SV72: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV389 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV72 @ SV389 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV72 @ SV240 @ SV389 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV72 @ SV240 )
        = $false )
      | ( ( cType___24t @ SV72 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4375]) ).

thf(4563,plain,
    ! [SV241: $i,SV390: $i,SV73: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
        = $false )
      | ( ( ! [SY1395: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SY1395 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SY1395 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SY1395 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4376]) ).

thf(4564,plain,
    ! [SV242: $i,SV391: $i,SV74: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4377]) ).

thf(4565,plain,
    ! [SV78: $i] :
      ( ( ( ! [SY657: $i] :
              ( ~ ( cProp___24t @ SY657 )
              | ( p @ SV78 )
              | ~ ( p @ SV78 )
              | ( p @ SY657 ) ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4378]) ).

thf(4566,plain,
    ! [SV78: $i] :
      ( ( ( ! [SY658: $i] :
              ( ~ ( cProp___24t @ SY658 )
              | ( p @ SV78 )
              | ~ ( p @ SY658 )
              | ( p @ SY658 ) ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4379]) ).

thf(4567,plain,
    ! [SV78: $i] :
      ( ( ( ! [SY659: $i] :
              ( ~ ( cProp___24t @ SY659 )
              | ~ ( p @ SY659 )
              | ~ ( p @ SV78 )
              | ( p @ SY659 ) ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4380]) ).

thf(4568,plain,
    ! [SV78: $i] :
      ( ( ( ! [SX1: $i] :
              ( ~ ( cProp___24t @ SX1 )
              | ~ ( p @ SX1 )
              | ~ ( p @ SX1 )
              | ( p @ SX1 ) ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4381]) ).

thf(4569,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4383]) ).

thf(4570,plain,
    ! [SV245: $i,SV392: $i] :
      ( ( ( cType___24t @ SV392 )
        = $false )
      | ( ( ! [SY1396: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ SY1396 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ ( happ @ ( happ @ SV245 @ SV392 ) @ SY1396 ) ) ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV245 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4384]) ).

thf(4571,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ! [SY1258: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1258 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1258 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1258 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4385]) ).

thf(4572,plain,
    ! [SV246: $i,SV79: $i] :
      ( ( ( ! [SY1259: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SY1259 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SY1259 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SY1259 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4386]) ).

thf(4573,plain,
    ! [SV431: $i,SV393: $i,SV161: $i,SV130: $i,SV81: $i] :
      ( ( ( ~ ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV393 @ SV431 ) )
        = $true )
      | ( ( ( p @ ( happ @ ( happ @ SV130 @ SV393 ) @ SV431 ) )
          | ( p @ ( happ @ ( happ @ SV161 @ SV393 ) @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4389]) ).

thf(4574,plain,
    ! [SV161: $i,SV81: $i,SV130: $i] :
      ( ( ! [SY1093: $i,SY1094: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV130 @ SY1093 ) @ SY1094 ) )
            | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1093 @ SY1094 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4390]) ).

thf(4575,plain,
    ! [SV130: $i,SV81: $i,SV161: $i] :
      ( ( ! [SY1095: $i,SY1096: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV161 @ SY1095 ) @ SY1096 ) )
            | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SY1095 @ SY1096 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4391]) ).

thf(4576,plain,
    ! [SV131: $i,SV82: $i,SV432: $i,SV394: $i,SV162: $i] :
      ( ( ( ( happ @ SV162 @ SV394 )
         != ( happ @ SV162 @ SV432 ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV394 @ SV432 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4392]) ).

thf(4577,plain,
    ! [SV433: $i,SV395: $i,SV162: $i,SV131: $i,SV82: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV395 @ SV433 ) )
        = $true )
      | ( ( ( happ @ SV162 @ SV395 )
          = ( happ @ SV162 @ SV433 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4393]) ).

thf(4578,plain,
    ! [SV249: $i,SV396: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
          | ! [SY1400: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1400 )
              | ~ ( ~ ! [SY1401: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1401 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1401 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1401 ) ) )
                  | ~ ! [SY1402: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1402 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1402 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1402 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4394]) ).

thf(4579,plain,
    ! [SV397: $i,SV303: $i,SV132: $i,SV84: $i] :
      ( ( ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV303 @ SV397 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV132 @ SV303 ) @ SV397 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4395]) ).

thf(4580,plain,
    ! [SV84: $i,SV398: $i,SV304: $i,SV132: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV132 @ SV304 ) @ SV398 ) )
        = $false )
      | ( ( c_24__lam__7591___24a4 @ SV84 @ SV132 @ SV304 @ SV398 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4396]) ).

thf(4581,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ! [SY1266: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1266 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1266 )
              | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
              | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1266 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4397]) ).

thf(4582,plain,
    ! [SV250: $i,SV85: $i] :
      ( ( ( ! [SY1267: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SY1267 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SY1267 )
              | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SY1267 ) )
              | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4398]) ).

thf(4583,plain,
    ! [SV251: $i] :
      ( ( ( cType___24t @ ( happ @ SV251 @ ( sK12_Vv__CANONICAL__0 @ SV251 ) ) )
        = $false )
      | ( ( c_24__type__28___24t @ SV251 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4400]) ).

thf(4584,plain,
    ! [SV252: $i,SV399: $i] :
      ( ( ( cType___24t @ SV399 )
        = $false )
      | ( ( cType___24t @ ( happ @ SV252 @ SV399 ) )
        = $true )
      | ( ( c_24__type__28___24t @ SV252 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4401]) ).

thf(4585,plain,
    ! [SV86: $i,SV305: $i,SV400: $i,SV133: $i] :
      ( ( ( ~ ( p @ ( happ @ SV133 @ SV400 ) ) )
        = $true )
      | ( ( p @ ( happ @ SV305 @ SV400 ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV305 @ SV400 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4402]) ).

thf(4586,plain,
    ! [SV460: $i,SV133: $i,SV86: $i] :
      ( ( ! [SY1441: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV460 @ SY1441 )
            | ( p @ ( happ @ SV133 @ SY1441 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4403]) ).

thf(4587,plain,
    ! [SV461: $i,SV133: $i,SV86: $i] :
      ( ( ! [SY1442: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV461 @ SY1442 )
            | ~ ( p @ ( happ @ SV461 @ SY1442 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4404]) ).

thf(4588,plain,
    ! [SV401: $i,SV306: $i,SV134: $i,SV87: $i] :
      ( ( ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV306 @ SV401 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV134 @ SV401 ) @ SV306 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4405]) ).

thf(4589,plain,
    ! [SV87: $i,SV307: $i,SV402: $i,SV134: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV134 @ SV402 ) @ SV307 ) )
        = $false )
      | ( ( c_24__lam__7587___24a4 @ SV87 @ SV134 @ SV307 @ SV402 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4406]) ).

thf(4590,plain,
    ! [SV88: $i,SV308: $i,SV280: $i] :
      ( ( ( p @ ( happ @ SV280 @ SV308 ) )
        = $false )
      | ( ( chahn_2eHahnSets_2eset__compl___24a3 @ SV88 @ SV280 @ SV308 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4407]) ).

thf(4591,plain,
    ! [SV253: $i,SV403: $i,SV89: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( ~ ( ~ ! [SY1403: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1403 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1403 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1403 ) ) ) )
              | ~ ! [SY1404: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1404 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1404 ) ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1404 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4408]) ).

thf(4592,plain,
    ! [SV434: $i,SV404: $i,SV163: $i,SV135: $i,SV90: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV404 @ SV434 ) )
        = $true )
      | ( ( ( p @ ( happ @ ( happ @ SV135 @ SV404 ) @ SV434 ) )
          | ( p @ ( happ @ ( happ @ SV163 @ SV404 ) @ SV434 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4409]) ).

thf(4593,plain,
    ! [SV163: $i,SV90: $i,SV135: $i] :
      ( ( ! [SY1103: $i,SY1104: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV135 @ SY1103 ) @ SY1104 ) )
            | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1103 @ SY1104 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4410]) ).

thf(4594,plain,
    ! [SV135: $i,SV90: $i,SV163: $i] :
      ( ( ! [SY1105: $i,SY1106: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV163 @ SY1105 ) @ SY1106 ) )
            | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SY1105 @ SY1106 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4411]) ).

thf(4595,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ~ ( ~ ! [SY1272: $i] :
                    ( ~ ( cProp___24t @ SY1272 )
                    | ( p @ SV91 )
                    | ~ ( p @ SV91 )
                    | ( p @ SV254 )
                    | ( p @ SY1272 ) )
              | ~ ! [SY1273: $i] :
                    ( ~ ( cProp___24t @ SY1273 )
                    | ( p @ SV91 )
                    | ~ ( p @ SY1273 )
                    | ( p @ SV254 )
                    | ( p @ SY1273 ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4412]) ).

thf(4596,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ( ~ ! [SY1274: $i] :
                    ( ~ ( cProp___24t @ SY1274 )
                    | ~ ( p @ SV254 )
                    | ~ ( p @ SV91 )
                    | ( p @ SV254 )
                    | ( p @ SY1274 ) )
              | ~ ! [SY1275: $i] :
                    ( ~ ( cProp___24t @ SY1275 )
                    | ~ ( p @ SV254 )
                    | ~ ( p @ SY1275 )
                    | ( p @ SV254 )
                    | ( p @ SY1275 ) ) ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4413]) ).

thf(4597,plain,
    ! [SV92: $i,SV435: $i,SV164: $i,SV405: $i,SV136: $i] :
      ( ( ( ~ ( p @ ( happ @ SV136 @ SV405 ) )
          | ~ ( p @ ( happ @ SV164 @ SV435 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV405 @ SV435 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4414]) ).

thf(4598,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ! [SY1109: $i] :
            ( ! [SY1110: $i] :
                ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1109 @ SY1110 )
            | ( p @ ( happ @ SV136 @ SY1109 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4415]) ).

thf(4599,plain,
    ! [SV164: $i,SV136: $i,SV92: $i] :
      ( ( ! [SY1111: $i,SY1112: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SY1111 @ SY1112 )
            | ( p @ ( happ @ SV164 @ SY1112 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4416]) ).

thf(4600,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) )
        = $true )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4417]) ).

thf(4601,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SV282 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) ) )
        = $true )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4418]) ).

thf(4602,plain,
    ! [SV283: $i,SV436: $i,SV256: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SV436 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SV283 @ SV436 ) )
        = $true )
      | ( ( c_24__type__11748___24t @ SV256 @ SV283 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4419]) ).

thf(4603,plain,
    ! [SV437: $i,SV406: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV406 @ SV437 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV406 ) @ SV437 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4420]) ).

thf(4604,plain,
    ! [SV438: $i,SV407: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV407 ) @ SV438 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV407 @ SV438 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4421]) ).

thf(4605,plain,
    ! [SV311: $i,SV285: $i,SV94: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV285 @ SV311 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV311 @ SV285 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV285 @ SV311 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4422]) ).

thf(4606,plain,
    ! [SV462: $i,SV439: $i,SV94: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV439 @ SV462 )
        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV439 @ SV462 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4423]) ).

thf(4607,plain,
    ! [SV463: $i,SV440: $i,SV94: $i] :
      ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV440 @ SV463 )
        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV463 @ SV440 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4424]) ).

thf(4608,plain,
    ! [SV95: $i,SV312: $i,SV408: $i,SV138: $i] :
      ( ( ( ~ ( p @ ( happ @ SV138 @ SV408 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV312 @ SV408 ) ) )
        = $true )
      | ( ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV312 @ SV408 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4426]) ).

thf(4609,plain,
    ! [SV464: $i,SV138: $i,SV95: $i] :
      ( ( ! [SY1443: $i] :
            ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV464 @ SY1443 )
            | ( p @ ( happ @ SV138 @ SY1443 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4427]) ).

thf(4610,plain,
    ! [SV465: $i,SV138: $i,SV95: $i] :
      ( ( ! [SY1444: $i] :
            ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV465 @ SY1444 )
            | ( p @ ( happ @ SV465 @ SY1444 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4428]) ).

thf(4611,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ! [SY1281: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1281 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1281 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1281 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4429]) ).

thf(4612,plain,
    ! [SV259: $i,SV96: $i] :
      ( ( ( ! [SY1282: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SY1282 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SY1282 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SY1282 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4430]) ).

thf(4613,plain,
    ! [SV409: $i,SV313: $i,SV139: $i,SV97: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV313 @ SV409 )
        = $false )
      | ( ( ( SV313 = SV409 )
          | ( p @ ( happ @ ( happ @ SV139 @ SV313 ) @ SV409 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4431]) ).

thf(4614,plain,
    ! [SV139: $i,SV97: $i,SV466: $i] :
      ( ( ! [SY1445: $i] :
            ( ( SV466 != SY1445 )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV466 @ SY1445 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4432]) ).

thf(4615,plain,
    ! [SV97: $i,SV467: $i,SV139: $i] :
      ( ( ! [SY1446: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV139 @ SV467 ) @ SY1446 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV467 @ SY1446 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4433]) ).

thf(4616,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( t @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) @ SV98 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4434]) ).

thf(4617,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ~ ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
                | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                      | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4434]) ).

thf(4618,plain,
    ! [SV315: $i,SV289: $i,SV98: $i,SV468: $i] :
      ( ( ( ~ ( t @ SV468 @ SV98 )
          | ! [SY1447: $i] :
              ( ~ ( t @ SY1447 @ SV98 )
              | ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SY1447 ) )
              | ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SY1447 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4435]) ).

thf(4619,plain,
    ! [SV410: $i,SV316: $i,SV140: $i,SV99: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV316 @ SV410 )
        = $false )
      | ( ( ( p @ ( happ @ ( happ @ SV140 @ SV316 ) @ SV410 ) )
          | ( p @ ( happ @ ( happ @ SV140 @ SV410 ) @ SV316 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4436]) ).

thf(4620,plain,
    ! [SV99: $i,SV469: $i,SV140: $i] :
      ( ( ! [SY1448: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV140 @ SV469 ) @ SY1448 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV469 @ SY1448 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4437]) ).

thf(4621,plain,
    ! [SV99: $i,SV470: $i,SV140: $i] :
      ( ( ! [SY1449: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV140 @ SY1449 ) @ SV470 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV470 @ SY1449 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4438]) ).

thf(4622,plain,
    ! [SV100: $i,SV166: $i,SV441: $i,SV411: $i,SV141: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV141 @ SV411 ) @ SV441 ) )
          | ( p @ ( happ @ ( happ @ SV166 @ SV411 ) @ SV441 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV411 @ SV441 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4439]) ).

thf(4623,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ! [SY1119: $i,SY1120: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1119 @ SY1120 )
            | ( p @ ( happ @ ( happ @ SV141 @ SY1119 ) @ SY1120 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4440]) ).

thf(4624,plain,
    ! [SV166: $i,SV141: $i,SV100: $i] :
      ( ( ! [SY1121: $i,SY1122: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SY1121 @ SY1122 )
            | ~ ( p @ ( happ @ ( happ @ SV166 @ SY1121 ) @ SY1122 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4441]) ).

thf(4625,plain,
    ! [SV290: $i,SV317: $i,SV101: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) )
        = $false )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4442]) ).

thf(4626,plain,
    ! [SV101: $i,SV317: $i,SV290: $i] :
      ( ( ( ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SV317 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) ) )
        = $false )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4442]) ).

thf(4627,plain,
    ! [SV318: $i,SV291: $i,SV471: $i,SV101: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SV471 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SV318 @ SV471 ) ) )
        = $true )
      | ( ( c_24__type__11699___24t @ SV101 @ SV291 @ SV318 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4443]) ).

thf(4628,plain,
    ! [SV442: $i,SV412: $i,SV167: $i,SV142: $i,SV102: $i] :
      ( ( ( ~ ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV412 @ SV442 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV167 @ SV412 ) @ SV442 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4444]) ).

thf(4629,plain,
    ! [SV142: $i,SV102: $i,SV443: $i,SV413: $i,SV167: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV167 @ SV413 ) @ SV443 ) ) )
        = $true )
      | ( ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV413 @ SV443 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4445]) ).

thf(4630,plain,
    ! [SV103: $i,SV319: $i,SV292: $i] :
      ( ( ( p @ SV292 )
        = $true )
      | ( ( p @ SV319 )
        = $true )
      | ( ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV292 @ SV319 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4446]) ).

thf(4631,plain,
    ! [SV103: $i,SV444: $i] :
      ( ( ( ~ ( p @ SV444 ) )
        = $true )
      | ( ( ! [SY1429: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV444 @ SY1429 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4447]) ).

thf(4632,plain,
    ! [SV445: $i,SV103: $i,SV472: $i] :
      ( ( ~ ( p @ SV472 )
        | ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV445 @ SV472 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4448]) ).

thf(4633,plain,
    ! [SV104: $i,SV143: $i,SV446: $i,SV414: $i,SV168: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) )
          | ~ ( p @ ( happ @ SV143 @ SV414 ) )
          | ~ ( p @ ( happ @ SV143 @ SV446 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4449]) ).

thf(4634,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ( ~ ! [SY1129: $i,SY1130: $i] :
                  ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
                  | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
            | ~ ! [SY1131: $i] :
                  ( ! [SY1132: $i] :
                      ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
                  | ( p @ ( happ @ SV143 @ SY1131 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4450]) ).

thf(4635,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ! [SY1133: $i,SY1134: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1133 @ SY1134 )
            | ( p @ ( happ @ SV143 @ SY1134 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4451]) ).

thf(4636,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4454]) ).

thf(4637,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4455]) ).

thf(4638,plain,
    ! [SV296: $i,SV447: $i,SV261: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV447 ) )
        = $true )
      | ( ( ! [SY1431: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1431 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SV447 ) @ SY1431 ) ) ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4456]) ).

thf(4639,plain,
    ! [SV415: $i,SV322: $i,SV144: $i,SV106: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV322 @ SV415 )
        = $false )
      | ( ( ( p @ ( happ @ ( happ @ SV144 @ SV415 ) @ SV322 ) )
          | ( SV322 = SV415 )
          | ( p @ ( happ @ ( happ @ SV144 @ SV322 ) @ SV415 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4457]) ).

thf(4640,plain,
    ! [SV106: $i,SV473: $i,SV144: $i] :
      ( ( ! [SY1450: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1450 ) @ SV473 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV473 @ SY1450 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4458]) ).

thf(4641,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ! [SY1023: $i,SY1024: $i] :
              ( ( SY1023 != SY1024 )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) )
        | ~ ! [SY1025: $i,SY1026: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4459]) ).

thf(4642,plain,
    ! [SV448: $i,SV416: $i,SV169: $i,SV145: $i,SV107: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV416 @ SV448 ) )
        = $true )
      | ( ( p @ ( happ @ SV416 @ ( happ @ SV169 @ SV448 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4460]) ).

thf(4643,plain,
    ! [SV145: $i,SV107: $i,SV449: $i,SV169: $i,SV417: $i] :
      ( ( ( ~ ( p @ ( happ @ SV417 @ ( happ @ SV169 @ SV449 ) ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV417 @ SV449 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4461]) ).

thf(4644,plain,
    ! [SV108: $i,SV146: $i,SV418: $i,SV323: $i] :
      ( ( ( SV323 != SV418 )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV146 @ SV323 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV323 @ SV418 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4462]) ).

thf(4645,plain,
    ! [SV474: $i,SV146: $i,SV108: $i] :
      ( ( ! [SY1451: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV474 @ SY1451 )
            | ( SV474 = SY1451 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4463]) ).

thf(4646,plain,
    ! [SV475: $i,SV146: $i,SV108: $i] :
      ( ( ! [SY1452: $i] :
            ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV475 @ SY1452 )
        | ( p @ ( happ @ SV146 @ SV475 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4464]) ).

thf(4647,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
          | ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4466]) ).

thf(4648,plain,
    ! [SV263: $i,SV419: $i] :
      ( ( ( cType___24t @ SV419 )
        = $false )
      | ( ( ! [SY1415: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1415 )
              | ! [SY1416: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1416 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SY1415 ) @ SY1416 ) ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4467]) ).

thf(4649,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ! [SY1290: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1290 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1290 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1290 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4468]) ).

thf(4650,plain,
    ! [SV264: $i,SV109: $i] :
      ( ( ( ! [SY1291: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SY1291 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SY1291 )
              | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SY1291 ) )
              | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4469]) ).

thf(4651,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) )
          | ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                      | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4471]) ).

thf(4652,plain,
    ! [SV266: $i,SV420: $i] :
      ( ( ( cType___24t @ SV420 )
        = $false )
      | ( ( ! [SY1417: $i] :
              ( ~ ( cType___24t @ SY1417 )
              | ! [SY1418: $i] :
                  ( ~ ( cType___24t @ SY1418 )
                  | ! [SY1419: $i] :
                      ( ~ ( cType___24t @ SY1419 )
                      | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SY1417 ) @ SY1418 ) @ SY1419 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4472]) ).

thf(4653,plain,
    ! [SV110: $i,SV170: $i,SV450: $i,SV421: $i,SV147: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV147 @ SV421 ) @ SV450 ) )
          | ~ ( p @ ( happ @ ( happ @ SV170 @ SV421 ) @ SV450 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV421 @ SV450 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4473]) ).

thf(4654,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ! [SY1141: $i,SY1142: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1141 @ SY1142 )
            | ( p @ ( happ @ ( happ @ SV147 @ SY1141 ) @ SY1142 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4474]) ).

thf(4655,plain,
    ! [SV170: $i,SV147: $i,SV110: $i] :
      ( ( ! [SY1143: $i,SY1144: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SY1143 @ SY1144 )
            | ( p @ ( happ @ ( happ @ SV170 @ SY1143 ) @ SY1144 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4475]) ).

thf(4656,plain,
    ! [SV422: $i,SV324: $i,SV148: $i,SV111: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV324 @ SV422 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV148 @ SV422 ) @ SV324 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4476]) ).

thf(4657,plain,
    ! [SV111: $i,SV325: $i,SV423: $i,SV148: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV148 @ SV423 ) @ SV325 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a4 @ SV111 @ SV148 @ SV325 @ SV423 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4477]) ).

thf(4658,plain,
    ! [SV112: $i,SV326: $i,SV297: $i] :
      ( ( ( p @ SV297 )
        = $false )
      | ( ( ~ ( p @ SV326 ) )
        = $true )
      | ( ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV297 @ SV326 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4478]) ).

thf(4659,plain,
    ! [SV451: $i,SV112: $i] :
      ( ( ( ! [SY1432: $i] :
              ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV451 @ SY1432 ) ) )
        = $true )
      | ( ( p @ SV451 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4479]) ).

thf(4660,plain,
    ! [SV476: $i,SV452: $i,SV112: $i] :
      ( ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV452 @ SV476 ) )
        | ( p @ SV476 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4480]) ).

thf(4661,plain,
    ! [SV424: $i,SV327: $i,SV149: $i,SV113: $i] :
      ( ( ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV327 @ SV424 )
        = $false )
      | ( ( ( p @ ( happ @ SV149 @ SV424 ) )
          | ( p @ ( happ @ SV327 @ SV424 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4481]) ).

thf(4662,plain,
    ! [SV477: $i,SV113: $i,SV149: $i] :
      ( ( ! [SY1453: $i] :
            ( ~ ( p @ ( happ @ SV149 @ SY1453 ) )
            | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV477 @ SY1453 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4482]) ).

thf(4663,plain,
    ! [SV149: $i,SV113: $i,SV478: $i] :
      ( ( ! [SY1454: $i] :
            ( ~ ( p @ ( happ @ SV478 @ SY1454 ) )
            | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV478 @ SY1454 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4483]) ).

thf(4664,plain,
    ! [SV114: $i,SV453: $i] :
      ( ( ( p @ SV453 )
        = $true )
      | ( ( ! [SY1434: $i] : ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV453 @ SY1434 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4484]) ).

thf(4665,plain,
    ! [SV454: $i,SV114: $i,SV479: $i] :
      ( ( ~ ( p @ SV479 )
        | ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV454 @ SV479 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4485]) ).

thf(4666,plain,
    ! [SV114: $i,SV328: $i,SV298: $i] :
      ( ( ( ~ ( p @ SV298 ) )
        = $true )
      | ( ( p @ SV328 )
        = $true )
      | ( ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV298 @ SV328 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4486]) ).

thf(4667,plain,
    ! [SV267: $i,SV425: $i,SV115: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
          | ! [SY1421: $i] :
              ( ~ ( t @ SY1421 @ SV115 )
              | ~ ( ~ ! [SY1422: $i] :
                        ( ~ ( t @ SY1422 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1422 ) )
                        | ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1422 ) ) )
                  | ~ ! [SY1423: $i] :
                        ( ~ ( t @ SY1423 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1423 ) )
                        | ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1423 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4487]) ).

thf(4668,plain,
    ! [SV116: $i,SV329: $i,SV426: $i,SV150: $i] :
      ( ( ( ~ ( p @ ( happ @ SV150 @ SV426 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV329 @ SV426 ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV329 @ SV426 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4488]) ).

thf(4669,plain,
    ! [SV480: $i,SV150: $i,SV116: $i] :
      ( ( ! [SY1455: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV480 @ SY1455 )
            | ( p @ ( happ @ SV150 @ SY1455 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4489]) ).

thf(4670,plain,
    ! [SV481: $i,SV150: $i,SV116: $i] :
      ( ( ! [SY1456: $i] :
            ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV481 @ SY1456 )
            | ( p @ ( happ @ SV481 @ SY1456 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4490]) ).

thf(4671,plain,
    ! [SV268: $i,SV427: $i,SV117: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( ~ ( ~ ! [SY1424: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1424 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1424 ) ) ) )
              | ~ ! [SY1425: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1425 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1425 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1425 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4491]) ).

thf(4672,plain,
    ! [SV482: $i,SV455: $i,SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV455 @ SV482 )
        | ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV455 ) ) @ ( happ @ SV171 @ SV482 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4492]) ).

thf(4673,plain,
    ! [SV151: $i,SV118: $i,SV483: $i,SV456: $i,SV171: $i,SV269: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV456 ) ) @ ( happ @ SV171 @ SV483 ) ) )
        | ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV456 @ SV483 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4493]) ).

thf(4674,plain,
    ! [SV484: $i,SV457: $i,SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV457 @ SV484 )
        | ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV457 ) ) @ ( happ @ SV172 @ SV484 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4494]) ).

thf(4675,plain,
    ! [SV152: $i,SV119: $i,SV485: $i,SV458: $i,SV172: $i,SV270: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV458 ) ) @ ( happ @ SV172 @ SV485 ) ) )
        | ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV458 @ SV485 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4495]) ).

thf(4676,plain,
    ! [SV120: $i,SV330: $i,SV299: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV299 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) )
        = $false )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4496]) ).

thf(4677,plain,
    ! [SV299: $i,SV330: $i,SV120: $i] :
      ( ( ( ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV330 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) ) )
        = $false )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4496]) ).

thf(4678,plain,
    ! [SV331: $i,SV120: $i,SV486: $i,SV300: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SV486 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV331 @ SV486 ) ) )
        = $true )
      | ( ( c_24__type__11787___24t @ SV120 @ SV300 @ SV331 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4497]) ).

thf(4679,plain,
    ! [SV153: $i,SV121: $i,SV428: $i,SV332: $i] :
      ( ( ( SV332 = SV428 )
        = $false )
      | ( ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV332 @ SV428 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4498]) ).

thf(4680,plain,
    ! [SV429: $i,SV333: $i,SV153: $i,SV121: $i] :
      ( ( ( p @ ( c_24__prop__35352___24a4 @ SV121 @ SV153 @ SV333 @ SV429 ) )
        = $false )
      | ( ( SV333 = SV429 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4499]) ).

thf(4681,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) )
          | ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4501]) ).

thf(4682,plain,
    ! [SV272: $i,SV430: $i] :
      ( ( ( cType___24t @ SV430 )
        = $false )
      | ( ( ! [SY1426: $i] :
              ( ~ ( cType___24t @ SY1426 )
              | ( cType___24t @ ( happ @ ( happ @ SV272 @ SV430 ) @ SY1426 ) ) ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV272 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4502]) ).

thf(4683,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV487: $i,SV459: $i,SV173: $i] :
      ( ( ( ( happ @ SV173 @ SV459 )
         != ( happ @ SV173 @ SV487 ) )
        | ~ ( p @ ( happ @ ( happ @ SV273 @ SV459 ) @ SV487 ) )
        | ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV459 @ SV487 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4503]) ).

thf(4684,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ! [SY1315: $i,SY1316: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
              | ( ( happ @ SV173 @ SY1315 )
                = ( happ @ SV173 @ SY1316 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4504]) ).

thf(4685,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ! [SY1317: $i,SY1318: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
              | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4504]) ).

thf(4686,plain,
    ! [SV334: $i,SV175: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 ) )
        = $true )
      | ( ( ! [SY1362: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1362 )
              | ! [SY1363: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1363 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1362 @ SY1363 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1362 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1363 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4505]) ).

thf(4687,plain,
    ! [SV10: $i,SV179: $i] :
      ( ( ( p @ SV179 )
        = $false )
      | ( ( p @ SV10 )
        = $false )
      | ( ( p @ SV10 )
        = $true )
      | ( ( cProp___24t @ SV179 )
        = $false )
      | ( ( cProp___24t @ SV10 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4506]) ).

thf(4688,plain,
    ! [SV335: $i,SV183: $i,SV15: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SV335 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV335 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV335 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
        = $false )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4508]) ).

thf(4689,plain,
    ! [SV336: $i,SV184: $i,SV16: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SV336 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV336 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV336 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
        = $false )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4509]) ).

thf(4690,plain,
    ! [SV337: $i,SV185: $i,SV17: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SV337 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV337 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV337 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
        = $false )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4510]) ).

thf(4691,plain,
    ! [SV338: $i,SV186: $i,SV18: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SV338 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV338 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV338 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
        = $false )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4511]) ).

thf(4692,plain,
    ! [SV339: $i,SV187: $i,SV19: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SV339 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV339 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV339 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
        = $false )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4512]) ).

thf(4693,plain,
    ! [SV340: $i,SV188: $i,SV20: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SV340 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV340 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV340 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
        = $false )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4513]) ).

thf(4694,plain,
    ! [SV341: $i,SV189: $i,SV21: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SV341 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV341 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV341 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
        = $false )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4514]) ).

thf(4695,plain,
    ! [SV342: $i,SV190: $i,SV488: $i,SV22: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV488 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SV342 ) @ SV488 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV342 @ SV488 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV342 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4515]) ).

thf(4696,plain,
    ! [SV343: $i,SV191: $i,SV489: $i,SV23: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV489 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ SV489 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SV489 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV343 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4516]) ).

thf(4697,plain,
    ! [SV345: $i,SV194: $i,SV26: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SV345 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SV345 @ SV194 ) @ SV194 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV345 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
        = $false )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4518]) ).

thf(4698,plain,
    ! [SV346: $i,SV195: $i,SV27: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SV346 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SV346 ) @ SV195 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV346 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
        = $false )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4519]) ).

thf(4699,plain,
    ! [SV348: $i,SV197: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 ) )
        = $true )
      | ( ( ! [SY1366: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1366 )
              | ! [SY1367: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1367 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1366 @ SY1367 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1366 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1367 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4521]) ).

thf(4700,plain,
    ! [SV349: $i,SV198: $i,SV30: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) ) )
        = $true )
      | ( ( ! [SY1368: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1368 )
              | ! [SY1369: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1369 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1368 @ SY1369 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1368 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1369 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4522]) ).

thf(4701,plain,
    ! [SV350: $i,SV199: $i,SV490: $i,SV31: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV490 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SV350 ) @ SV490 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SV490 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV350 @ SV490 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV350 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4523]) ).

thf(4702,plain,
    ! [SV351: $i,SV200: $i,SV491: $i,SV32: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV491 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SV351 ) @ SV491 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV351 @ SV491 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV351 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4524]) ).

thf(4703,plain,
    ! [SV352: $i,SV201: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 ) )
        = $true )
      | ( ( ! [SY1372: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1372 )
              | ! [SY1373: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1373 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1372 @ SY1373 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1372 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1373 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4525]) ).

thf(4704,plain,
    ! [SV353: $i,SV202: $i,SV34: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) ) )
        = $true )
      | ( ( ! [SY1374: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1374 )
              | ! [SY1375: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1375 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1374 @ SY1375 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1374 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1375 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4526]) ).

thf(4705,plain,
    ! [SV354: $i,SV203: $i,SV35: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SV354 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV354 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV354 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
        = $false )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4527]) ).

thf(4706,plain,
    ! [SV355: $i,SV204: $i,SV36: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SV355 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV355 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV355 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
        = $false )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4528]) ).

thf(4707,plain,
    ! [SV356: $i,SV205: $i,SV492: $i,SV37: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV492 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SV356 ) @ SV492 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV356 @ SV492 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV356 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4529]) ).

thf(4708,plain,
    ! [SV357: $i,SV206: $i,SV493: $i,SV38: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV493 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ SV493 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SV493 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV357 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4530]) ).

thf(4709,plain,
    ! [SV359: $i,SV209: $i,SV41: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SV359 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SV359 ) @ SV359 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV359 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
        = $false )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4532]) ).

thf(4710,plain,
    ! [SV360: $i,SV210: $i,SV42: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SV360 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SV360 @ SV210 ) @ SV360 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV360 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
        = $false )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4533]) ).

thf(4711,plain,
    ! [SV361: $i,SV211: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 ) )
        = $true )
      | ( ( ! [SY1378: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1378 )
              | ! [SY1379: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1379 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1378 @ SY1379 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1378 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1379 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4534]) ).

thf(4712,plain,
    ! [SV362: $i,SV212: $i,SV44: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) ) )
        = $true )
      | ( ( ! [SY1380: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1380 )
              | ! [SY1381: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1381 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1380 @ SY1381 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1380 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1381 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4535]) ).

thf(4713,plain,
    ! [SV363: $i,SV213: $i,SV45: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SV363 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SV363 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV363 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
        = $false )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4536]) ).

thf(4714,plain,
    ! [SV364: $i,SV214: $i,SV46: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SV364 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SV364 @ SV214 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV364 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
        = $false )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4537]) ).

thf(4715,plain,
    ! [SV365: $i,SV215: $i,SV47: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SV365 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV365 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
        = $false )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4538]) ).

thf(4716,plain,
    ! [SV366: $i,SV216: $i,SV48: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4539]) ).

thf(4717,plain,
    ! [SV368: $i,SV218: $i,SV494: $i,SV50: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV494 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SV494 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SV494 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4541]) ).

thf(4718,plain,
    ! [SV220: $i,SV370: $i,SV495: $i,SV52: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV495 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SV495 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SV495 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4543]) ).

thf(4719,plain,
    ! [SV371: $i,SV221: $i,SV496: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
          | ! [SY1457: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1457 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SY1457 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SY1457 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4544]) ).

thf(4720,plain,
    ! [SV372: $i,SV222: $i,SV497: $i,SV54: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4545]) ).

thf(4721,plain,
    ! [SV373: $i,SV223: $i,SV498: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
          | ! [SY1458: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1458 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1458 @ SV498 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SY1458 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4546]) ).

thf(4722,plain,
    ! [SV375: $i,SV225: $i,SV57: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SV375 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV375 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV375 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
        = $false )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4548]) ).

thf(4723,plain,
    ! [SV376: $i,SV227: $i,SV59: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SV376 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV376 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV376 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
        = $false )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4549]) ).

thf(4724,plain,
    ! [SV377: $i,SV228: $i,SV60: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV377 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
        = $false )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4550]) ).

thf(4725,plain,
    ! [SV378: $i,SV229: $i,SV499: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
          | ! [SY1459: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1459 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SY1459 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SY1459 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4551]) ).

thf(4726,plain,
    ! [SV379: $i,SV230: $i,SV62: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SV379 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SV379 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV379 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
        = $false )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4552]) ).

thf(4727,plain,
    ! [SV380: $i,SV231: $i,SV63: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SV380 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SV380 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV380 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
        = $false )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4553]) ).

thf(4728,plain,
    ! [SV381: $i,SV232: $i,SV64: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SV381 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SV381 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV381 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
        = $false )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4554]) ).

thf(4729,plain,
    ! [SV382: $i,SV233: $i,SV65: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SV382 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV382 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV382 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
        = $false )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4555]) ).

thf(4730,plain,
    ! [SV383: $i,SV234: $i,SV66: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV383 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
        = $false )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4556]) ).

thf(4731,plain,
    ! [SV384: $i,SV235: $i,SV500: $i,SV67: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4557]) ).

thf(4732,plain,
    ! [SV386: $i,SV237: $i,SV501: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
          | ! [SY1460: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1460 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SY1460 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SY1460 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4559]) ).

thf(4733,plain,
    ! [SV388: $i,SV239: $i,SV502: $i,SV71: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV502 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SV502 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4561]) ).

thf(4734,plain,
    ! [SV390: $i,SV241: $i,SV503: $i,SV73: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV503 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SV503 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SV503 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4563]) ).

thf(4735,plain,
    ! [SV391: $i,SV242: $i,SV74: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4564]) ).

thf(4736,plain,
    ! [SV78: $i,SV504: $i] :
      ( ( ( ~ ( cProp___24t @ SV504 )
          | ( p @ SV78 )
          | ~ ( p @ SV78 )
          | ( p @ SV504 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4565]) ).

thf(4737,plain,
    ! [SV78: $i,SV505: $i] :
      ( ( ( ~ ( cProp___24t @ SV505 )
          | ( p @ SV78 )
          | ~ ( p @ SV505 )
          | ( p @ SV505 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4566]) ).

thf(4738,plain,
    ! [SV78: $i,SV506: $i] :
      ( ( ( ~ ( cProp___24t @ SV506 )
          | ~ ( p @ SV506 )
          | ~ ( p @ SV78 )
          | ( p @ SV506 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4567]) ).

thf(4739,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( ~ ( cProp___24t @ SV507 )
          | ~ ( p @ SV507 )
          | ~ ( p @ SV507 )
          | ( p @ SV507 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4568]) ).

thf(4740,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4569]) ).

thf(4741,plain,
    ! [SV244: $i] :
      ( ( ( ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4569]) ).

thf(4742,plain,
    ! [SV245: $i,SV508: $i,SV392: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ SV508 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ ( happ @ ( happ @ SV245 @ SV392 ) @ SV508 ) ) )
        = $true )
      | ( ( cType___24t @ SV392 )
        = $false )
      | ( ( c_24__type__96___24t @ SV245 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4570]) ).

thf(4743,plain,
    ! [SV246: $i,SV509: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4571]) ).

thf(4744,plain,
    ! [SV246: $i,SV510: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4572]) ).

thf(4745,plain,
    ! [SV431: $i,SV393: $i,SV161: $i,SV130: $i,SV81: $i] :
      ( ( ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV393 @ SV431 )
        = $false )
      | ( ( ( p @ ( happ @ ( happ @ SV130 @ SV393 ) @ SV431 ) )
          | ( p @ ( happ @ ( happ @ SV161 @ SV393 ) @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4573]) ).

thf(4746,plain,
    ! [SV161: $i,SV81: $i,SV511: $i,SV130: $i] :
      ( ( ! [SY1461: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV130 @ SV511 ) @ SY1461 ) )
            | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV511 @ SY1461 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4574]) ).

thf(4747,plain,
    ! [SV130: $i,SV81: $i,SV512: $i,SV161: $i] :
      ( ( ! [SY1462: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV161 @ SV512 ) @ SY1462 ) )
            | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV512 @ SY1462 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4575]) ).

thf(4748,plain,
    ! [SV131: $i,SV82: $i,SV432: $i,SV394: $i,SV162: $i] :
      ( ( ( ( happ @ SV162 @ SV394 )
          = ( happ @ SV162 @ SV432 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV394 @ SV432 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4576]) ).

thf(4749,plain,
    ! [SV433: $i,SV395: $i,SV162: $i,SV131: $i,SV82: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eeq__rel___24a5 @ SV82 @ SV131 @ SV162 @ SV395 @ SV433 )
        = $false )
      | ( ( ( happ @ SV162 @ SV395 )
          = ( happ @ SV162 @ SV433 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4577]) ).

thf(4750,plain,
    ! [SV396: $i,SV249: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 ) )
        = $true )
      | ( ( ! [SY1400: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1400 )
              | ~ ( ~ ! [SY1401: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1401 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1401 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1401 ) ) )
                  | ~ ! [SY1402: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1402 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1402 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1402 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4578]) ).

thf(4751,plain,
    ! [SV250: $i,SV513: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 )
          | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4581]) ).

thf(4752,plain,
    ! [SV250: $i,SV514: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 )
          | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4582]) ).

thf(4753,plain,
    ! [SV86: $i,SV305: $i,SV400: $i,SV133: $i] :
      ( ( ( p @ ( happ @ SV133 @ SV400 ) )
        = $false )
      | ( ( p @ ( happ @ SV305 @ SV400 ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV305 @ SV400 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4585]) ).

thf(4754,plain,
    ! [SV515: $i,SV460: $i,SV133: $i,SV86: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV460 @ SV515 )
        | ( p @ ( happ @ SV133 @ SV515 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4586]) ).

thf(4755,plain,
    ! [SV516: $i,SV461: $i,SV133: $i,SV86: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV461 @ SV516 )
        | ~ ( p @ ( happ @ SV461 @ SV516 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4587]) ).

thf(4756,plain,
    ! [SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ~ ! [SY1403: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1403 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1403 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1403 ) ) ) )
          | ~ ! [SY1404: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1404 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1404 ) ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1404 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4591]) ).

thf(4757,plain,
    ! [SV434: $i,SV404: $i,SV163: $i,SV135: $i,SV90: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV404 @ SV434 )
        = $false )
      | ( ( ( p @ ( happ @ ( happ @ SV135 @ SV404 ) @ SV434 ) )
          | ( p @ ( happ @ ( happ @ SV163 @ SV404 ) @ SV434 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4592]) ).

thf(4758,plain,
    ! [SV163: $i,SV90: $i,SV517: $i,SV135: $i] :
      ( ( ! [SY1463: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV135 @ SV517 ) @ SY1463 ) )
            | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV517 @ SY1463 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4593]) ).

thf(4759,plain,
    ! [SV135: $i,SV90: $i,SV518: $i,SV163: $i] :
      ( ( ! [SY1464: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV163 @ SV518 ) @ SY1464 ) )
            | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV518 @ SY1464 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4594]) ).

thf(4760,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ~ ! [SY1272: $i] :
                ( ~ ( cProp___24t @ SY1272 )
                | ( p @ SV91 )
                | ~ ( p @ SV91 )
                | ( p @ SV254 )
                | ( p @ SY1272 ) )
          | ~ ! [SY1273: $i] :
                ( ~ ( cProp___24t @ SY1273 )
                | ( p @ SV91 )
                | ~ ( p @ SY1273 )
                | ( p @ SV254 )
                | ( p @ SY1273 ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4595]) ).

thf(4761,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ! [SY1274: $i] :
                ( ~ ( cProp___24t @ SY1274 )
                | ~ ( p @ SV254 )
                | ~ ( p @ SV91 )
                | ( p @ SV254 )
                | ( p @ SY1274 ) )
          | ~ ! [SY1275: $i] :
                ( ~ ( cProp___24t @ SY1275 )
                | ~ ( p @ SV254 )
                | ~ ( p @ SY1275 )
                | ( p @ SV254 )
                | ( p @ SY1275 ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4596]) ).

thf(4762,plain,
    ! [SV92: $i,SV435: $i,SV164: $i,SV405: $i,SV136: $i] :
      ( ( ( ~ ( p @ ( happ @ SV136 @ SV405 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV164 @ SV435 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV405 @ SV435 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4597]) ).

thf(4763,plain,
    ! [SV519: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ! [SY1465: $i] :
            ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV519 @ SY1465 )
        | ( p @ ( happ @ SV136 @ SV519 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4598]) ).

thf(4764,plain,
    ! [SV520: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ! [SY1466: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV520 @ SY1466 )
            | ( p @ ( happ @ SV164 @ SY1466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4599]) ).

thf(4765,plain,
    ! [SV282: $i,SV255: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV255 @ ( happ @ SV282 @ ( sK16_Vv__CANONICAL__1 @ SV282 @ SV255 ) ) )
        = $false )
      | ( ( c_24__type__11748___24t @ SV255 @ SV282 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4601]) ).

thf(4766,plain,
    ! [SV283: $i,SV436: $i,SV256: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ SV436 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV256 @ ( happ @ SV283 @ SV436 ) )
        = $true )
      | ( ( c_24__type__11748___24t @ SV256 @ SV283 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4602]) ).

thf(4767,plain,
    ! [SV437: $i,SV406: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV406 @ SV437 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV406 ) @ SV437 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4603]) ).

thf(4768,plain,
    ! [SV438: $i,SV407: $i,SV165: $i,SV137: $i,SV93: $i] :
      ( ( ( p @ ( happ @ ( happ @ ( happ @ ( happ @ ( happ @ chahn_2eHahnRelationsBasic_2eminus__rel @ SV93 ) @ SV137 ) @ SV165 ) @ SV407 ) @ SV438 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV93 @ SV137 @ SV165 @ SV407 @ SV438 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4604]) ).

thf(4769,plain,
    ! [SV285: $i,SV311: $i,SV94: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV311 @ SV285 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV285 @ SV311 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV285 @ SV311 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4605]) ).

thf(4770,plain,
    ! [SV462: $i,SV439: $i,SV94: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV439 @ SV462 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV439 @ SV462 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4606]) ).

thf(4771,plain,
    ! [SV463: $i,SV440: $i,SV94: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV440 @ SV463 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV463 @ SV440 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4607]) ).

thf(4772,plain,
    ! [SV95: $i,SV312: $i,SV408: $i,SV138: $i] :
      ( ( ( p @ ( happ @ SV138 @ SV408 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV312 @ SV408 ) ) )
        = $true )
      | ( ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV312 @ SV408 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4608]) ).

thf(4773,plain,
    ! [SV521: $i,SV464: $i,SV138: $i,SV95: $i] :
      ( ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV464 @ SV521 )
        | ( p @ ( happ @ SV138 @ SV521 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4609]) ).

thf(4774,plain,
    ! [SV522: $i,SV465: $i,SV138: $i,SV95: $i] :
      ( ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV465 @ SV522 )
        | ( p @ ( happ @ SV465 @ SV522 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4610]) ).

thf(4775,plain,
    ! [SV259: $i,SV523: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4611]) ).

thf(4776,plain,
    ! [SV259: $i,SV524: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4612]) ).

thf(4777,plain,
    ! [SV97: $i,SV139: $i,SV409: $i,SV313: $i] :
      ( ( ( SV313 = SV409 )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV139 @ SV313 ) @ SV409 ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV313 @ SV409 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4613]) ).

thf(4778,plain,
    ! [SV139: $i,SV97: $i,SV525: $i,SV466: $i] :
      ( ( ( SV466 != SV525 )
        | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV466 @ SV525 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4614]) ).

thf(4779,plain,
    ! [SV97: $i,SV526: $i,SV467: $i,SV139: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV139 @ SV467 ) @ SV526 ) )
        | ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV467 @ SV526 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4615]) ).

thf(4780,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( t @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) @ SV98 )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4616]) ).

thf(4781,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
              | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                    | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4617]) ).

thf(4782,plain,
    ! [SV315: $i,SV289: $i,SV98: $i,SV468: $i] :
      ( ( ( ~ ( t @ SV468 @ SV98 ) )
        = $true )
      | ( ( ! [SY1447: $i] :
              ( ~ ( t @ SY1447 @ SV98 )
              | ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SY1447 ) )
              | ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SY1447 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4618]) ).

thf(4783,plain,
    ! [SV99: $i,SV410: $i,SV316: $i,SV140: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV140 @ SV316 ) @ SV410 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV140 @ SV410 ) @ SV316 ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV316 @ SV410 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4619]) ).

thf(4784,plain,
    ! [SV99: $i,SV527: $i,SV469: $i,SV140: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV140 @ SV469 ) @ SV527 ) )
        | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV469 @ SV527 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4620]) ).

thf(4785,plain,
    ! [SV99: $i,SV470: $i,SV528: $i,SV140: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV140 @ SV528 ) @ SV470 ) )
        | ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV470 @ SV528 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4621]) ).

thf(4786,plain,
    ! [SV100: $i,SV166: $i,SV441: $i,SV411: $i,SV141: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV141 @ SV411 ) @ SV441 ) ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV166 @ SV411 ) @ SV441 ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV411 @ SV441 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4622]) ).

thf(4787,plain,
    ! [SV529: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ! [SY1467: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV529 @ SY1467 )
            | ( p @ ( happ @ ( happ @ SV141 @ SV529 ) @ SY1467 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4623]) ).

thf(4788,plain,
    ! [SV530: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ! [SY1468: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV530 @ SY1468 )
            | ~ ( p @ ( happ @ ( happ @ SV166 @ SV530 ) @ SY1468 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4624]) ).

thf(4789,plain,
    ! [SV290: $i,SV317: $i,SV101: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) )
        = $true )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4625]) ).

thf(4790,plain,
    ! [SV101: $i,SV317: $i,SV290: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SV317 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) ) )
        = $true )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4626]) ).

thf(4791,plain,
    ! [SV318: $i,SV291: $i,SV471: $i,SV101: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SV471 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SV318 @ SV471 ) )
        = $true )
      | ( ( c_24__type__11699___24t @ SV101 @ SV291 @ SV318 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4627]) ).

thf(4792,plain,
    ! [SV442: $i,SV412: $i,SV167: $i,SV142: $i,SV102: $i] :
      ( ( ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV412 @ SV442 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV167 @ SV412 ) @ SV442 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4628]) ).

thf(4793,plain,
    ! [SV142: $i,SV102: $i,SV443: $i,SV413: $i,SV167: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV167 @ SV413 ) @ SV443 ) )
        = $false )
      | ( ( c_24__lam__16___24a5 @ SV102 @ SV142 @ SV167 @ SV413 @ SV443 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4629]) ).

thf(4794,plain,
    ! [SV103: $i,SV444: $i] :
      ( ( ( p @ SV444 )
        = $false )
      | ( ( ! [SY1429: $i] : ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV444 @ SY1429 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4631]) ).

thf(4795,plain,
    ! [SV445: $i,SV103: $i,SV472: $i] :
      ( ( ( ~ ( p @ SV472 ) )
        = $true )
      | ( ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV445 @ SV472 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4632]) ).

thf(4796,plain,
    ! [SV104: $i,SV143: $i,SV446: $i,SV414: $i,SV168: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) )
          | ~ ( p @ ( happ @ SV143 @ SV414 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV143 @ SV446 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4633]) ).

thf(4797,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ! [SY1129: $i,SY1130: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
              | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) )
        | ~ ! [SY1131: $i] :
              ( ! [SY1132: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
              | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[4634]) ).

thf(4798,plain,
    ! [SV531: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ! [SY1469: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV531 @ SY1469 )
            | ( p @ ( happ @ SV143 @ SY1469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4635]) ).

thf(4799,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4637]) ).

thf(4800,plain,
    ! [SV296: $i,SV447: $i,SV261: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV447 )
        = $false )
      | ( ( ! [SY1431: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SY1431 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SV447 ) @ SY1431 ) ) ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4638]) ).

thf(4801,plain,
    ! [SV106: $i,SV322: $i,SV415: $i,SV144: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV144 @ SV415 ) @ SV322 ) )
        = $true )
      | ( ( ( SV322 = SV415 )
          | ( p @ ( happ @ ( happ @ SV144 @ SV322 ) @ SV415 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV322 @ SV415 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4639]) ).

thf(4802,plain,
    ! [SV106: $i,SV473: $i,SV532: $i,SV144: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV144 @ SV532 ) @ SV473 ) )
        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV473 @ SV532 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4640]) ).

thf(4803,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ~ ! [SY1023: $i,SY1024: $i] :
              ( ( SY1023 != SY1024 )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4641]) ).

thf(4804,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ~ ! [SY1025: $i,SY1026: $i] :
              ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
              | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4641]) ).

thf(4805,plain,
    ! [SV448: $i,SV416: $i,SV169: $i,SV145: $i,SV107: $i] :
      ( ( ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV416 @ SV448 )
        = $false )
      | ( ( p @ ( happ @ SV416 @ ( happ @ SV169 @ SV448 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4642]) ).

thf(4806,plain,
    ! [SV145: $i,SV107: $i,SV449: $i,SV169: $i,SV417: $i] :
      ( ( ( p @ ( happ @ SV417 @ ( happ @ SV169 @ SV449 ) ) )
        = $false )
      | ( ( chahn_2eHahnSets_2eset__map___24a5 @ SV107 @ SV145 @ SV169 @ SV417 @ SV449 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4643]) ).

thf(4807,plain,
    ! [SV108: $i,SV146: $i,SV418: $i,SV323: $i] :
      ( ( ( SV323 = SV418 )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV146 @ SV323 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV323 @ SV418 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4644]) ).

thf(4808,plain,
    ! [SV533: $i,SV474: $i,SV146: $i,SV108: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV474 @ SV533 )
        | ( SV474 = SV533 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4645]) ).

thf(4809,plain,
    ! [SV475: $i,SV146: $i,SV108: $i] :
      ( ( ( ! [SY1452: $i] :
              ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV475 @ SY1452 ) )
        = $true )
      | ( ( p @ ( happ @ SV146 @ SV475 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4646]) ).

thf(4810,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4647]) ).

thf(4811,plain,
    ! [SV262: $i] :
      ( ( ( ~ ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
                | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4647]) ).

thf(4812,plain,
    ! [SV263: $i,SV534: $i,SV419: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV534 )
          | ! [SY1470: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1470 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SV534 ) @ SY1470 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV419 )
        = $false )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4648]) ).

thf(4813,plain,
    ! [SV264: $i,SV535: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4649]) ).

thf(4814,plain,
    ! [SV264: $i,SV536: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4650]) ).

thf(4815,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK9_SY473 @ SV265 ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4651]) ).

thf(4816,plain,
    ! [SV265: $i] :
      ( ( ( ~ ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
                | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                      | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4651]) ).

thf(4817,plain,
    ! [SV420: $i,SV266: $i,SV537: $i] :
      ( ( ( ~ ( cType___24t @ SV537 )
          | ! [SY1471: $i] :
              ( ~ ( cType___24t @ SY1471 )
              | ! [SY1472: $i] :
                  ( ~ ( cType___24t @ SY1472 )
                  | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SY1471 ) @ SY1472 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4652]) ).

thf(4818,plain,
    ! [SV110: $i,SV170: $i,SV450: $i,SV421: $i,SV147: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV147 @ SV421 ) @ SV450 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV170 @ SV421 ) @ SV450 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV421 @ SV450 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4653]) ).

thf(4819,plain,
    ! [SV538: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ! [SY1473: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV538 @ SY1473 )
            | ( p @ ( happ @ ( happ @ SV147 @ SV538 ) @ SY1473 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4654]) ).

thf(4820,plain,
    ! [SV539: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ! [SY1474: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV539 @ SY1474 )
            | ( p @ ( happ @ ( happ @ SV170 @ SV539 ) @ SY1474 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4655]) ).

thf(4821,plain,
    ! [SV112: $i,SV297: $i,SV326: $i] :
      ( ( ( p @ SV326 )
        = $false )
      | ( ( p @ SV297 )
        = $false )
      | ( ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV297 @ SV326 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4658]) ).

thf(4822,plain,
    ! [SV540: $i,SV451: $i,SV112: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV451 @ SV540 ) ) )
        = $true )
      | ( ( p @ SV451 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4659]) ).

thf(4823,plain,
    ! [SV476: $i,SV452: $i,SV112: $i] :
      ( ( ( ~ ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV452 @ SV476 ) ) )
        = $true )
      | ( ( p @ SV476 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4660]) ).

thf(4824,plain,
    ! [SV113: $i,SV327: $i,SV424: $i,SV149: $i] :
      ( ( ( p @ ( happ @ SV149 @ SV424 ) )
        = $true )
      | ( ( p @ ( happ @ SV327 @ SV424 ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV327 @ SV424 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4661]) ).

thf(4825,plain,
    ! [SV477: $i,SV113: $i,SV541: $i,SV149: $i] :
      ( ( ~ ( p @ ( happ @ SV149 @ SV541 ) )
        | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV477 @ SV541 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4662]) ).

thf(4826,plain,
    ! [SV149: $i,SV113: $i,SV542: $i,SV478: $i] :
      ( ( ~ ( p @ ( happ @ SV478 @ SV542 ) )
        | ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV478 @ SV542 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4663]) ).

thf(4827,plain,
    ! [SV543: $i,SV453: $i,SV114: $i] :
      ( ( ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV453 @ SV543 ) )
        = $true )
      | ( ( p @ SV453 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4664]) ).

thf(4828,plain,
    ! [SV454: $i,SV114: $i,SV479: $i] :
      ( ( ( ~ ( p @ SV479 ) )
        = $true )
      | ( ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV454 @ SV479 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4665]) ).

thf(4829,plain,
    ! [SV114: $i,SV328: $i,SV298: $i] :
      ( ( ( p @ SV298 )
        = $false )
      | ( ( p @ SV328 )
        = $true )
      | ( ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV298 @ SV328 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4666]) ).

thf(4830,plain,
    ! [SV425: $i,SV267: $i,SV115: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 ) )
        = $true )
      | ( ( ! [SY1421: $i] :
              ( ~ ( t @ SY1421 @ SV115 )
              | ~ ( ~ ! [SY1422: $i] :
                        ( ~ ( t @ SY1422 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1422 ) )
                        | ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1422 ) ) )
                  | ~ ! [SY1423: $i] :
                        ( ~ ( t @ SY1423 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1423 ) )
                        | ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1423 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4667]) ).

thf(4831,plain,
    ! [SV116: $i,SV329: $i,SV426: $i,SV150: $i] :
      ( ( ( p @ ( happ @ SV150 @ SV426 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV329 @ SV426 ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV329 @ SV426 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4668]) ).

thf(4832,plain,
    ! [SV544: $i,SV480: $i,SV150: $i,SV116: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV480 @ SV544 )
        | ( p @ ( happ @ SV150 @ SV544 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4669]) ).

thf(4833,plain,
    ! [SV545: $i,SV481: $i,SV150: $i,SV116: $i] :
      ( ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV481 @ SV545 )
        | ( p @ ( happ @ SV481 @ SV545 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4670]) ).

thf(4834,plain,
    ! [SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( ~ ! [SY1424: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1424 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1424 ) ) ) )
          | ~ ! [SY1425: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1425 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1425 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1425 ) ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4671]) ).

thf(4835,plain,
    ! [SV482: $i,SV455: $i,SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ( ~ ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV455 @ SV482 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV455 ) ) @ ( happ @ SV171 @ SV482 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4672]) ).

thf(4836,plain,
    ! [SV151: $i,SV118: $i,SV483: $i,SV456: $i,SV171: $i,SV269: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV456 ) ) @ ( happ @ SV171 @ SV483 ) ) ) )
        = $true )
      | ( ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV456 @ SV483 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4673]) ).

thf(4837,plain,
    ! [SV484: $i,SV457: $i,SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV457 @ SV484 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV457 ) ) @ ( happ @ SV172 @ SV484 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4674]) ).

thf(4838,plain,
    ! [SV152: $i,SV119: $i,SV485: $i,SV458: $i,SV172: $i,SV270: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV458 ) ) @ ( happ @ SV172 @ SV485 ) ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV458 @ SV485 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4675]) ).

thf(4839,plain,
    ! [SV120: $i,SV330: $i,SV299: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV299 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) )
        = $true )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4676]) ).

thf(4840,plain,
    ! [SV299: $i,SV330: $i,SV120: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV330 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) ) )
        = $true )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4677]) ).

thf(4841,plain,
    ! [SV331: $i,SV120: $i,SV486: $i,SV300: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SV486 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV331 @ SV486 ) )
        = $true )
      | ( ( c_24__type__11787___24t @ SV120 @ SV300 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4678]) ).

thf(4842,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( cType___24t @ ( sK7_SY472 @ SV271 ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4681]) ).

thf(4843,plain,
    ! [SV271: $i] :
      ( ( ( ~ ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4681]) ).

thf(4844,plain,
    ! [SV430: $i,SV272: $i,SV546: $i] :
      ( ( ( ~ ( cType___24t @ SV546 )
          | ( cType___24t @ ( happ @ ( happ @ SV272 @ SV430 ) @ SV546 ) ) )
        = $true )
      | ( ( cType___24t @ SV430 )
        = $false )
      | ( ( c_24__type__52___24t @ SV272 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4682]) ).

thf(4845,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV487: $i,SV459: $i,SV173: $i] :
      ( ( ( ( ( happ @ SV173 @ SV459 )
           != ( happ @ SV173 @ SV487 ) )
          | ~ ( p @ ( happ @ ( happ @ SV273 @ SV459 ) @ SV487 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV459 @ SV487 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4683]) ).

thf(4846,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ! [SY1315: $i,SY1316: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1315 @ SY1316 )
            | ( ( happ @ SV173 @ SY1315 )
              = ( happ @ SV173 @ SY1316 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4684]) ).

thf(4847,plain,
    ! [SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ! [SY1317: $i,SY1318: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SY1317 @ SY1318 )
            | ( p @ ( happ @ ( happ @ SV273 @ SY1317 ) @ SY1318 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4685]) ).

thf(4848,plain,
    ! [SV334: $i,SV175: $i,SV5: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( ! [SY1362: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1362 )
              | ! [SY1363: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1363 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SY1362 @ SY1363 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SY1362 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1363 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4686]) ).

thf(4849,plain,
    ! [SV335: $i,SV183: $i,SV15: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ SV183 @ SV335 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV15 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV183 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV15 @ SV335 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV335 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV15 @ SV183 )
        = $false )
      | ( ( cType___24t @ SV15 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4688]) ).

thf(4850,plain,
    ! [SV336: $i,SV184: $i,SV16: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ SV184 @ SV336 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV16 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV184 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV16 @ SV336 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV336 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV16 @ SV184 )
        = $false )
      | ( ( cType___24t @ SV16 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4689]) ).

thf(4851,plain,
    ! [SV337: $i,SV185: $i,SV17: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ SV185 @ SV337 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV17 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV185 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV17 @ SV337 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV337 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV17 @ SV185 )
        = $false )
      | ( ( cType___24t @ SV17 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4690]) ).

thf(4852,plain,
    ! [SV338: $i,SV186: $i,SV18: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ SV186 @ SV338 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV18 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV186 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV18 @ SV338 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV338 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV18 @ SV186 )
        = $false )
      | ( ( cType___24t @ SV18 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4691]) ).

thf(4853,plain,
    ! [SV339: $i,SV187: $i,SV19: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ SV187 @ SV339 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV19 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV187 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV19 @ SV339 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV339 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV19 @ SV187 )
        = $false )
      | ( ( cType___24t @ SV19 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4692]) ).

thf(4854,plain,
    ! [SV340: $i,SV188: $i,SV20: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ SV188 @ SV340 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV20 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV188 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV20 @ SV340 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV340 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV20 @ SV188 )
        = $false )
      | ( ( cType___24t @ SV20 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4693]) ).

thf(4855,plain,
    ! [SV341: $i,SV189: $i,SV21: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ SV189 @ SV341 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV21 @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV189 ) @ ( chahn_2eHahnRelationsBasic_2eimmediate___24a2 @ SV21 @ SV341 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV341 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV21 @ SV189 )
        = $false )
      | ( ( cType___24t @ SV21 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4694]) ).

thf(4856,plain,
    ! [SV342: $i,SV190: $i,SV488: $i,SV22: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV488 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SV342 ) @ SV488 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV342 @ SV488 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV342 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4695]) ).

thf(4857,plain,
    ! [SV343: $i,SV191: $i,SV489: $i,SV23: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV489 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ SV489 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SV489 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV343 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4696]) ).

thf(4858,plain,
    ! [SV345: $i,SV194: $i,SV26: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV26 @ SV194 @ SV345 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV26 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV26 @ SV345 @ SV194 ) @ SV194 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV345 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV26 @ SV194 )
        = $false )
      | ( ( cType___24t @ SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4697]) ).

thf(4859,plain,
    ! [SV346: $i,SV195: $i,SV27: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV27 @ SV195 @ SV346 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV27 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV27 @ SV195 @ SV346 ) @ SV195 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV346 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV27 @ SV195 )
        = $false )
      | ( ( cType___24t @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4698]) ).

thf(4860,plain,
    ! [SV348: $i,SV197: $i,SV29: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( ! [SY1366: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1366 )
              | ! [SY1367: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1367 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SY1366 @ SY1367 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SY1366 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1367 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4699]) ).

thf(4861,plain,
    ! [SV349: $i,SV198: $i,SV30: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( ! [SY1368: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1368 )
              | ! [SY1369: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1369 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SY1368 @ SY1369 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SY1368 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1369 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4700]) ).

thf(4862,plain,
    ! [SV350: $i,SV199: $i,SV490: $i,SV31: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV490 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SV350 ) @ SV490 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SV490 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV350 @ SV490 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV350 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4701]) ).

thf(4863,plain,
    ! [SV351: $i,SV200: $i,SV491: $i,SV32: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV491 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SV351 ) @ SV491 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV351 @ SV491 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV351 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4702]) ).

thf(4864,plain,
    ! [SV352: $i,SV201: $i,SV33: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( ! [SY1372: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1372 )
              | ! [SY1373: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1373 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SY1372 @ SY1373 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SY1372 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1373 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4703]) ).

thf(4865,plain,
    ! [SV353: $i,SV202: $i,SV34: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( ! [SY1374: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1374 )
              | ! [SY1375: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1375 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SY1374 @ SY1375 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SY1374 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1375 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4704]) ).

thf(4866,plain,
    ! [SV354: $i,SV203: $i,SV35: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ SV203 @ SV354 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV35 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV203 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV35 @ SV354 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV354 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV35 @ SV203 )
        = $false )
      | ( ( cType___24t @ SV35 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4705]) ).

thf(4867,plain,
    ! [SV355: $i,SV204: $i,SV36: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ SV204 @ SV355 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV36 @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV204 ) @ ( cCoq_2eRelations_2eRelation__Operators_2etransp___24a2 @ SV36 @ SV355 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV355 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV36 @ SV204 )
        = $false )
      | ( ( cType___24t @ SV36 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4706]) ).

thf(4868,plain,
    ! [SV356: $i,SV205: $i,SV492: $i,SV37: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV492 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SV356 ) @ SV492 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV356 @ SV492 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV356 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4707]) ).

thf(4869,plain,
    ! [SV357: $i,SV206: $i,SV493: $i,SV38: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV493 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ SV493 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SV493 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV357 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4708]) ).

thf(4870,plain,
    ! [SV359: $i,SV209: $i,SV41: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV41 @ SV209 @ SV359 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV41 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV41 @ SV209 @ SV359 ) @ SV359 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV359 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV41 @ SV209 )
        = $false )
      | ( ( cType___24t @ SV41 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4709]) ).

thf(4871,plain,
    ! [SV360: $i,SV210: $i,SV42: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV42 @ SV210 @ SV360 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV42 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV42 @ SV360 @ SV210 ) @ SV360 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV360 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV42 @ SV210 )
        = $false )
      | ( ( cType___24t @ SV42 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4710]) ).

thf(4872,plain,
    ! [SV361: $i,SV211: $i,SV43: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( ! [SY1378: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1378 )
              | ! [SY1379: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1379 )
                  | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SY1378 @ SY1379 )
                  | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SY1378 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1379 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4711]) ).

thf(4873,plain,
    ! [SV362: $i,SV212: $i,SV44: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( ! [SY1380: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1380 )
              | ! [SY1381: $i] :
                  ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1381 )
                  | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SY1380 @ SY1381 ) )
                  | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SY1380 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1381 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4712]) ).

thf(4874,plain,
    ! [SV363: $i,SV213: $i,SV45: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV45 @ SV213 @ SV363 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV45 @ SV213 @ SV363 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV363 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV45 @ SV213 )
        = $false )
      | ( ( cType___24t @ SV45 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4713]) ).

thf(4875,plain,
    ! [SV364: $i,SV214: $i,SV46: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV46 @ SV214 @ SV364 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV46 @ SV364 @ SV214 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV364 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV46 @ SV214 )
        = $false )
      | ( ( cType___24t @ SV46 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4714]) ).

thf(4876,plain,
    ! [SV365: $i,SV215: $i,SV47: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ SV215 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2efunctional___24a2 @ SV47 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV47 @ SV215 @ SV365 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV365 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV47 @ SV215 )
        = $false )
      | ( ( cType___24t @ SV47 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4715]) ).

thf(4877,plain,
    ! [SV366: $i,SV216: $i,SV48: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4716]) ).

thf(4878,plain,
    ! [SV368: $i,SV218: $i,SV494: $i,SV50: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV494 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SV494 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SV494 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4717]) ).

thf(4879,plain,
    ! [SV220: $i,SV370: $i,SV495: $i,SV52: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV495 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SV495 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SV495 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4718]) ).

thf(4880,plain,
    ! [SV371: $i,SV221: $i,SV496: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 ) )
        = $true )
      | ( ( ! [SY1457: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1457 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SY1457 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SY1457 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4719]) ).

thf(4881,plain,
    ! [SV372: $i,SV222: $i,SV497: $i,SV54: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4720]) ).

thf(4882,plain,
    ! [SV373: $i,SV223: $i,SV498: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 ) )
        = $true )
      | ( ( ! [SY1458: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1458 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1458 @ SV498 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SY1458 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4721]) ).

thf(4883,plain,
    ! [SV375: $i,SV225: $i,SV57: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ SV225 @ SV375 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV57 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV225 ) @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV57 @ SV375 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV375 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV57 @ SV225 )
        = $false )
      | ( ( cType___24t @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4722]) ).

thf(4884,plain,
    ! [SV376: $i,SV227: $i,SV59: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ SV227 @ SV376 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV59 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV227 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV59 @ SV376 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV376 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV59 @ SV227 )
        = $false )
      | ( ( cType___24t @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4723]) ).

thf(4885,plain,
    ! [SV377: $i,SV228: $i,SV60: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ SV228 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV60 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV228 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV60 @ SV377 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV377 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV60 @ SV228 )
        = $false )
      | ( ( cType___24t @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4724]) ).

thf(4886,plain,
    ! [SV378: $i,SV229: $i,SV499: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 ) )
        = $true )
      | ( ( ! [SY1459: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1459 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SY1459 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SY1459 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4725]) ).

thf(4887,plain,
    ! [SV379: $i,SV230: $i,SV62: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ SV379 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV62 @ SV230 @ ( chahn_2eHahnRelationsBasic_2eclos__refl___24a2 @ SV62 @ SV379 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV379 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV62 @ SV230 )
        = $false )
      | ( ( cType___24t @ SV62 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4726]) ).

thf(4888,plain,
    ! [SV380: $i,SV231: $i,SV63: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ SV380 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV63 @ SV231 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a2 @ SV63 @ SV380 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV380 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV63 @ SV231 )
        = $false )
      | ( ( cType___24t @ SV63 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4727]) ).

thf(4889,plain,
    ! [SV381: $i,SV232: $i,SV64: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ SV381 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV64 @ SV232 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV64 @ SV381 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV381 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV64 @ SV232 )
        = $false )
      | ( ( cType___24t @ SV64 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4728]) ).

thf(4890,plain,
    ! [SV382: $i,SV233: $i,SV65: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ SV233 @ SV382 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV65 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV233 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV65 @ SV382 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV382 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV65 @ SV233 )
        = $false )
      | ( ( cType___24t @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4729]) ).

thf(4891,plain,
    ! [SV383: $i,SV234: $i,SV66: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ SV234 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV66 @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV234 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a2 @ SV66 @ SV383 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV383 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV66 @ SV234 )
        = $false )
      | ( ( cType___24t @ SV66 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4730]) ).

thf(4892,plain,
    ! [SV384: $i,SV235: $i,SV500: $i,SV67: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4731]) ).

thf(4893,plain,
    ! [SV386: $i,SV237: $i,SV501: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 ) )
        = $true )
      | ( ( ! [SY1460: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1460 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SY1460 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SY1460 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4732]) ).

thf(4894,plain,
    ! [SV388: $i,SV239: $i,SV502: $i,SV71: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV502 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SV502 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4733]) ).

thf(4895,plain,
    ! [SV390: $i,SV241: $i,SV503: $i,SV73: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV503 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SV503 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SV503 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4734]) ).

thf(4896,plain,
    ! [SV391: $i,SV242: $i,SV74: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4735]) ).

thf(4897,plain,
    ! [SV78: $i,SV504: $i] :
      ( ( ( ~ ( cProp___24t @ SV504 ) )
        = $true )
      | ( ( ( p @ SV78 )
          | ~ ( p @ SV78 )
          | ( p @ SV504 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4736]) ).

thf(4898,plain,
    ! [SV78: $i,SV505: $i] :
      ( ( ( ~ ( cProp___24t @ SV505 ) )
        = $true )
      | ( ( ( p @ SV78 )
          | ~ ( p @ SV505 )
          | ( p @ SV505 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4737]) ).

thf(4899,plain,
    ! [SV78: $i,SV506: $i] :
      ( ( ( ~ ( cProp___24t @ SV506 ) )
        = $true )
      | ( ( ~ ( p @ SV506 )
          | ~ ( p @ SV78 )
          | ( p @ SV506 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4738]) ).

thf(4900,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( ~ ( cProp___24t @ SV507 ) )
        = $true )
      | ( ( ~ ( p @ SV507 )
          | ~ ( p @ SV507 )
          | ( p @ SV507 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4739]) ).

thf(4901,plain,
    ! [SV244: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( sK2_SY468 @ SV244 ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4740]) ).

thf(4902,plain,
    ! [SV244: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) ) )
        = $true )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4741]) ).

thf(4903,plain,
    ! [SV245: $i,SV508: $i,SV392: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ SV508 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ ( happ @ ( happ @ SV245 @ SV392 ) @ SV508 ) )
        = $true )
      | ( ( cType___24t @ SV392 )
        = $false )
      | ( ( c_24__type__96___24t @ SV245 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4742]) ).

thf(4904,plain,
    ! [SV246: $i,SV509: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4743]) ).

thf(4905,plain,
    ! [SV246: $i,SV510: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4744]) ).

thf(4906,plain,
    ! [SV81: $i,SV161: $i,SV431: $i,SV393: $i,SV130: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV130 @ SV393 ) @ SV431 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV161 @ SV393 ) @ SV431 ) )
        = $true )
      | ( ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV393 @ SV431 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4745]) ).

thf(4907,plain,
    ! [SV161: $i,SV81: $i,SV547: $i,SV511: $i,SV130: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV130 @ SV511 ) @ SV547 ) )
        | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV511 @ SV547 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4746]) ).

thf(4908,plain,
    ! [SV130: $i,SV81: $i,SV548: $i,SV512: $i,SV161: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV161 @ SV512 ) @ SV548 ) )
        | ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV512 @ SV548 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4747]) ).

thf(4909,plain,
    ! [SV396: $i,SV249: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( ! [SY1400: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1400 )
              | ~ ( ~ ! [SY1401: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1401 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1401 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1401 ) ) )
                  | ~ ! [SY1402: $i] :
                        ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1402 )
                        | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SY1400 @ SY1402 )
                        | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1402 ) )
                        | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SY1400 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4750]) ).

thf(4910,plain,
    ! [SV250: $i,SV513: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 )
          | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4751]) ).

thf(4911,plain,
    ! [SV250: $i,SV514: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 )
          | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4752]) ).

thf(4912,plain,
    ! [SV515: $i,SV460: $i,SV133: $i,SV86: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV460 @ SV515 ) )
        = $true )
      | ( ( p @ ( happ @ SV133 @ SV515 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4754]) ).

thf(4913,plain,
    ! [SV516: $i,SV461: $i,SV133: $i,SV86: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV461 @ SV516 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV461 @ SV516 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4755]) ).

thf(4914,plain,
    ! [SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ~ ! [SY1403: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1403 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1403 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1403 ) ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4756]) ).

thf(4915,plain,
    ! [SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ~ ! [SY1404: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1404 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1404 ) ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1404 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4756]) ).

thf(4916,plain,
    ! [SV90: $i,SV163: $i,SV434: $i,SV404: $i,SV135: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV135 @ SV404 ) @ SV434 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV163 @ SV404 ) @ SV434 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV404 @ SV434 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4757]) ).

thf(4917,plain,
    ! [SV163: $i,SV90: $i,SV549: $i,SV517: $i,SV135: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV135 @ SV517 ) @ SV549 ) )
        | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV517 @ SV549 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4758]) ).

thf(4918,plain,
    ! [SV135: $i,SV90: $i,SV550: $i,SV518: $i,SV163: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV163 @ SV518 ) @ SV550 ) )
        | ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV518 @ SV550 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4759]) ).

thf(4919,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ~ ! [SY1272: $i] :
                ( ~ ( cProp___24t @ SY1272 )
                | ( p @ SV91 )
                | ~ ( p @ SV91 )
                | ( p @ SV254 )
                | ( p @ SY1272 ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4760]) ).

thf(4920,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ~ ! [SY1273: $i] :
                ( ~ ( cProp___24t @ SY1273 )
                | ( p @ SV91 )
                | ~ ( p @ SY1273 )
                | ( p @ SV254 )
                | ( p @ SY1273 ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4760]) ).

thf(4921,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ! [SY1274: $i] :
                ( ~ ( cProp___24t @ SY1274 )
                | ~ ( p @ SV254 )
                | ~ ( p @ SV91 )
                | ( p @ SV254 )
                | ( p @ SY1274 ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4761]) ).

thf(4922,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ~ ! [SY1275: $i] :
                ( ~ ( cProp___24t @ SY1275 )
                | ~ ( p @ SV254 )
                | ~ ( p @ SY1275 )
                | ( p @ SV254 )
                | ( p @ SY1275 ) ) )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4761]) ).

thf(4923,plain,
    ! [SV92: $i,SV435: $i,SV164: $i,SV405: $i,SV136: $i] :
      ( ( ( p @ ( happ @ SV136 @ SV405 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV164 @ SV435 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV405 @ SV435 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4762]) ).

thf(4924,plain,
    ! [SV519: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ( ! [SY1465: $i] :
              ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV519 @ SY1465 ) )
        = $true )
      | ( ( p @ ( happ @ SV136 @ SV519 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4763]) ).

thf(4925,plain,
    ! [SV551: $i,SV520: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV520 @ SV551 )
        | ( p @ ( happ @ SV164 @ SV551 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4764]) ).

thf(4926,plain,
    ! [SV462: $i,SV439: $i,SV94: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV439 @ SV462 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV439 @ SV462 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4770]) ).

thf(4927,plain,
    ! [SV463: $i,SV440: $i,SV94: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV94 @ SV440 @ SV463 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV94 @ SV463 @ SV440 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4771]) ).

thf(4928,plain,
    ! [SV95: $i,SV138: $i,SV408: $i,SV312: $i] :
      ( ( ( p @ ( happ @ SV312 @ SV408 ) )
        = $false )
      | ( ( p @ ( happ @ SV138 @ SV408 ) )
        = $false )
      | ( ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV312 @ SV408 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4772]) ).

thf(4929,plain,
    ! [SV521: $i,SV464: $i,SV138: $i,SV95: $i] :
      ( ( ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV464 @ SV521 ) )
        = $true )
      | ( ( p @ ( happ @ SV138 @ SV521 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4773]) ).

thf(4930,plain,
    ! [SV522: $i,SV465: $i,SV138: $i,SV95: $i] :
      ( ( ( ~ ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV465 @ SV522 ) )
        = $true )
      | ( ( p @ ( happ @ SV465 @ SV522 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4774]) ).

thf(4931,plain,
    ! [SV259: $i,SV523: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4775]) ).

thf(4932,plain,
    ! [SV259: $i,SV524: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4776]) ).

thf(4933,plain,
    ! [SV139: $i,SV97: $i,SV525: $i,SV466: $i] :
      ( ( ( SV466 != SV525 )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV466 @ SV525 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4778]) ).

thf(4934,plain,
    ! [SV97: $i,SV526: $i,SV467: $i,SV139: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV139 @ SV467 ) @ SV526 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV467 @ SV526 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4779]) ).

thf(4935,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
          | ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4781]) ).

thf(4936,plain,
    ! [SV315: $i,SV289: $i,SV98: $i,SV468: $i] :
      ( ( ( t @ SV468 @ SV98 )
        = $false )
      | ( ( ! [SY1447: $i] :
              ( ~ ( t @ SY1447 @ SV98 )
              | ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SY1447 ) )
              | ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SY1447 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4782]) ).

thf(4937,plain,
    ! [SV99: $i,SV527: $i,SV469: $i,SV140: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV140 @ SV469 ) @ SV527 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV469 @ SV527 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4784]) ).

thf(4938,plain,
    ! [SV99: $i,SV470: $i,SV528: $i,SV140: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV140 @ SV528 ) @ SV470 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV470 @ SV528 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4785]) ).

thf(4939,plain,
    ! [SV100: $i,SV166: $i,SV441: $i,SV411: $i,SV141: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV141 @ SV411 ) @ SV441 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV166 @ SV411 ) @ SV441 ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV411 @ SV441 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4786]) ).

thf(4940,plain,
    ! [SV552: $i,SV529: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV529 @ SV552 )
        | ( p @ ( happ @ ( happ @ SV141 @ SV529 ) @ SV552 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4787]) ).

thf(4941,plain,
    ! [SV553: $i,SV530: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV530 @ SV553 )
        | ~ ( p @ ( happ @ ( happ @ SV166 @ SV530 ) @ SV553 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4788]) ).

thf(4942,plain,
    ! [SV101: $i,SV317: $i,SV290: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV290 @ ( happ @ SV317 @ ( sK17_Vv__CANONICAL__2 @ SV317 @ SV290 @ SV101 ) ) )
        = $false )
      | ( ( c_24__type__11699___24t @ SV101 @ SV290 @ SV317 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4790]) ).

thf(4943,plain,
    ! [SV318: $i,SV291: $i,SV471: $i,SV101: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV101 @ SV471 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV291 @ ( happ @ SV318 @ SV471 ) )
        = $true )
      | ( ( c_24__type__11699___24t @ SV101 @ SV291 @ SV318 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4791]) ).

thf(4944,plain,
    ! [SV554: $i,SV444: $i,SV103: $i] :
      ( ( ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV444 @ SV554 ) )
        = $true )
      | ( ( p @ SV444 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4794]) ).

thf(4945,plain,
    ! [SV445: $i,SV103: $i,SV472: $i] :
      ( ( ( p @ SV472 )
        = $false )
      | ( ( p @ ( c_24__prop__35356___24a3 @ SV103 @ SV445 @ SV472 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4795]) ).

thf(4946,plain,
    ! [SV104: $i,SV143: $i,SV446: $i,SV414: $i,SV168: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV143 @ SV414 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV143 @ SV446 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4796]) ).

thf(4947,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ! [SY1129: $i,SY1130: $i] :
              ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
              | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4797]) ).

thf(4948,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ! [SY1131: $i] :
              ( ! [SY1132: $i] :
                  ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
              | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[4797]) ).

thf(4949,plain,
    ! [SV555: $i,SV531: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV531 @ SV555 )
        | ( p @ ( happ @ SV143 @ SV555 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4798]) ).

thf(4950,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4799]) ).

thf(4951,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4799]) ).

thf(4952,plain,
    ! [SV447: $i,SV296: $i,SV556: $i,SV261: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV556 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SV447 ) @ SV556 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV447 )
        = $false )
      | ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4800]) ).

thf(4953,plain,
    ! [SV106: $i,SV144: $i,SV415: $i,SV322: $i] :
      ( ( ( SV322 = SV415 )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV144 @ SV322 ) @ SV415 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV144 @ SV415 ) @ SV322 ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV322 @ SV415 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4801]) ).

thf(4954,plain,
    ! [SV106: $i,SV473: $i,SV532: $i,SV144: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV144 @ SV532 ) @ SV473 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV473 @ SV532 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4802]) ).

thf(4955,plain,
    ! [SV144: $i,SV106: $i] :
      ( ( ! [SY1023: $i,SY1024: $i] :
            ( ( SY1023 != SY1024 )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1023 @ SY1024 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4803]) ).

thf(4956,plain,
    ! [SV106: $i,SV144: $i] :
      ( ( ! [SY1025: $i,SY1026: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV144 @ SY1025 ) @ SY1026 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SY1025 @ SY1026 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4804]) ).

thf(4957,plain,
    ! [SV108: $i,SV418: $i,SV323: $i,SV146: $i] :
      ( ( ( p @ ( happ @ SV146 @ SV323 ) )
        = $false )
      | ( ( SV323 = SV418 )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV323 @ SV418 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4807]) ).

thf(4958,plain,
    ! [SV533: $i,SV474: $i,SV146: $i,SV108: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV474 @ SV533 ) )
        = $true )
      | ( ( SV474 = SV533 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4808]) ).

thf(4959,plain,
    ! [SV557: $i,SV475: $i,SV146: $i,SV108: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV475 @ SV557 ) )
        = $true )
      | ( ( p @ ( happ @ SV146 @ SV475 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4809]) ).

thf(4960,plain,
    ! [SV262: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK4_SY469 @ SV262 ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4810]) ).

thf(4961,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
              | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4811]) ).

thf(4962,plain,
    ! [SV263: $i,SV534: $i,SV419: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV534 ) )
        = $true )
      | ( ( ! [SY1470: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1470 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SV534 ) @ SY1470 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV419 )
        = $false )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4812]) ).

thf(4963,plain,
    ! [SV264: $i,SV535: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4813]) ).

thf(4964,plain,
    ! [SV264: $i,SV536: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4814]) ).

thf(4965,plain,
    ! [SV265: $i] :
      ( ( ( cType___24t @ ( sK9_SY473 @ SV265 ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4815]) ).

thf(4966,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
              | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                    | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4816]) ).

thf(4967,plain,
    ! [SV420: $i,SV266: $i,SV537: $i] :
      ( ( ( ~ ( cType___24t @ SV537 ) )
        = $true )
      | ( ( ! [SY1471: $i] :
              ( ~ ( cType___24t @ SY1471 )
              | ! [SY1472: $i] :
                  ( ~ ( cType___24t @ SY1472 )
                  | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SY1471 ) @ SY1472 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4817]) ).

thf(4968,plain,
    ! [SV110: $i,SV170: $i,SV450: $i,SV421: $i,SV147: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV147 @ SV421 ) @ SV450 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV170 @ SV421 ) @ SV450 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV421 @ SV450 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4818]) ).

thf(4969,plain,
    ! [SV558: $i,SV538: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV538 @ SV558 )
        | ( p @ ( happ @ ( happ @ SV147 @ SV538 ) @ SV558 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4819]) ).

thf(4970,plain,
    ! [SV559: $i,SV539: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV539 @ SV559 )
        | ( p @ ( happ @ ( happ @ SV170 @ SV539 ) @ SV559 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4820]) ).

thf(4971,plain,
    ! [SV540: $i,SV451: $i,SV112: $i] :
      ( ( ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV451 @ SV540 ) )
        = $false )
      | ( ( p @ SV451 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4822]) ).

thf(4972,plain,
    ! [SV476: $i,SV452: $i,SV112: $i] :
      ( ( ( p @ ( c_24__prop__35355___24a3 @ SV112 @ SV452 @ SV476 ) )
        = $false )
      | ( ( p @ SV476 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4823]) ).

thf(4973,plain,
    ! [SV477: $i,SV113: $i,SV541: $i,SV149: $i] :
      ( ( ( ~ ( p @ ( happ @ SV149 @ SV541 ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV477 @ SV541 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4825]) ).

thf(4974,plain,
    ! [SV149: $i,SV113: $i,SV542: $i,SV478: $i] :
      ( ( ( ~ ( p @ ( happ @ SV478 @ SV542 ) ) )
        = $true )
      | ( ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV478 @ SV542 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4826]) ).

thf(4975,plain,
    ! [SV454: $i,SV114: $i,SV479: $i] :
      ( ( ( p @ SV479 )
        = $false )
      | ( ( p @ ( c_24__prop__35357___24a3 @ SV114 @ SV454 @ SV479 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4828]) ).

thf(4976,plain,
    ! [SV425: $i,SV267: $i,SV115: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( ! [SY1421: $i] :
              ( ~ ( t @ SY1421 @ SV115 )
              | ~ ( ~ ! [SY1422: $i] :
                        ( ~ ( t @ SY1422 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1422 ) )
                        | ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1422 ) ) )
                  | ~ ! [SY1423: $i] :
                        ( ~ ( t @ SY1423 @ SV115 )
                        | ~ ( p @ ( happ @ ( happ @ SV425 @ SY1421 ) @ SY1423 ) )
                        | ( p @ ( happ @ ( happ @ SV267 @ SY1421 ) @ SY1423 ) ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4830]) ).

thf(4977,plain,
    ! [SV116: $i,SV150: $i,SV426: $i,SV329: $i] :
      ( ( ( p @ ( happ @ SV329 @ SV426 ) )
        = $false )
      | ( ( p @ ( happ @ SV150 @ SV426 ) )
        = $false )
      | ( ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV329 @ SV426 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4831]) ).

thf(4978,plain,
    ! [SV544: $i,SV480: $i,SV150: $i,SV116: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV480 @ SV544 ) )
        = $true )
      | ( ( p @ ( happ @ SV150 @ SV544 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4832]) ).

thf(4979,plain,
    ! [SV545: $i,SV481: $i,SV150: $i,SV116: $i] :
      ( ( ( ~ ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV481 @ SV545 ) )
        = $true )
      | ( ( p @ ( happ @ SV481 @ SV545 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4833]) ).

thf(4980,plain,
    ! [SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( ~ ! [SY1424: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1424 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1424 ) ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4834]) ).

thf(4981,plain,
    ! [SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( ~ ! [SY1425: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1425 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1425 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1425 ) ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4834]) ).

thf(4982,plain,
    ! [SV482: $i,SV455: $i,SV269: $i,SV171: $i,SV151: $i,SV118: $i] :
      ( ( ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV455 @ SV482 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV455 ) ) @ ( happ @ SV171 @ SV482 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4835]) ).

thf(4983,plain,
    ! [SV151: $i,SV118: $i,SV483: $i,SV456: $i,SV171: $i,SV269: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV269 @ ( happ @ SV171 @ SV456 ) ) @ ( happ @ SV171 @ SV483 ) ) )
        = $false )
      | ( ( c_24__lam__7800___24a6 @ SV118 @ SV151 @ SV171 @ SV269 @ SV456 @ SV483 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4836]) ).

thf(4984,plain,
    ! [SV484: $i,SV457: $i,SV270: $i,SV172: $i,SV152: $i,SV119: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV457 @ SV484 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV457 ) ) @ ( happ @ SV172 @ SV484 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4837]) ).

thf(4985,plain,
    ! [SV152: $i,SV119: $i,SV485: $i,SV458: $i,SV172: $i,SV270: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV270 @ ( happ @ SV172 @ SV458 ) ) @ ( happ @ SV172 @ SV485 ) ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2emap__rel___24a6 @ SV119 @ SV152 @ SV172 @ SV270 @ SV458 @ SV485 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4838]) ).

thf(4986,plain,
    ! [SV299: $i,SV330: $i,SV120: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV330 @ ( sK15_Vv__CANONICAL__2 @ SV330 @ SV299 @ SV120 ) ) )
        = $false )
      | ( ( c_24__type__11787___24t @ SV120 @ SV299 @ SV330 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4840]) ).

thf(4987,plain,
    ! [SV331: $i,SV120: $i,SV486: $i,SV300: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV300 @ SV486 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV120 @ ( happ @ SV331 @ SV486 ) )
        = $true )
      | ( ( c_24__type__11787___24t @ SV120 @ SV300 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4841]) ).

thf(4988,plain,
    ! [SV271: $i] :
      ( ( ( cType___24t @ ( sK7_SY472 @ SV271 ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4842]) ).

thf(4989,plain,
    ! [SV271: $i] :
      ( ( ( ~ ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) ) )
        = $true )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4843]) ).

thf(4990,plain,
    ! [SV430: $i,SV272: $i,SV546: $i] :
      ( ( ( ~ ( cType___24t @ SV546 ) )
        = $true )
      | ( ( cType___24t @ ( happ @ ( happ @ SV272 @ SV430 ) @ SV546 ) )
        = $true )
      | ( ( cType___24t @ SV430 )
        = $false )
      | ( ( c_24__type__52___24t @ SV272 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4844]) ).

thf(4991,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV487: $i,SV459: $i,SV173: $i] :
      ( ( ( ( happ @ SV173 @ SV459 )
         != ( happ @ SV173 @ SV487 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV273 @ SV459 ) @ SV487 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV459 @ SV487 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4845]) ).

thf(4992,plain,
    ! [SV560: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ! [SY1475: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV560 @ SY1475 )
            | ( ( happ @ SV173 @ SV560 )
              = ( happ @ SV173 @ SY1475 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4846]) ).

thf(4993,plain,
    ! [SV561: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ! [SY1476: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV561 @ SY1476 )
            | ( p @ ( happ @ ( happ @ SV273 @ SV561 ) @ SY1476 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4847]) ).

thf(4994,plain,
    ! [SV334: $i,SV175: $i,SV562: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
          | ! [SY1477: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1477 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SY1477 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1477 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4848]) ).

thf(4995,plain,
    ! [SV342: $i,SV190: $i,SV488: $i,SV22: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV488 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ SV342 ) @ SV488 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV190 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV22 @ SV342 @ SV488 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV342 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV22 @ SV190 )
        = $false )
      | ( ( cType___24t @ SV22 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4856]) ).

thf(4996,plain,
    ! [SV343: $i,SV191: $i,SV489: $i,SV23: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV489 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV23 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ SV489 ) ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV343 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV23 @ SV191 @ SV489 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV343 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV23 @ SV191 )
        = $false )
      | ( ( cType___24t @ SV23 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4857]) ).

thf(4997,plain,
    ! [SV348: $i,SV197: $i,SV563: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
          | ! [SY1478: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1478 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SY1478 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1478 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4860]) ).

thf(4998,plain,
    ! [SV349: $i,SV198: $i,SV564: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
          | ! [SY1479: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1479 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SY1479 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1479 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4861]) ).

thf(4999,plain,
    ! [SV350: $i,SV199: $i,SV490: $i,SV31: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV490 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ SV199 @ SV350 ) @ SV490 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV31 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV199 @ SV490 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV31 @ SV350 @ SV490 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV350 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV31 @ SV199 )
        = $false )
      | ( ( cType___24t @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4862]) ).

thf(5000,plain,
    ! [SV351: $i,SV200: $i,SV491: $i,SV32: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV491 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ SV351 ) @ SV491 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV200 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV32 @ SV351 @ SV491 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV351 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV32 @ SV200 )
        = $false )
      | ( ( cType___24t @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4863]) ).

thf(5001,plain,
    ! [SV352: $i,SV201: $i,SV565: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
          | ! [SY1480: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1480 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SY1480 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1480 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4864]) ).

thf(5002,plain,
    ! [SV353: $i,SV202: $i,SV566: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
          | ! [SY1481: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1481 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SY1481 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1481 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4865]) ).

thf(5003,plain,
    ! [SV356: $i,SV205: $i,SV492: $i,SV37: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV492 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ SV356 ) @ SV492 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV205 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV37 @ SV356 @ SV492 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV356 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV37 @ SV205 )
        = $false )
      | ( ( cType___24t @ SV37 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4868]) ).

thf(5004,plain,
    ! [SV357: $i,SV206: $i,SV493: $i,SV38: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV493 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV38 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ SV493 ) ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV357 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV38 @ SV206 @ SV493 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV357 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV38 @ SV206 )
        = $false )
      | ( ( cType___24t @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4869]) ).

thf(5005,plain,
    ! [SV361: $i,SV211: $i,SV567: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
          | ! [SY1482: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1482 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SY1482 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1482 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4872]) ).

thf(5006,plain,
    ! [SV362: $i,SV212: $i,SV568: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
          | ! [SY1483: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1483 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SY1483 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1483 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4873]) ).

thf(5007,plain,
    ! [SV216: $i,SV366: $i,SV48: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4877]) ).

thf(5008,plain,
    ! [SV368: $i,SV218: $i,SV494: $i,SV50: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV494 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SV494 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SV494 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4878]) ).

thf(5009,plain,
    ! [SV220: $i,SV370: $i,SV495: $i,SV52: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV495 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SV495 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SV495 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4879]) ).

thf(5010,plain,
    ! [SV371: $i,SV221: $i,SV496: $i,SV53: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( ! [SY1457: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SY1457 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SY1457 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SY1457 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4880]) ).

thf(5011,plain,
    ! [SV372: $i,SV222: $i,SV497: $i,SV54: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4881]) ).

thf(5012,plain,
    ! [SV373: $i,SV223: $i,SV498: $i,SV55: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( ! [SY1458: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SY1458 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SY1458 @ SV498 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SY1458 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4882]) ).

thf(5013,plain,
    ! [SV378: $i,SV229: $i,SV499: $i,SV61: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( ! [SY1459: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SY1459 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SY1459 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SY1459 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4886]) ).

thf(5014,plain,
    ! [SV384: $i,SV235: $i,SV500: $i,SV67: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4892]) ).

thf(5015,plain,
    ! [SV386: $i,SV237: $i,SV501: $i,SV69: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( ! [SY1460: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SY1460 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SY1460 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SY1460 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4893]) ).

thf(5016,plain,
    ! [SV388: $i,SV239: $i,SV502: $i,SV71: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV502 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SV502 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4894]) ).

thf(5017,plain,
    ! [SV390: $i,SV241: $i,SV503: $i,SV73: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV503 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SV503 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SV503 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4895]) ).

thf(5018,plain,
    ! [SV242: $i,SV391: $i,SV74: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4896]) ).

thf(5019,plain,
    ! [SV78: $i,SV504: $i] :
      ( ( ( cProp___24t @ SV504 )
        = $false )
      | ( ( ( p @ SV78 )
          | ~ ( p @ SV78 )
          | ( p @ SV504 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4897]) ).

thf(5020,plain,
    ! [SV78: $i,SV505: $i] :
      ( ( ( cProp___24t @ SV505 )
        = $false )
      | ( ( ( p @ SV78 )
          | ~ ( p @ SV505 )
          | ( p @ SV505 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4898]) ).

thf(5021,plain,
    ! [SV78: $i,SV506: $i] :
      ( ( ( cProp___24t @ SV506 )
        = $false )
      | ( ( ~ ( p @ SV506 )
          | ~ ( p @ SV78 )
          | ( p @ SV506 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4899]) ).

thf(5022,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( cProp___24t @ SV507 )
        = $false )
      | ( ( ~ ( p @ SV507 )
          | ~ ( p @ SV507 )
          | ( p @ SV507 ) )
        = $true )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4900]) ).

thf(5023,plain,
    ! [SV244: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK1_Vv__CANONICAL__0 @ SV244 ) @ ( happ @ ( happ @ SV244 @ ( sK1_Vv__CANONICAL__0 @ SV244 ) ) @ ( sK2_SY468 @ SV244 ) ) )
        = $false )
      | ( ( c_24__type__96___24t @ SV244 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4902]) ).

thf(5024,plain,
    ! [SV245: $i,SV508: $i,SV392: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ SV508 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV392 @ ( happ @ ( happ @ SV245 @ SV392 ) @ SV508 ) )
        = $true )
      | ( ( cType___24t @ SV392 )
        = $false )
      | ( ( c_24__type__96___24t @ SV245 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4903]) ).

thf(5025,plain,
    ! [SV246: $i,SV509: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4904]) ).

thf(5026,plain,
    ! [SV246: $i,SV510: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4905]) ).

thf(5027,plain,
    ! [SV161: $i,SV81: $i,SV547: $i,SV511: $i,SV130: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV130 @ SV511 ) @ SV547 ) ) )
        = $true )
      | ( ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV511 @ SV547 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4907]) ).

thf(5028,plain,
    ! [SV130: $i,SV81: $i,SV548: $i,SV512: $i,SV161: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV161 @ SV512 ) @ SV548 ) ) )
        = $true )
      | ( ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV512 @ SV548 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4908]) ).

thf(5029,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
          | ~ ( ~ ! [SY1484: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1484 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1484 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1484 ) ) )
              | ~ ! [SY1485: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1485 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1485 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1485 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4909]) ).

thf(5030,plain,
    ! [SV250: $i,SV513: $i,SV85: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 )
          | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4910]) ).

thf(5031,plain,
    ! [SV250: $i,SV514: $i,SV85: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 )
          | ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4911]) ).

thf(5032,plain,
    ! [SV515: $i,SV460: $i,SV133: $i,SV86: $i] :
      ( ( ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV460 @ SV515 )
        = $false )
      | ( ( p @ ( happ @ SV133 @ SV515 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4912]) ).

thf(5033,plain,
    ! [SV516: $i,SV461: $i,SV133: $i,SV86: $i] :
      ( ( ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV461 @ SV516 )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV461 @ SV516 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4913]) ).

thf(5034,plain,
    ! [SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ! [SY1403: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1403 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1403 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1403 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4914]) ).

thf(5035,plain,
    ! [SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ! [SY1404: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SY1404 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SY1404 ) ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SY1404 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4915]) ).

thf(5036,plain,
    ! [SV163: $i,SV90: $i,SV549: $i,SV517: $i,SV135: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV135 @ SV517 ) @ SV549 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV517 @ SV549 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4917]) ).

thf(5037,plain,
    ! [SV135: $i,SV90: $i,SV550: $i,SV518: $i,SV163: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV163 @ SV518 ) @ SV550 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV518 @ SV550 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4918]) ).

thf(5038,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ! [SY1272: $i] :
              ( ~ ( cProp___24t @ SY1272 )
              | ( p @ SV91 )
              | ~ ( p @ SV91 )
              | ( p @ SV254 )
              | ( p @ SY1272 ) ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4919]) ).

thf(5039,plain,
    ! [SV254: $i,SV91: $i] :
      ( ( ( ! [SY1273: $i] :
              ( ~ ( cProp___24t @ SY1273 )
              | ( p @ SV91 )
              | ~ ( p @ SY1273 )
              | ( p @ SV254 )
              | ( p @ SY1273 ) ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4920]) ).

thf(5040,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ! [SY1274: $i] :
              ( ~ ( cProp___24t @ SY1274 )
              | ~ ( p @ SV254 )
              | ~ ( p @ SV91 )
              | ( p @ SV254 )
              | ( p @ SY1274 ) ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4921]) ).

thf(5041,plain,
    ! [SV91: $i,SV254: $i] :
      ( ( ( ! [SY1275: $i] :
              ( ~ ( cProp___24t @ SY1275 )
              | ~ ( p @ SV254 )
              | ~ ( p @ SY1275 )
              | ( p @ SV254 )
              | ( p @ SY1275 ) ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4922]) ).

thf(5042,plain,
    ! [SV92: $i,SV405: $i,SV136: $i,SV435: $i,SV164: $i] :
      ( ( ( p @ ( happ @ SV164 @ SV435 ) )
        = $false )
      | ( ( p @ ( happ @ SV136 @ SV405 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV405 @ SV435 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4923]) ).

thf(5043,plain,
    ! [SV570: $i,SV519: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV519 @ SV570 ) )
        = $true )
      | ( ( p @ ( happ @ SV136 @ SV519 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4924]) ).

thf(5044,plain,
    ! [SV551: $i,SV520: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV520 @ SV551 ) )
        = $true )
      | ( ( p @ ( happ @ SV164 @ SV551 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4925]) ).

thf(5045,plain,
    ! [SV521: $i,SV464: $i,SV138: $i,SV95: $i] :
      ( ( ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV464 @ SV521 )
        = $false )
      | ( ( p @ ( happ @ SV138 @ SV521 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4929]) ).

thf(5046,plain,
    ! [SV522: $i,SV465: $i,SV138: $i,SV95: $i] :
      ( ( ( c_24__lam__40532___24a4 @ SV95 @ SV138 @ SV465 @ SV522 )
        = $false )
      | ( ( p @ ( happ @ SV465 @ SV522 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4930]) ).

thf(5047,plain,
    ! [SV259: $i,SV523: $i,SV96: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4931]) ).

thf(5048,plain,
    ! [SV259: $i,SV524: $i,SV96: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4932]) ).

thf(5049,plain,
    ! [SV139: $i,SV97: $i,SV525: $i,SV466: $i] :
      ( ( ( SV466 = SV525 )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV466 @ SV525 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4933]) ).

thf(5050,plain,
    ! [SV97: $i,SV526: $i,SV467: $i,SV139: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV139 @ SV467 ) @ SV526 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl___24a4 @ SV97 @ SV139 @ SV467 @ SV526 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4934]) ).

thf(5051,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4935]) ).

thf(5052,plain,
    ! [SV98: $i,SV314: $i,SV288: $i] :
      ( ( ( ~ ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
                | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4935]) ).

thf(5053,plain,
    ! [SV315: $i,SV468: $i,SV289: $i,SV98: $i,SV571: $i] :
      ( ( ( ~ ( t @ SV571 @ SV98 )
          | ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SV571 ) )
          | ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SV571 ) ) )
        = $true )
      | ( ( t @ SV468 @ SV98 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4936]) ).

thf(5054,plain,
    ! [SV99: $i,SV527: $i,SV469: $i,SV140: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV140 @ SV469 ) @ SV527 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV469 @ SV527 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4937]) ).

thf(5055,plain,
    ! [SV99: $i,SV470: $i,SV528: $i,SV140: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV140 @ SV528 ) @ SV470 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__sym___24a4 @ SV99 @ SV140 @ SV470 @ SV528 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4938]) ).

thf(5056,plain,
    ! [SV552: $i,SV529: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV529 @ SV552 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV141 @ SV529 ) @ SV552 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4940]) ).

thf(5057,plain,
    ! [SV553: $i,SV530: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV530 @ SV553 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV166 @ SV530 ) @ SV553 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4941]) ).

thf(5058,plain,
    ! [SV104: $i,SV143: $i,SV446: $i,SV414: $i,SV168: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV143 @ SV414 ) ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ SV143 @ SV446 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4946]) ).

thf(5059,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ! [SY1129: $i,SY1130: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1129 @ SY1130 )
            | ( p @ ( happ @ ( happ @ SV168 @ SY1129 ) @ SY1130 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4947]) ).

thf(5060,plain,
    ! [SV168: $i,SV143: $i,SV104: $i] :
      ( ( ! [SY1131: $i] :
            ( ! [SY1132: $i] :
                ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SY1131 @ SY1132 )
            | ( p @ ( happ @ SV143 @ SY1131 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[4948]) ).

thf(5061,plain,
    ! [SV555: $i,SV531: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV531 @ SV555 ) )
        = $true )
      | ( ( p @ ( happ @ SV143 @ SV555 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4949]) ).

thf(5062,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( sK14_SY479 @ SV295 @ SV260 ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4950]) ).

thf(5063,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) ) )
        = $true )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4951]) ).

thf(5064,plain,
    ! [SV447: $i,SV296: $i,SV556: $i,SV261: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV556 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SV447 ) @ SV556 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV447 )
        = $false )
      | ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4952]) ).

thf(5065,plain,
    ! [SV106: $i,SV473: $i,SV532: $i,SV144: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV144 @ SV532 ) @ SV473 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV473 @ SV532 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4954]) ).

thf(5066,plain,
    ! [SV144: $i,SV106: $i,SV572: $i] :
      ( ( ! [SY1486: $i] :
            ( ( SV572 != SY1486 )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV572 @ SY1486 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4955]) ).

thf(5067,plain,
    ! [SV106: $i,SV573: $i,SV144: $i] :
      ( ( ! [SY1487: $i] :
            ( ~ ( p @ ( happ @ ( happ @ SV144 @ SV573 ) @ SY1487 ) )
            | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV573 @ SY1487 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4956]) ).

thf(5068,plain,
    ! [SV533: $i,SV474: $i,SV146: $i,SV108: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV474 @ SV533 )
        = $false )
      | ( ( SV474 = SV533 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4958]) ).

thf(5069,plain,
    ! [SV557: $i,SV475: $i,SV146: $i,SV108: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eeqv__rel___24a4 @ SV108 @ SV146 @ SV475 @ SV557 )
        = $false )
      | ( ( p @ ( happ @ SV146 @ SV475 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4959]) ).

thf(5070,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
          | ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4961]) ).

thf(5071,plain,
    ! [SV263: $i,SV534: $i,SV419: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV534 )
        = $false )
      | ( ( ! [SY1470: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SY1470 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SV534 ) @ SY1470 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV419 )
        = $false )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4962]) ).

thf(5072,plain,
    ! [SV264: $i,SV535: $i,SV109: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4963]) ).

thf(5073,plain,
    ! [SV264: $i,SV536: $i,SV109: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 )
          | ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4964]) ).

thf(5074,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) )
          | ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4966]) ).

thf(5075,plain,
    ! [SV420: $i,SV266: $i,SV537: $i] :
      ( ( ( cType___24t @ SV537 )
        = $false )
      | ( ( ! [SY1471: $i] :
              ( ~ ( cType___24t @ SY1471 )
              | ! [SY1472: $i] :
                  ( ~ ( cType___24t @ SY1472 )
                  | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SY1471 ) @ SY1472 ) ) ) ) )
        = $true )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4967]) ).

thf(5076,plain,
    ! [SV110: $i,SV147: $i,SV450: $i,SV421: $i,SV170: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV170 @ SV421 ) @ SV450 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV147 @ SV421 ) @ SV450 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV421 @ SV450 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4968]) ).

thf(5077,plain,
    ! [SV558: $i,SV538: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV538 @ SV558 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV147 @ SV538 ) @ SV558 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4969]) ).

thf(5078,plain,
    ! [SV559: $i,SV539: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV539 @ SV559 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV170 @ SV539 ) @ SV559 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4970]) ).

thf(5079,plain,
    ! [SV477: $i,SV113: $i,SV541: $i,SV149: $i] :
      ( ( ( p @ ( happ @ SV149 @ SV541 ) )
        = $false )
      | ( ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV477 @ SV541 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4973]) ).

thf(5080,plain,
    ! [SV149: $i,SV113: $i,SV542: $i,SV478: $i] :
      ( ( ( p @ ( happ @ SV478 @ SV542 ) )
        = $false )
      | ( ( chahn_2eHahnSets_2eset__union___24a4 @ SV113 @ SV149 @ SV478 @ SV542 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4974]) ).

thf(5081,plain,
    ! [SV425: $i,SV267: $i,SV115: $i,SV574: $i] :
      ( ( ( ~ ( t @ SV574 @ SV115 )
          | ~ ( ~ ! [SY1488: $i] :
                    ( ~ ( t @ SY1488 @ SV115 )
                    | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1488 ) )
                    | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1488 ) ) )
              | ~ ! [SY1489: $i] :
                    ( ~ ( t @ SY1489 @ SV115 )
                    | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1489 ) )
                    | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1489 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4976]) ).

thf(5082,plain,
    ! [SV544: $i,SV480: $i,SV150: $i,SV116: $i] :
      ( ( ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV480 @ SV544 )
        = $false )
      | ( ( p @ ( happ @ SV150 @ SV544 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4978]) ).

thf(5083,plain,
    ! [SV545: $i,SV481: $i,SV150: $i,SV116: $i] :
      ( ( ( chahn_2eHahnSets_2eset__inter___24a4 @ SV116 @ SV150 @ SV481 @ SV545 )
        = $false )
      | ( ( p @ ( happ @ SV481 @ SV545 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4979]) ).

thf(5084,plain,
    ! [SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( ! [SY1424: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1424 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1424 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4980]) ).

thf(5085,plain,
    ! [SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( ! [SY1425: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SY1425 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SY1425 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SY1425 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4981]) ).

thf(5086,plain,
    ! [SV271: $i] :
      ( ( ( cType___24t @ ( happ @ ( happ @ SV271 @ ( sK6_Vv__CANONICAL__0 @ SV271 ) ) @ ( sK7_SY472 @ SV271 ) ) )
        = $false )
      | ( ( c_24__type__52___24t @ SV271 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4989]) ).

thf(5087,plain,
    ! [SV430: $i,SV272: $i,SV546: $i] :
      ( ( ( cType___24t @ SV546 )
        = $false )
      | ( ( cType___24t @ ( happ @ ( happ @ SV272 @ SV430 ) @ SV546 ) )
        = $true )
      | ( ( cType___24t @ SV430 )
        = $false )
      | ( ( c_24__type__52___24t @ SV272 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4990]) ).

thf(5088,plain,
    ! [SV154: $i,SV122: $i,SV273: $i,SV487: $i,SV459: $i,SV173: $i] :
      ( ( ( ( happ @ SV173 @ SV459 )
          = ( happ @ SV173 @ SV487 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV273 @ SV459 ) @ SV487 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV459 @ SV487 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4991]) ).

thf(5089,plain,
    ! [SV575: $i,SV560: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV560 @ SV575 )
        | ( ( happ @ SV173 @ SV560 )
          = ( happ @ SV173 @ SV575 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4992]) ).

thf(5090,plain,
    ! [SV576: $i,SV561: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV561 @ SV576 )
        | ( p @ ( happ @ ( happ @ SV273 @ SV561 ) @ SV576 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[4993]) ).

thf(5091,plain,
    ! [SV334: $i,SV175: $i,SV562: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 ) )
        = $true )
      | ( ( ! [SY1477: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1477 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SY1477 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1477 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4994]) ).

thf(5092,plain,
    ! [SV348: $i,SV197: $i,SV563: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 ) )
        = $true )
      | ( ( ! [SY1478: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1478 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SY1478 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1478 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4997]) ).

thf(5093,plain,
    ! [SV349: $i,SV198: $i,SV564: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 ) )
        = $true )
      | ( ( ! [SY1479: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1479 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SY1479 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1479 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4998]) ).

thf(5094,plain,
    ! [SV352: $i,SV201: $i,SV565: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 ) )
        = $true )
      | ( ( ! [SY1480: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1480 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SY1480 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1480 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5001]) ).

thf(5095,plain,
    ! [SV353: $i,SV202: $i,SV566: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 ) )
        = $true )
      | ( ( ! [SY1481: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1481 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SY1481 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1481 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5002]) ).

thf(5096,plain,
    ! [SV361: $i,SV211: $i,SV567: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 ) )
        = $true )
      | ( ( ! [SY1482: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1482 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SY1482 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1482 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5005]) ).

thf(5097,plain,
    ! [SV362: $i,SV212: $i,SV568: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 ) )
        = $true )
      | ( ( ! [SY1483: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1483 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SY1483 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1483 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5006]) ).

thf(5098,plain,
    ! [SV216: $i,SV366: $i,SV48: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV366 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV48 @ SV216 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV48 @ SV216 @ SV366 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV366 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV48 @ SV216 )
        = $false )
      | ( ( cType___24t @ SV48 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5007]) ).

thf(5099,plain,
    ! [SV368: $i,SV494: $i,SV218: $i,SV50: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SV494 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SV494 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV494 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5008]) ).

thf(5100,plain,
    ! [SV220: $i,SV495: $i,SV370: $i,SV52: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SV495 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SV495 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV495 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5009]) ).

thf(5101,plain,
    ! [SV496: $i,SV371: $i,SV221: $i,SV577: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5010]) ).

thf(5102,plain,
    ! [SV497: $i,SV372: $i,SV222: $i,SV54: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5011]) ).

thf(5103,plain,
    ! [SV498: $i,SV373: $i,SV223: $i,SV578: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5012]) ).

thf(5104,plain,
    ! [SV499: $i,SV378: $i,SV229: $i,SV579: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5013]) ).

thf(5105,plain,
    ! [SV384: $i,SV500: $i,SV235: $i,SV67: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5014]) ).

thf(5106,plain,
    ! [SV501: $i,SV386: $i,SV237: $i,SV580: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5015]) ).

thf(5107,plain,
    ! [SV502: $i,SV388: $i,SV239: $i,SV71: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SV502 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV502 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5016]) ).

thf(5108,plain,
    ! [SV390: $i,SV503: $i,SV241: $i,SV73: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SV503 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SV503 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV503 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5017]) ).

thf(5109,plain,
    ! [SV242: $i,SV391: $i,SV74: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV391 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV74 @ SV242 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV74 @ SV242 @ SV391 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV391 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV74 @ SV242 )
        = $false )
      | ( ( cType___24t @ SV74 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5018]) ).

thf(5110,plain,
    ! [SV504: $i,SV78: $i] :
      ( ( ( p @ SV78 )
        = $true )
      | ( ( ~ ( p @ SV78 )
          | ( p @ SV504 ) )
        = $true )
      | ( ( cProp___24t @ SV504 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5019]) ).

thf(5111,plain,
    ! [SV505: $i,SV78: $i] :
      ( ( ( p @ SV78 )
        = $true )
      | ( ( ~ ( p @ SV505 )
          | ( p @ SV505 ) )
        = $true )
      | ( ( cProp___24t @ SV505 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5020]) ).

thf(5112,plain,
    ! [SV78: $i,SV506: $i] :
      ( ( ( ~ ( p @ SV506 ) )
        = $true )
      | ( ( ~ ( p @ SV78 )
          | ( p @ SV506 ) )
        = $true )
      | ( ( cProp___24t @ SV506 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5021]) ).

thf(5113,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( ~ ( p @ SV507 ) )
        = $true )
      | ( ( ~ ( p @ SV507 )
          | ( p @ SV507 ) )
        = $true )
      | ( ( cProp___24t @ SV507 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5022]) ).

thf(5114,plain,
    ! [SV509: $i,SV246: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5025]) ).

thf(5115,plain,
    ! [SV510: $i,SV246: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5026]) ).

thf(5116,plain,
    ! [SV161: $i,SV81: $i,SV547: $i,SV511: $i,SV130: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV130 @ SV511 ) @ SV547 ) )
        = $false )
      | ( ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV511 @ SV547 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5027]) ).

thf(5117,plain,
    ! [SV130: $i,SV81: $i,SV548: $i,SV512: $i,SV161: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV161 @ SV512 ) @ SV548 ) )
        = $false )
      | ( ( c_24__lam__3971___24a5 @ SV81 @ SV130 @ SV161 @ SV512 @ SV548 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5028]) ).

thf(5118,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1484: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1484 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1484 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1484 ) ) )
              | ~ ! [SY1485: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1485 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1485 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1485 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5029]) ).

thf(5119,plain,
    ! [SV513: $i,SV250: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5030]) ).

thf(5120,plain,
    ! [SV514: $i,SV250: $i,SV85: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5031]) ).

thf(5121,plain,
    ! [SV133: $i,SV86: $i,SV516: $i,SV461: $i] :
      ( ( ( p @ ( happ @ SV461 @ SV516 ) )
        = $false )
      | ( ( chahn_2eHahnSets_2eset__minus___24a4 @ SV86 @ SV133 @ SV461 @ SV516 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5033]) ).

thf(5122,plain,
    ! [SV403: $i,SV253: $i,SV581: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV581 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV581 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV581 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5034]) ).

thf(5123,plain,
    ! [SV403: $i,SV253: $i,SV582: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV582 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV582 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV582 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5035]) ).

thf(5124,plain,
    ! [SV163: $i,SV90: $i,SV549: $i,SV517: $i,SV135: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV135 @ SV517 ) @ SV549 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV517 @ SV549 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5036]) ).

thf(5125,plain,
    ! [SV135: $i,SV90: $i,SV550: $i,SV518: $i,SV163: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV163 @ SV518 ) @ SV550 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a5 @ SV90 @ SV135 @ SV163 @ SV518 @ SV550 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5037]) ).

thf(5126,plain,
    ! [SV254: $i,SV91: $i,SV583: $i] :
      ( ( ( ~ ( cProp___24t @ SV583 )
          | ( p @ SV91 )
          | ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV583 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5038]) ).

thf(5127,plain,
    ! [SV254: $i,SV91: $i,SV584: $i] :
      ( ( ( ~ ( cProp___24t @ SV584 )
          | ( p @ SV91 )
          | ~ ( p @ SV584 )
          | ( p @ SV254 )
          | ( p @ SV584 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5039]) ).

thf(5128,plain,
    ! [SV91: $i,SV254: $i,SV585: $i] :
      ( ( ( ~ ( cProp___24t @ SV585 )
          | ~ ( p @ SV254 )
          | ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5040]) ).

thf(5129,plain,
    ! [SV91: $i,SV254: $i,SV586: $i] :
      ( ( ( ~ ( cProp___24t @ SV586 )
          | ~ ( p @ SV254 )
          | ~ ( p @ SV586 )
          | ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5041]) ).

thf(5130,plain,
    ! [SV570: $i,SV519: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV519 @ SV570 )
        = $false )
      | ( ( p @ ( happ @ SV136 @ SV519 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5043]) ).

thf(5131,plain,
    ! [SV551: $i,SV520: $i,SV164: $i,SV136: $i,SV92: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2ecross__rel___24a5 @ SV92 @ SV136 @ SV164 @ SV520 @ SV551 )
        = $false )
      | ( ( p @ ( happ @ SV164 @ SV551 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5044]) ).

thf(5132,plain,
    ! [SV523: $i,SV259: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5047]) ).

thf(5133,plain,
    ! [SV524: $i,SV259: $i,SV96: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5048]) ).

thf(5134,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( t @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) @ SV98 )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5051]) ).

thf(5135,plain,
    ! [SV98: $i,SV314: $i,SV288: $i] :
      ( ( ( ~ ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
              | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5052]) ).

thf(5136,plain,
    ! [SV315: $i,SV468: $i,SV289: $i,SV98: $i,SV571: $i] :
      ( ( ( ~ ( t @ SV571 @ SV98 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SV571 ) )
          | ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SV571 ) ) )
        = $true )
      | ( ( t @ SV468 @ SV98 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5053]) ).

thf(5137,plain,
    ! [SV552: $i,SV529: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV529 @ SV552 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV141 @ SV529 ) @ SV552 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5056]) ).

thf(5138,plain,
    ! [SV553: $i,SV530: $i,SV166: $i,SV141: $i,SV100: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV530 @ SV553 )
        = $false )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV166 @ SV530 ) @ SV553 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5057]) ).

thf(5139,plain,
    ! [SV104: $i,SV446: $i,SV168: $i,SV414: $i,SV143: $i] :
      ( ( ( p @ ( happ @ SV143 @ SV414 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) )
        = $false )
      | ( ( ~ ( p @ ( happ @ SV143 @ SV446 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5058]) ).

thf(5140,plain,
    ! [SV587: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ! [SY1490: $i] :
            ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV587 @ SY1490 )
            | ( p @ ( happ @ ( happ @ SV168 @ SV587 ) @ SY1490 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5059]) ).

thf(5141,plain,
    ! [SV588: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ! [SY1491: $i] :
            ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV588 @ SY1491 )
        | ( p @ ( happ @ SV143 @ SV588 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5060]) ).

thf(5142,plain,
    ! [SV555: $i,SV531: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV531 @ SV555 )
        = $false )
      | ( ( p @ ( happ @ SV143 @ SV555 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5061]) ).

thf(5143,plain,
    ! [SV295: $i,SV260: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV260 @ ( happ @ ( happ @ SV295 @ ( sK13_Vv__CANONICAL__1 @ SV295 @ SV260 ) ) @ ( sK14_SY479 @ SV295 @ SV260 ) ) )
        = $false )
      | ( ( c_24__type__11829___24t @ SV260 @ SV295 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5063]) ).

thf(5144,plain,
    ! [SV447: $i,SV296: $i,SV556: $i,SV261: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV556 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ ( happ @ ( happ @ SV296 @ SV447 ) @ SV556 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV261 @ SV447 )
        = $false )
      | ( ( c_24__type__11829___24t @ SV261 @ SV296 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5064]) ).

thf(5145,plain,
    ! [SV144: $i,SV106: $i,SV589: $i,SV572: $i] :
      ( ( ( SV572 != SV589 )
        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV572 @ SV589 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5066]) ).

thf(5146,plain,
    ! [SV106: $i,SV590: $i,SV573: $i,SV144: $i] :
      ( ( ~ ( p @ ( happ @ ( happ @ SV144 @ SV573 ) @ SV590 ) )
        | ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV573 @ SV590 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5067]) ).

thf(5147,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5070]) ).

thf(5148,plain,
    ! [SV262: $i] :
      ( ( ( ~ ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5070]) ).

thf(5149,plain,
    ! [SV534: $i,SV263: $i,SV591: $i,SV419: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV591 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SV534 ) @ SV591 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV534 )
        = $false )
      | ( ( cType___24t @ SV419 )
        = $false )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5071]) ).

thf(5150,plain,
    ! [SV535: $i,SV264: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5072]) ).

thf(5151,plain,
    ! [SV536: $i,SV264: $i,SV109: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 ) )
        = $true )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5073]) ).

thf(5152,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK10_SY476 @ SV265 ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5074]) ).

thf(5153,plain,
    ! [SV265: $i] :
      ( ( ( ~ ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
                | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5074]) ).

thf(5154,plain,
    ! [SV537: $i,SV420: $i,SV266: $i,SV592: $i] :
      ( ( ( ~ ( cType___24t @ SV592 )
          | ! [SY1492: $i] :
              ( ~ ( cType___24t @ SY1492 )
              | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SV592 ) @ SY1492 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV537 )
        = $false )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5075]) ).

thf(5155,plain,
    ! [SV558: $i,SV538: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV538 @ SV558 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV147 @ SV538 ) @ SV558 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5077]) ).

thf(5156,plain,
    ! [SV559: $i,SV539: $i,SV170: $i,SV147: $i,SV110: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2einter__rel___24a5 @ SV110 @ SV147 @ SV170 @ SV539 @ SV559 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV170 @ SV539 ) @ SV559 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5078]) ).

thf(5157,plain,
    ! [SV425: $i,SV267: $i,SV115: $i,SV574: $i] :
      ( ( ( ~ ( t @ SV574 @ SV115 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY1488: $i] :
                    ( ~ ( t @ SY1488 @ SV115 )
                    | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1488 ) )
                    | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1488 ) ) )
              | ~ ! [SY1489: $i] :
                    ( ~ ( t @ SY1489 @ SV115 )
                    | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1489 ) )
                    | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1489 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5081]) ).

thf(5158,plain,
    ! [SV427: $i,SV268: $i,SV593: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV593 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV593 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5084]) ).

thf(5159,plain,
    ! [SV427: $i,SV268: $i,SV594: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV594 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV594 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV594 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5085]) ).

thf(5160,plain,
    ! [SV154: $i,SV122: $i,SV173: $i,SV487: $i,SV459: $i,SV273: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV273 @ SV459 ) @ SV487 ) )
        = $false )
      | ( ( ( happ @ SV173 @ SV459 )
          = ( happ @ SV173 @ SV487 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV459 @ SV487 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5088]) ).

thf(5161,plain,
    ! [SV575: $i,SV560: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV560 @ SV575 ) )
        = $true )
      | ( ( ( happ @ SV173 @ SV560 )
          = ( happ @ SV173 @ SV575 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5089]) ).

thf(5162,plain,
    ! [SV576: $i,SV561: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV561 @ SV576 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV273 @ SV561 ) @ SV576 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5090]) ).

thf(5163,plain,
    ! [SV334: $i,SV175: $i,SV562: $i,SV5: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
        = $false )
      | ( ( ! [SY1477: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SY1477 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SY1477 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SY1477 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5091]) ).

thf(5164,plain,
    ! [SV348: $i,SV197: $i,SV563: $i,SV29: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
        = $false )
      | ( ( ! [SY1478: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SY1478 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SY1478 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SY1478 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5092]) ).

thf(5165,plain,
    ! [SV349: $i,SV198: $i,SV564: $i,SV30: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
        = $false )
      | ( ( ! [SY1479: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SY1479 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SY1479 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SY1479 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5093]) ).

thf(5166,plain,
    ! [SV352: $i,SV201: $i,SV565: $i,SV33: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
        = $false )
      | ( ( ! [SY1480: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SY1480 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SY1480 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SY1480 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5094]) ).

thf(5167,plain,
    ! [SV353: $i,SV202: $i,SV566: $i,SV34: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
        = $false )
      | ( ( ! [SY1481: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SY1481 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SY1481 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SY1481 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5095]) ).

thf(5168,plain,
    ! [SV361: $i,SV211: $i,SV567: $i,SV43: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
        = $false )
      | ( ( ! [SY1482: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SY1482 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SY1482 )
              | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SY1482 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5096]) ).

thf(5169,plain,
    ! [SV362: $i,SV212: $i,SV568: $i,SV44: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
        = $false )
      | ( ( ! [SY1483: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SY1483 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SY1483 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SY1483 ) ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5097]) ).

thf(5170,plain,
    ! [SV368: $i,SV494: $i,SV218: $i,SV50: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ SV218 @ SV494 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV50 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV50 @ SV218 @ SV368 ) @ SV494 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV494 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV368 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV50 @ SV218 )
        = $false )
      | ( ( cType___24t @ SV50 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5099]) ).

thf(5171,plain,
    ! [SV220: $i,SV495: $i,SV370: $i,SV52: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ SV370 @ SV495 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV52 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV52 @ SV220 @ SV370 ) @ SV495 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV495 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV370 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV52 @ SV220 )
        = $false )
      | ( ( cType___24t @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5100]) ).

thf(5172,plain,
    ! [SV496: $i,SV371: $i,SV221: $i,SV577: $i,SV53: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5101]) ).

thf(5173,plain,
    ! [SV497: $i,SV372: $i,SV222: $i,SV54: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5102]) ).

thf(5174,plain,
    ! [SV498: $i,SV373: $i,SV223: $i,SV578: $i,SV55: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5103]) ).

thf(5175,plain,
    ! [SV499: $i,SV378: $i,SV229: $i,SV579: $i,SV61: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5104]) ).

thf(5176,plain,
    ! [SV384: $i,SV500: $i,SV235: $i,SV67: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5105]) ).

thf(5177,plain,
    ! [SV501: $i,SV386: $i,SV237: $i,SV580: $i,SV69: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5106]) ).

thf(5178,plain,
    ! [SV502: $i,SV388: $i,SV239: $i,SV71: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ SV388 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV71 @ SV239 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV71 @ SV388 @ SV502 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV502 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV388 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV71 @ SV239 )
        = $false )
      | ( ( cType___24t @ SV71 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5107]) ).

thf(5179,plain,
    ! [SV390: $i,SV503: $i,SV241: $i,SV73: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ SV503 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV73 @ SV241 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV73 @ SV390 @ SV503 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV503 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV390 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV73 @ SV241 )
        = $false )
      | ( ( cType___24t @ SV73 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5108]) ).

thf(5180,plain,
    ! [SV504: $i,SV78: $i] :
      ( ( ( ~ ( p @ SV78 ) )
        = $true )
      | ( ( p @ SV504 )
        = $true )
      | ( ( p @ SV78 )
        = $true )
      | ( ( cProp___24t @ SV504 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5110]) ).

thf(5181,plain,
    ! [SV78: $i,SV505: $i] :
      ( ( ( ~ ( p @ SV505 ) )
        = $true )
      | ( ( p @ SV505 )
        = $true )
      | ( ( p @ SV78 )
        = $true )
      | ( ( cProp___24t @ SV505 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5111]) ).

thf(5182,plain,
    ! [SV78: $i,SV506: $i] :
      ( ( ( p @ SV506 )
        = $false )
      | ( ( ~ ( p @ SV78 )
          | ( p @ SV506 ) )
        = $true )
      | ( ( cProp___24t @ SV506 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5112]) ).

thf(5183,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( p @ SV507 )
        = $false )
      | ( ( ~ ( p @ SV507 )
          | ( p @ SV507 ) )
        = $true )
      | ( ( cProp___24t @ SV507 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5113]) ).

thf(5184,plain,
    ! [SV509: $i,SV246: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5114]) ).

thf(5185,plain,
    ! [SV510: $i,SV246: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5115]) ).

thf(5186,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( ~ ( ~ ! [SY1484: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1484 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1484 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1484 ) ) )
              | ~ ! [SY1485: $i] :
                    ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1485 )
                    | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1485 )
                    | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1485 ) )
                    | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5118]) ).

thf(5187,plain,
    ! [SV513: $i,SV250: $i,SV85: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5119]) ).

thf(5188,plain,
    ! [SV514: $i,SV250: $i,SV85: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) )
          | ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5120]) ).

thf(5189,plain,
    ! [SV403: $i,SV253: $i,SV581: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV581 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV581 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV581 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5122]) ).

thf(5190,plain,
    ! [SV403: $i,SV253: $i,SV582: $i,SV89: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV582 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV582 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV582 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5123]) ).

thf(5191,plain,
    ! [SV254: $i,SV91: $i,SV583: $i] :
      ( ( ( ~ ( cProp___24t @ SV583 ) )
        = $true )
      | ( ( ( p @ SV91 )
          | ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV583 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5126]) ).

thf(5192,plain,
    ! [SV254: $i,SV91: $i,SV584: $i] :
      ( ( ( ~ ( cProp___24t @ SV584 ) )
        = $true )
      | ( ( ( p @ SV91 )
          | ~ ( p @ SV584 )
          | ( p @ SV254 )
          | ( p @ SV584 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5127]) ).

thf(5193,plain,
    ! [SV91: $i,SV254: $i,SV585: $i] :
      ( ( ( ~ ( cProp___24t @ SV585 ) )
        = $true )
      | ( ( ~ ( p @ SV254 )
          | ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5128]) ).

thf(5194,plain,
    ! [SV91: $i,SV254: $i,SV586: $i] :
      ( ( ( ~ ( cProp___24t @ SV586 ) )
        = $true )
      | ( ( ~ ( p @ SV254 )
          | ~ ( p @ SV586 )
          | ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5129]) ).

thf(5195,plain,
    ! [SV523: $i,SV259: $i,SV96: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5132]) ).

thf(5196,plain,
    ! [SV524: $i,SV259: $i,SV96: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5133]) ).

thf(5197,plain,
    ! [SV98: $i,SV314: $i,SV288: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
          | ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5135]) ).

thf(5198,plain,
    ! [SV315: $i,SV468: $i,SV289: $i,SV98: $i,SV571: $i] :
      ( ( ( t @ SV571 @ SV98 )
        = $false )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SV571 ) )
          | ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SV571 ) ) )
        = $true )
      | ( ( t @ SV468 @ SV98 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5136]) ).

thf(5199,plain,
    ! [SV141: $i,SV100: $i,SV553: $i,SV530: $i,SV166: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV166 @ SV530 ) @ SV553 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eminus__rel___24a5 @ SV100 @ SV141 @ SV166 @ SV530 @ SV553 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5138]) ).

thf(5200,plain,
    ! [SV104: $i,SV414: $i,SV168: $i,SV446: $i,SV143: $i] :
      ( ( ( p @ ( happ @ SV143 @ SV446 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV168 @ SV414 ) @ SV446 ) )
        = $false )
      | ( ( p @ ( happ @ SV143 @ SV414 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV414 @ SV446 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5139]) ).

thf(5201,plain,
    ! [SV595: $i,SV587: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV587 @ SV595 )
        | ( p @ ( happ @ ( happ @ SV168 @ SV587 ) @ SV595 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[5140]) ).

thf(5202,plain,
    ! [SV588: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( ! [SY1491: $i] :
              ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV588 @ SY1491 ) )
        = $true )
      | ( ( p @ ( happ @ SV143 @ SV588 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5141]) ).

thf(5203,plain,
    ! [SV144: $i,SV106: $i,SV589: $i,SV572: $i] :
      ( ( ( SV572 != SV589 )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV572 @ SV589 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5145]) ).

thf(5204,plain,
    ! [SV106: $i,SV590: $i,SV573: $i,SV144: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV144 @ SV573 ) @ SV590 ) ) )
        = $true )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV573 @ SV590 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5146]) ).

thf(5205,plain,
    ! [SV262: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( sK5_SY471 @ SV262 ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5147]) ).

thf(5206,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) ) )
        = $true )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5148]) ).

thf(5207,plain,
    ! [SV534: $i,SV263: $i,SV591: $i,SV419: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV591 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SV534 ) @ SV591 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV534 )
        = $false )
      | ( ( cType___24t @ SV419 )
        = $false )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5149]) ).

thf(5208,plain,
    ! [SV535: $i,SV264: $i,SV109: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5150]) ).

thf(5209,plain,
    ! [SV536: $i,SV264: $i,SV109: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 )
        = $false )
      | ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) )
          | ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5151]) ).

thf(5210,plain,
    ! [SV265: $i] :
      ( ( ( cType___24t @ ( sK10_SY476 @ SV265 ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5152]) ).

thf(5211,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
              | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5153]) ).

thf(5212,plain,
    ! [SV537: $i,SV420: $i,SV266: $i,SV592: $i] :
      ( ( ( ~ ( cType___24t @ SV592 ) )
        = $true )
      | ( ( ! [SY1492: $i] :
              ( ~ ( cType___24t @ SY1492 )
              | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SV592 ) @ SY1492 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV537 )
        = $false )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5154]) ).

thf(5213,plain,
    ! [SV425: $i,SV267: $i,SV115: $i,SV574: $i] :
      ( ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( ~ ( ~ ! [SY1488: $i] :
                    ( ~ ( t @ SY1488 @ SV115 )
                    | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1488 ) )
                    | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1488 ) ) )
              | ~ ! [SY1489: $i] :
                    ( ~ ( t @ SY1489 @ SV115 )
                    | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1489 ) )
                    | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1489 ) ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5157]) ).

thf(5214,plain,
    ! [SV427: $i,SV268: $i,SV593: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV593 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV593 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5158]) ).

thf(5215,plain,
    ! [SV427: $i,SV268: $i,SV594: $i,SV117: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV594 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV594 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV594 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5159]) ).

thf(5216,plain,
    ! [SV575: $i,SV560: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV560 @ SV575 )
        = $false )
      | ( ( ( happ @ SV173 @ SV560 )
          = ( happ @ SV173 @ SV575 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5161]) ).

thf(5217,plain,
    ! [SV576: $i,SV561: $i,SV273: $i,SV173: $i,SV154: $i,SV122: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2erestr__eq__rel___24a6 @ SV122 @ SV154 @ SV173 @ SV273 @ SV561 @ SV576 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV273 @ SV561 ) @ SV576 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5162]) ).

thf(5218,plain,
    ! [SV334: $i,SV175: $i,SV562: $i,SV596: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV596 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SV596 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SV596 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5163]) ).

thf(5219,plain,
    ! [SV348: $i,SV197: $i,SV563: $i,SV597: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV597 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SV597 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SV597 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5164]) ).

thf(5220,plain,
    ! [SV349: $i,SV198: $i,SV564: $i,SV598: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV598 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SV598 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SV598 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5165]) ).

thf(5221,plain,
    ! [SV352: $i,SV201: $i,SV565: $i,SV599: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV599 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SV599 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SV599 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5166]) ).

thf(5222,plain,
    ! [SV353: $i,SV202: $i,SV566: $i,SV600: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV600 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SV600 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SV600 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5167]) ).

thf(5223,plain,
    ! [SV361: $i,SV211: $i,SV567: $i,SV601: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV601 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SV601 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SV601 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5168]) ).

thf(5224,plain,
    ! [SV362: $i,SV212: $i,SV568: $i,SV602: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV602 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SV602 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SV602 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5169]) ).

thf(5225,plain,
    ! [SV496: $i,SV371: $i,SV221: $i,SV577: $i,SV53: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5172]) ).

thf(5226,plain,
    ! [SV372: $i,SV497: $i,SV222: $i,SV54: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5173]) ).

thf(5227,plain,
    ! [SV498: $i,SV373: $i,SV223: $i,SV578: $i,SV55: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5174]) ).

thf(5228,plain,
    ! [SV499: $i,SV378: $i,SV229: $i,SV579: $i,SV61: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5175]) ).

thf(5229,plain,
    ! [SV235: $i,SV500: $i,SV384: $i,SV67: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5176]) ).

thf(5230,plain,
    ! [SV501: $i,SV386: $i,SV237: $i,SV580: $i,SV69: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5177]) ).

thf(5231,plain,
    ! [SV504: $i,SV78: $i] :
      ( ( ( p @ SV78 )
        = $false )
      | ( ( p @ SV504 )
        = $true )
      | ( ( p @ SV78 )
        = $true )
      | ( ( cProp___24t @ SV504 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5180]) ).

thf(5232,plain,
    ! [SV78: $i,SV505: $i] :
      ( ( ( p @ SV505 )
        = $false )
      | ( ( p @ SV505 )
        = $true )
      | ( ( p @ SV78 )
        = $true )
      | ( ( cProp___24t @ SV505 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5181]) ).

thf(5233,plain,
    ! [SV506: $i,SV78: $i] :
      ( ( ( ~ ( p @ SV78 ) )
        = $true )
      | ( ( p @ SV506 )
        = $true )
      | ( ( p @ SV506 )
        = $false )
      | ( ( cProp___24t @ SV506 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5182]) ).

thf(5234,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( ~ ( p @ SV507 ) )
        = $true )
      | ( ( p @ SV507 )
        = $true )
      | ( ( p @ SV507 )
        = $false )
      | ( ( cProp___24t @ SV507 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5183]) ).

thf(5235,plain,
    ! [SV509: $i,SV246: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5184]) ).

thf(5236,plain,
    ! [SV246: $i,SV510: $i,SV79: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5185]) ).

thf(5237,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ! [SY1484: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1484 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1484 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1484 ) ) )
          | ~ ! [SY1485: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1485 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1485 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1485 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5186]) ).

thf(5238,plain,
    ! [SV513: $i,SV250: $i,SV85: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5187]) ).

thf(5239,plain,
    ! [SV250: $i,SV514: $i,SV85: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5188]) ).

thf(5240,plain,
    ! [SV403: $i,SV253: $i,SV581: $i,SV89: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV581 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV581 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV581 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5189]) ).

thf(5241,plain,
    ! [SV403: $i,SV253: $i,SV582: $i,SV89: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV582 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV582 ) ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV582 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5190]) ).

thf(5242,plain,
    ! [SV254: $i,SV91: $i,SV583: $i] :
      ( ( ( cProp___24t @ SV583 )
        = $false )
      | ( ( ( p @ SV91 )
          | ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV583 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5191]) ).

thf(5243,plain,
    ! [SV254: $i,SV91: $i,SV584: $i] :
      ( ( ( cProp___24t @ SV584 )
        = $false )
      | ( ( ( p @ SV91 )
          | ~ ( p @ SV584 )
          | ( p @ SV254 )
          | ( p @ SV584 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5192]) ).

thf(5244,plain,
    ! [SV91: $i,SV254: $i,SV585: $i] :
      ( ( ( cProp___24t @ SV585 )
        = $false )
      | ( ( ~ ( p @ SV254 )
          | ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5193]) ).

thf(5245,plain,
    ! [SV91: $i,SV254: $i,SV586: $i] :
      ( ( ( cProp___24t @ SV586 )
        = $false )
      | ( ( ~ ( p @ SV254 )
          | ~ ( p @ SV586 )
          | ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5194]) ).

thf(5246,plain,
    ! [SV523: $i,SV259: $i,SV96: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5195]) ).

thf(5247,plain,
    ! [SV259: $i,SV524: $i,SV96: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5196]) ).

thf(5248,plain,
    ! [SV98: $i,SV314: $i,SV288: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5197]) ).

thf(5249,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5197]) ).

thf(5250,plain,
    ! [SV98: $i,SV315: $i,SV571: $i,SV468: $i,SV289: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SV571 ) ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SV571 ) )
        = $true )
      | ( ( t @ SV571 @ SV98 )
        = $false )
      | ( ( t @ SV468 @ SV98 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5198]) ).

thf(5251,plain,
    ! [SV595: $i,SV587: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV587 @ SV595 ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV168 @ SV587 ) @ SV595 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[5201]) ).

thf(5252,plain,
    ! [SV603: $i,SV588: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( ~ ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV588 @ SV603 ) )
        = $true )
      | ( ( p @ ( happ @ SV143 @ SV588 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[5202]) ).

thf(5253,plain,
    ! [SV144: $i,SV106: $i,SV589: $i,SV572: $i] :
      ( ( ( SV572 = SV589 )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV572 @ SV589 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5203]) ).

thf(5254,plain,
    ! [SV106: $i,SV590: $i,SV573: $i,SV144: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV144 @ SV573 ) @ SV590 ) )
        = $false )
      | ( ( chahn_2eHahnRelationsBasic_2eclos__refl__sym___24a4 @ SV106 @ SV144 @ SV573 @ SV590 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5204]) ).

thf(5255,plain,
    ! [SV262: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ ( sK3_Vv__CANONICAL__0 @ SV262 ) @ ( happ @ ( happ @ ( happ @ SV262 @ ( sK3_Vv__CANONICAL__0 @ SV262 ) ) @ ( sK4_SY469 @ SV262 ) ) @ ( sK5_SY471 @ SV262 ) ) )
        = $false )
      | ( ( c_24__type__90___24t @ SV262 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5206]) ).

thf(5256,plain,
    ! [SV534: $i,SV263: $i,SV591: $i,SV419: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV591 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ ( happ @ ( happ @ ( happ @ SV263 @ SV419 ) @ SV534 ) @ SV591 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV419 @ SV534 )
        = $false )
      | ( ( cType___24t @ SV419 )
        = $false )
      | ( ( c_24__type__90___24t @ SV263 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5207]) ).

thf(5257,plain,
    ! [SV535: $i,SV264: $i,SV109: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5208]) ).

thf(5258,plain,
    ! [SV264: $i,SV536: $i,SV109: $i] :
      ( ( ( ~ ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) ) )
        = $true )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5209]) ).

thf(5259,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) )
          | ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5211]) ).

thf(5260,plain,
    ! [SV537: $i,SV420: $i,SV266: $i,SV592: $i] :
      ( ( ( cType___24t @ SV592 )
        = $false )
      | ( ( ! [SY1492: $i] :
              ( ~ ( cType___24t @ SY1492 )
              | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SV592 ) @ SY1492 ) ) ) )
        = $true )
      | ( ( cType___24t @ SV537 )
        = $false )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5212]) ).

thf(5261,plain,
    ! [SV425: $i,SV574: $i,SV267: $i,SV115: $i] :
      ( ( ( ~ ! [SY1488: $i] :
                ( ~ ( t @ SY1488 @ SV115 )
                | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1488 ) )
                | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1488 ) ) )
          | ~ ! [SY1489: $i] :
                ( ~ ( t @ SY1489 @ SV115 )
                | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1489 ) )
                | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1489 ) ) ) )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5213]) ).

thf(5262,plain,
    ! [SV427: $i,SV268: $i,SV593: $i,SV117: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV593 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV593 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5214]) ).

thf(5263,plain,
    ! [SV427: $i,SV268: $i,SV594: $i,SV117: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV594 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV594 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV594 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5215]) ).

thf(5264,plain,
    ! [SV334: $i,SV175: $i,SV562: $i,SV596: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV596 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SV596 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SV596 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5218]) ).

thf(5265,plain,
    ! [SV348: $i,SV197: $i,SV563: $i,SV597: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV597 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SV597 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SV597 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5219]) ).

thf(5266,plain,
    ! [SV349: $i,SV198: $i,SV564: $i,SV598: $i,SV30: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV598 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SV598 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SV598 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5220]) ).

thf(5267,plain,
    ! [SV352: $i,SV201: $i,SV565: $i,SV599: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV599 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SV599 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SV599 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5221]) ).

thf(5268,plain,
    ! [SV353: $i,SV202: $i,SV566: $i,SV600: $i,SV34: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV600 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SV600 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SV600 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5222]) ).

thf(5269,plain,
    ! [SV361: $i,SV211: $i,SV567: $i,SV601: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV601 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SV601 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SV601 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5223]) ).

thf(5270,plain,
    ! [SV362: $i,SV212: $i,SV568: $i,SV602: $i,SV44: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV602 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SV602 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SV602 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5224]) ).

thf(5271,plain,
    ! [SV577: $i,SV496: $i,SV371: $i,SV221: $i,SV53: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5225]) ).

thf(5272,plain,
    ! [SV372: $i,SV497: $i,SV222: $i,SV54: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV497 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV54 @ SV372 @ SV497 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV54 @ SV222 @ SV372 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV497 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV372 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV54 @ SV222 )
        = $false )
      | ( ( cType___24t @ SV54 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5226]) ).

thf(5273,plain,
    ! [SV498: $i,SV578: $i,SV373: $i,SV223: $i,SV55: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5227]) ).

thf(5274,plain,
    ! [SV579: $i,SV499: $i,SV378: $i,SV229: $i,SV61: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5228]) ).

thf(5275,plain,
    ! [SV235: $i,SV500: $i,SV384: $i,SV67: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV384 @ SV500 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV67 @ SV235 @ SV384 ) @ SV500 ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV67 @ SV235 @ SV500 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV500 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV384 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV67 @ SV235 )
        = $false )
      | ( ( cType___24t @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5229]) ).

thf(5276,plain,
    ! [SV580: $i,SV501: $i,SV386: $i,SV237: $i,SV69: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5230]) ).

thf(5277,plain,
    ! [SV506: $i,SV78: $i] :
      ( ( ( p @ SV78 )
        = $false )
      | ( ( p @ SV506 )
        = $true )
      | ( ( p @ SV506 )
        = $false )
      | ( ( cProp___24t @ SV506 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5233]) ).

thf(5278,plain,
    ! [SV78: $i,SV507: $i] :
      ( ( ( p @ SV507 )
        = $false )
      | ( ( p @ SV507 )
        = $true )
      | ( ( p @ SV507 )
        = $false )
      | ( ( cProp___24t @ SV507 )
        = $false )
      | ( ( cProp___24t @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5234]) ).

thf(5279,plain,
    ! [SV509: $i,SV246: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV509 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV509 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV509 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5235]) ).

thf(5280,plain,
    ! [SV246: $i,SV510: $i,SV79: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2 @ SV79 @ SV246 )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV79 @ SV246 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV510 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV79 @ SV246 )
        = $false )
      | ( ( cType___24t @ SV79 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5236]) ).

thf(5281,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ! [SY1484: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1484 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1484 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1484 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[5237]) ).

thf(5282,plain,
    ! [SV249: $i,SV396: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ! [SY1485: $i] :
                ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1485 )
                | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1485 )
                | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1485 ) )
                | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[5237]) ).

thf(5283,plain,
    ! [SV513: $i,SV250: $i,SV85: $i] :
      ( ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
        = $false )
      | ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV513 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV513 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV513 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5238]) ).

thf(5284,plain,
    ! [SV250: $i,SV514: $i,SV85: $i] :
      ( ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV514 ) )
        = $false )
      | ( ( p @ ( cCoq_2eInit_2eWf_2ewell__founded___24a2 @ SV85 @ SV250 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV85 @ SV250 @ SV514 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV514 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV85 @ SV250 )
        = $false )
      | ( ( cType___24t @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5239]) ).

thf(5285,plain,
    ! [SV581: $i,SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV581 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV581 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV581 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5240]) ).

thf(5286,plain,
    ! [SV582: $i,SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV582 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV582 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV582 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5241]) ).

thf(5287,plain,
    ! [SV583: $i,SV254: $i,SV91: $i] :
      ( ( ( p @ SV91 )
        = $true )
      | ( ( ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV583 ) )
        = $true )
      | ( ( cProp___24t @ SV583 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5242]) ).

thf(5288,plain,
    ! [SV254: $i,SV584: $i,SV91: $i] :
      ( ( ( p @ SV91 )
        = $true )
      | ( ( ~ ( p @ SV584 )
          | ( p @ SV254 )
          | ( p @ SV584 ) )
        = $true )
      | ( ( cProp___24t @ SV584 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5243]) ).

thf(5289,plain,
    ! [SV585: $i,SV91: $i,SV254: $i] :
      ( ( ( ~ ( p @ SV254 ) )
        = $true )
      | ( ( ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( cProp___24t @ SV585 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5244]) ).

thf(5290,plain,
    ! [SV91: $i,SV586: $i,SV254: $i] :
      ( ( ( ~ ( p @ SV254 ) )
        = $true )
      | ( ( ~ ( p @ SV586 )
          | ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( cProp___24t @ SV586 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5245]) ).

thf(5291,plain,
    ! [SV523: $i,SV259: $i,SV96: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV523 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV523 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV523 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5246]) ).

thf(5292,plain,
    ! [SV259: $i,SV524: $i,SV96: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV524 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eirreflexive___24a2 @ SV96 @ SV259 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV96 @ SV259 @ SV524 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV524 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV96 @ SV259 )
        = $false )
      | ( ( cType___24t @ SV96 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5247]) ).

thf(5293,plain,
    ! [SV98: $i,SV314: $i,SV288: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV288 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5248]) ).

thf(5294,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5249]) ).

thf(5295,plain,
    ! [SV98: $i,SV315: $i,SV571: $i,SV468: $i,SV289: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV289 @ SV468 ) @ SV571 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV315 @ SV468 ) @ SV571 ) )
        = $true )
      | ( ( t @ SV571 @ SV98 )
        = $false )
      | ( ( t @ SV468 @ SV98 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV289 @ SV315 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5250]) ).

thf(5296,plain,
    ! [SV595: $i,SV587: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV587 @ SV595 )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV168 @ SV587 ) @ SV595 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5251]) ).

thf(5297,plain,
    ! [SV603: $i,SV588: $i,SV168: $i,SV143: $i,SV104: $i] :
      ( ( ( chahn_2eHahnRelationsBasic_2erestr__rel___24a5 @ SV104 @ SV143 @ SV168 @ SV588 @ SV603 )
        = $false )
      | ( ( p @ ( happ @ SV143 @ SV588 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5252]) ).

thf(5298,plain,
    ! [SV535: $i,SV264: $i,SV109: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV535 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV535 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV535 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5257]) ).

thf(5299,plain,
    ! [SV264: $i,SV536: $i,SV109: $i] :
      ( ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV536 ) )
        = $false )
      | ( ( p @ ( chahn_2eHahnRelationsBasic_2eacyclic___24a2 @ SV109 @ SV264 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV109 @ SV264 @ SV536 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV536 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV109 @ SV264 )
        = $false )
      | ( ( cType___24t @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5258]) ).

thf(5300,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( sK11_SY478 @ SV265 ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5259]) ).

thf(5301,plain,
    ! [SV265: $i] :
      ( ( ( ~ ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[5259]) ).

thf(5302,plain,
    ! [SV592: $i,SV537: $i,SV420: $i,SV266: $i,SV604: $i] :
      ( ( ( ~ ( cType___24t @ SV604 )
          | ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SV592 ) @ SV604 ) ) )
        = $true )
      | ( ( cType___24t @ SV592 )
        = $false )
      | ( ( cType___24t @ SV537 )
        = $false )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5260]) ).

thf(5303,plain,
    ! [SV425: $i,SV574: $i,SV267: $i,SV115: $i] :
      ( ( ( ~ ! [SY1488: $i] :
                ( ~ ( t @ SY1488 @ SV115 )
                | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1488 ) )
                | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1488 ) ) ) )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[5261]) ).

thf(5304,plain,
    ! [SV267: $i,SV574: $i,SV425: $i,SV115: $i] :
      ( ( ( ~ ! [SY1489: $i] :
                ( ~ ( t @ SY1489 @ SV115 )
                | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1489 ) )
                | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1489 ) ) ) )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[5261]) ).

thf(5305,plain,
    ! [SV593: $i,SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV593 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV593 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5262]) ).

thf(5306,plain,
    ! [SV427: $i,SV594: $i,SV268: $i,SV117: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV594 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV594 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV594 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5263]) ).

thf(5307,plain,
    ! [SV334: $i,SV175: $i,SV562: $i,SV596: $i,SV5: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV596 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SV596 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SV596 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5264]) ).

thf(5308,plain,
    ! [SV348: $i,SV197: $i,SV563: $i,SV597: $i,SV29: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV597 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SV597 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SV597 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5265]) ).

thf(5309,plain,
    ! [SV349: $i,SV198: $i,SV564: $i,SV598: $i,SV30: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV598 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SV598 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SV598 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5266]) ).

thf(5310,plain,
    ! [SV352: $i,SV201: $i,SV565: $i,SV599: $i,SV33: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV599 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SV599 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SV599 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5267]) ).

thf(5311,plain,
    ! [SV353: $i,SV202: $i,SV566: $i,SV600: $i,SV34: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV600 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SV600 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SV600 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5268]) ).

thf(5312,plain,
    ! [SV361: $i,SV211: $i,SV567: $i,SV601: $i,SV43: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV601 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SV601 )
          | ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SV601 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5269]) ).

thf(5313,plain,
    ! [SV362: $i,SV212: $i,SV568: $i,SV602: $i,SV44: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV602 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SV602 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SV602 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5270]) ).

thf(5314,plain,
    ! [SV577: $i,SV496: $i,SV371: $i,SV221: $i,SV53: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5271]) ).

thf(5315,plain,
    ! [SV498: $i,SV578: $i,SV373: $i,SV223: $i,SV55: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5273]) ).

thf(5316,plain,
    ! [SV579: $i,SV499: $i,SV378: $i,SV229: $i,SV61: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5274]) ).

thf(5317,plain,
    ! [SV580: $i,SV501: $i,SV386: $i,SV237: $i,SV69: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5276]) ).

thf(5318,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV83: $i] :
      ( ( ( ! [SY1484: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1484 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1484 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1484 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[5281]) ).

thf(5319,plain,
    ! [SV249: $i,SV396: $i,SV569: $i,SV83: $i] :
      ( ( ( ! [SY1485: $i] :
              ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SY1485 )
              | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SY1485 )
              | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SY1485 ) )
              | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[5282]) ).

thf(5320,plain,
    ! [SV581: $i,SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV581 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV581 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV581 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5285]) ).

thf(5321,plain,
    ! [SV582: $i,SV403: $i,SV253: $i,SV89: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ SV253 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV89 @ SV403 @ SV582 ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV89 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV89 @ SV253 @ SV403 ) @ SV582 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV582 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV403 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV89 @ SV253 )
        = $false )
      | ( ( cType___24t @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5286]) ).

thf(5322,plain,
    ! [SV583: $i,SV254: $i,SV91: $i] :
      ( ( ( ~ ( p @ SV91 ) )
        = $true )
      | ( ( ( p @ SV254 )
          | ( p @ SV583 ) )
        = $true )
      | ( ( p @ SV91 )
        = $true )
      | ( ( cProp___24t @ SV583 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5287]) ).

thf(5323,plain,
    ! [SV91: $i,SV254: $i,SV584: $i] :
      ( ( ( ~ ( p @ SV584 ) )
        = $true )
      | ( ( ( p @ SV254 )
          | ( p @ SV584 ) )
        = $true )
      | ( ( p @ SV91 )
        = $true )
      | ( ( cProp___24t @ SV584 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5288]) ).

thf(5324,plain,
    ! [SV585: $i,SV91: $i,SV254: $i] :
      ( ( ( p @ SV254 )
        = $false )
      | ( ( ~ ( p @ SV91 )
          | ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( cProp___24t @ SV585 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5289]) ).

thf(5325,plain,
    ! [SV91: $i,SV586: $i,SV254: $i] :
      ( ( ( p @ SV254 )
        = $false )
      | ( ( ~ ( p @ SV586 )
          | ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( cProp___24t @ SV586 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5290]) ).

thf(5326,plain,
    ! [SV98: $i,SV288: $i,SV314: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV314 @ ( sK18_V3__x @ SV314 @ SV288 @ SV98 ) ) @ ( sK19_SY480 @ SV314 @ SV288 @ SV98 ) ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV98 @ SV288 @ SV314 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5294]) ).

thf(5327,plain,
    ! [SV265: $i] :
      ( ( ( cType___24t @ ( sK11_SY478 @ SV265 ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5300]) ).

thf(5328,plain,
    ! [SV265: $i] :
      ( ( ( ~ ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) ) )
        = $true )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[5301]) ).

thf(5329,plain,
    ! [SV592: $i,SV537: $i,SV420: $i,SV266: $i,SV604: $i] :
      ( ( ( ~ ( cType___24t @ SV604 ) )
        = $true )
      | ( ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SV592 ) @ SV604 ) )
        = $true )
      | ( ( cType___24t @ SV592 )
        = $false )
      | ( ( cType___24t @ SV537 )
        = $false )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5302]) ).

thf(5330,plain,
    ! [SV425: $i,SV574: $i,SV267: $i,SV115: $i] :
      ( ( ( ! [SY1488: $i] :
              ( ~ ( t @ SY1488 @ SV115 )
              | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1488 ) )
              | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1488 ) ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[5303]) ).

thf(5331,plain,
    ! [SV267: $i,SV574: $i,SV425: $i,SV115: $i] :
      ( ( ( ! [SY1489: $i] :
              ( ~ ( t @ SY1489 @ SV115 )
              | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SY1489 ) )
              | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SY1489 ) ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[5304]) ).

thf(5332,plain,
    ! [SV593: $i,SV427: $i,SV268: $i,SV117: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV427 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV593 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV593 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5305]) ).

thf(5333,plain,
    ! [SV427: $i,SV594: $i,SV268: $i,SV117: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ SV594 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV117 @ SV268 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV117 @ SV427 @ SV594 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV594 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV427 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV117 @ SV268 )
        = $false )
      | ( ( cType___24t @ SV117 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5306]) ).

thf(5334,plain,
    ! [SV334: $i,SV175: $i,SV596: $i,SV562: $i,SV5: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SV596 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SV596 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV596 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5307]) ).

thf(5335,plain,
    ! [SV348: $i,SV197: $i,SV597: $i,SV563: $i,SV29: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SV597 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SV597 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV597 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5308]) ).

thf(5336,plain,
    ! [SV349: $i,SV198: $i,SV598: $i,SV564: $i,SV30: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SV598 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SV598 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV598 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5309]) ).

thf(5337,plain,
    ! [SV352: $i,SV201: $i,SV599: $i,SV565: $i,SV33: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SV599 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SV599 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV599 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5310]) ).

thf(5338,plain,
    ! [SV353: $i,SV202: $i,SV600: $i,SV566: $i,SV34: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SV600 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SV600 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV600 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5311]) ).

thf(5339,plain,
    ! [SV361: $i,SV211: $i,SV601: $i,SV567: $i,SV43: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SV601 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SV601 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV601 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5312]) ).

thf(5340,plain,
    ! [SV362: $i,SV212: $i,SV602: $i,SV568: $i,SV44: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SV602 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SV602 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV602 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5313]) ).

thf(5341,plain,
    ! [SV371: $i,SV221: $i,SV577: $i,SV496: $i,SV53: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5314]) ).

thf(5342,plain,
    ! [SV373: $i,SV223: $i,SV498: $i,SV578: $i,SV55: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5315]) ).

thf(5343,plain,
    ! [SV378: $i,SV229: $i,SV579: $i,SV499: $i,SV61: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5316]) ).

thf(5344,plain,
    ! [SV386: $i,SV237: $i,SV580: $i,SV501: $i,SV69: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5317]) ).

thf(5345,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV605: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5318]) ).

thf(5346,plain,
    ! [SV249: $i,SV396: $i,SV569: $i,SV606: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 )
          | ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5319]) ).

thf(5347,plain,
    ! [SV583: $i,SV254: $i,SV91: $i] :
      ( ( ( p @ SV91 )
        = $false )
      | ( ( ( p @ SV254 )
          | ( p @ SV583 ) )
        = $true )
      | ( ( p @ SV91 )
        = $true )
      | ( ( cProp___24t @ SV583 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5322]) ).

thf(5348,plain,
    ! [SV91: $i,SV254: $i,SV584: $i] :
      ( ( ( p @ SV584 )
        = $false )
      | ( ( ( p @ SV254 )
          | ( p @ SV584 ) )
        = $true )
      | ( ( p @ SV91 )
        = $true )
      | ( ( cProp___24t @ SV584 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5323]) ).

thf(5349,plain,
    ! [SV585: $i,SV254: $i,SV91: $i] :
      ( ( ( ~ ( p @ SV91 ) )
        = $true )
      | ( ( ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( p @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV585 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5324]) ).

thf(5350,plain,
    ! [SV91: $i,SV254: $i,SV586: $i] :
      ( ( ( ~ ( p @ SV586 ) )
        = $true )
      | ( ( ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( p @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV586 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5325]) ).

thf(5351,plain,
    ! [SV265: $i] :
      ( ( ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV265 @ ( sK8_Vv__CANONICAL__0 @ SV265 ) ) @ ( sK9_SY473 @ SV265 ) ) @ ( sK10_SY476 @ SV265 ) ) @ ( sK11_SY478 @ SV265 ) ) )
        = $false )
      | ( ( c_24__type__4733___24t @ SV265 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[5328]) ).

thf(5352,plain,
    ! [SV592: $i,SV537: $i,SV420: $i,SV266: $i,SV604: $i] :
      ( ( ( cType___24t @ SV604 )
        = $false )
      | ( ( cType___24t @ ( happ @ ( happ @ ( happ @ ( happ @ SV266 @ SV420 ) @ SV537 ) @ SV592 ) @ SV604 ) )
        = $true )
      | ( ( cType___24t @ SV592 )
        = $false )
      | ( ( cType___24t @ SV537 )
        = $false )
      | ( ( cType___24t @ SV420 )
        = $false )
      | ( ( c_24__type__4733___24t @ SV266 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5329]) ).

thf(5353,plain,
    ! [SV425: $i,SV574: $i,SV267: $i,SV115: $i,SV607: $i] :
      ( ( ( ~ ( t @ SV607 @ SV115 )
          | ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV607 ) )
          | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV607 ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5330]) ).

thf(5354,plain,
    ! [SV267: $i,SV574: $i,SV425: $i,SV115: $i,SV608: $i] :
      ( ( ( ~ ( t @ SV608 @ SV115 )
          | ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV608 ) )
          | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV608 ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[5331]) ).

thf(5355,plain,
    ! [SV334: $i,SV175: $i,SV596: $i,SV562: $i,SV5: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV562 @ SV596 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV175 @ SV562 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV5 @ SV334 @ SV596 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV596 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV562 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV5 @ SV175 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV334 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV5 @ SV175 )
        = $false )
      | ( ( cType___24t @ SV5 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5334]) ).

thf(5356,plain,
    ! [SV348: $i,SV197: $i,SV597: $i,SV563: $i,SV29: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV563 @ SV597 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV197 @ SV563 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV29 @ SV348 @ SV597 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV597 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV563 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV29 @ SV197 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV348 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV29 @ SV197 )
        = $false )
      | ( ( cType___24t @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5335]) ).

thf(5357,plain,
    ! [SV349: $i,SV198: $i,SV598: $i,SV564: $i,SV30: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV564 @ SV598 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV198 @ SV564 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV30 @ SV349 @ SV598 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV598 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV564 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV30 @ SV198 @ SV349 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV349 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV30 @ SV198 )
        = $false )
      | ( ( cType___24t @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5336]) ).

thf(5358,plain,
    ! [SV352: $i,SV201: $i,SV599: $i,SV565: $i,SV33: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV565 @ SV599 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV201 @ SV565 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV33 @ SV352 @ SV599 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV599 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV565 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV33 @ SV201 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV352 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV33 @ SV201 )
        = $false )
      | ( ( cType___24t @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5337]) ).

thf(5359,plain,
    ! [SV353: $i,SV202: $i,SV600: $i,SV566: $i,SV34: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV566 @ SV600 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV202 @ SV566 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV34 @ SV353 @ SV600 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV600 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV566 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV34 @ SV202 @ SV353 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV353 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV34 @ SV202 )
        = $false )
      | ( ( cType___24t @ SV34 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5338]) ).

thf(5360,plain,
    ! [SV361: $i,SV211: $i,SV601: $i,SV567: $i,SV43: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV567 @ SV601 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV211 @ SV567 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV43 @ SV361 @ SV601 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV601 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV567 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV43 @ SV211 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV361 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV43 @ SV211 )
        = $false )
      | ( ( cType___24t @ SV43 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5339]) ).

thf(5361,plain,
    ! [SV362: $i,SV212: $i,SV602: $i,SV568: $i,SV44: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV568 @ SV602 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV212 @ SV568 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV44 @ SV362 @ SV602 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV602 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV568 )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV44 @ SV212 @ SV362 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV362 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV44 @ SV212 )
        = $false )
      | ( ( cType___24t @ SV44 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5340]) ).

thf(5362,plain,
    ! [SV371: $i,SV221: $i,SV577: $i,SV496: $i,SV53: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV496 @ SV577 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV221 @ SV496 ) @ ( chahn_2eHahnRelationsBasic_2einter__rel___24a3 @ SV53 @ SV371 @ SV577 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV53 @ SV221 @ SV371 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV577 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV496 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV371 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV53 @ SV221 )
        = $false )
      | ( ( cType___24t @ SV53 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5341]) ).

thf(5363,plain,
    ! [SV373: $i,SV223: $i,SV498: $i,SV578: $i,SV55: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV578 @ SV498 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV223 @ SV498 ) @ ( chahn_2eHahnRelationsBasic_2eminus__rel___24a3 @ SV55 @ SV373 @ SV578 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV55 @ SV223 @ SV373 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV578 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV498 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV373 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV55 @ SV223 )
        = $false )
      | ( ( cType___24t @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5342]) ).

thf(5364,plain,
    ! [SV378: $i,SV229: $i,SV579: $i,SV499: $i,SV61: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV499 @ SV579 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV229 @ SV499 ) @ ( chahn_2eHahnRelationsBasic_2eseq___24a3 @ SV61 @ SV378 @ SV579 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV61 @ SV229 @ SV378 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV579 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV499 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV378 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV61 @ SV229 )
        = $false )
      | ( ( cType___24t @ SV61 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5343]) ).

thf(5365,plain,
    ! [SV386: $i,SV237: $i,SV580: $i,SV501: $i,SV69: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV501 @ SV580 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV237 @ SV501 ) @ ( cCoq_2eRelations_2eRelation__Operators_2eunion___24a3 @ SV69 @ SV386 @ SV580 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV69 @ SV237 @ SV386 ) )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV580 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV501 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV386 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV69 @ SV237 )
        = $false )
      | ( ( cType___24t @ SV69 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5344]) ).

thf(5366,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV605: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5345]) ).

thf(5367,plain,
    ! [SV249: $i,SV396: $i,SV569: $i,SV606: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 ) )
        = $true )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5346]) ).

thf(5368,plain,
    ! [SV91: $i,SV583: $i,SV254: $i] :
      ( ( ( p @ SV254 )
        = $true )
      | ( ( p @ SV583 )
        = $true )
      | ( ( p @ SV91 )
        = $false )
      | ( ( p @ SV91 )
        = $true )
      | ( ( cProp___24t @ SV583 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5347]) ).

thf(5369,plain,
    ! [SV91: $i,SV584: $i,SV254: $i] :
      ( ( ( p @ SV254 )
        = $true )
      | ( ( p @ SV584 )
        = $true )
      | ( ( p @ SV584 )
        = $false )
      | ( ( p @ SV91 )
        = $true )
      | ( ( cProp___24t @ SV584 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5348]) ).

thf(5370,plain,
    ! [SV585: $i,SV254: $i,SV91: $i] :
      ( ( ( p @ SV91 )
        = $false )
      | ( ( ( p @ SV254 )
          | ( p @ SV585 ) )
        = $true )
      | ( ( p @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV585 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5349]) ).

thf(5371,plain,
    ! [SV91: $i,SV254: $i,SV586: $i] :
      ( ( ( p @ SV586 )
        = $false )
      | ( ( ( p @ SV254 )
          | ( p @ SV586 ) )
        = $true )
      | ( ( p @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV586 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5350]) ).

thf(5372,plain,
    ! [SV425: $i,SV574: $i,SV267: $i,SV115: $i,SV607: $i] :
      ( ( ( ~ ( t @ SV607 @ SV115 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV607 ) )
          | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV607 ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5353]) ).

thf(5373,plain,
    ! [SV267: $i,SV574: $i,SV425: $i,SV115: $i,SV608: $i] :
      ( ( ( ~ ( t @ SV608 @ SV115 ) )
        = $true )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV608 ) )
          | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV608 ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5354]) ).

thf(5374,plain,
    ! [SV396: $i,SV249: $i,SV569: $i,SV605: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5366]) ).

thf(5375,plain,
    ! [SV249: $i,SV396: $i,SV569: $i,SV606: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 )
        = $false )
      | ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 )
          | ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5367]) ).

thf(5376,plain,
    ! [SV91: $i,SV585: $i,SV254: $i] :
      ( ( ( p @ SV254 )
        = $true )
      | ( ( p @ SV585 )
        = $true )
      | ( ( p @ SV91 )
        = $false )
      | ( ( p @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV585 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5370]) ).

thf(5377,plain,
    ! [SV91: $i,SV586: $i,SV254: $i] :
      ( ( ( p @ SV254 )
        = $true )
      | ( ( p @ SV586 )
        = $true )
      | ( ( p @ SV586 )
        = $false )
      | ( ( p @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV586 )
        = $false )
      | ( ( cProp___24t @ SV254 )
        = $false )
      | ( ( cProp___24t @ SV91 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5371]) ).

thf(5378,plain,
    ! [SV425: $i,SV574: $i,SV267: $i,SV115: $i,SV607: $i] :
      ( ( ( t @ SV607 @ SV115 )
        = $false )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV607 ) )
          | ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV607 ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5372]) ).

thf(5379,plain,
    ! [SV267: $i,SV574: $i,SV425: $i,SV115: $i,SV608: $i] :
      ( ( ( t @ SV608 @ SV115 )
        = $false )
      | ( ( ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV608 ) )
          | ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV608 ) ) )
        = $true )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5373]) ).

thf(5380,plain,
    ! [SV396: $i,SV249: $i,SV605: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5374]) ).

thf(5381,plain,
    ! [SV249: $i,SV396: $i,SV606: $i,SV569: $i,SV83: $i] :
      ( ( ( ~ ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 ) )
        = $true )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5375]) ).

thf(5382,plain,
    ! [SV115: $i,SV425: $i,SV607: $i,SV574: $i,SV267: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV607 ) ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV607 ) )
        = $true )
      | ( ( t @ SV607 @ SV115 )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5378]) ).

thf(5383,plain,
    ! [SV115: $i,SV267: $i,SV608: $i,SV574: $i,SV425: $i] :
      ( ( ( ~ ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV608 ) ) )
        = $true )
      | ( ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV608 ) )
        = $true )
      | ( ( t @ SV608 @ SV115 )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5379]) ).

thf(5384,plain,
    ! [SV396: $i,SV249: $i,SV605: $i,SV569: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5380]) ).

thf(5385,plain,
    ! [SV249: $i,SV396: $i,SV606: $i,SV569: $i,SV83: $i] :
      ( ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 )
        = $false )
      | ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) )
          | ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5381]) ).

thf(5386,plain,
    ! [SV115: $i,SV425: $i,SV607: $i,SV574: $i,SV267: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV607 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV607 ) )
        = $true )
      | ( ( t @ SV607 @ SV115 )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5382]) ).

thf(5387,plain,
    ! [SV115: $i,SV267: $i,SV608: $i,SV574: $i,SV425: $i] :
      ( ( ( p @ ( happ @ ( happ @ SV425 @ SV574 ) @ SV608 ) )
        = $false )
      | ( ( p @ ( happ @ ( happ @ SV267 @ SV574 ) @ SV608 ) )
        = $true )
      | ( ( t @ SV608 @ SV115 )
        = $false )
      | ( ( t @ SV574 @ SV115 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV115 @ SV267 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV425 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV115 @ SV267 )
        = $false )
      | ( ( cType___24t @ SV115 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5383]) ).

thf(5388,plain,
    ! [SV605: $i,SV396: $i,SV569: $i,SV249: $i,SV83: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5384]) ).

thf(5389,plain,
    ! [SV569: $i,SV249: $i,SV606: $i,SV396: $i,SV83: $i] :
      ( ( ( ~ ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) ) )
        = $true )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[5385]) ).

thf(5390,plain,
    ! [SV605: $i,SV396: $i,SV569: $i,SV249: $i,SV83: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV605 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV605 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV605 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5388]) ).

thf(5391,plain,
    ! [SV569: $i,SV249: $i,SV606: $i,SV396: $i,SV83: $i] :
      ( ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV396 @ SV606 ) )
        = $false )
      | ( ( p @ ( cCoq_2eRelations_2eRelation__Definitions_2einclusion___24a3 @ SV83 @ SV249 @ SV569 ) )
        = $true )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV569 @ SV606 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV606 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV569 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2esame__relation___24a3 @ SV83 @ SV249 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV396 )
        = $false )
      | ( ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t @ SV83 @ SV249 )
        = $false )
      | ( ( cType___24t @ SV83 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[5389]) ).

thf(5392,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[2976,5391,5390,5387,5386,5377,5376,5369,5368,5365,5364,5363,5362,5361,5360,5359,5358,5357,5356,5355,5352,5351,5333,5332,5327,5326,5321,5320,5299,5298,5297,5296,5295,5293,5292,5291,5284,5283,5280,5279,5278,5277,5275,5272,5256,5255,5254,5253,5232,5231,5217,5216,5210,5205,5200,5199,5179,5178,5171,5170,5160,5156,5155,5144,5143,5142,5137,5134,5131,5130,5125,5124,5121,5117,5116,5109,5098,5087,5086,5083,5082,5080,5079,5076,5069,5068,5065,5062,5055,5054,5050,5049,5046,5045,5042,5032,5024,5023,5004,5003,5000,4999,4996,4995,4988,4987,4986,4985,4984,4983,4982,4977,4975,4972,4971,4965,4960,4957,4953,4945,4944,4943,4942,4939,4928,4927,4926,4916,4906,4901,4891,4890,4889,4888,4887,4885,4884,4883,4876,4875,4874,4871,4870,4867,4866,4859,4858,4855,4854,4853,4852,4851,4850,4849,4839,4829,4827,4824,4821,4806,4805,4793,4792,4789,4783,4780,4777,4769,4768,4767,4766,4765,4753,4749,4748,4687,4680,4679,4657,4656,4636,4630,4600,4590,4589,4588,4584,4583,4580,4579,4562,4560,4558,4547,4542,4540,4531,4520,4517,4507,4500,4470,4465,4453,4452,4425,4399,4388,4387,4382,4230,4212,4211,4079,4072,4071,4021,4003,3988,3977,3976,3973,3873,3809,3805,3651,3650,3571,3506,3501,3498,3497,3496,3297,3294,3225,3079,3078,3077,3076,3075,3074,3073,3072,3071,3070,3069,3068,3067,3066,3065,3064,3063,3062,3061,3060,3059,3058,3057,3056,3055,3054,3053,3052,3051,3050,3049,3048,3047,3046,3045,3044,3043,3042,3041,3040,3039,3038,3037,3036,3035,3034,3033,3032,2988,2986,2983,2978,2977]) ).

thf(5393,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[5392]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEV617+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.21  % Computer : n015.cluster.edu
% 0.09/0.21  % Model    : x86_64 x86_64
% 0.09/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21  % Memory   : 8046.5625MB
% 0.09/0.21  % OS       : Linux 6.8.0-71-generic
% 0.09/0.21  % CPULimit : 300
% 0.09/0.21  % WCLimit  : 300
% 0.09/0.21  % DateTime : Tue Oct  6 15:53:14 UTC 2026
% 0.09/0.21  % CPUTime  : 
% 0.09/0.21  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 211.96/42.71  .........................
% 211.96/42.71  
% 211.96/42.71   No.of.Axioms: 2655
% 211.96/42.71  
% 211.96/42.71   Length.of.Defs: 0
% 211.96/42.71  
% 211.96/42.71   Contains.Choice.Funs: false
% 211.96/42.71  ...........................................................................................................................................................
% 211.96/42.71  
% 211.96/42.71  ********************************
% 211.96/42.71  *   All subproblems solved!    *
% 211.96/42.71  ********************************
% 211.96/42.71  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:188,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:70,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5392,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 211.96/42.71  
% 211.96/42.71  %**** Beginning of derivation protocol ****
% 211.96/42.71  % SZS output start CNFRefutation
% See solution above
% 211.96/42.77  
% 211.96/42.77  %**** End of derivation protocol ****
% 211.96/42.77  %**** no. of clauses in derivation: 2926 ****
% 211.96/42.77  %**** clause counter: 5392 ****
% 211.96/42.77  
% 211.96/42.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:188,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:70,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5392,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------