%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX239-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:02:38 AM UTC 2026
% Result : Unsatisfiable 224.50s 37.65s
% Output : CNFRefutation 224.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 114
% Syntax : Number of formulae : 562 ( 562 unt; 0 typ; 0 def)
% Number of atoms : 1456 (1001 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3985 ( 8 ~; 0 |; 0 &;3977 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 12 con; 0-4 aty)
% Number of variables : 1214 ( 0 ^;1214 !; 0 ?;1214 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_andb,type,
andb: $i > $i > $i ).
thf(tp_atom,type,
atom: $i > $i ).
thf(tp_aux,type,
aux: $i > $i > $i > $i ).
thf(tp_aux2,type,
aux2: $i > $i > $i > $i > $i ).
thf(tp_aux3,type,
aux3: $i > $i > $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_cons2,type,
cons2: $i > $i > $i ).
thf(tp_cons3,type,
cons3: $i > $i > $i ).
thf(tp_eps,type,
eps: $i ).
thf(tp_eps2,type,
eps2: $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_eq2,type,
eq2: $i > $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_nil2,type,
nil2: $i ).
thf(tp_nil3,type,
nil3: $i ).
thf(tp_nil4,type,
nil4: $i ).
thf(tp_notb,type,
notb: $i > $i ).
thf(tp_or2,type,
or2: $i > $i ).
thf(tp_orb,type,
orb: $i > $i > $i ).
thf(tp_pair2,type,
pair2: $i > $i > $i ).
thf(tp_prop_same,type,
prop_same: $i > $i > $i ).
thf(tp_rec,type,
rec: $i > $i > $i ).
thf(tp_reck,type,
reck: $i > $i > $i > $i ).
thf(tp_reck2,type,
reck2: $i > $i > $i ).
thf(tp_splits,type,
splits: $i > $i > $i ).
thf(tp_splits2,type,
splits2: $i > $i ).
thf(tp_star,type,
star: $i > $i ).
thf(tp_step,type,
step: $i > $i > $i ).
thf(tp_x,type,
x: $i > $i > $i ).
thf(tp_x2,type,
x2: $i > $i > $i ).
thf(tp_y,type,
y: $i > $i > $i ).
thf(tp_z,type,
z: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( eq2 @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_111) ).
thf(2,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_110) ).
thf(3,axiom,
( ( eq2 @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_109) ).
thf(4,axiom,
( ( eq2 @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_108) ).
thf(5,axiom,
( ( eq @ c @ b )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_107) ).
thf(6,axiom,
( ( eq @ c @ a )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_106) ).
thf(7,axiom,
( ( eq @ b @ c )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_105) ).
thf(8,axiom,
( ( eq @ b @ a )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_104) ).
thf(9,axiom,
( ( eq @ a @ c )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_103) ).
thf(10,axiom,
( ( eq @ a @ b )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_102) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( prop_same @ X @ Y )
= ( eq2 @ ( rec @ X @ Y ) @ ( reck2 @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_101) ).
thf(12,axiom,
! [P2: $i,X6: $i,X7: $i] :
( ( reck2 @ ( star @ P2 ) @ ( cons2 @ X6 @ X7 ) )
= ( aux3 @ P2 @ X6 @ X7 @ ( notb @ ( eps2 @ P2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_100) ).
thf(13,axiom,
! [P2: $i] :
( ( reck2 @ ( star @ P2 ) @ nil2 )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_099) ).
thf(14,axiom,
! [R: $i,Q2: $i,Y: $i] :
( ( reck2 @ ( y @ R @ Q2 ) @ Y )
= ( or2 @ ( reck @ R @ Q2 @ ( splits2 @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_098) ).
thf(15,axiom,
! [P: $i,Q: $i,Y: $i] :
( ( reck2 @ ( x @ P @ Q ) @ Y )
= ( orb @ ( reck2 @ P @ Y ) @ ( reck2 @ Q @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_097) ).
thf(16,axiom,
! [C: $i,B2: $i,X4: $i,X5: $i] :
( ( reck2 @ ( atom @ C ) @ ( cons2 @ B2 @ ( cons2 @ X4 @ X5 ) ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_096) ).
thf(17,axiom,
! [C: $i,B2: $i] :
( ( reck2 @ ( atom @ C ) @ ( cons2 @ B2 @ nil2 ) )
= ( eq @ C @ B2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_095) ).
thf(18,axiom,
! [C: $i] :
( ( reck2 @ ( atom @ C ) @ nil2 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_094) ).
thf(19,axiom,
! [Z: $i,X2: $i] :
( ( reck2 @ eps @ ( cons2 @ Z @ X2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_093) ).
thf(20,axiom,
( ( reck2 @ eps @ nil2 )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_092) ).
thf(21,axiom,
! [Y: $i] :
( ( reck2 @ nil4 @ Y )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_091) ).
thf(22,axiom,
! [P: $i,Q: $i,L: $i,R: $i,Z: $i] :
( ( reck @ P @ Q @ ( cons @ ( pair2 @ L @ R ) @ Z ) )
= ( cons3 @ ( andb @ ( reck2 @ P @ L ) @ ( rec @ Q @ R ) ) @ ( reck @ P @ Q @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_090) ).
thf(23,axiom,
! [P: $i,Q: $i] :
( ( reck @ P @ Q @ nil )
= nil3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_089) ).
thf(24,axiom,
! [X: $i,Z: $i,Xs: $i] :
( ( rec @ X @ ( cons2 @ Z @ Xs ) )
= ( rec @ ( step @ X @ Z ) @ Xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_088) ).
thf(25,axiom,
! [X: $i] :
( ( rec @ X @ nil2 )
= ( eps2 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_087) ).
thf(26,axiom,
! [Y: $i] :
( ( step @ eps @ Y )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_086) ).
thf(27,axiom,
! [Y: $i] :
( ( step @ nil4 @ Y )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_085) ).
thf(28,axiom,
! [P2: $i,Y: $i] :
( ( step @ ( star @ P2 ) @ Y )
= ( y @ ( step @ P2 @ Y ) @ ( star @ P2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_084) ).
thf(29,axiom,
! [R: $i,Q2: $i,Y: $i] :
( ( step @ ( y @ R @ Q2 ) @ Y )
= ( aux2 @ Y @ R @ Q2 @ ( eps2 @ R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_083) ).
thf(30,axiom,
! [P: $i,Q: $i,Y: $i] :
( ( step @ ( x @ P @ Q ) @ Y )
= ( x @ ( step @ P @ Y ) @ ( step @ Q @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_082) ).
thf(31,axiom,
! [B: $i,Y: $i] :
( ( step @ ( atom @ B ) @ Y )
= ( aux @ Y @ B @ ( eq @ B @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_081) ).
thf(32,axiom,
! [X: $i] :
( ( eps2 @ ( atom @ X ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_080) ).
thf(33,axiom,
( ( eps2 @ nil4 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_079) ).
thf(34,axiom,
! [Y: $i] :
( ( eps2 @ ( star @ Y ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_078) ).
thf(35,axiom,
! [R: $i,Q2: $i] :
( ( eps2 @ ( y @ R @ Q2 ) )
= ( andb @ ( eps2 @ R ) @ ( eps2 @ Q2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_077) ).
thf(36,axiom,
! [P: $i,Q: $i] :
( ( eps2 @ ( x @ P @ Q ) )
= ( orb @ ( eps2 @ P ) @ ( eps2 @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_076) ).
thf(37,axiom,
( ( eps2 @ eps )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_075) ).
thf(38,axiom,
! [Q: $i] :
( ( andb @ bfalse @ Q )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_074) ).
thf(39,axiom,
! [Q: $i] :
( ( andb @ btrue @ Q )
= Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_073) ).
thf(40,axiom,
( ( notb @ bfalse )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_072) ).
thf(41,axiom,
( ( notb @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
thf(42,axiom,
! [Y: $i,Xs: $i] :
( ( or2 @ ( cons3 @ Y @ Xs ) )
= ( orb @ Y @ ( or2 @ Xs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_070) ).
thf(43,axiom,
( ( or2 @ nil3 )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_069) ).
thf(44,axiom,
! [Q: $i] :
( ( orb @ bfalse @ Q )
= Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_068) ).
thf(45,axiom,
! [Q: $i] :
( ( orb @ btrue @ Q )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_067) ).
thf(46,axiom,
! [Y: $i,Xs: $i] :
( ( splits2 @ ( cons2 @ Y @ Xs ) )
= ( cons @ ( pair2 @ nil2 @ ( cons2 @ Y @ Xs ) ) @ ( splits @ Y @ ( splits2 @ Xs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_066) ).
thf(47,axiom,
( ( splits2 @ nil2 )
= ( cons @ ( pair2 @ nil2 @ nil2 ) @ nil ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_065) ).
thf(48,axiom,
! [X: $i,Bs: $i,Cs: $i,X2: $i] :
( ( splits @ X @ ( cons @ ( pair2 @ Bs @ Cs ) @ X2 ) )
= ( cons @ ( pair2 @ ( cons2 @ X @ Bs ) @ Cs ) @ ( splits @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_064) ).
thf(49,axiom,
! [X: $i] :
( ( splits @ X @ nil )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
thf(50,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( star @ X ) @ ( star @ X2 ) )
= ( x @ ( star @ X ) @ ( star @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_062) ).
thf(51,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( star @ X ) @ ( y @ X2 @ X3 ) )
= ( x @ ( star @ X ) @ ( y @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_061) ).
thf(52,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( star @ X ) @ ( x @ X2 @ X3 ) )
= ( x @ ( star @ X ) @ ( x @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_060) ).
thf(53,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( star @ X ) @ ( atom @ X2 ) )
= ( x @ ( star @ X ) @ ( atom @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_059) ).
thf(54,axiom,
! [X: $i] :
( ( x2 @ ( star @ X ) @ eps )
= ( x @ ( star @ X ) @ eps ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_058) ).
thf(55,axiom,
! [X: $i] :
( ( x2 @ ( star @ X ) @ nil4 )
= ( star @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_057) ).
thf(56,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( star @ X3 ) )
= ( x @ ( y @ X @ X2 ) @ ( star @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_056) ).
thf(57,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( x @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_055) ).
thf(58,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( x @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
thf(59,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( atom @ X3 ) )
= ( x @ ( y @ X @ X2 ) @ ( atom @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
thf(60,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( y @ X @ X2 ) @ eps )
= ( x @ ( y @ X @ X2 ) @ eps ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
thf(61,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( y @ X @ X2 ) @ nil4 )
= ( y @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
thf(62,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( star @ X3 ) )
= ( x @ ( x @ X @ X2 ) @ ( star @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
thf(63,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( x @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_049) ).
thf(64,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( x @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_048) ).
thf(65,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( atom @ X3 ) )
= ( x @ ( x @ X @ X2 ) @ ( atom @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
thf(66,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( x @ X @ X2 ) @ eps )
= ( x @ ( x @ X @ X2 ) @ eps ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
thf(67,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( x @ X @ X2 ) @ nil4 )
= ( x @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
thf(68,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( atom @ X ) @ ( star @ X2 ) )
= ( x @ ( atom @ X ) @ ( star @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
thf(69,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( atom @ X ) @ ( y @ X2 @ X3 ) )
= ( x @ ( atom @ X ) @ ( y @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
thf(70,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( atom @ X ) @ ( x @ X2 @ X3 ) )
= ( x @ ( atom @ X ) @ ( x @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
thf(71,axiom,
! [X: $i,X2: $i] :
( ( x2 @ ( atom @ X ) @ ( atom @ X2 ) )
= ( x @ ( atom @ X ) @ ( atom @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_041) ).
thf(72,axiom,
! [X: $i] :
( ( x2 @ ( atom @ X ) @ eps )
= ( x @ ( atom @ X ) @ eps ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_040) ).
thf(73,axiom,
! [X: $i] :
( ( x2 @ ( atom @ X ) @ nil4 )
= ( atom @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
thf(74,axiom,
! [X: $i] :
( ( x2 @ eps @ ( star @ X ) )
= ( x @ eps @ ( star @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
thf(75,axiom,
! [X: $i,X2: $i] :
( ( x2 @ eps @ ( y @ X @ X2 ) )
= ( x @ eps @ ( y @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
thf(76,axiom,
! [X: $i,X2: $i] :
( ( x2 @ eps @ ( x @ X @ X2 ) )
= ( x @ eps @ ( x @ X @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
thf(77,axiom,
! [X: $i] :
( ( x2 @ eps @ ( atom @ X ) )
= ( x @ eps @ ( atom @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
thf(78,axiom,
( ( x2 @ eps @ eps )
= ( x @ eps @ eps ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
thf(79,axiom,
( ( x2 @ eps @ nil4 )
= eps ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
thf(80,axiom,
! [Y: $i] :
( ( x2 @ nil4 @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
thf(81,axiom,
! [X: $i,X2: $i] :
( ( z @ ( star @ X ) @ ( star @ X2 ) )
= ( y @ ( star @ X ) @ ( star @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(82,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( star @ X ) @ ( y @ X2 @ X3 ) )
= ( y @ ( star @ X ) @ ( y @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(83,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( star @ X ) @ ( x @ X2 @ X3 ) )
= ( y @ ( star @ X ) @ ( x @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(84,axiom,
! [X: $i,X2: $i] :
( ( z @ ( star @ X ) @ ( atom @ X2 ) )
= ( y @ ( star @ X ) @ ( atom @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(85,axiom,
! [X: $i] :
( ( z @ ( star @ X ) @ eps )
= ( star @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(86,axiom,
! [X: $i] :
( ( z @ ( star @ X ) @ nil4 )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(87,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( y @ X @ X2 ) @ ( star @ X3 ) )
= ( y @ ( y @ X @ X2 ) @ ( star @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(88,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( y @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(89,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( y @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(90,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( y @ X @ X2 ) @ ( atom @ X3 ) )
= ( y @ ( y @ X @ X2 ) @ ( atom @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(91,axiom,
! [X: $i,X2: $i] :
( ( z @ ( y @ X @ X2 ) @ eps )
= ( y @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(92,axiom,
! [X: $i,X2: $i] :
( ( z @ ( y @ X @ X2 ) @ nil4 )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(93,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( x @ X @ X2 ) @ ( star @ X3 ) )
= ( y @ ( x @ X @ X2 ) @ ( star @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(94,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( y @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(95,axiom,
! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( y @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(96,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( x @ X @ X2 ) @ ( atom @ X3 ) )
= ( y @ ( x @ X @ X2 ) @ ( atom @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(97,axiom,
! [X: $i,X2: $i] :
( ( z @ ( x @ X @ X2 ) @ eps )
= ( x @ X @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(98,axiom,
! [X: $i,X2: $i] :
( ( z @ ( x @ X @ X2 ) @ nil4 )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(99,axiom,
! [X: $i,X2: $i] :
( ( z @ ( atom @ X ) @ ( star @ X2 ) )
= ( y @ ( atom @ X ) @ ( star @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(100,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( atom @ X ) @ ( y @ X2 @ X3 ) )
= ( y @ ( atom @ X ) @ ( y @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(101,axiom,
! [X: $i,X2: $i,X3: $i] :
( ( z @ ( atom @ X ) @ ( x @ X2 @ X3 ) )
= ( y @ ( atom @ X ) @ ( x @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(102,axiom,
! [X: $i,X2: $i] :
( ( z @ ( atom @ X ) @ ( atom @ X2 ) )
= ( y @ ( atom @ X ) @ ( atom @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(103,axiom,
! [X: $i] :
( ( z @ ( atom @ X ) @ eps )
= ( atom @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(104,axiom,
! [X: $i] :
( ( z @ ( atom @ X ) @ nil4 )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(105,axiom,
! [Y: $i] :
( ( z @ eps @ Y )
= Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(106,axiom,
! [Y: $i] :
( ( z @ nil4 @ Y )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(107,axiom,
! [P2: $i,X6: $i,X7: $i] :
( ( aux3 @ P2 @ X6 @ X7 @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(108,axiom,
! [P2: $i,X6: $i,X7: $i] :
( ( aux3 @ P2 @ X6 @ X7 @ btrue )
= ( rec @ ( y @ P2 @ ( star @ P2 ) ) @ ( cons2 @ X6 @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(109,axiom,
! [Y: $i,R: $i,Q2: $i] :
( ( aux2 @ Y @ R @ Q2 @ bfalse )
= ( x @ ( y @ ( step @ R @ Y ) @ Q2 ) @ nil4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(110,axiom,
! [Y: $i,R: $i,Q2: $i] :
( ( aux2 @ Y @ R @ Q2 @ btrue )
= ( x @ ( y @ ( step @ R @ Y ) @ Q2 ) @ ( step @ Q2 @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(111,axiom,
! [Y: $i,B: $i] :
( ( aux @ Y @ B @ bfalse )
= nil4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(112,axiom,
! [Y: $i,B: $i] :
( ( aux @ Y @ B @ btrue )
= eps ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(113,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(114,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[113]) ).
thf(115,negated_conjecture,
! [X: $i,Y: $i] :
( ( eq2 @ ( prop_same @ X @ Y ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(116,plain,
$false = $false,
inference(unfold_def,[status(thm)],[114]) ).
thf(117,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(118,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(119,plain,
( ( ( eq2 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(120,plain,
( ( ( eq2 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(121,plain,
( ( ( eq @ c @ b )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(122,plain,
( ( ( eq @ c @ a )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(123,plain,
( ( ( eq @ b @ c )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(124,plain,
( ( ( eq @ b @ a )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(125,plain,
( ( ( eq @ a @ c )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(126,plain,
( ( ( eq @ a @ b )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(127,plain,
( ( ! [X: $i,Y: $i] :
( ( prop_same @ X @ Y )
= ( eq2 @ ( rec @ X @ Y ) @ ( reck2 @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(128,plain,
( ( ! [P2: $i,X6: $i,X7: $i] :
( ( reck2 @ ( star @ P2 ) @ ( cons2 @ X6 @ X7 ) )
= ( aux3 @ P2 @ X6 @ X7 @ ( notb @ ( eps2 @ P2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(129,plain,
( ( ! [P2: $i] :
( ( reck2 @ ( star @ P2 ) @ nil2 )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(130,plain,
( ( ! [R: $i,Q2: $i,Y: $i] :
( ( reck2 @ ( y @ R @ Q2 ) @ Y )
= ( or2 @ ( reck @ R @ Q2 @ ( splits2 @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(131,plain,
( ( ! [P: $i,Q: $i,Y: $i] :
( ( reck2 @ ( x @ P @ Q ) @ Y )
= ( orb @ ( reck2 @ P @ Y ) @ ( reck2 @ Q @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(132,plain,
( ( ! [C: $i,B2: $i,X4: $i,X5: $i] :
( ( reck2 @ ( atom @ C ) @ ( cons2 @ B2 @ ( cons2 @ X4 @ X5 ) ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(133,plain,
( ( ! [C: $i,B2: $i] :
( ( reck2 @ ( atom @ C ) @ ( cons2 @ B2 @ nil2 ) )
= ( eq @ C @ B2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(134,plain,
( ( ! [C: $i] :
( ( reck2 @ ( atom @ C ) @ nil2 )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(135,plain,
( ( ! [Z: $i,X2: $i] :
( ( reck2 @ eps @ ( cons2 @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(136,plain,
( ( ( reck2 @ eps @ nil2 )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(137,plain,
( ( ! [Y: $i] :
( ( reck2 @ nil4 @ Y )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(138,plain,
( ( ! [P: $i,Q: $i,L: $i,R: $i,Z: $i] :
( ( reck @ P @ Q @ ( cons @ ( pair2 @ L @ R ) @ Z ) )
= ( cons3 @ ( andb @ ( reck2 @ P @ L ) @ ( rec @ Q @ R ) ) @ ( reck @ P @ Q @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(139,plain,
( ( ! [P: $i,Q: $i] :
( ( reck @ P @ Q @ nil )
= nil3 ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(140,plain,
( ( ! [X: $i,Z: $i,Xs: $i] :
( ( rec @ X @ ( cons2 @ Z @ Xs ) )
= ( rec @ ( step @ X @ Z ) @ Xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(141,plain,
( ( ! [X: $i] :
( ( rec @ X @ nil2 )
= ( eps2 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(142,plain,
( ( ! [Y: $i] :
( ( step @ eps @ Y )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(143,plain,
( ( ! [Y: $i] :
( ( step @ nil4 @ Y )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(144,plain,
( ( ! [P2: $i,Y: $i] :
( ( step @ ( star @ P2 ) @ Y )
= ( y @ ( step @ P2 @ Y ) @ ( star @ P2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(145,plain,
( ( ! [R: $i,Q2: $i,Y: $i] :
( ( step @ ( y @ R @ Q2 ) @ Y )
= ( aux2 @ Y @ R @ Q2 @ ( eps2 @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(146,plain,
( ( ! [P: $i,Q: $i,Y: $i] :
( ( step @ ( x @ P @ Q ) @ Y )
= ( x @ ( step @ P @ Y ) @ ( step @ Q @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(147,plain,
( ( ! [B: $i,Y: $i] :
( ( step @ ( atom @ B ) @ Y )
= ( aux @ Y @ B @ ( eq @ B @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(148,plain,
( ( ! [X: $i] :
( ( eps2 @ ( atom @ X ) )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(149,plain,
( ( ( eps2 @ nil4 )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(150,plain,
( ( ! [Y: $i] :
( ( eps2 @ ( star @ Y ) )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(151,plain,
( ( ! [R: $i,Q2: $i] :
( ( eps2 @ ( y @ R @ Q2 ) )
= ( andb @ ( eps2 @ R ) @ ( eps2 @ Q2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(152,plain,
( ( ! [P: $i,Q: $i] :
( ( eps2 @ ( x @ P @ Q ) )
= ( orb @ ( eps2 @ P ) @ ( eps2 @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(153,plain,
( ( ( eps2 @ eps )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(154,plain,
( ( ! [Q: $i] :
( ( andb @ bfalse @ Q )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(155,plain,
( ( ! [Q: $i] :
( ( andb @ btrue @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(156,plain,
( ( ( notb @ bfalse )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(157,plain,
( ( ( notb @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(158,plain,
( ( ! [Y: $i,Xs: $i] :
( ( or2 @ ( cons3 @ Y @ Xs ) )
= ( orb @ Y @ ( or2 @ Xs ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(159,plain,
( ( ( or2 @ nil3 )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(160,plain,
( ( ! [Q: $i] :
( ( orb @ bfalse @ Q )
= Q ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(161,plain,
( ( ! [Q: $i] :
( ( orb @ btrue @ Q )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(162,plain,
( ( ! [Y: $i,Xs: $i] :
( ( splits2 @ ( cons2 @ Y @ Xs ) )
= ( cons @ ( pair2 @ nil2 @ ( cons2 @ Y @ Xs ) ) @ ( splits @ Y @ ( splits2 @ Xs ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(163,plain,
( ( ( splits2 @ nil2 )
= ( cons @ ( pair2 @ nil2 @ nil2 ) @ nil ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(164,plain,
( ( ! [X: $i,Bs: $i,Cs: $i,X2: $i] :
( ( splits @ X @ ( cons @ ( pair2 @ Bs @ Cs ) @ X2 ) )
= ( cons @ ( pair2 @ ( cons2 @ X @ Bs ) @ Cs ) @ ( splits @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(165,plain,
( ( ! [X: $i] :
( ( splits @ X @ nil )
= nil ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(166,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( star @ X ) @ ( star @ X2 ) )
= ( x @ ( star @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(167,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( star @ X ) @ ( y @ X2 @ X3 ) )
= ( x @ ( star @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(168,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( star @ X ) @ ( x @ X2 @ X3 ) )
= ( x @ ( star @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(169,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( star @ X ) @ ( atom @ X2 ) )
= ( x @ ( star @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(170,plain,
( ( ! [X: $i] :
( ( x2 @ ( star @ X ) @ eps )
= ( x @ ( star @ X ) @ eps ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(171,plain,
( ( ! [X: $i] :
( ( x2 @ ( star @ X ) @ nil4 )
= ( star @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(172,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( star @ X3 ) )
= ( x @ ( y @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(173,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( x @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(174,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( x @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(175,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( atom @ X3 ) )
= ( x @ ( y @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(176,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( y @ X @ X2 ) @ eps )
= ( x @ ( y @ X @ X2 ) @ eps ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(177,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( y @ X @ X2 ) @ nil4 )
= ( y @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(178,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( star @ X3 ) )
= ( x @ ( x @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(179,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( x @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(180,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( x @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(181,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( atom @ X3 ) )
= ( x @ ( x @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(182,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( x @ X @ X2 ) @ eps )
= ( x @ ( x @ X @ X2 ) @ eps ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(183,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( x @ X @ X2 ) @ nil4 )
= ( x @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(184,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( atom @ X ) @ ( star @ X2 ) )
= ( x @ ( atom @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(185,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( atom @ X ) @ ( y @ X2 @ X3 ) )
= ( x @ ( atom @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(186,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( atom @ X ) @ ( x @ X2 @ X3 ) )
= ( x @ ( atom @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(187,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( atom @ X ) @ ( atom @ X2 ) )
= ( x @ ( atom @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(188,plain,
( ( ! [X: $i] :
( ( x2 @ ( atom @ X ) @ eps )
= ( x @ ( atom @ X ) @ eps ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(189,plain,
( ( ! [X: $i] :
( ( x2 @ ( atom @ X ) @ nil4 )
= ( atom @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(190,plain,
( ( ! [X: $i] :
( ( x2 @ eps @ ( star @ X ) )
= ( x @ eps @ ( star @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(191,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ eps @ ( y @ X @ X2 ) )
= ( x @ eps @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(192,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ eps @ ( x @ X @ X2 ) )
= ( x @ eps @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(193,plain,
( ( ! [X: $i] :
( ( x2 @ eps @ ( atom @ X ) )
= ( x @ eps @ ( atom @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(194,plain,
( ( ( x2 @ eps @ eps )
= ( x @ eps @ eps ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(195,plain,
( ( ( x2 @ eps @ nil4 )
= eps )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(196,plain,
( ( ! [Y: $i] :
( ( x2 @ nil4 @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(197,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( star @ X ) @ ( star @ X2 ) )
= ( y @ ( star @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(198,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( star @ X ) @ ( y @ X2 @ X3 ) )
= ( y @ ( star @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(199,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( star @ X ) @ ( x @ X2 @ X3 ) )
= ( y @ ( star @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(200,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( star @ X ) @ ( atom @ X2 ) )
= ( y @ ( star @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(201,plain,
( ( ! [X: $i] :
( ( z @ ( star @ X ) @ eps )
= ( star @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(202,plain,
( ( ! [X: $i] :
( ( z @ ( star @ X ) @ nil4 )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(203,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( y @ X @ X2 ) @ ( star @ X3 ) )
= ( y @ ( y @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(204,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( y @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(205,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( y @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(206,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( y @ X @ X2 ) @ ( atom @ X3 ) )
= ( y @ ( y @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(207,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( y @ X @ X2 ) @ eps )
= ( y @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(208,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( y @ X @ X2 ) @ nil4 )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(209,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( x @ X @ X2 ) @ ( star @ X3 ) )
= ( y @ ( x @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(210,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( y @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(211,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( y @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(212,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( x @ X @ X2 ) @ ( atom @ X3 ) )
= ( y @ ( x @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(213,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( x @ X @ X2 ) @ eps )
= ( x @ X @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(214,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( x @ X @ X2 ) @ nil4 )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(215,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( atom @ X ) @ ( star @ X2 ) )
= ( y @ ( atom @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(216,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( atom @ X ) @ ( y @ X2 @ X3 ) )
= ( y @ ( atom @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(217,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( atom @ X ) @ ( x @ X2 @ X3 ) )
= ( y @ ( atom @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(218,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( atom @ X ) @ ( atom @ X2 ) )
= ( y @ ( atom @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(219,plain,
( ( ! [X: $i] :
( ( z @ ( atom @ X ) @ eps )
= ( atom @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(220,plain,
( ( ! [X: $i] :
( ( z @ ( atom @ X ) @ nil4 )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(221,plain,
( ( ! [Y: $i] :
( ( z @ eps @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(222,plain,
( ( ! [Y: $i] :
( ( z @ nil4 @ Y )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(223,plain,
( ( ! [P2: $i,X6: $i,X7: $i] :
( ( aux3 @ P2 @ X6 @ X7 @ bfalse )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(224,plain,
( ( ! [P2: $i,X6: $i,X7: $i] :
( ( aux3 @ P2 @ X6 @ X7 @ btrue )
= ( rec @ ( y @ P2 @ ( star @ P2 ) ) @ ( cons2 @ X6 @ X7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(225,plain,
( ( ! [Y: $i,R: $i,Q2: $i] :
( ( aux2 @ Y @ R @ Q2 @ bfalse )
= ( x @ ( y @ ( step @ R @ Y ) @ Q2 ) @ nil4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(226,plain,
( ( ! [Y: $i,R: $i,Q2: $i] :
( ( aux2 @ Y @ R @ Q2 @ btrue )
= ( x @ ( y @ ( step @ R @ Y ) @ Q2 ) @ ( step @ Q2 @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(227,plain,
( ( ! [Y: $i,B: $i] :
( ( aux @ Y @ B @ bfalse )
= nil4 ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(228,plain,
( ( ! [Y: $i,B: $i] :
( ( aux @ Y @ B @ btrue )
= eps ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(229,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( prop_same @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(230,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[116]) ).
thf(231,plain,
( ( ! [X: $i,Y: $i] :
( ( eq2 @ ( prop_same @ X @ Y ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(232,plain,
( ( ! [Y: $i,B: $i] :
( ( aux @ Y @ B @ btrue )
= eps ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(233,plain,
( ( ! [Y: $i,B: $i] :
( ( aux @ Y @ B @ bfalse )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(234,plain,
( ( ! [Y: $i,R: $i,Q2: $i] :
( ( aux2 @ Y @ R @ Q2 @ btrue )
= ( x @ ( y @ ( step @ R @ Y ) @ Q2 ) @ ( step @ Q2 @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(235,plain,
( ( ! [Y: $i,R: $i,Q2: $i] :
( ( aux2 @ Y @ R @ Q2 @ bfalse )
= ( x @ ( y @ ( step @ R @ Y ) @ Q2 ) @ nil4 ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(236,plain,
( ( ! [P2: $i,X6: $i,X7: $i] :
( ( aux3 @ P2 @ X6 @ X7 @ btrue )
= ( rec @ ( y @ P2 @ ( star @ P2 ) ) @ ( cons2 @ X6 @ X7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(237,plain,
( ( ! [P2: $i,X6: $i,X7: $i] :
( ( aux3 @ P2 @ X6 @ X7 @ bfalse )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(238,plain,
( ( ! [Y: $i] :
( ( z @ nil4 @ Y )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(239,plain,
( ( ! [Y: $i] :
( ( z @ eps @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(240,plain,
( ( ! [X: $i] :
( ( z @ ( atom @ X ) @ nil4 )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(241,plain,
( ( ! [X: $i] :
( ( z @ ( atom @ X ) @ eps )
= ( atom @ X ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(242,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( atom @ X ) @ ( atom @ X2 ) )
= ( y @ ( atom @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(243,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( atom @ X ) @ ( x @ X2 @ X3 ) )
= ( y @ ( atom @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(244,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( atom @ X ) @ ( y @ X2 @ X3 ) )
= ( y @ ( atom @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(245,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( atom @ X ) @ ( star @ X2 ) )
= ( y @ ( atom @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(246,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( x @ X @ X2 ) @ nil4 )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(247,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( x @ X @ X2 ) @ eps )
= ( x @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(248,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( x @ X @ X2 ) @ ( atom @ X3 ) )
= ( y @ ( x @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(249,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( y @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(250,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( y @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(251,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( x @ X @ X2 ) @ ( star @ X3 ) )
= ( y @ ( x @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(252,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( y @ X @ X2 ) @ nil4 )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(253,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( y @ X @ X2 ) @ eps )
= ( y @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(254,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( y @ X @ X2 ) @ ( atom @ X3 ) )
= ( y @ ( y @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(255,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( y @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(256,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( z @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( y @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(257,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( y @ X @ X2 ) @ ( star @ X3 ) )
= ( y @ ( y @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(258,plain,
( ( ! [X: $i] :
( ( z @ ( star @ X ) @ nil4 )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(259,plain,
( ( ! [X: $i] :
( ( z @ ( star @ X ) @ eps )
= ( star @ X ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(260,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( star @ X ) @ ( atom @ X2 ) )
= ( y @ ( star @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(261,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( star @ X ) @ ( x @ X2 @ X3 ) )
= ( y @ ( star @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(262,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( z @ ( star @ X ) @ ( y @ X2 @ X3 ) )
= ( y @ ( star @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(263,plain,
( ( ! [X: $i,X2: $i] :
( ( z @ ( star @ X ) @ ( star @ X2 ) )
= ( y @ ( star @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(264,plain,
( ( ! [Y: $i] :
( ( x2 @ nil4 @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(265,plain,
( ( ( x2 @ eps @ nil4 )
= eps )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(266,plain,
( ( ( x2 @ eps @ eps )
= ( x @ eps @ eps ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(267,plain,
( ( ! [X: $i] :
( ( x2 @ eps @ ( atom @ X ) )
= ( x @ eps @ ( atom @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(268,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ eps @ ( x @ X @ X2 ) )
= ( x @ eps @ ( x @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(269,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ eps @ ( y @ X @ X2 ) )
= ( x @ eps @ ( y @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(270,plain,
( ( ! [X: $i] :
( ( x2 @ eps @ ( star @ X ) )
= ( x @ eps @ ( star @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(271,plain,
( ( ! [X: $i] :
( ( x2 @ ( atom @ X ) @ nil4 )
= ( atom @ X ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(272,plain,
( ( ! [X: $i] :
( ( x2 @ ( atom @ X ) @ eps )
= ( x @ ( atom @ X ) @ eps ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(273,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( atom @ X ) @ ( atom @ X2 ) )
= ( x @ ( atom @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(274,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( atom @ X ) @ ( x @ X2 @ X3 ) )
= ( x @ ( atom @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(275,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( atom @ X ) @ ( y @ X2 @ X3 ) )
= ( x @ ( atom @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(276,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( atom @ X ) @ ( star @ X2 ) )
= ( x @ ( atom @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(277,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( x @ X @ X2 ) @ nil4 )
= ( x @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(278,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( x @ X @ X2 ) @ eps )
= ( x @ ( x @ X @ X2 ) @ eps ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(279,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( atom @ X3 ) )
= ( x @ ( x @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(280,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( x @ ( x @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(281,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( x @ ( x @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(282,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( x @ X @ X2 ) @ ( star @ X3 ) )
= ( x @ ( x @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(283,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( y @ X @ X2 ) @ nil4 )
= ( y @ X @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(284,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( y @ X @ X2 ) @ eps )
= ( x @ ( y @ X @ X2 ) @ eps ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(285,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( atom @ X3 ) )
= ( x @ ( y @ X @ X2 ) @ ( atom @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(286,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) )
= ( x @ ( y @ X @ X2 ) @ ( x @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(287,plain,
( ( ! [X: $i,X2: $i,X3: $i,X4: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) )
= ( x @ ( y @ X @ X2 ) @ ( y @ X3 @ X4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(288,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( y @ X @ X2 ) @ ( star @ X3 ) )
= ( x @ ( y @ X @ X2 ) @ ( star @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(289,plain,
( ( ! [X: $i] :
( ( x2 @ ( star @ X ) @ nil4 )
= ( star @ X ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(290,plain,
( ( ! [X: $i] :
( ( x2 @ ( star @ X ) @ eps )
= ( x @ ( star @ X ) @ eps ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(291,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( star @ X ) @ ( atom @ X2 ) )
= ( x @ ( star @ X ) @ ( atom @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(292,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( star @ X ) @ ( x @ X2 @ X3 ) )
= ( x @ ( star @ X ) @ ( x @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(293,plain,
( ( ! [X: $i,X2: $i,X3: $i] :
( ( x2 @ ( star @ X ) @ ( y @ X2 @ X3 ) )
= ( x @ ( star @ X ) @ ( y @ X2 @ X3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(294,plain,
( ( ! [X: $i,X2: $i] :
( ( x2 @ ( star @ X ) @ ( star @ X2 ) )
= ( x @ ( star @ X ) @ ( star @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(295,plain,
( ( ! [X: $i] :
( ( splits @ X @ nil )
= nil ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(296,plain,
( ( ! [X: $i,Bs: $i,Cs: $i,X2: $i] :
( ( splits @ X @ ( cons @ ( pair2 @ Bs @ Cs ) @ X2 ) )
= ( cons @ ( pair2 @ ( cons2 @ X @ Bs ) @ Cs ) @ ( splits @ X @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(297,plain,
( ( ( splits2 @ nil2 )
= ( cons @ ( pair2 @ nil2 @ nil2 ) @ nil ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(298,plain,
( ( ! [Y: $i,Xs: $i] :
( ( splits2 @ ( cons2 @ Y @ Xs ) )
= ( cons @ ( pair2 @ nil2 @ ( cons2 @ Y @ Xs ) ) @ ( splits @ Y @ ( splits2 @ Xs ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(299,plain,
( ( ! [Q: $i] :
( ( orb @ btrue @ Q )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(300,plain,
( ( ! [Q: $i] :
( ( orb @ bfalse @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(301,plain,
( ( ( or2 @ nil3 )
= bfalse )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(302,plain,
( ( ! [Y: $i,Xs: $i] :
( ( or2 @ ( cons3 @ Y @ Xs ) )
= ( orb @ Y @ ( or2 @ Xs ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(303,plain,
( ( ( notb @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(304,plain,
( ( ( notb @ bfalse )
= btrue )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(305,plain,
( ( ! [Q: $i] :
( ( andb @ btrue @ Q )
= Q ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(306,plain,
( ( ! [Q: $i] :
( ( andb @ bfalse @ Q )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(307,plain,
( ( ( eps2 @ eps )
= btrue )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(308,plain,
( ( ! [P: $i,Q: $i] :
( ( eps2 @ ( x @ P @ Q ) )
= ( orb @ ( eps2 @ P ) @ ( eps2 @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(309,plain,
( ( ! [R: $i,Q2: $i] :
( ( eps2 @ ( y @ R @ Q2 ) )
= ( andb @ ( eps2 @ R ) @ ( eps2 @ Q2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(310,plain,
( ( ! [Y: $i] :
( ( eps2 @ ( star @ Y ) )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(311,plain,
( ( ( eps2 @ nil4 )
= bfalse )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(312,plain,
( ( ! [X: $i] :
( ( eps2 @ ( atom @ X ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(313,plain,
( ( ! [B: $i,Y: $i] :
( ( step @ ( atom @ B ) @ Y )
= ( aux @ Y @ B @ ( eq @ B @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(314,plain,
( ( ! [P: $i,Q: $i,Y: $i] :
( ( step @ ( x @ P @ Q ) @ Y )
= ( x @ ( step @ P @ Y ) @ ( step @ Q @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(315,plain,
( ( ! [R: $i,Q2: $i,Y: $i] :
( ( step @ ( y @ R @ Q2 ) @ Y )
= ( aux2 @ Y @ R @ Q2 @ ( eps2 @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(316,plain,
( ( ! [P2: $i,Y: $i] :
( ( step @ ( star @ P2 ) @ Y )
= ( y @ ( step @ P2 @ Y ) @ ( star @ P2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(317,plain,
( ( ! [Y: $i] :
( ( step @ nil4 @ Y )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(318,plain,
( ( ! [Y: $i] :
( ( step @ eps @ Y )
= nil4 ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(319,plain,
( ( ! [X: $i] :
( ( rec @ X @ nil2 )
= ( eps2 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(320,plain,
( ( ! [X: $i,Z: $i,Xs: $i] :
( ( rec @ X @ ( cons2 @ Z @ Xs ) )
= ( rec @ ( step @ X @ Z ) @ Xs ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(321,plain,
( ( ! [P: $i,Q: $i] :
( ( reck @ P @ Q @ nil )
= nil3 ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(322,plain,
( ( ! [P: $i,Q: $i,L: $i,R: $i,Z: $i] :
( ( reck @ P @ Q @ ( cons @ ( pair2 @ L @ R ) @ Z ) )
= ( cons3 @ ( andb @ ( reck2 @ P @ L ) @ ( rec @ Q @ R ) ) @ ( reck @ P @ Q @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(323,plain,
( ( ! [Y: $i] :
( ( reck2 @ nil4 @ Y )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(324,plain,
( ( ( reck2 @ eps @ nil2 )
= btrue )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(325,plain,
( ( ! [Z: $i,X2: $i] :
( ( reck2 @ eps @ ( cons2 @ Z @ X2 ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(326,plain,
( ( ! [C: $i] :
( ( reck2 @ ( atom @ C ) @ nil2 )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(327,plain,
( ( ! [C: $i,B2: $i] :
( ( reck2 @ ( atom @ C ) @ ( cons2 @ B2 @ nil2 ) )
= ( eq @ C @ B2 ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(328,plain,
( ( ! [C: $i,B2: $i,X4: $i,X5: $i] :
( ( reck2 @ ( atom @ C ) @ ( cons2 @ B2 @ ( cons2 @ X4 @ X5 ) ) )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(329,plain,
( ( ! [P: $i,Q: $i,Y: $i] :
( ( reck2 @ ( x @ P @ Q ) @ Y )
= ( orb @ ( reck2 @ P @ Y ) @ ( reck2 @ Q @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(330,plain,
( ( ! [R: $i,Q2: $i,Y: $i] :
( ( reck2 @ ( y @ R @ Q2 ) @ Y )
= ( or2 @ ( reck @ R @ Q2 @ ( splits2 @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(331,plain,
( ( ! [P2: $i] :
( ( reck2 @ ( star @ P2 ) @ nil2 )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(332,plain,
( ( ! [P2: $i,X6: $i,X7: $i] :
( ( reck2 @ ( star @ P2 ) @ ( cons2 @ X6 @ X7 ) )
= ( aux3 @ P2 @ X6 @ X7 @ ( notb @ ( eps2 @ P2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(333,plain,
( ( ! [X: $i,Y: $i] :
( ( prop_same @ X @ Y )
= ( eq2 @ ( rec @ X @ Y ) @ ( reck2 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(334,plain,
( ( ( eq @ a @ b )
= bfalse )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(335,plain,
( ( ( eq @ a @ c )
= bfalse )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(336,plain,
( ( ( eq @ b @ a )
= bfalse )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(337,plain,
( ( ( eq @ b @ c )
= bfalse )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(338,plain,
( ( ( eq @ c @ a )
= bfalse )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(339,plain,
( ( ( eq @ c @ b )
= bfalse )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(340,plain,
( ( ( eq2 @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(341,plain,
( ( ( eq2 @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(342,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(343,plain,
( ( ! [X: $i] :
( ( eq2 @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(344,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[230]) ).
thf(345,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( eq2 @ ( prop_same @ SX0 @ SX1 ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(346,plain,
! [SV1: $i] :
( ( ! [SY213: $i] :
( ( aux @ SV1 @ SY213 @ btrue )
= eps ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(347,plain,
! [SV2: $i] :
( ( ! [SY214: $i] :
( ( aux @ SV2 @ SY214 @ bfalse )
= nil4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(348,plain,
! [SV3: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ( aux2 @ SV3 @ SY215 @ SY216 @ btrue )
= ( x @ ( y @ ( step @ SY215 @ SV3 ) @ SY216 ) @ ( step @ SY216 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(349,plain,
! [SV4: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ( aux2 @ SV4 @ SY217 @ SY218 @ bfalse )
= ( x @ ( y @ ( step @ SY217 @ SV4 ) @ SY218 ) @ nil4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(350,plain,
! [SV5: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ( aux3 @ SV5 @ SY219 @ SY220 @ btrue )
= ( rec @ ( y @ SV5 @ ( star @ SV5 ) ) @ ( cons2 @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(351,plain,
! [SV6: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ( aux3 @ SV6 @ SY221 @ SY222 @ bfalse )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(352,plain,
! [SV7: $i] :
( ( ( z @ nil4 @ SV7 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(353,plain,
! [SV8: $i] :
( ( ( z @ eps @ SV8 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(354,plain,
! [SV9: $i] :
( ( ( z @ ( atom @ SV9 ) @ nil4 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(355,plain,
! [SV10: $i] :
( ( ( z @ ( atom @ SV10 ) @ eps )
= ( atom @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(356,plain,
! [SV11: $i] :
( ( ! [SY223: $i] :
( ( z @ ( atom @ SV11 ) @ ( atom @ SY223 ) )
= ( y @ ( atom @ SV11 ) @ ( atom @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(357,plain,
! [SV12: $i] :
( ( ! [SY224: $i,SY225: $i] :
( ( z @ ( atom @ SV12 ) @ ( x @ SY224 @ SY225 ) )
= ( y @ ( atom @ SV12 ) @ ( x @ SY224 @ SY225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(358,plain,
! [SV13: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ( z @ ( atom @ SV13 ) @ ( y @ SY226 @ SY227 ) )
= ( y @ ( atom @ SV13 ) @ ( y @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(359,plain,
! [SV14: $i] :
( ( ! [SY228: $i] :
( ( z @ ( atom @ SV14 ) @ ( star @ SY228 ) )
= ( y @ ( atom @ SV14 ) @ ( star @ SY228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(360,plain,
! [SV15: $i] :
( ( ! [SY229: $i] :
( ( z @ ( x @ SV15 @ SY229 ) @ nil4 )
= nil4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(361,plain,
! [SV16: $i] :
( ( ! [SY230: $i] :
( ( z @ ( x @ SV16 @ SY230 ) @ eps )
= ( x @ SV16 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(362,plain,
! [SV17: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ( z @ ( x @ SV17 @ SY231 ) @ ( atom @ SY232 ) )
= ( y @ ( x @ SV17 @ SY231 ) @ ( atom @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(363,plain,
! [SV18: $i] :
( ( ! [SY233: $i,SY234: $i,SY235: $i] :
( ( z @ ( x @ SV18 @ SY233 ) @ ( x @ SY234 @ SY235 ) )
= ( y @ ( x @ SV18 @ SY233 ) @ ( x @ SY234 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(364,plain,
! [SV19: $i] :
( ( ! [SY236: $i,SY237: $i,SY238: $i] :
( ( z @ ( x @ SV19 @ SY236 ) @ ( y @ SY237 @ SY238 ) )
= ( y @ ( x @ SV19 @ SY236 ) @ ( y @ SY237 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(365,plain,
! [SV20: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( z @ ( x @ SV20 @ SY239 ) @ ( star @ SY240 ) )
= ( y @ ( x @ SV20 @ SY239 ) @ ( star @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(366,plain,
! [SV21: $i] :
( ( ! [SY241: $i] :
( ( z @ ( y @ SV21 @ SY241 ) @ nil4 )
= nil4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(367,plain,
! [SV22: $i] :
( ( ! [SY242: $i] :
( ( z @ ( y @ SV22 @ SY242 ) @ eps )
= ( y @ SV22 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(368,plain,
! [SV23: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ( z @ ( y @ SV23 @ SY243 ) @ ( atom @ SY244 ) )
= ( y @ ( y @ SV23 @ SY243 ) @ ( atom @ SY244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(369,plain,
! [SV24: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i] :
( ( z @ ( y @ SV24 @ SY245 ) @ ( x @ SY246 @ SY247 ) )
= ( y @ ( y @ SV24 @ SY245 ) @ ( x @ SY246 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(370,plain,
! [SV25: $i] :
( ( ! [SY248: $i,SY249: $i,SY250: $i] :
( ( z @ ( y @ SV25 @ SY248 ) @ ( y @ SY249 @ SY250 ) )
= ( y @ ( y @ SV25 @ SY248 ) @ ( y @ SY249 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(371,plain,
! [SV26: $i] :
( ( ! [SY251: $i,SY252: $i] :
( ( z @ ( y @ SV26 @ SY251 ) @ ( star @ SY252 ) )
= ( y @ ( y @ SV26 @ SY251 ) @ ( star @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(372,plain,
! [SV27: $i] :
( ( ( z @ ( star @ SV27 ) @ nil4 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(373,plain,
! [SV28: $i] :
( ( ( z @ ( star @ SV28 ) @ eps )
= ( star @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(374,plain,
! [SV29: $i] :
( ( ! [SY253: $i] :
( ( z @ ( star @ SV29 ) @ ( atom @ SY253 ) )
= ( y @ ( star @ SV29 ) @ ( atom @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(375,plain,
! [SV30: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ( z @ ( star @ SV30 ) @ ( x @ SY254 @ SY255 ) )
= ( y @ ( star @ SV30 ) @ ( x @ SY254 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(376,plain,
! [SV31: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ( z @ ( star @ SV31 ) @ ( y @ SY256 @ SY257 ) )
= ( y @ ( star @ SV31 ) @ ( y @ SY256 @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(377,plain,
! [SV32: $i] :
( ( ! [SY258: $i] :
( ( z @ ( star @ SV32 ) @ ( star @ SY258 ) )
= ( y @ ( star @ SV32 ) @ ( star @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(378,plain,
! [SV33: $i] :
( ( ( x2 @ nil4 @ SV33 )
= SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(379,plain,
! [SV34: $i] :
( ( ( x2 @ eps @ ( atom @ SV34 ) )
= ( x @ eps @ ( atom @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(380,plain,
! [SV35: $i] :
( ( ! [SY259: $i] :
( ( x2 @ eps @ ( x @ SV35 @ SY259 ) )
= ( x @ eps @ ( x @ SV35 @ SY259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(381,plain,
! [SV36: $i] :
( ( ! [SY260: $i] :
( ( x2 @ eps @ ( y @ SV36 @ SY260 ) )
= ( x @ eps @ ( y @ SV36 @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(382,plain,
! [SV37: $i] :
( ( ( x2 @ eps @ ( star @ SV37 ) )
= ( x @ eps @ ( star @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(383,plain,
! [SV38: $i] :
( ( ( x2 @ ( atom @ SV38 ) @ nil4 )
= ( atom @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(384,plain,
! [SV39: $i] :
( ( ( x2 @ ( atom @ SV39 ) @ eps )
= ( x @ ( atom @ SV39 ) @ eps ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(385,plain,
! [SV40: $i] :
( ( ! [SY261: $i] :
( ( x2 @ ( atom @ SV40 ) @ ( atom @ SY261 ) )
= ( x @ ( atom @ SV40 ) @ ( atom @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(386,plain,
! [SV41: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ( x2 @ ( atom @ SV41 ) @ ( x @ SY262 @ SY263 ) )
= ( x @ ( atom @ SV41 ) @ ( x @ SY262 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(387,plain,
! [SV42: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ( x2 @ ( atom @ SV42 ) @ ( y @ SY264 @ SY265 ) )
= ( x @ ( atom @ SV42 ) @ ( y @ SY264 @ SY265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(388,plain,
! [SV43: $i] :
( ( ! [SY266: $i] :
( ( x2 @ ( atom @ SV43 ) @ ( star @ SY266 ) )
= ( x @ ( atom @ SV43 ) @ ( star @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(389,plain,
! [SV44: $i] :
( ( ! [SY267: $i] :
( ( x2 @ ( x @ SV44 @ SY267 ) @ nil4 )
= ( x @ SV44 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(390,plain,
! [SV45: $i] :
( ( ! [SY268: $i] :
( ( x2 @ ( x @ SV45 @ SY268 ) @ eps )
= ( x @ ( x @ SV45 @ SY268 ) @ eps ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(391,plain,
! [SV46: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ( x2 @ ( x @ SV46 @ SY269 ) @ ( atom @ SY270 ) )
= ( x @ ( x @ SV46 @ SY269 ) @ ( atom @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(392,plain,
! [SV47: $i] :
( ( ! [SY271: $i,SY272: $i,SY273: $i] :
( ( x2 @ ( x @ SV47 @ SY271 ) @ ( x @ SY272 @ SY273 ) )
= ( x @ ( x @ SV47 @ SY271 ) @ ( x @ SY272 @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(393,plain,
! [SV48: $i] :
( ( ! [SY274: $i,SY275: $i,SY276: $i] :
( ( x2 @ ( x @ SV48 @ SY274 ) @ ( y @ SY275 @ SY276 ) )
= ( x @ ( x @ SV48 @ SY274 ) @ ( y @ SY275 @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(394,plain,
! [SV49: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ( x2 @ ( x @ SV49 @ SY277 ) @ ( star @ SY278 ) )
= ( x @ ( x @ SV49 @ SY277 ) @ ( star @ SY278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(395,plain,
! [SV50: $i] :
( ( ! [SY279: $i] :
( ( x2 @ ( y @ SV50 @ SY279 ) @ nil4 )
= ( y @ SV50 @ SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(396,plain,
! [SV51: $i] :
( ( ! [SY280: $i] :
( ( x2 @ ( y @ SV51 @ SY280 ) @ eps )
= ( x @ ( y @ SV51 @ SY280 ) @ eps ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(397,plain,
! [SV52: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ( x2 @ ( y @ SV52 @ SY281 ) @ ( atom @ SY282 ) )
= ( x @ ( y @ SV52 @ SY281 ) @ ( atom @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(398,plain,
! [SV53: $i] :
( ( ! [SY283: $i,SY284: $i,SY285: $i] :
( ( x2 @ ( y @ SV53 @ SY283 ) @ ( x @ SY284 @ SY285 ) )
= ( x @ ( y @ SV53 @ SY283 ) @ ( x @ SY284 @ SY285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(399,plain,
! [SV54: $i] :
( ( ! [SY286: $i,SY287: $i,SY288: $i] :
( ( x2 @ ( y @ SV54 @ SY286 ) @ ( y @ SY287 @ SY288 ) )
= ( x @ ( y @ SV54 @ SY286 ) @ ( y @ SY287 @ SY288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(400,plain,
! [SV55: $i] :
( ( ! [SY289: $i,SY290: $i] :
( ( x2 @ ( y @ SV55 @ SY289 ) @ ( star @ SY290 ) )
= ( x @ ( y @ SV55 @ SY289 ) @ ( star @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(401,plain,
! [SV56: $i] :
( ( ( x2 @ ( star @ SV56 ) @ nil4 )
= ( star @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(402,plain,
! [SV57: $i] :
( ( ( x2 @ ( star @ SV57 ) @ eps )
= ( x @ ( star @ SV57 ) @ eps ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(403,plain,
! [SV58: $i] :
( ( ! [SY291: $i] :
( ( x2 @ ( star @ SV58 ) @ ( atom @ SY291 ) )
= ( x @ ( star @ SV58 ) @ ( atom @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(404,plain,
! [SV59: $i] :
( ( ! [SY292: $i,SY293: $i] :
( ( x2 @ ( star @ SV59 ) @ ( x @ SY292 @ SY293 ) )
= ( x @ ( star @ SV59 ) @ ( x @ SY292 @ SY293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(405,plain,
! [SV60: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ( x2 @ ( star @ SV60 ) @ ( y @ SY294 @ SY295 ) )
= ( x @ ( star @ SV60 ) @ ( y @ SY294 @ SY295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(406,plain,
! [SV61: $i] :
( ( ! [SY296: $i] :
( ( x2 @ ( star @ SV61 ) @ ( star @ SY296 ) )
= ( x @ ( star @ SV61 ) @ ( star @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(407,plain,
! [SV62: $i] :
( ( ( splits @ SV62 @ nil )
= nil )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(408,plain,
! [SV63: $i] :
( ( ! [SY297: $i,SY298: $i,SY299: $i] :
( ( splits @ SV63 @ ( cons @ ( pair2 @ SY297 @ SY298 ) @ SY299 ) )
= ( cons @ ( pair2 @ ( cons2 @ SV63 @ SY297 ) @ SY298 ) @ ( splits @ SV63 @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(409,plain,
! [SV64: $i] :
( ( ! [SY300: $i] :
( ( splits2 @ ( cons2 @ SV64 @ SY300 ) )
= ( cons @ ( pair2 @ nil2 @ ( cons2 @ SV64 @ SY300 ) ) @ ( splits @ SV64 @ ( splits2 @ SY300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(410,plain,
! [SV65: $i] :
( ( ( orb @ btrue @ SV65 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(411,plain,
! [SV66: $i] :
( ( ( orb @ bfalse @ SV66 )
= SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(412,plain,
! [SV67: $i] :
( ( ! [SY301: $i] :
( ( or2 @ ( cons3 @ SV67 @ SY301 ) )
= ( orb @ SV67 @ ( or2 @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(413,plain,
! [SV68: $i] :
( ( ( andb @ btrue @ SV68 )
= SV68 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(414,plain,
! [SV69: $i] :
( ( ( andb @ bfalse @ SV69 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(415,plain,
! [SV70: $i] :
( ( ! [SY302: $i] :
( ( eps2 @ ( x @ SV70 @ SY302 ) )
= ( orb @ ( eps2 @ SV70 ) @ ( eps2 @ SY302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(416,plain,
! [SV71: $i] :
( ( ! [SY303: $i] :
( ( eps2 @ ( y @ SV71 @ SY303 ) )
= ( andb @ ( eps2 @ SV71 ) @ ( eps2 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(417,plain,
! [SV72: $i] :
( ( ( eps2 @ ( star @ SV72 ) )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(418,plain,
! [SV73: $i] :
( ( ( eps2 @ ( atom @ SV73 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(419,plain,
! [SV74: $i] :
( ( ! [SY304: $i] :
( ( step @ ( atom @ SV74 ) @ SY304 )
= ( aux @ SY304 @ SV74 @ ( eq @ SV74 @ SY304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(420,plain,
! [SV75: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ( step @ ( x @ SV75 @ SY305 ) @ SY306 )
= ( x @ ( step @ SV75 @ SY306 ) @ ( step @ SY305 @ SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(421,plain,
! [SV76: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ( step @ ( y @ SV76 @ SY307 ) @ SY308 )
= ( aux2 @ SY308 @ SV76 @ SY307 @ ( eps2 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(422,plain,
! [SV77: $i] :
( ( ! [SY309: $i] :
( ( step @ ( star @ SV77 ) @ SY309 )
= ( y @ ( step @ SV77 @ SY309 ) @ ( star @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(423,plain,
! [SV78: $i] :
( ( ( step @ nil4 @ SV78 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(424,plain,
! [SV79: $i] :
( ( ( step @ eps @ SV79 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(425,plain,
! [SV80: $i] :
( ( ( rec @ SV80 @ nil2 )
= ( eps2 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(426,plain,
! [SV81: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ( rec @ SV81 @ ( cons2 @ SY310 @ SY311 ) )
= ( rec @ ( step @ SV81 @ SY310 ) @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(427,plain,
! [SV82: $i] :
( ( ! [SY312: $i] :
( ( reck @ SV82 @ SY312 @ nil )
= nil3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(428,plain,
! [SV83: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i,SY316: $i] :
( ( reck @ SV83 @ SY313 @ ( cons @ ( pair2 @ SY314 @ SY315 ) @ SY316 ) )
= ( cons3 @ ( andb @ ( reck2 @ SV83 @ SY314 ) @ ( rec @ SY313 @ SY315 ) ) @ ( reck @ SV83 @ SY313 @ SY316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(429,plain,
! [SV84: $i] :
( ( ( reck2 @ nil4 @ SV84 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(430,plain,
! [SV85: $i] :
( ( ! [SY317: $i] :
( ( reck2 @ eps @ ( cons2 @ SV85 @ SY317 ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(431,plain,
! [SV86: $i] :
( ( ( reck2 @ ( atom @ SV86 ) @ nil2 )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(432,plain,
! [SV87: $i] :
( ( ! [SY318: $i] :
( ( reck2 @ ( atom @ SV87 ) @ ( cons2 @ SY318 @ nil2 ) )
= ( eq @ SV87 @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(433,plain,
! [SV88: $i] :
( ( ! [SY319: $i,SY320: $i,SY321: $i] :
( ( reck2 @ ( atom @ SV88 ) @ ( cons2 @ SY319 @ ( cons2 @ SY320 @ SY321 ) ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(434,plain,
! [SV89: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ( reck2 @ ( x @ SV89 @ SY322 ) @ SY323 )
= ( orb @ ( reck2 @ SV89 @ SY323 ) @ ( reck2 @ SY322 @ SY323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(435,plain,
! [SV90: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ( reck2 @ ( y @ SV90 @ SY324 ) @ SY325 )
= ( or2 @ ( reck @ SV90 @ SY324 @ ( splits2 @ SY325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(436,plain,
! [SV91: $i] :
( ( ( reck2 @ ( star @ SV91 ) @ nil2 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(437,plain,
! [SV92: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ( reck2 @ ( star @ SV92 ) @ ( cons2 @ SY326 @ SY327 ) )
= ( aux3 @ SV92 @ SY326 @ SY327 @ ( notb @ ( eps2 @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(438,plain,
! [SV93: $i] :
( ( ! [SY328: $i] :
( ( prop_same @ SV93 @ SY328 )
= ( eq2 @ ( rec @ SV93 @ SY328 ) @ ( reck2 @ SV93 @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(439,plain,
! [SV94: $i] :
( ( ( eq @ SV94 @ SV94 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(440,plain,
! [SV95: $i] :
( ( ( eq2 @ SV95 @ SV95 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(441,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(442,plain,
! [SV96: $i] :
( ( ! [SY329: $i] :
( ( eq2 @ ( prop_same @ SV96 @ SY329 ) @ bfalse )
!= btrue ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(443,plain,
! [SV97: $i,SV1: $i] :
( ( ( aux @ SV1 @ SV97 @ btrue )
= eps )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(444,plain,
! [SV98: $i,SV2: $i] :
( ( ( aux @ SV2 @ SV98 @ bfalse )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(445,plain,
! [SV99: $i,SV3: $i] :
( ( ! [SY330: $i] :
( ( aux2 @ SV3 @ SV99 @ SY330 @ btrue )
= ( x @ ( y @ ( step @ SV99 @ SV3 ) @ SY330 ) @ ( step @ SY330 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(446,plain,
! [SV100: $i,SV4: $i] :
( ( ! [SY331: $i] :
( ( aux2 @ SV4 @ SV100 @ SY331 @ bfalse )
= ( x @ ( y @ ( step @ SV100 @ SV4 ) @ SY331 ) @ nil4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(447,plain,
! [SV101: $i,SV5: $i] :
( ( ! [SY332: $i] :
( ( aux3 @ SV5 @ SV101 @ SY332 @ btrue )
= ( rec @ ( y @ SV5 @ ( star @ SV5 ) ) @ ( cons2 @ SV101 @ SY332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(448,plain,
! [SV102: $i,SV6: $i] :
( ( ! [SY333: $i] :
( ( aux3 @ SV6 @ SV102 @ SY333 @ bfalse )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(449,plain,
! [SV103: $i,SV11: $i] :
( ( ( z @ ( atom @ SV11 ) @ ( atom @ SV103 ) )
= ( y @ ( atom @ SV11 ) @ ( atom @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(450,plain,
! [SV104: $i,SV12: $i] :
( ( ! [SY334: $i] :
( ( z @ ( atom @ SV12 ) @ ( x @ SV104 @ SY334 ) )
= ( y @ ( atom @ SV12 ) @ ( x @ SV104 @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(451,plain,
! [SV105: $i,SV13: $i] :
( ( ! [SY335: $i] :
( ( z @ ( atom @ SV13 ) @ ( y @ SV105 @ SY335 ) )
= ( y @ ( atom @ SV13 ) @ ( y @ SV105 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(452,plain,
! [SV106: $i,SV14: $i] :
( ( ( z @ ( atom @ SV14 ) @ ( star @ SV106 ) )
= ( y @ ( atom @ SV14 ) @ ( star @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(453,plain,
! [SV107: $i,SV15: $i] :
( ( ( z @ ( x @ SV15 @ SV107 ) @ nil4 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(454,plain,
! [SV108: $i,SV16: $i] :
( ( ( z @ ( x @ SV16 @ SV108 ) @ eps )
= ( x @ SV16 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(455,plain,
! [SV109: $i,SV17: $i] :
( ( ! [SY336: $i] :
( ( z @ ( x @ SV17 @ SV109 ) @ ( atom @ SY336 ) )
= ( y @ ( x @ SV17 @ SV109 ) @ ( atom @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(456,plain,
! [SV110: $i,SV18: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ( z @ ( x @ SV18 @ SV110 ) @ ( x @ SY337 @ SY338 ) )
= ( y @ ( x @ SV18 @ SV110 ) @ ( x @ SY337 @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(457,plain,
! [SV111: $i,SV19: $i] :
( ( ! [SY339: $i,SY340: $i] :
( ( z @ ( x @ SV19 @ SV111 ) @ ( y @ SY339 @ SY340 ) )
= ( y @ ( x @ SV19 @ SV111 ) @ ( y @ SY339 @ SY340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(458,plain,
! [SV112: $i,SV20: $i] :
( ( ! [SY341: $i] :
( ( z @ ( x @ SV20 @ SV112 ) @ ( star @ SY341 ) )
= ( y @ ( x @ SV20 @ SV112 ) @ ( star @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(459,plain,
! [SV113: $i,SV21: $i] :
( ( ( z @ ( y @ SV21 @ SV113 ) @ nil4 )
= nil4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(460,plain,
! [SV114: $i,SV22: $i] :
( ( ( z @ ( y @ SV22 @ SV114 ) @ eps )
= ( y @ SV22 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(461,plain,
! [SV115: $i,SV23: $i] :
( ( ! [SY342: $i] :
( ( z @ ( y @ SV23 @ SV115 ) @ ( atom @ SY342 ) )
= ( y @ ( y @ SV23 @ SV115 ) @ ( atom @ SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(462,plain,
! [SV116: $i,SV24: $i] :
( ( ! [SY343: $i,SY344: $i] :
( ( z @ ( y @ SV24 @ SV116 ) @ ( x @ SY343 @ SY344 ) )
= ( y @ ( y @ SV24 @ SV116 ) @ ( x @ SY343 @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(463,plain,
! [SV117: $i,SV25: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ( z @ ( y @ SV25 @ SV117 ) @ ( y @ SY345 @ SY346 ) )
= ( y @ ( y @ SV25 @ SV117 ) @ ( y @ SY345 @ SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(464,plain,
! [SV118: $i,SV26: $i] :
( ( ! [SY347: $i] :
( ( z @ ( y @ SV26 @ SV118 ) @ ( star @ SY347 ) )
= ( y @ ( y @ SV26 @ SV118 ) @ ( star @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(465,plain,
! [SV119: $i,SV29: $i] :
( ( ( z @ ( star @ SV29 ) @ ( atom @ SV119 ) )
= ( y @ ( star @ SV29 ) @ ( atom @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(466,plain,
! [SV120: $i,SV30: $i] :
( ( ! [SY348: $i] :
( ( z @ ( star @ SV30 ) @ ( x @ SV120 @ SY348 ) )
= ( y @ ( star @ SV30 ) @ ( x @ SV120 @ SY348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(467,plain,
! [SV121: $i,SV31: $i] :
( ( ! [SY349: $i] :
( ( z @ ( star @ SV31 ) @ ( y @ SV121 @ SY349 ) )
= ( y @ ( star @ SV31 ) @ ( y @ SV121 @ SY349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(468,plain,
! [SV122: $i,SV32: $i] :
( ( ( z @ ( star @ SV32 ) @ ( star @ SV122 ) )
= ( y @ ( star @ SV32 ) @ ( star @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(469,plain,
! [SV123: $i,SV35: $i] :
( ( ( x2 @ eps @ ( x @ SV35 @ SV123 ) )
= ( x @ eps @ ( x @ SV35 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(470,plain,
! [SV124: $i,SV36: $i] :
( ( ( x2 @ eps @ ( y @ SV36 @ SV124 ) )
= ( x @ eps @ ( y @ SV36 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(471,plain,
! [SV125: $i,SV40: $i] :
( ( ( x2 @ ( atom @ SV40 ) @ ( atom @ SV125 ) )
= ( x @ ( atom @ SV40 ) @ ( atom @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(472,plain,
! [SV126: $i,SV41: $i] :
( ( ! [SY350: $i] :
( ( x2 @ ( atom @ SV41 ) @ ( x @ SV126 @ SY350 ) )
= ( x @ ( atom @ SV41 ) @ ( x @ SV126 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(473,plain,
! [SV127: $i,SV42: $i] :
( ( ! [SY351: $i] :
( ( x2 @ ( atom @ SV42 ) @ ( y @ SV127 @ SY351 ) )
= ( x @ ( atom @ SV42 ) @ ( y @ SV127 @ SY351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(474,plain,
! [SV128: $i,SV43: $i] :
( ( ( x2 @ ( atom @ SV43 ) @ ( star @ SV128 ) )
= ( x @ ( atom @ SV43 ) @ ( star @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(475,plain,
! [SV129: $i,SV44: $i] :
( ( ( x2 @ ( x @ SV44 @ SV129 ) @ nil4 )
= ( x @ SV44 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(476,plain,
! [SV130: $i,SV45: $i] :
( ( ( x2 @ ( x @ SV45 @ SV130 ) @ eps )
= ( x @ ( x @ SV45 @ SV130 ) @ eps ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(477,plain,
! [SV131: $i,SV46: $i] :
( ( ! [SY352: $i] :
( ( x2 @ ( x @ SV46 @ SV131 ) @ ( atom @ SY352 ) )
= ( x @ ( x @ SV46 @ SV131 ) @ ( atom @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(478,plain,
! [SV132: $i,SV47: $i] :
( ( ! [SY353: $i,SY354: $i] :
( ( x2 @ ( x @ SV47 @ SV132 ) @ ( x @ SY353 @ SY354 ) )
= ( x @ ( x @ SV47 @ SV132 ) @ ( x @ SY353 @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(479,plain,
! [SV133: $i,SV48: $i] :
( ( ! [SY355: $i,SY356: $i] :
( ( x2 @ ( x @ SV48 @ SV133 ) @ ( y @ SY355 @ SY356 ) )
= ( x @ ( x @ SV48 @ SV133 ) @ ( y @ SY355 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(480,plain,
! [SV134: $i,SV49: $i] :
( ( ! [SY357: $i] :
( ( x2 @ ( x @ SV49 @ SV134 ) @ ( star @ SY357 ) )
= ( x @ ( x @ SV49 @ SV134 ) @ ( star @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(481,plain,
! [SV135: $i,SV50: $i] :
( ( ( x2 @ ( y @ SV50 @ SV135 ) @ nil4 )
= ( y @ SV50 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(482,plain,
! [SV136: $i,SV51: $i] :
( ( ( x2 @ ( y @ SV51 @ SV136 ) @ eps )
= ( x @ ( y @ SV51 @ SV136 ) @ eps ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(483,plain,
! [SV137: $i,SV52: $i] :
( ( ! [SY358: $i] :
( ( x2 @ ( y @ SV52 @ SV137 ) @ ( atom @ SY358 ) )
= ( x @ ( y @ SV52 @ SV137 ) @ ( atom @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(484,plain,
! [SV138: $i,SV53: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ( x2 @ ( y @ SV53 @ SV138 ) @ ( x @ SY359 @ SY360 ) )
= ( x @ ( y @ SV53 @ SV138 ) @ ( x @ SY359 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(485,plain,
! [SV139: $i,SV54: $i] :
( ( ! [SY361: $i,SY362: $i] :
( ( x2 @ ( y @ SV54 @ SV139 ) @ ( y @ SY361 @ SY362 ) )
= ( x @ ( y @ SV54 @ SV139 ) @ ( y @ SY361 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(486,plain,
! [SV140: $i,SV55: $i] :
( ( ! [SY363: $i] :
( ( x2 @ ( y @ SV55 @ SV140 ) @ ( star @ SY363 ) )
= ( x @ ( y @ SV55 @ SV140 ) @ ( star @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(487,plain,
! [SV141: $i,SV58: $i] :
( ( ( x2 @ ( star @ SV58 ) @ ( atom @ SV141 ) )
= ( x @ ( star @ SV58 ) @ ( atom @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(488,plain,
! [SV142: $i,SV59: $i] :
( ( ! [SY364: $i] :
( ( x2 @ ( star @ SV59 ) @ ( x @ SV142 @ SY364 ) )
= ( x @ ( star @ SV59 ) @ ( x @ SV142 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(489,plain,
! [SV143: $i,SV60: $i] :
( ( ! [SY365: $i] :
( ( x2 @ ( star @ SV60 ) @ ( y @ SV143 @ SY365 ) )
= ( x @ ( star @ SV60 ) @ ( y @ SV143 @ SY365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(490,plain,
! [SV144: $i,SV61: $i] :
( ( ( x2 @ ( star @ SV61 ) @ ( star @ SV144 ) )
= ( x @ ( star @ SV61 ) @ ( star @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(491,plain,
! [SV145: $i,SV63: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ( splits @ SV63 @ ( cons @ ( pair2 @ SV145 @ SY366 ) @ SY367 ) )
= ( cons @ ( pair2 @ ( cons2 @ SV63 @ SV145 ) @ SY366 ) @ ( splits @ SV63 @ SY367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(492,plain,
! [SV146: $i,SV64: $i] :
( ( ( splits2 @ ( cons2 @ SV64 @ SV146 ) )
= ( cons @ ( pair2 @ nil2 @ ( cons2 @ SV64 @ SV146 ) ) @ ( splits @ SV64 @ ( splits2 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(493,plain,
! [SV147: $i,SV67: $i] :
( ( ( or2 @ ( cons3 @ SV67 @ SV147 ) )
= ( orb @ SV67 @ ( or2 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(494,plain,
! [SV148: $i,SV70: $i] :
( ( ( eps2 @ ( x @ SV70 @ SV148 ) )
= ( orb @ ( eps2 @ SV70 ) @ ( eps2 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(495,plain,
! [SV149: $i,SV71: $i] :
( ( ( eps2 @ ( y @ SV71 @ SV149 ) )
= ( andb @ ( eps2 @ SV71 ) @ ( eps2 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(496,plain,
! [SV150: $i,SV74: $i] :
( ( ( step @ ( atom @ SV74 ) @ SV150 )
= ( aux @ SV150 @ SV74 @ ( eq @ SV74 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(497,plain,
! [SV151: $i,SV75: $i] :
( ( ! [SY368: $i] :
( ( step @ ( x @ SV75 @ SV151 ) @ SY368 )
= ( x @ ( step @ SV75 @ SY368 ) @ ( step @ SV151 @ SY368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(498,plain,
! [SV152: $i,SV76: $i] :
( ( ! [SY369: $i] :
( ( step @ ( y @ SV76 @ SV152 ) @ SY369 )
= ( aux2 @ SY369 @ SV76 @ SV152 @ ( eps2 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(499,plain,
! [SV153: $i,SV77: $i] :
( ( ( step @ ( star @ SV77 ) @ SV153 )
= ( y @ ( step @ SV77 @ SV153 ) @ ( star @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(500,plain,
! [SV154: $i,SV81: $i] :
( ( ! [SY370: $i] :
( ( rec @ SV81 @ ( cons2 @ SV154 @ SY370 ) )
= ( rec @ ( step @ SV81 @ SV154 ) @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(501,plain,
! [SV155: $i,SV82: $i] :
( ( ( reck @ SV82 @ SV155 @ nil )
= nil3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(502,plain,
! [SV156: $i,SV83: $i] :
( ( ! [SY371: $i,SY372: $i,SY373: $i] :
( ( reck @ SV83 @ SV156 @ ( cons @ ( pair2 @ SY371 @ SY372 ) @ SY373 ) )
= ( cons3 @ ( andb @ ( reck2 @ SV83 @ SY371 ) @ ( rec @ SV156 @ SY372 ) ) @ ( reck @ SV83 @ SV156 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(503,plain,
! [SV157: $i,SV85: $i] :
( ( ( reck2 @ eps @ ( cons2 @ SV85 @ SV157 ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(504,plain,
! [SV158: $i,SV87: $i] :
( ( ( reck2 @ ( atom @ SV87 ) @ ( cons2 @ SV158 @ nil2 ) )
= ( eq @ SV87 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(505,plain,
! [SV159: $i,SV88: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ( reck2 @ ( atom @ SV88 ) @ ( cons2 @ SV159 @ ( cons2 @ SY374 @ SY375 ) ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(506,plain,
! [SV160: $i,SV89: $i] :
( ( ! [SY376: $i] :
( ( reck2 @ ( x @ SV89 @ SV160 ) @ SY376 )
= ( orb @ ( reck2 @ SV89 @ SY376 ) @ ( reck2 @ SV160 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(507,plain,
! [SV161: $i,SV90: $i] :
( ( ! [SY377: $i] :
( ( reck2 @ ( y @ SV90 @ SV161 ) @ SY377 )
= ( or2 @ ( reck @ SV90 @ SV161 @ ( splits2 @ SY377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(508,plain,
! [SV162: $i,SV92: $i] :
( ( ! [SY378: $i] :
( ( reck2 @ ( star @ SV92 ) @ ( cons2 @ SV162 @ SY378 ) )
= ( aux3 @ SV92 @ SV162 @ SY378 @ ( notb @ ( eps2 @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(509,plain,
! [SV163: $i,SV93: $i] :
( ( ( prop_same @ SV93 @ SV163 )
= ( eq2 @ ( rec @ SV93 @ SV163 ) @ ( reck2 @ SV93 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(510,plain,
! [SV164: $i,SV96: $i] :
( ( ( eq2 @ ( prop_same @ SV96 @ SV164 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(511,plain,
! [SV165: $i,SV99: $i,SV3: $i] :
( ( ( aux2 @ SV3 @ SV99 @ SV165 @ btrue )
= ( x @ ( y @ ( step @ SV99 @ SV3 ) @ SV165 ) @ ( step @ SV165 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(512,plain,
! [SV166: $i,SV100: $i,SV4: $i] :
( ( ( aux2 @ SV4 @ SV100 @ SV166 @ bfalse )
= ( x @ ( y @ ( step @ SV100 @ SV4 ) @ SV166 ) @ nil4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(513,plain,
! [SV167: $i,SV101: $i,SV5: $i] :
( ( ( aux3 @ SV5 @ SV101 @ SV167 @ btrue )
= ( rec @ ( y @ SV5 @ ( star @ SV5 ) ) @ ( cons2 @ SV101 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(514,plain,
! [SV168: $i,SV102: $i,SV6: $i] :
( ( ( aux3 @ SV6 @ SV102 @ SV168 @ bfalse )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(515,plain,
! [SV169: $i,SV104: $i,SV12: $i] :
( ( ( z @ ( atom @ SV12 ) @ ( x @ SV104 @ SV169 ) )
= ( y @ ( atom @ SV12 ) @ ( x @ SV104 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(516,plain,
! [SV170: $i,SV105: $i,SV13: $i] :
( ( ( z @ ( atom @ SV13 ) @ ( y @ SV105 @ SV170 ) )
= ( y @ ( atom @ SV13 ) @ ( y @ SV105 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(517,plain,
! [SV171: $i,SV109: $i,SV17: $i] :
( ( ( z @ ( x @ SV17 @ SV109 ) @ ( atom @ SV171 ) )
= ( y @ ( x @ SV17 @ SV109 ) @ ( atom @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(518,plain,
! [SV172: $i,SV110: $i,SV18: $i] :
( ( ! [SY379: $i] :
( ( z @ ( x @ SV18 @ SV110 ) @ ( x @ SV172 @ SY379 ) )
= ( y @ ( x @ SV18 @ SV110 ) @ ( x @ SV172 @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(519,plain,
! [SV173: $i,SV111: $i,SV19: $i] :
( ( ! [SY380: $i] :
( ( z @ ( x @ SV19 @ SV111 ) @ ( y @ SV173 @ SY380 ) )
= ( y @ ( x @ SV19 @ SV111 ) @ ( y @ SV173 @ SY380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(520,plain,
! [SV174: $i,SV112: $i,SV20: $i] :
( ( ( z @ ( x @ SV20 @ SV112 ) @ ( star @ SV174 ) )
= ( y @ ( x @ SV20 @ SV112 ) @ ( star @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(521,plain,
! [SV175: $i,SV115: $i,SV23: $i] :
( ( ( z @ ( y @ SV23 @ SV115 ) @ ( atom @ SV175 ) )
= ( y @ ( y @ SV23 @ SV115 ) @ ( atom @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(522,plain,
! [SV176: $i,SV116: $i,SV24: $i] :
( ( ! [SY381: $i] :
( ( z @ ( y @ SV24 @ SV116 ) @ ( x @ SV176 @ SY381 ) )
= ( y @ ( y @ SV24 @ SV116 ) @ ( x @ SV176 @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(523,plain,
! [SV177: $i,SV117: $i,SV25: $i] :
( ( ! [SY382: $i] :
( ( z @ ( y @ SV25 @ SV117 ) @ ( y @ SV177 @ SY382 ) )
= ( y @ ( y @ SV25 @ SV117 ) @ ( y @ SV177 @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(524,plain,
! [SV178: $i,SV118: $i,SV26: $i] :
( ( ( z @ ( y @ SV26 @ SV118 ) @ ( star @ SV178 ) )
= ( y @ ( y @ SV26 @ SV118 ) @ ( star @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(525,plain,
! [SV179: $i,SV120: $i,SV30: $i] :
( ( ( z @ ( star @ SV30 ) @ ( x @ SV120 @ SV179 ) )
= ( y @ ( star @ SV30 ) @ ( x @ SV120 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(526,plain,
! [SV180: $i,SV121: $i,SV31: $i] :
( ( ( z @ ( star @ SV31 ) @ ( y @ SV121 @ SV180 ) )
= ( y @ ( star @ SV31 ) @ ( y @ SV121 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(527,plain,
! [SV181: $i,SV126: $i,SV41: $i] :
( ( ( x2 @ ( atom @ SV41 ) @ ( x @ SV126 @ SV181 ) )
= ( x @ ( atom @ SV41 ) @ ( x @ SV126 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(528,plain,
! [SV182: $i,SV127: $i,SV42: $i] :
( ( ( x2 @ ( atom @ SV42 ) @ ( y @ SV127 @ SV182 ) )
= ( x @ ( atom @ SV42 ) @ ( y @ SV127 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(529,plain,
! [SV183: $i,SV131: $i,SV46: $i] :
( ( ( x2 @ ( x @ SV46 @ SV131 ) @ ( atom @ SV183 ) )
= ( x @ ( x @ SV46 @ SV131 ) @ ( atom @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(530,plain,
! [SV184: $i,SV132: $i,SV47: $i] :
( ( ! [SY383: $i] :
( ( x2 @ ( x @ SV47 @ SV132 ) @ ( x @ SV184 @ SY383 ) )
= ( x @ ( x @ SV47 @ SV132 ) @ ( x @ SV184 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(531,plain,
! [SV185: $i,SV133: $i,SV48: $i] :
( ( ! [SY384: $i] :
( ( x2 @ ( x @ SV48 @ SV133 ) @ ( y @ SV185 @ SY384 ) )
= ( x @ ( x @ SV48 @ SV133 ) @ ( y @ SV185 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(532,plain,
! [SV186: $i,SV134: $i,SV49: $i] :
( ( ( x2 @ ( x @ SV49 @ SV134 ) @ ( star @ SV186 ) )
= ( x @ ( x @ SV49 @ SV134 ) @ ( star @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(533,plain,
! [SV187: $i,SV137: $i,SV52: $i] :
( ( ( x2 @ ( y @ SV52 @ SV137 ) @ ( atom @ SV187 ) )
= ( x @ ( y @ SV52 @ SV137 ) @ ( atom @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(534,plain,
! [SV188: $i,SV138: $i,SV53: $i] :
( ( ! [SY385: $i] :
( ( x2 @ ( y @ SV53 @ SV138 ) @ ( x @ SV188 @ SY385 ) )
= ( x @ ( y @ SV53 @ SV138 ) @ ( x @ SV188 @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(535,plain,
! [SV189: $i,SV139: $i,SV54: $i] :
( ( ! [SY386: $i] :
( ( x2 @ ( y @ SV54 @ SV139 ) @ ( y @ SV189 @ SY386 ) )
= ( x @ ( y @ SV54 @ SV139 ) @ ( y @ SV189 @ SY386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(536,plain,
! [SV190: $i,SV140: $i,SV55: $i] :
( ( ( x2 @ ( y @ SV55 @ SV140 ) @ ( star @ SV190 ) )
= ( x @ ( y @ SV55 @ SV140 ) @ ( star @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(537,plain,
! [SV191: $i,SV142: $i,SV59: $i] :
( ( ( x2 @ ( star @ SV59 ) @ ( x @ SV142 @ SV191 ) )
= ( x @ ( star @ SV59 ) @ ( x @ SV142 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(538,plain,
! [SV192: $i,SV143: $i,SV60: $i] :
( ( ( x2 @ ( star @ SV60 ) @ ( y @ SV143 @ SV192 ) )
= ( x @ ( star @ SV60 ) @ ( y @ SV143 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(539,plain,
! [SV193: $i,SV145: $i,SV63: $i] :
( ( ! [SY387: $i] :
( ( splits @ SV63 @ ( cons @ ( pair2 @ SV145 @ SV193 ) @ SY387 ) )
= ( cons @ ( pair2 @ ( cons2 @ SV63 @ SV145 ) @ SV193 ) @ ( splits @ SV63 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(540,plain,
! [SV194: $i,SV151: $i,SV75: $i] :
( ( ( step @ ( x @ SV75 @ SV151 ) @ SV194 )
= ( x @ ( step @ SV75 @ SV194 ) @ ( step @ SV151 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(541,plain,
! [SV195: $i,SV152: $i,SV76: $i] :
( ( ( step @ ( y @ SV76 @ SV152 ) @ SV195 )
= ( aux2 @ SV195 @ SV76 @ SV152 @ ( eps2 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(542,plain,
! [SV196: $i,SV154: $i,SV81: $i] :
( ( ( rec @ SV81 @ ( cons2 @ SV154 @ SV196 ) )
= ( rec @ ( step @ SV81 @ SV154 ) @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(543,plain,
! [SV197: $i,SV156: $i,SV83: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ( reck @ SV83 @ SV156 @ ( cons @ ( pair2 @ SV197 @ SY388 ) @ SY389 ) )
= ( cons3 @ ( andb @ ( reck2 @ SV83 @ SV197 ) @ ( rec @ SV156 @ SY388 ) ) @ ( reck @ SV83 @ SV156 @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(544,plain,
! [SV198: $i,SV159: $i,SV88: $i] :
( ( ! [SY390: $i] :
( ( reck2 @ ( atom @ SV88 ) @ ( cons2 @ SV159 @ ( cons2 @ SV198 @ SY390 ) ) )
= bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(545,plain,
! [SV199: $i,SV160: $i,SV89: $i] :
( ( ( reck2 @ ( x @ SV89 @ SV160 ) @ SV199 )
= ( orb @ ( reck2 @ SV89 @ SV199 ) @ ( reck2 @ SV160 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(546,plain,
! [SV200: $i,SV161: $i,SV90: $i] :
( ( ( reck2 @ ( y @ SV90 @ SV161 ) @ SV200 )
= ( or2 @ ( reck @ SV90 @ SV161 @ ( splits2 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(547,plain,
! [SV201: $i,SV162: $i,SV92: $i] :
( ( ( reck2 @ ( star @ SV92 ) @ ( cons2 @ SV162 @ SV201 ) )
= ( aux3 @ SV92 @ SV162 @ SV201 @ ( notb @ ( eps2 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(548,plain,
! [SV164: $i,SV96: $i] :
( ( ( eq2 @ ( prop_same @ SV96 @ SV164 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(549,plain,
! [SV202: $i,SV172: $i,SV110: $i,SV18: $i] :
( ( ( z @ ( x @ SV18 @ SV110 ) @ ( x @ SV172 @ SV202 ) )
= ( y @ ( x @ SV18 @ SV110 ) @ ( x @ SV172 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(550,plain,
! [SV203: $i,SV173: $i,SV111: $i,SV19: $i] :
( ( ( z @ ( x @ SV19 @ SV111 ) @ ( y @ SV173 @ SV203 ) )
= ( y @ ( x @ SV19 @ SV111 ) @ ( y @ SV173 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(551,plain,
! [SV204: $i,SV176: $i,SV116: $i,SV24: $i] :
( ( ( z @ ( y @ SV24 @ SV116 ) @ ( x @ SV176 @ SV204 ) )
= ( y @ ( y @ SV24 @ SV116 ) @ ( x @ SV176 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(552,plain,
! [SV205: $i,SV177: $i,SV117: $i,SV25: $i] :
( ( ( z @ ( y @ SV25 @ SV117 ) @ ( y @ SV177 @ SV205 ) )
= ( y @ ( y @ SV25 @ SV117 ) @ ( y @ SV177 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(553,plain,
! [SV206: $i,SV184: $i,SV132: $i,SV47: $i] :
( ( ( x2 @ ( x @ SV47 @ SV132 ) @ ( x @ SV184 @ SV206 ) )
= ( x @ ( x @ SV47 @ SV132 ) @ ( x @ SV184 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(554,plain,
! [SV207: $i,SV185: $i,SV133: $i,SV48: $i] :
( ( ( x2 @ ( x @ SV48 @ SV133 ) @ ( y @ SV185 @ SV207 ) )
= ( x @ ( x @ SV48 @ SV133 ) @ ( y @ SV185 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(555,plain,
! [SV208: $i,SV188: $i,SV138: $i,SV53: $i] :
( ( ( x2 @ ( y @ SV53 @ SV138 ) @ ( x @ SV188 @ SV208 ) )
= ( x @ ( y @ SV53 @ SV138 ) @ ( x @ SV188 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(556,plain,
! [SV209: $i,SV189: $i,SV139: $i,SV54: $i] :
( ( ( x2 @ ( y @ SV54 @ SV139 ) @ ( y @ SV189 @ SV209 ) )
= ( x @ ( y @ SV54 @ SV139 ) @ ( y @ SV189 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(557,plain,
! [SV210: $i,SV193: $i,SV145: $i,SV63: $i] :
( ( ( splits @ SV63 @ ( cons @ ( pair2 @ SV145 @ SV193 ) @ SV210 ) )
= ( cons @ ( pair2 @ ( cons2 @ SV63 @ SV145 ) @ SV193 ) @ ( splits @ SV63 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(558,plain,
! [SV211: $i,SV197: $i,SV156: $i,SV83: $i] :
( ( ! [SY391: $i] :
( ( reck @ SV83 @ SV156 @ ( cons @ ( pair2 @ SV197 @ SV211 ) @ SY391 ) )
= ( cons3 @ ( andb @ ( reck2 @ SV83 @ SV197 ) @ ( rec @ SV156 @ SV211 ) ) @ ( reck @ SV83 @ SV156 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(559,plain,
! [SV212: $i,SV198: $i,SV159: $i,SV88: $i] :
( ( ( reck2 @ ( atom @ SV88 ) @ ( cons2 @ SV159 @ ( cons2 @ SV198 @ SV212 ) ) )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(560,plain,
! [SV213: $i,SV211: $i,SV197: $i,SV156: $i,SV83: $i] :
( ( ( reck @ SV83 @ SV156 @ ( cons @ ( pair2 @ SV197 @ SV211 ) @ SV213 ) )
= ( cons3 @ ( andb @ ( reck2 @ SV83 @ SV197 ) @ ( rec @ SV156 @ SV211 ) ) @ ( reck @ SV83 @ SV156 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(561,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[265,560,559,557,556,555,554,553,552,551,550,549,548,547,546,545,542,541,540,538,537,536,533,532,529,528,527,526,525,524,521,520,517,516,515,514,513,512,511,509,504,503,501,499,496,495,494,493,492,490,487,482,481,476,475,474,471,470,469,468,465,460,459,454,453,452,449,444,443,441,440,439,436,431,429,425,424,423,418,417,414,413,411,410,407,402,401,384,383,382,379,378,373,372,355,354,353,352,341,340,339,338,337,336,335,334,324,311,307,304,303,301,297,266]) ).
thf(562,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[561]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX239-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n018.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 17:17:06 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 224.50/37.65
% 224.50/37.65 No.of.Axioms: 113
% 224.50/37.65
% 224.50/37.65 Length.of.Defs: 0
% 224.50/37.65
% 224.50/37.65 Contains.Choice.Funs: false
% 224.50/37.65 ..............
% 224.50/37.65
% 224.50/37.65 ********************************
% 224.50/37.65 * All subproblems solved! *
% 224.50/37.65 ********************************
% 224.50/37.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:113,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:561,loop_count:0,foatp_calls:1,translation:fof_full)
% 224.50/37.65
% 224.50/37.65 %**** Beginning of derivation protocol ****
% 224.50/37.65 % SZS output start CNFRefutation
% See solution above
% 224.50/37.65
% 224.50/37.65 %**** End of derivation protocol ****
% 224.50/37.65 %**** no. of clauses in derivation: 562 ****
% 224.50/37.65 %**** clause counter: 561 ****
% 224.50/37.65
% 224.50/37.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:113,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:561,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------